An Introduction to Foundational Logic 9780976037095, 0976037092

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An Introduction to Foundational Logic
 9780976037095, 0976037092

Table of contents :
Contents
P reface
....................................................................................................
...................xiii
Introduction—What Is
Logic?.................................................................................. 1
Correct Thinking Is Directed
Thinking.................................................................1
What Is Foundational
Logic?.................................................................................2
Logic Is a
Science.............................................................................................
..... 3
The Special Mind-Set Required for the Study of Logic..................................... 4
Logic Is a Practical
Science....................................................................................5
Logic Is an A
rt..................................................................................................
......5
Logic and Truth
....................................................................................................
.. 6
Being Logical and Being “Logical”
......................................................................7
Formal and Material
Logic.....................................................................................7
Chapter O ne—The Sources of Logic: The Three Acts of the Intellect......... 9
The Approach Taken by This
Book.......................................................................9
The First Act of the Intellect: Simple Apprehension........................................... 9
The Genesis of
Ideas.............................................................................................
11
The Internal
Senses..............................................................................................
. 11
The Sense Image As the Product of External and Internal Sensation................13
The Distinction Between Sense Images and Intellectual Images....................... 14
The Relation Between Sense Knowledge and Intellectual Knowledge............. 15
The Idea As
Means...............................................................................................
16
The Second Act of the Intellect: Judgment.........................................................
18
Composition and
Division................................................................................... 19
Propositions and Truth and
Falsity...................................................................... 20
The Third Act of the Intellect:
Reasoning...........................................................21
Inference...........................................................................................
.....................21
Reasoning and
Argument.....................................................................................22
Review Item
s...................................................................................................
...... 23
Exercises...........................................................................................
.....................23
Chapter Two—Ideas and Their
Expression..........................................................25
Distinctions........................................................................................
................... 2^
The T hing
....................................................................................................
..........27
The Idea
....................................................................................................
............ 2^
The
Word................................................................................................
..............
The Idea As
Universal.........................................................................................


VI C o n t e n t s
In What Sense Are Universals
Real?......................................................................30
Signs...............................................................................................
............................ 31
Natural Signs and Conventional Sign s
.................................................................. 31
Instrumental Signs and Formal
Signs.................................................................... 33
The Interpretation of
Signs..................................................................................... 34
Terms...............................................................................................
........................... 36
The Comprehension and Extension of Terms....................................................... 36
The
Predicables.........................................................................................
................38
Review Item
s...................................................................................................
.......... 41
Exercises...........................................................................................
......................... 42
Chapter Three—The Varieties of
Ideas...................................................................43
Complexity in
Ideas...............................................................................................
.. 43
Concrete and Abstract
Ideas....................................................................................44
Singular Terms and General
Terms....................................................................... 45
Uni vocal, Equivocal, and Analogous Terms........................................................47
The Analogy of
Attribution....................................................................................50
Metaphor............................................................................................
........................ 51
The Opposition of
Terms......................................................................................... 52
Sound and Unsound
Ideas....................................................................................... 55
Creative
Ideas...............................................................................................
............ 58
Review Item
s...................................................................................................
.......... 59
Exercises...........................................................................................
......................... 60
Chapter Four—The C
ategories................................................................................. 61
What Are the
Categories?........................................................................................6
1
Primary Substance and Secondary Substance.......................................................63
The General Nature of
Accident............................................................................. 65
The Accident of
Quantity....................................................................................... 65
The Accident of
Quality......................................................................................... 67
Action and
Passivity...........................................................................................
..... 73
Time and P lace
....................................................................................................
..... 74
Position and
Habit...............................................................................................
.... 76
Summary Comments on the Accidents.................................................................
76
Review Item
s...................................................................................................
.......... 77
Exercises...........................................................................................
.........................78
Chapter Five—Definition and Division
.................................................................. 79
The Need for Clarity in
Ideas................................................................................ 79
Definition and Division
.......................................................................................... 80
Essential
Definition..........................................................................................
.......80
The Rules for Essential
Definition........................................................................84
The Difficulties with Essential
Definition........................................................... 86
The Limitations of Essential
Definition............................................................... 87
Descriptive
Definition..........................................................................................
.. 89
Descriptive Definition by
Property.......................................................................90
Descriptive Definition by
Accident.......................................................................90
Descriptive Definition by
Cause........................................................................... 91
Descriptive Definition by Nam
e........................................................................... 92
Descriptive Definition by
Narration..................................................................... 93


C o n t e n t s vii




Division
....................................................................................................
.............. 93
Physical Division or
Partition.............................................................................. 94
Logical
Division............................................................................................
.........95
The Rules for Logical
Division............................................................................96
Classification......................................................................................
................... 100
Review Item
s...................................................................................................
....... 101
Exercises...........................................................................................
...................... 101
Chapter
Six—Judgment........................................................................................
.... 103
The Second Act of the
Intellect............................................................................ 103
Predication.........................................................................................
......................104
The First Principles of All Human Reasoning................................................... 105
The Principle of
Identity........................................................................................107
The Principle of
Contradiction............................................................................. 107
The Principle of Excluded
Middle....................................................................... 108
The Principle of Sufficient
Reason...................................................................... 109
The Categorical
Proposition.................................................................................109
The Anatomy of a
Proposition............................................................................. 110
The Logical Form of
Propositions....................................................................... 112
The Quantity of
Propositions............................................................................... 113
The Quality of
Propositions..................................................................................116
Modal
Propositions........................................................................................
....... 116
The Distribution of Terms in Propositions........................................................
119
Diagraming
Propositions......................................................................................12
1
Propositions Are Either True or
False................................................................ 122
The Correspondence Criterion of
Truth.............................................................123
The Coherence Criterion of
Truth...................................................................... 124
Propositional Truth Is Absolute
Truth............................................................... 124
Review Item
s...................................................................................................
.......126
Exercises...........................................................................................
......................127
Chapter Seven—The Varieties of Propositions.................................................
128
Complex
Propositions........................................................................................
.. 128
Compound
Propositions.......................................................................................1
29
Inference,
Again...............................................................................................
..... 130
Conjunctive
Propositions.....................................................................................130

Disjunctive
Propositions......................................................................................13
2
Inferences To Be Drawn from Conjunctive and Disjunctive Propositions.....134
Truth
Tables..............................................................................................
.............136
The Obversion of
Propositions............................................................................138
The Conversion of
Propositions..........................................................................140
Review Item
s...................................................................................................
...... 144
Exercises...........................................................................................
..................... 144
Chapter Eight—Further Explorations in Immediate Inference.....................146
The Interrelations Among General Propositions............................................. 146
Shorthand Ways of Expressing General Propositions..................................... 147
The Opposition of
Propositions......................................................................... 148
Contradictory
Opposition....................................................................................149
Contrary Opposition...............................................................................
..............152


viii

C o n t e n t s



Subcontrary
Opposition.........................................................................................
155
Subalternation......................................................................................
....................156
Summary of Possible Inferences Among General Propositions....................... 158
The Square of
Opposition..................................................................................... 159
Other Forms of Immediate
Inference...................................................................164
Review Item
s...................................................................................................
........ 166
Exercises...........................................................................................
....................... 166
Chapter
Nine—Reasoning......................................................................................
...168
The Third Act of the
Intellect................................................................................ 168
Reasoning and
Argument.......................................................................................169
Complexity in
Argument........................................................................................171
Deductive
Reasoning...........................................................................................
.. 174
Mediate
Reasoning...........................................................................................
..... 177
Syllogistic
Reasoning...........................................................................................
178
Validity and
Truth...............................................................................................
.. 179
The Anatomy of a Syllogism
................................................................................180
The Essence of Syllogistic
Reasoning................................................................ 182
The Principle of the Identifying
Third................................................................ 184
The Principle of the Separating
Third................................................................. 185
The Dictum de Omni
Principle.............................................................................. 187
The Dictum de Nullo
Principle.............................................................................. 187
Diagraming Syllogism
s........................................................................................ 188
Review Item
s...................................................................................................
........190
Exercises...........................................................................................
...................... 191
Chapter Ten—The Figures and Moods of the Syllogism................................ 192
The Categorical Syllogism
................................................................................... 192
The Figure of a Syllogism
.................................................................................... 193
The Mood of a Syllogism
.....................................................................................194
The Darii and Ferio Moods of the First Figure ..................................................197
The Potency and Versatility of First Figure Syllogism s..................................199
Are There Only Four Valid Moods in the First Figure?...................................200
The Valid Moods of the Second Figure: Cesare and Camestres...................... 201
The Valid Moods of the Second Figure: Baroco and Festino........................... 205
The Valid Moods of the Third Figure: Darapti, Datisi, Disamis..................... 207
The Valid Moods of the Third Figure: Bocardo, Felapton, Ferison.................209
The Controversial Fourth Figure
........................................................................ 211
Reducing Imperfect Syllogisms to the First Figure.......................................... 213
Categorical Syllogisms Containing Non-Factual Propositions....................... 215
Review
....................................................................................................
................ 216
Exercises...........................................................................................
..................... 217
Chapter Eleven—The Rules of the Syllogism................................................... 219
Determining Validity by Figure and M ood...................................................... 219
The Rules of the Syllogism
.................................................................................220
The Rule Governing the Number of Terms....................................................... 221
The Problem of Equivocation in Argument...................................................... 222
The Rule Governing the Extreme Terms...........................................................225
The Problem of the Illicit
Minor........................................................................ 226


C o n t e n t s IX
The Problem of the Illicit
Major.........................................................................227
The Rule Governing the Middle Term...............................................................
228
Guilt by
Association.........................................................................................
.....229
The Rule Governing Negative Premisses...........................................................
231
The Rule Governing Particular Premisses..........................................................
232
The Rule Governing Weaknesses in Premisses.................................................235
Summary of the Rules of the Syllogism ............................................................
236
False Premisses and a True Conclusion?...........................................................
237
Review
....................................................................................................
............... 240
Exercises...........................................................................................
.................... 240
Chapter Twelve—Variations oh Syllogistic Reasoning;
Making
Arguments........................................................................................
244
Polysyllogisms......................................................................................
...............244
The Advantages and Disadvantages of Polysyllogistic Argument................. 245
The Rules of the Polysyllogism
...........................................................................246
The Logical Limitations of Polysyllogistic Reasoning................................... 247
Sorites.............................................................................................
...................... 249
The Rules of the Sorites
Argument................................................................... 250
Enthymemes..........................................................................................
............... 252
The Ways in Which Syllogisms Are Commonly Abbreviated....................... 253
Responding to
Enthymemes.............................................................................. 254
Making an Argument: the Conclusion................................................................
257
Making an Argument: The Premisses.................................................................
260
A Psychological N
ote............................................................................................ 264
Review Item
s...................................................................................................
........265
Exercises...........................................................................................
...................... 266
Chapter Thirteen—Conditional
Reasoning..........................................................269
The Conditional Way of
Thinking...................................................................... 269
Hypothetical
Argument........................................................................................
270
The Anatomy of the Hypothetical Syllogism .....................................................271
The Pure Hypothetical Syllogism
........................................................................273
The Mixed Hypothetical Syllogism:Modus Ponens........................................ 275
The Mixed Hypothetical SyllogismrAforfws Tollens............................... 276
Affirming the
Consequent.................................................................................... 277
A Reciprocal Relation Between Antecedent and Consequent.......................... 279
Denying the
Antecedent.......................................................................................
280
The Relation Between Categorical Syllogisms and
Hypothetical Syllogism
s...................................................................................282
The Dilemma Argument: Modus Ponens............................................................283
The Dilemma Argument: Modus Tollens............................................................285
Probable Hypothetical
Arguments....................................................................... 287
Review
....................................................................................................
.................290
Exercises...........................................................................................
...................... 291
Chapter Fourteen—Inductive Reasoning.............................................................
294
Deduction and
Induction...................................................................................... 294
Where Inductive Reasoning
Begins....................................................................295
The Uniformity of Nature .......................................................
296


X C o n t e n t s
Inductive Reasoning as Ordered to the Discovery of Causes........................... 299
Scientific
Method..............................................................................................
...... 302
Observation and
Experiment.................................................................................303
Forming
Hypotheses..........................................................................................
.... 305
Testing
Hypotheses..........................................................................................
....... 307
From Hypotheses to
Laws..................................................................................... 309
The Canons of
Induction.......................................................................................
310
Inductive Reasoning as Ordered to the Confirmation of Properties................313
Opinion P olls .............................................................
317
Inductive Reasoning and the Social Sciences.....................................................
318
Argument by
Analogy............................................................................................
320
Review Item
s...................................................................................................
.........322
Exercises...........................................................................................
....................... 322
Chapter Fifteen—Fallacious
Reasoning.................................................................325
What Is Fallacious
Reasoning?............................................................................ 325
Why Study Fallacious
Reasoning?.......................................................................327
Formal and Informal
Fallacies.............................................................................. 327
General Review of the Formal
Fallacies.............................................................. 328
Fallacies Related to
Language.............................................................................. 329
Begging the
Question............................................................................................
. 332
Missing the
Point...............................................................................................
..... 333
Straw M an
....................................................................................................
............334
Hasty
Conclusion..........................................................................................
..........335
Sweeping
Generalization......................................................................................
. 337
False
Dilemma.............................................................................................
........... 337
Fallacy of
Composition.........................................................................................
339
The Appeal to
Ignorance.......................................................................................340
Improper Appeal to
Authority.............................................................................. 340
Two Wrongs Make a
Right................................................................................... 342
The End Justifies the M
eans................................................................................. 343
Tu
Quoque..............................................................................................
................. 344
Ad
Hominem.............................................................................................
............... 345
The Genetic
Fallacy.............................................................................................
...346
Simplistic
Reductionism........................................................................................
347
Special
Pleading............................................................................................
......... 348
Dismissive
Ridicule............................................................................................
....349
Red
Herring.............................................................................................
................ 350
Ad Populum
....................................................................................................
......... 351
Ad Misericordiam
..................................................................................................
352
Ad Baculum
....................................................................................................
.........352
The Last Word:
Truth............................................................................................
353
Review Item
s...................................................................................................
........354
Exercises...........................................................................................
.......................354
A
ppendices...........................................................................................
.........................359
Chapter O n e
....................................................................................................
........ 359
Chapter T w o
....................................................................................................
........ 362
Chapter
Three...............................................................................................
.......... 367

C o n t e n t s
XI
Chapter
Four................................................................................................
...........370
Chapter
Five................................................................................................
............374
Chapter S ix
....................................................................................................
..........375
Chapter Seven
....................................................................................................
.....377
Chapter
Eight...............................................................................................
...........381
Chapter N ine
....................................................................................................
.......382
ChapterTen..........................................................................................
...................385
Chapter Eleven
....................................................................................................
... 390
ChapterTwelve.......................................................................................
............... 391
Chapter
Thirteen............................................................................................
........ 395
Chapter
Fourteen............................................................................................
........ 396
Chapter
Fifteen.............................................................................................
.......... 399
N o te s
....................................................................................................
.......................... 403
Bibliography........................................................................................
..........................405
In d e x
....................................................................................................
.......................... 411

Citation preview

AN INTRODUCTION L OGIC D. Q. Mclnerny

An Introduction to Foundational Logic

D.Q. Mclnerny

T h e P r ie s tly F r a te r n ity o f S t. P e te r E lm h u r s t T o w n s h i p , P e n n s y lv a n ia

2012

Other books in this series: A Course in Thomistic Ethics ( 1997; 3d ed. 2010) The Philosophy o f Nature (1998; 3d ed. forthcoming) Philosophical Psychology (1999; 2d printing 2002) Metaphysics (2004) Natural Theology (2005) Epistemology (2007)

Cover and book design by Nancy LaRoza

ISBN 978-0-9760370-9-5 Copyright © 2012 by D.Q. Mclnerny All rights reserved. Printed in the United States of America

In M em oriam M atthew John Coulom be (1963-1981)

Contents

P re fa c e .......................................................................................................................xiii Introduction—What Is Logic?.................................................................................. 1 Correct Thinking Is Directed Thinking.................................................................1 What Is Foundational Logic?.................................................................................2 Logic Is a Science.................................................................................................. 3 The Special Mind-Set Required for the Study of Logic..................................... 4 Logic Is a Practical Science....................................................................................5 Logic Is an A rt........................................................................................................5 Logic and T ruth...................................................................................................... 6 Being Logical and Being “Logical” ......................................................................7 Formal and Material Logic.....................................................................................7 Chapter O ne—The Sources of Logic: The Three Acts of the Intellect......... 9 The Approach Taken by This Book.......................................................................9 The First Act of the Intellect: Simple Apprehension........................................... 9 The Genesis of Ideas............................................................................................. 11 The Internal Senses............................................................................................... 11 The Sense Image As the Product of External and Internal Sensation................13 The Distinction Between Sense Images and Intellectual Images....................... 14 The Relation Between Sense Knowledge and Intellectual Knowledge............. 15 The Idea As M eans............................................................................................... 16 The Second Act of the Intellect: Judgment......................................................... 18 Composition and D ivision................................................................................... 19 Propositions and Truth and Falsity...................................................................... 20 The Third Act of the Intellect: Reasoning...........................................................21 Inference................................................................................................................21 Reasoning and A rgum ent.....................................................................................22 Review Item s......................................................................................................... 23 Exercises................................................................................................................23 Chapter Two—Ideas and Their Expression..........................................................25 Distinctions........................................................................................................... 2^ The T h in g ..............................................................................................................27 The Id e a ................................................................................................................ 2^ The W ord.............................................................................................................. The Idea As Universal.........................................................................................

VI

C ontents

In What Sense Are Universals Real?......................................................................30 Signs........................................................................................................................... 31 Natural Signs and Conventional S ig n s..................................................................31 Instrumental Signs and Formal S ign s.................................................................... 33 The Interpretation of S ig n s..................................................................................... 34 Terms.......................................................................................................................... 36 The Comprehension and Extension of Terms....................................................... 36 The Predicables.........................................................................................................38 Review Item s............................................................................................................. 41 Exercises.................................................................................................................... 42 Chapter Three—The Varieties of Ideas...................................................................43 Complexity in Ideas................................................................................................. 43 Concrete and Abstract Ideas....................................................................................44 Singular Terms and General Terms....................................................................... 45 Uni vocal, Equivocal, and Analogous T erm s........................................................47 The Analogy of Attribution....................................................................................50 Metaphor.................................................................................................................... 51 The Opposition of Terms......................................................................................... 52 Sound and Unsound Ideas....................................................................................... 55 Creative Ideas........................................................................................................... 58 Review Item s............................................................................................................. 59 Exercises.................................................................................................................... 60 Chapter Four—The C ategories................................................................................. 61 What Are the Categories?........................................................................................61 Primary Substance and Secondary Substance.......................................................63 The General Nature of Accident.............................................................................65 The Accident of Quantity....................................................................................... 65 The Accident of Q uality......................................................................................... 67 Action and Passivity................................................................................................ 73 Time and P la ce......................................................................................................... 74 Position and H abit................................................................................................... 76 Summary Comments on the Accidents................................................................. 76 Review Item s............................................................................................................. 77 Exercises....................................................................................................................78 Chapter Five—Definition and D ivision.................................................................. 79 The Need for Clarity in Ideas................................................................................ 79 Definition and D ivision.......................................................................................... 80 Essential Definition.................................................................................................80 The Rules for Essential D efinition........................................................................84 The Difficulties with Essential Definition........................................................... 86 The Limitations of Essential D efinition............................................................... 87 Descriptive D efinition............................................................................................89 Descriptive Definition by Property.......................................................................90 Descriptive Definition by Accident.......................................................................90 Descriptive Definition by Cause........................................................................... 91 Descriptive Definition by N am e........................................................................... 92 Descriptive Definition by Narration..................................................................... 93

C ontents

vii

D ivision.................................................................................................................. 93 Physical Division or Partition..............................................................................94 Logical Division.....................................................................................................95 The Rules for Logical D ivision............................................................................96 Classification......................................................................................................... 100 Review Item s.......................................................................................................... 101 Exercises................................................................................................................. 101 Chapter Six—Judgm ent............................................................................................ 103 The Second Act of the Intellect............................................................................103 Predication...............................................................................................................104 The First Principles of All Human Reasoning................................................... 105 The Principle of Identity........................................................................................107 The Principle of Contradiction............................................................................. 107 The Principle of Excluded Middle....................................................................... 108 The Principle of Sufficient Reason...................................................................... 109 The Categorical Proposition.................................................................................109 The Anatomy of a Proposition............................................................................. 110 The Logical Form of Propositions....................................................................... 112 The Quantity of Propositions............................................................................... 113 The Quality of Propositions..................................................................................116 Modal Propositions............................................................................................... 116 The Distribution of Terms in Propositions........................................................ 119 Diagraming Propositions......................................................................................121 Propositions Are Either True or False................................................................ 122 The Correspondence Criterion of Truth.............................................................123 The Coherence Criterion of Truth...................................................................... 124 Propositional Truth Is Absolute Truth............................................................... 124 Review Item s..........................................................................................................126 Exercises.................................................................................................................127 Chapter Seven—The Varieties o f Propositions................................................. 128 Complex Propositions.......................................................................................... 128 Compound Propositions.......................................................................................129 Inference, A gain.................................................................................................... 130 Conjunctive Propositions.....................................................................................130 Disjunctive Propositions......................................................................................132 Inferences To Be Drawn from Conjunctive and Disjunctive Propositions.....134 Truth Tables...........................................................................................................136 The Obversion of Propositions............................................................................138 The Conversion of Propositions..........................................................................140 Review Item s......................................................................................................... 144 Exercises................................................................................................................ 144 Chapter Eight—Further Explorations in Immediate Inference.....................146 The Interrelations Among General Propositions............................................. 146 Shorthand Ways of Expressing General Propositions..................................... 147 The Opposition of Propositions......................................................................... 148 Contradictory Opposition....................................................................................149 Contrary Opposition............................................................................... ..............152

viii

C ontents

Subcontrary Opposition......................................................................................... 155 Subalternation..........................................................................................................156 Summary of Possible Inferences Among General Propositions....................... 158 The Square of Opposition..................................................................................... 159 Other Forms of Immediate Inference...................................................................164 Review Item s........................................................................................................... 166 Exercises.................................................................................................................. 166

Chapter Nine—Reasoning .........................................................................................168 The Third Act of the Intellect................................................................................168 Reasoning and Argument.......................................................................................169 Complexity in Argument........................................................................................171 Deductive Reasoning............................................................................................. 174 Mediate Reasoning................................................................................................ 177 Syllogistic R easoning........................................................................................... 178 Validity and Truth................................................................................................. 179 The Anatomy of a Syllogism ................................................................................180 The Essence of Syllogistic Reasoning................................................................ 182 The Principle of the Identifying Third................................................................ 184 The Principle of the Separating Third................................................................. 185 The Dictum de Omni Principle.............................................................................. 187 The Dictum de Nullo Principle.............................................................................. 187 Diagraming Syllogism s........................................................................................ 188 Review Item s...........................................................................................................190 Exercises................................................................................................................. 191

Chapter Ten—The Figures and Moods of the Syllogism................................ 192 The Categorical Syllogism ................................................................................... 192 The Figure of a Syllogism ....................................................................................193 The Mood of a Syllogism .....................................................................................194 The Darii and Ferio Moods of the First Figure ..................................................197 The Potency and Versatility of First Figure Syllogism s..................................199 Are There Only Four Valid Moods in the First Figure?...................................200 The Valid Moods of the Second Figure: Cesare and Camestres...................... 201 The Valid Moods of the Second Figure: Baroco and Festino........................... 205 The Valid Moods of the Third Figure: Darapti, Datisi, D isam is..................... 207 The Valid Moods of the Third Figure: Bocardo, Felapton, Ferison.................209 The Controversial Fourth Figure ........................................................................ 211 Reducing Imperfect Syllogisms to the First Figure.......................................... 213 Categorical Syllogisms Containing Non-Factual Propositions....................... 215 R eview .................................................................................................................... 216 Exercises................................................................................................................ 217

Chapter Eleven—The Rules of the Syllogism................................................... 219 Determining Validity by Figure and M ood...................................................... 219 The Rules of the Syllogism .................................................................................220 The Rule Governing the Number of Terms....................................................... 221 The Problem of Equivocation in Argument...................................................... 222 The Rule Governing the Extreme Terms...........................................................225 The Problem of the Illicit Minor........................................................................ 226

C ontents

IX

The Problem of the Illicit Major.........................................................................227 The Rule Governing the Middle Term............................................................... 228 Guilt by Association..............................................................................................229 The Rule Governing Negative Premisses........................................................... 231 The Rule Governing Particular Premisses.......................................................... 232 The Rule Governing Weaknesses in Premisses.................................................235 Summary of the Rules of the Syllogism............................................................ 236 False Premisses and a True Conclusion?........................................................... 237 R eview ................................................................................................................... 240 Exercises............................................................................................................... 240

Chapter Twelve—Variations oh Syllogistic Reasoning; Making Arguments ........................................................................................ 244 Polysyllogism s.....................................................................................................244 The Advantages and Disadvantages of Polysyllogistic Argument.................245 The Rules of the Polysyllogism ...........................................................................246 The Logical Limitations of Polysyllogistic Reasoning...................................247 Sorites................................................................................................................... 249 The Rules of the Sorites Argument................................................................... 250 Enthymemes......................................................................................................... 252 The Ways in Which Syllogisms Are Commonly Abbreviated....................... 253 Responding to Enthymemes.............................................................................. 254 Making an Argument: the Conclusion................................................................ 257 Making an Argument: The Premisses................................................................. 260 A Psychological N ote............................................................................................ 264 Review Item s...........................................................................................................265 Exercises................................................................................................................. 266

Chapter Thirteen—Conditional Reasoning ..........................................................269 The Conditional Way of Thinking...................................................................... 269 Hypothetical Argument........................................................................................ 270 The Anatomy of the Hypothetical Syllogism .....................................................271 The Pure Hypothetical Syllogism ........................................................................273 The Mixed Hypothetical Syllogism:Modus Ponens........................................ 275 The Mixed Hypothetical SyllogismrAforfws Tollens............................... 276 Affirming the Consequent.................................................................................... 277 A Reciprocal Relation Between Antecedent and Consequent.......................... 279 Denying the Antecedent....................................................................................... 280 The Relation Between Categorical Syllogisms and Hypothetical Syllogism s...................................................................................282 The Dilemma Argument: Modus Ponens............................................................283 The Dilemma Argument: Modus Tollens............................................................285 Probable Hypothetical Arguments....................................................................... 287 R eview .....................................................................................................................290 Exercises................................................................................................................. 291

Chapter Fourteen—Inductive Reasoning............................................................. 294 Deduction and Induction...................................................................................... 294 Where Inductive Reasoning B egins....................................................................295 The Uniformity of Nature ....................................................... 296

X

C ontents

Inductive Reasoning as Ordered to the Discovery of Causes........................... 299 Scientific Method.................................................................................................... 302 Observation and Experiment.................................................................................303 Forming Hypotheses.............................................................................................. 305 Testing Hypotheses................................................................................................. 307 From Hypotheses to L aw s..................................................................................... 309 The Canons of Induction....................................................................................... 310 Inductive Reasoning as Ordered to the Confirmation of Properties................313 Opinion P o lls............................................................. 317 Inductive Reasoning and the Social Sciences..................................................... 318 Argument by Analogy............................................................................................ 320 Review Item s............................................................................................................322 Exercises.................................................................................................................. 322 Chapter Fifteen—Fallacious R easoning.................................................................325 What Is Fallacious Reasoning?............................................................................ 325 Why Study Fallacious Reasoning?.......................................................................327 Formal and Informal Fallacies.............................................................................. 327 General Review of the Formal Fallacies.............................................................. 328 Fallacies Related to Language.............................................................................. 329 Begging the Question............................................................................................. 332 Missing the Point.................................................................................................... 333 Straw M an................................................................................................................334 Hasty Conclusion....................................................................................................335 Sweeping Generalization.......................................................................................337 False Dilemma........................................................................................................ 337 Fallacy of Composition.........................................................................................339 The Appeal to Ignorance.......................................................................................340 Improper Appeal to Authority.............................................................................. 340 Two Wrongs Make a R ight................................................................................... 342 The End Justifies the M eans................................................................................. 343 Tu Q uoque............................................................................................................... 344 Ad Hominem............................................................................................................ 345 The Genetic Fallacy................................................................................................346 Simplistic Reductionism........................................................................................ 347 Special Pleading..................................................................................................... 348 Dismissive Ridicule................................................................................................349 Red Herring............................................................................................................. 350 Ad Populum.............................................................................................................351 Ad M isericordiam .................................................................................................. 352 Ad Baculum.............................................................................................................352 The Last Word: Truth............................................................................................ 353 Review Item s...........................................................................................................354 Exercises..................................................................................................................354 A p p en d ices....................................................................................................................359 Chapter O n e ............................................................................................................ 359 Chapter T w o ............................................................................................................ 362 Chapter T hree......................................................................................................... 367

C ontents

XI

Chapter Four...........................................................................................................370 Chapter F ive............................................................................................................374 Chapter S ix ..............................................................................................................375 Chapter Seven.........................................................................................................377 Chapter Eight..........................................................................................................381 Chapter N in e...........................................................................................................382 ChapterTen.............................................................................................................385 Chapter E leven....................................................................................................... 390 ChapterTwelve......................................................................................................391 Chapter Thirteen.................................................................................................... 395 Chapter Fourteen.................................................................................................... 396 Chapter Fifteen....................................................................................................... 399

N o te s .............................................................................................................................. 403 Bibliography ..................................................................................................................405 I n d e x .............................................................................................................................. 411

X1U

Preface

is book has its remote origins in the set of lecture notes I had been sing for a large number of years for the course in logic which I taught at number of institutions in the M idwest and in the East, usually in the fall term only, but sometimes in the spring term as well. In 2003, at the time happily ensconced as a m em ber of the faculty of Our Lady o f Guadalupe Seminary, Denton, Nebraska, I decided to expand those notes, give them more rigid organization, and cast them in the shape of a book, a book which, though it had a certain completeness to it, still needed considerable fleshing out, and in the form it then took could perhaps best be described as a work in progress. We would have it printed locally on a year to year basis, running off just enough copies to cover the num ber o f students in my logic course. Subsequently I subjected the original book to a thorough revamping, and for two years used the new and im proved version in my logic course. So, first in its somewhat crude then in a more polished form, the book which is now being presented to the public has been put to the test in the classroom for eight consecutive years, and, in the considered opinion o f the instructor/author who had charge of that classroom — which opinion one hopes is not overly biased— it passed the test rather handsomely. It answered, with appreciable success, the practical demands that can reasonably be required of any textbook. Several years ago I had published a small book on logic (Being Logical, 2004), which I had written very much with a general audience in mind; I did not at all intend that it do service as a textbook, and I myself have never used it in the classroom . As it happened, however, and not a little to my pleasant surprise, a few institutions, mainly colleges and universities but at least one secondary school I know of, have adopted it for classroom use. This book, An Introduction to Foundational L ogic, was from the outset intended to serve as a college textbook, and in a rather special way, for I saw it as meeting a need which is not always met, or met only imperfectly, by the many college logic textbooks which are now available in the marketplace. Most of these books, excellent though they are in so many other ways, tend to assume too much in terms of the background of the average student, and therefor do not begin where they should begin— at the beginning. O f the many deficiencies that can be cited

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regarding secondary education in this country, especially in the public schools, one of the most prominent is the fact that rarely if ever are our students exposed to the subject o f logic. This state of affairs is all the more unfortunate because, so at least it seems to me, the subject o f logic should compose a standard part o f the secondary school curriculum . Every high school student should be carefully instructed in the principles that found clear and cogent thinking. But the situation being in fact what it is, almost all of the students who study logic on the college level come to it for the first time, and therefore they need to have available to them textbooks which take into account the severe limitations of their academic backgrounds in the subject. Too many of our current textbooks, in assuming too much, too quickly get into rather exotic realms such as symbolic logic, for exam ple, and this, besides often baffling and confusing students, leaves them with the erroneous impression that logic is a purely theoretical subject, and has little im m ediate application to our everyday lives. It is for those students, representing the majority of those who study logic on the college level, that this book was written. Its approach endeavors to take into account, I hope successfully, the actual situation, in terms of their background, in which most students find themselves today. Any book owes its existence in the first instance to its author, but no author ever works alone, and his book would never see the light of day were it not for the assistance and cooperation o f many others, more perhaps, if he were to consider the matter carefully, than he would be capable of counting. Here I can acknowledge only a few of those many. First of all, I wish to express my gratitude to the Priestly Fraternity of St. Peter, and specifically to Fr. Eric Flood, F.S.S.P., District Superior for North America, for their gracious willingness to publish this volume. In this regard, I owe special thanks also to Patricia McGovern, the M anager o f Fraternity Publications Service, printer and distributor of this book. I w ant also to express my gratitude to Fr. Josef Bisig, F.S.S.P., the Rector of Our Lady o f Guadalupe Seminary, to my colleagues on the faculty and staff of that rem arkable institution, and particularly to the many students it has been my privilege to teach over my sixteen year tenure here, students who, as a group, are possessed of an intellectual alertness and avidity to learn which I have encountered nowhere else, and from whose association I have benefitted greatly. Am ong my colleagues here at the seminary I want to make special mention, with deep appreciation but not without sorrow, of Dr. John Thombrugh, a fellow philosopher and our Academic Dean, who died quite suddenly early in the spring semester of 2011. John was a good philosopher, which is no small accom plishm ent given the times in which we live, but he was something significantly m ore, in any times: he was a good man. Among my students I want to single out for special thanks Mr. Joshua Curtis, who, without so much as a suggestion on my part, magnanimously volunteered to go through the entire manuscript o f this book in the early stages of production, and whose meticulous reading called attention to any number of glitches in the text.

I

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XV

If I were to attempt to cite all the people to whom I am permanently in debt for whatever knowledge o f logic, or o f philosophy in general, I have acquired, this Preface would rival the length o f die book itself, so I will limit m yself to two names only, Dr. Francis X. Owens, to whom I was first introduced to the subject o f logic as an undergraduate at the College o f St. Thomas in St. Paul, and Dr. Ralph M clnem y, whose telling influence on me was of the kind that could only have been provided by a brother. And then there is Nancy LaRoza. It is no exaggeration to say— I cannot avoid that proform a phrase simply because it happens to be literally true— that this book would never have become a book were it not for her assiduous efforts and the complete dedication she gave to it from start to finish. Her sure eye as a proofreader consistently showed up the limitations of the author in that respect, and her editorial advice and direction provided very valuable help throughout the process of putting the book together. It was she who was responsible for the design o f the book, and she did not shy away from the somewhat irksome task o f assembling the index. My very special thanks to Nancy LaRoza. D. Q. Mclnemy Department of Philosophy Our Lady of Guadalupe Seminary

)

I

1

Introduction What Is Logic? efore em barking on the serious study of any subject, we first need to have a clear idea o f the exact nature of the subject we will be studying, so we begin with a question: W hat is logic? To which question this concise response can be given: logic is the science o f correct thinking. In a m om ent we will explain the implications of identifying logic as a science, but first let us consider that phrase “correct thinking.” W e could use different adjectives to express the same key idea the definition presents to us, describing logic as the science of successful thinking, or the science of efficient thinking. W hat, then, is correct, or successful, or efficient thinking? It is simply thinking w hich fulfills the very purpose o f thinking, which is to arrive at the truth of things. To think logically m eans to think in such a way that one is on the right track to discovering the truth o f whatever it is one is thinking about. To identify thinking as “correct” o f course im plies that there is such a thing as incorrect thinking, and indeed there is. Incorrect thinking is thinking that does not m easure up to its proper purpose because it ends up with false conclusions rather than true ones.

B

C orrect T hinking I s D irected T hinking The ultimate test o f correct thinking is that it arrives at the truth regarding the subject on which it is focused. It is possible at times simply to stumble upon the truth, but that is ju st a m atter o f good luck, and logical thinking can never be a m atter o f luck. Logic is concerned with directed thinking, thinking which is consciously controlled and ordered toward achieving a specific end. It’s im possible to be exact about such matters, but we can guess that a fair portion o f the thinking we do on a daily basis is non-directed, or at least very loosely directed. Perhaps the conscious thought which is most opposite to directed thinking is daydreaming. When we are lost in a brown study it seems that we are com pletely passive with respect to our own minds, and we watch thoughts roll by as if we were mere spectators. But when we are trying to solve a problem,or

2

I ntroduction - W hat I s L ogic ?

trying to remember where we left our car keys, we cannot afford simply to let our mind wander. We have to bring our thought under rigid control, ai m it in a very specific direction. The logician Susan Stebbing nicely summed up the directed quality of thought with the phrase “thinking to some purpose,” which she used as the title to one of her books.1 W hat I s F oundational L o g ic ? Logic is a very large and a very rich subject. Some textbooks focus on a particular kind of logic, such as, for example, symbolic logic. Symbolic logic is an elaborate system of symbols which are intended to serve as replacements for words, and it may thus be understood as a kind of algebraic substitute for any of the natural languages. It was devised for the purpose of bringing to the forefront the bare structures of language and of arguments. It simplifies things by getting rid o f the distractions o f words, with all their denotative and connotative baggage. So, instead o f saying, “If George is running, then George is moving,” we put it in symbolic terms, and write: “P =>Q.” Employing symbols in logic can be quite helpful, and I will be m aking limited use of them in this book. O ther textbooks attem pt to give a sampling of various forms that logic can take, the different ways it can be em ployed. There is much to be said for this approach, for if done well, it can provide the reader with an instructive overview of the whole field. This textbook will not follow that approach, however, neither will it seek to concentrate on a specialized form of logic such as symbolic logic. Our intention here is to give as complete and competent an account as possible o f what I call foundational logic. In order to explain what that is, a very brief incursion into history is necessary. It was the Greek philosopher Aristotle (384322 b .c .) who was the first to think about thinking in an ordered and systematic way, and because o f the seminal work he did in exploring the workings of the human mind he fully deserves to be recognized as the father of the science of logic. He wrote six books on the subject, which are collectively known as the O rganon, and in them he laid the foundation for, and gave the basic shape and direction to, all the logic which was to follow.2 W hat I am calling foundational logic, then, can ju st as well be called Aristotelian logic, or classical logic. The premiss that underlies this book can be simply stated: for anyone who is new to logic and wants to learn the subject, the place to start is where logic itself started, with A ristotle. He has provided us with the basic principles that govern all sound hum an reasoning, and once we thoroughly fam iliarize ourselves with those principles, then we are in the best possible position to deal effectively with all the developm ents in logic subsequent to Aristotle. The philosopher Alfred North W hitehead once quipped that all of Western philosophy is a footnote to Plato. T hat m ight be paraphrased by claim ing that all logic is a footnote to Aristotle.

I ntroduction ~ W hat I s L ogic ?

L ogic I s

a

3

S cience

Every science has three basic features: (1) it is an organized body o f knowledge; (2) it is founded upon first principles; (3) it seeks knowledge founded in causality. A science is an organized body o f knowledge. This is the most obvious feature of any science. Every science has a subject matter, what it actually studies, and w hich traditionally has been known as the m aterial objectof the science. A science is in fact identified by its subject matter, so botany is the study o f plant life; m eteorology, the study o f the atm osphere; .o ceanography, the study of the w o rld ’s oceans and the life form s w ithin them . The longer a science has been around, the larger its body of know ledge, and the more active a science, the faster its body of knowledge grows during any period of its history. The science of biology dates back to the time o f A ristotle, well over two m illennia ago, and it accordingly has a huge body o f know ledge, more than even the most com petent o f biologists could hope to master in a lifetime. A science’s body of knowledge is organized, i.e., given logical order, and it is ju st that which makes it a “body.” A loose collection of ideas, disparate bits and pieces of knowledge with no discernible relations among them, would serve no scientific purpose. What accounts for the organization of a science’s body of knowledge is the logical thinking that is carried on within the context of the science. And how about logic itself, what is its body of knowledge? The book that you are holding in your hands attempts to provide you with a reliable sense of logic’s body of knowledge, the subject matter with which it is concerned. It by no means contains logic’s whole body o f knowledge— it would require several hefty tomes to do that— but it does endeavor to give you the essence of it, that core knowledge around which all the rest is structured. A science is fo u n d ed upon fir s t principles. Every science, if it is going to stand, and succeed in discovering genuine truths about its subject matter, must be built upon a sound foundation, and that foundation takes the form of the first principles of the science. A first principle is simply a fundamental or elementary truth, and it is characterized by the fact that it self-evident. Every science needs a starting point, and that starting point is represented by its first principles. They must be so basic and obvious that there is no need to prove them; as soon as they are expressed and we understand them, we immediately see that they are true. One o f the first principles, or axioms, of mathematics is, “the whole is greater than any o f its parts.” If we understand what “whole” means and what “part” means, we know that the statement cannot be anything but true. If there were no self-evident truths that serve as the basis for every science, if it was felt that every rudimentary statement about a science had to be proven, then the science could never even get started. But it is the very nature of self-evident statements that any attem pt to try to prove them would be silly. How would you try to “prove” to someone that a whole is greater than a part? They either see it, or they

4

Introduction ~ W hat Is L ogic?

don’t. And if they don’t, there is no going on from there. It is the self-evident nature of a statement that allows it to serve as the first principle of a science. The first principles of logic are unique in that not only do they serve as the starting points of our science, they also serve as the elementary truths which govern all of human reasoning. We can readily see how this is so, for logic is the science of correct thinking, and we must think correctly whatever other particular science we might be involved in, or, for that matter, in whatever we do. There are four basic first principles of logic: the principle of identity; the principle of contradiction; the principle of excluded middle; the principle of sufficient reason. For the moment, we simply state them; later we will be giving them close consideration. A science seeks knowledge which isfounded on causality. The most valuable knowledge we can have of anything is knowledge which does not simply tell us that something is so but also tells us why it is so. To be sure, knowledge that something is so is o f the utmost importance; this is factual knowledge. But if we know not only that a fact is a fact, but can explain just why it is the fact it is, then we have genuine scientific knowledge. It is the knowledge of the causes of things which answers that innocent but most provocative of all questions, “W hy?” Someone who is caught in the midst of a hurricane does not need a meteorologist to apprise him of that fact, but the meteorologist could enlighten him as to the causes of the hurricane, and could have given him some fairly reliable estimates as to the path it was going to take, which, had he paid attention to them beforehand, could have saved him from the plight in which he now finds himself. In logic we concentrate on two types of causes. Most importantly, we want to discover the causes of sound reasoning, so that, knowing those causes, we may put them to work in our own thinking. But it is also important that we be aware o f the causes of incorrect, or fallacious, reasoning. One of the best ways o f avoiding mistakes is knowing their causes. T he S pecial M ind-S et R equired

for the

Study

of

Logic

Logic, we say, is the science of correct thinking. In order profitably to pursue this science we must do something which is rather unusual: we must think about thinking. This is an occupation which, it seems safe to say, most of us seldom engage in. We do not think about thinking, we simply do it, and indeed, so it would appear, non-stop. We even think when we sleep, while engaged in that peculiar form o f mental activity we call dreaming. So, when we study logic we must attune ourselves to a kind of activity which we are not used to. We must not simply think— in any event we cannot avoid doing that— but we must observe the way we think, so as to make sure that we are thinking correctly. In this little drama we are both actor and audience.

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L ogic I s

a

5

P ractical S cience

Not everyone would agree with the assertion that logic is a practical science. Some logicians would want to maintain that logic can be regarded much as we would regard pure mathematics, that is, as having no direct reference or application to “the real world,” the world o f our everyday experiences. That logic can be regarded in that way is simply a matter of fact, and there are some real benefits from doing so. But the point o f view I am taking in this book, the conviction with which it is written, is that logic is essentially a practical science. We should want to learn logic, school ourselves in the ways of correct thinking, not simply to engage in mental gymnastics or to make our way freely and ably in the realm of pure theory, but so that we can function as rational agents in our day to day lives. The knowledge we gain from the study of logic is meant to be put to use. There is, of course, plenty of theory associated with logic, as you will soon discover, but it is theory that is directed toward action. To “be logical,” in the best sense, m eans more than ju st having ready-to-hand a certain type of knowledge, im portant though that is; it means that the knowledge makes a difference, practically, in the whole o f your life. L ogic I s

an

A rt

To say that logic is a practical science is almost the same thing as saying that it is an art. So, let us make the matter explicit: logic, as well as being a science, is an art as well. And it is an art of a very special kind. St. Thomas Aquinas, in his Preface to his commentary on Aristotle’s Posterior Analytics (one of the six books Aristotle devotes to the subject of logic), goes so far as to describe logic as the “art of arts.” It deserves that honored title, he explains, because it “directs the acts of reason, from which all the arts proceed.” 3 The gist o f his thinking there could be expressed in the following way: because logic has principally to do with reason, and because reason should govern all human activity, logic should govern all human activity. In w hat sense can logic be considered an art? In order to provide an adequate answer to that question we must first ask a more basic one: W hat is art? St. Thomas provides a solid answer to that question by describing art as “correct thinking as applied to m aking.” 4Every artist is a maker, turning out “products” of one kind or another. The quality of the artist’s product will depend fundamentally on two things: the artist must be in possession of the knowledge which is proper to his art; and he must have the know-how, the peculiar skill, to be able properly to apply that knowledge. Logic, as an art, is a making activity, and the principal product it is con­ cerned with turning out takes the form o f good arguments, which is to say, arguments whose structure and contents are such that they consistently yield true conclusions. To be a maker o f good arguments, the artist/logician must have a firm grasp of logical theory, and he must be adept in applying that theory.

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A critically important part of every art is practice, for it is only by practice that the art is perfected. Consider the medical profession, whose members, in­ terestingly, we commonly refer to as being engaged in “the practice of medicine.” M edicine, like logic, is both a science and an art. A doctor must have at his beck and call extensive theoretical know ledge, in the form, say, o f an easy fam iliarity with specific sciences such as chem istry and human physiology. But what really makes a good doctor is his artistry, his skill as a practitioner, his ability to put theory to work to achieve beneficial therapeutic results. We would naturally suppose that a doctor who has been practicing for ten years would be more skilled in the art of medicine than when he first started out, and of course the explanation for that is the practice itself. There is but a single path to be followed in order to become proficient in any art form, and that is the path o f practice. And so it is with the art o f logic. There is no warrant for minimizing the im portance o f m astering logical theory, but theory alone is not enough. We m ust develop the skills that allow us ably to apply that theory, and we gain those skills only through practice. Specifically, we must learn the diagnostic skills which allow us to distinguish good arguments from bad ones, and, more importantly, we must ourselves become proficient makers of good arguments. As rational creatures, there is no activity more natural for us than thinking. Thinking is natural; thinking well is not. We have to work at perfecting the latter. And we have ready to hand the perfect means of doing so, and that is logic— the science and the art. We should not consider it to be at all odd that we can become better thinkers simply by consciously and perseveringly practicing better thinking. Clear, cogent thinking, keen reasoning, is developed and perfected by clear, cogent thinking, by keen reasoning. It’s really as uncomplicated as that. The mind, like the body, must first be gotten in shape by exercise, then, once in shape, it must be kept in shape by continuing exercise. L ogic

and

T ruth

Logic is, must be, uncompromisingly committed to the truth. To say that is ju st another way o f calling attention to logic’s practical orientation. Truth is essentially a relation, a relation between the mental and the extra-mental, betw een our thoughts and those things in the external world to which our thoughts refer. If the ultimate test of correct thinking, as we have said, is that it leads us to the truth, then correct thinking is that whereby we keep in healthy touch with the objective order of things, the way things actually are in the real world, for truth is sim ply the bond between the subjective realm and the objective realm.

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B eing L ogical

and

7

B eing " L ogical "

There are two ways in which the adjective “logical” can be applied to thinking, only one of which is fully authentic. We can refer to people as being logical simply because they are consistent in the way they think. Consistency, just in itself, is a good thing, but as Ralph Waldo Emerson once pointedly observed, “a foolish consistency is the hobgoblin of little minds.” 5Thinking is foolishly consistent if it is consistently wrong-headed. Adolf Hitler can be said to have been remarkably consistent in his thought, but the problem, and a very grave problem indeed, was that the principles from which most of that thought proceeded were radically erroneous. There is no merit whatsoever in being a consistent thinker— “logical” in that sense only— if the thought about which one is being consistent is completely divorced from reality. If someone is in Peoria and wants to get to Chicago, and embarks upon his journey by heading due south, he may show marvelous consistency as he bravely forges ahead, but he will never make it to Chicago, unless, that is, he manages to circle the globe. We must necessarily strive to be consistent, but consistency alone is not enough. The only authentic way o f being logical, according to foundational logic, is to achieve a consistency which is not simply internal to our own thought— a madman can do that— but one which marries our minds with the objective order o f things. In other words, we want our thought to be consistent with, to reflect, the way things really are. This simply comes back to the critical importance of truth for logic. F ormal

and

M aterial L ogic

One o f the distinctions that figures rather large in the classical logic which is the subject o f this book is betw eenform al logic and material logic. Formal logic, as its name suggests, focuses on the forms, or structures, o f thinking, whereas material logic gives its attention to the actual contents of thought, the ideas them selves and what they refer to. Thus, formal logic is primarily interested in, say, the way terms are arranged in an argument, how they are physically placed in relation to one another, so as to make up a certain configuration. This is not a trivial interest, for how an argument is configured can make a big difference with respect to its validity. Material logic, on the other hand, is more concerned with what an argument is actually saying, what it is about, and whether or not the propositions it contains square with the state of affairs in the real world. Foundational logic occupies itself with both formal and material logic. We are very much concerned with how arguments are put together, their form, but we are no less concerned with what they say, their content. And this is how it should be, for the two, form and content, are inextricably tied up with one another. How we say things and what we say are certainly distinct, but they

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I ntroduction ~ W hat I s L ogic ?

cannot be completely separated, and they constantly play upon one another. We can say the right thing in the wrong way, and the wrong thing can be put in such a way to make it sound right. One o f the values o f learning logic is that it makes us more sensitive to the uses and the abuses o f language.

9

Chapter One The Sources of Logic: The Three Acts of the Intellect T he A

pproach

T aken

by

T his B ook

As is the case with any other discipline, so too with logic, there is more than one way in which it can be effectively approached. The approach which we will take in this book can be broadly described as inductive, in that we will begin with the particular and proceed to the general, or, to put it another way, we will begin with what is simpler and then work our way systematically to and through what is more complex. In more concrete terms, that means that we will begin with ideas, which are the basic building blocks of that large and impressive edifice we call the science of logic. More than that, ideas are the basic building blocks, the seminal sources, of all human thought. From the study of ideas we will m ove to studying how ideas are put together to form meaningful statements. Finally, we will busy ourselves in exploring how statements are put together to form arguments, which are the linguistic vehicles that convey the efforts of the human mind to arrive at the truth of things. This third stage of our journey will occupy most of our time and attention, for argumentative discourse represents the very heart of logic. What I have just briefly described have been traditionally known as the three acts o f the intellect. The human mind— the intellect— is a powerful and versatile instrum ent, whose activities are many and varied and seemingly incessant, but all its complex operations have their source in, are elaborated expressions of, three basic acts: simple apprehension; judgment, reasoning. T he F irst A ct

of the

Intellect: S imple A pprehension

Sim ple apprehension is that mental activity whereby we form ideas. To apprehend something, from a logical point of view, means to grasp it mentally, to understand it. And we do that through the medium of ideas. We have already described an idea, metaphorically, as the basic building block of logic, indeed, o f all human thought. When we think, about anything whatever, it is ideas with

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T he S ources of L ogic : T he T hree A cts of the I ntellect

which we are dealing most directly. This is where we necessarily start. It would provide us with a more precise understanding of the nature of an idea if we were to describe it as a mental image whose function is to be a bearer of meaning. And now, an exact definition: An idea is a m ental im age that reflects the nature o f its o bject. It is not expected that that definition will be immediately com prehensible to you, but in due course it will be, for in later pages we will give it close examination. For the time being, two brief points of clarification are in order. First, the “image” referred to in the definition is not necessarily a visual image, though it may involve the visual. What is being referred to, in the most general terms, is simply a mental entity, a “thing” existing within, rather than outside, the mind. Second, the “object” of an idea is that to which it refers, what the idea is “about.” To better fam iliarize ourselves with the nature of an idea, in these early stages o f our investigation, let’s consider two other words that serve as synonym s for “idea” : notion and concept. Our English word “notion” (“I once had the notion o f becom ing a farm er”) comes from the Latin n o tu s , the past participle o f the verb n oscere, which means “to know.” An idea, then, can be regarded as the basic m eans by which we come to know anything at all. It represents the first step in human intellection. The word “concept” (“Entropy is one o f the m ajor concepts in modern physics”) also comes from Latin, in this case from the noun con ceptu s , which means “that which is conceived.” This bit of etymological lore is especially revealing because it alludes to two important facts: (a) ideas are not part of the original “equipment” of the mind; and (b) they do not spring forth spontaneously from the mind, but result from the m ind’s encounter with the world. Ideas are engendered in the mind by our experiences with what lies outside the mind. We speak tellingly of “conceiving” ideas; they are the result of mental conception, and mental conception is just another way of saying “simple apprehension.” We are not bom with ideas, then, but ideas are continually being born within us. Just as there is no spontaneous generation in the biological realm, neither is there in the mental realm. An animal cannot conceive unless it is im pregnated. In a com parable way, the mind cannot conceive ideas unless it is caused to do so by the active influence of things in the external world. Ideas, we may say, are our knowing response to that world. A less common but especially provocative synonym for “idea” is “mental word.” A mental word is a word that we first speak to ourselves. A word, even one we address exclusively to ourselves, only makes sense if we grasp the nature of that to which the word refers. If I say to myself “gumbowlzee” (aword I ju st made up), and if I say it out loud, it is sound without meaning, and that is because it has no referent, no “object.” To be able to speak a real word, mental or oral, implies knowledge. An idea is a unit of knowledge, and this emphasizes its role, noted above, as a bearer of meaning. Simple apprehension, the first act of the intellect, is that mental operation by which ideas are brought into being.

T he S ources of L ogic : T he T hree A cts of the I ntellect

T he G enesis

of

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I deas

W here do our ideas come from? We have already made two negative assertions about the genesis o f ideas: there are no innate ideas; they are not generated spontaneously. It is the business of psychology, not logic, to give us a detailed, credible account of how ideas originate, but, as students of logic, it is im portant that we have at least a general understanding of the matter, given the critically important role ideas play in our science. We have said that the conceiving o f ideas inside the mind is a response to what is happening outside the mind. This fact is articulated in one of the fundamental principles governing hum an psychology, stated as follows: There is nothing in the mind which does not come through the senses. All of our ideas have their source in sensation. And because ideas are the foundation o f all of our knowledge, this means that all of our knowledge has its source in sensation. H um an know ledge is divisible into two realms, sense knowledge and intellectual knowledge, and it is the latter which is the realm of ideas. But it all begins with sense know ledge, and sense knowledge begins with the five external senses with which we are all quite familiar: sight, hearing, smell, taste, and touch. The external senses are passive, in that they are not self-activating, but depend upon external stimuli in order to perform their proper functions. The eyes, the organs of sight, might be in perfect condition, physiologically, but they are activated only when there is light. By the same token, the ears hear only in the stim ulating presence o f sound waves. And so it is with all the external senses. T heir action is essentially a form of reaction, a response to stimuli. A sensible is simply anything that can be sensed, whatever activates any of the external senses. A proper sensible is one which activates a specific sense organ; it is “proper” to that organ, pertains to it alone. Thus, the proper sensibles o f the five external senses can be stated as follows: sight— the visible; hearing— the audible; smell— the odoriferous (i.e., that which emits a smell); taste— the saporous (i.e., that which yields some kind of taste); touch— the tangible. (See Appendix A for further discussion of the principle, There is nothing in the m ind that does not come through the senses.) T he I nternal S enses The five external senses do not represent all of our powers of sensation. To be added to them are the four internal senses: the common sense, imagination, m em ory, and the estim ative sense. The internal senses are called “internal” because, unlike the external senses, they do not have specific physical organs through which they exercise their power; they are called “senses” because they have directly to do with sense knowledge, not intellectual knowledge. What we are calling the common sense here is not to be confused with the phenomenon which in ordinary parlance we call common sense, as when we say, for example, “Jack has a lot o f common sense,” meaning thereby to convey the idea that he

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is possessed o f a good deal o f practical wisdom. The rationale for positing the. existence o f the com m on sense is based upon the twin facts that each of the external senses knows only its proper sensible, and they do not communicate with one another. The eyes know only the visible, and the ears only the audible, and they do not inform one another o f the specialized sense data each has gathered from the external world. There is thus the need for an additional power, comm on to all the external senses, which brings together the data gathered by each o f those senses and integrates them in a single sense image. It is the com m on sense that enables us to know that different sensations that we are experiencing have their source in one, particular object. So, for example, it is through the action o f the comm on sense that I relate the colors of black and white I see, the very pungent odor I smell, and the sound of tiny feet scampering over the ground I am hearing, to that fleeing animal to which I give the name “skunk.” The task o f the internal sense called imagination is to record and store the information we receive from our external senses. Memory is the internal sense which recognizes and recalls the information which has been stored away by the imagination. The estimative sense receives its name because it “estimates” the value o f what is being sensed in term s o f its positive or negative effect on the sensing subject. The smell of fresh coffee brings a positive response on my part, but I experience a strong negative response if I catch the whiff of a skunk. All of your internal senses are in action while you are actually undergoing any sense experience. You can easily prove this by reflecting on any specific experience. Let us say that yesterday afternoon, while driving to the superm arket, you came very close to having a serious accident. You had just entered an intersection, traveling well under the speed limit, when all of a sudden a speeding car on the cross street comes bearing down on you, going through a red light. You slam on your brakes, swerve sharply, and because of complementary actions taken by the other driver, there is no collision. It was the comm on sense that brought all the various particular sensations you were experiencing in those few seconds into a single event. The fact that you could tell people about the event later shows that imagination was at work at the time, recording it and storing it away. And memory tells you that what imagination recorded was som ething that actually happened in real time— yesterday afternoon, at around 2:45. Finally, the accelerated heart beat and the flow of adrenalin you experienced is explained by the response of the estimative sense. The fact that this was a sense response accounts for its immediacy. Y ou did not have to pause and think about it in order to know that you were in a precarious situation. There was no time for cogitation. The special value of the estimative sense is that it serves as a kind of “first responder,” going into action before any thought processes begin. W e know that m em ory is operative while we are actually experiencing sensation because o f the phenomenon o f recognition, our ability to know that

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what we are sensing right now is som ething we have sensed on a previous occasion. You are able immediately to recognize the face or the voice of your friend because of the information instantaneously provided to you by memory. The im agination records, and the memory remembers, images that have their origin in each o f the external senses. T he S ense I mage A s the P roduct Internal S ensation

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Once the individualized sense data provided by each of the external senses is identified by the common sense as having its source in a single object (let us say, a rose bush), and then is responded to by each of the other three internal senses (im agination, memory, estim ative sense), then we have what may be called a completed sense image. It is called a sense image because it is limited to the kind of knowledge which is provided to us by our senses. The way I have ju st described the actions o f the external and internal senses may leave the erroneous im pression that our sense knowledge results from a somewhat plodding sequence of events, with first the external senses offering their data, and then the internal senses responding, one after another, to that data. But actually the whole process takes place instantaneously. Picture seven-year-old Joan standing transfixed before a rosebush in her grandm other’s backyard, staring steadily and admiringly at it. She has in her mind a sense image of what she is looking at. She has a clear visual image of the rosebush. She takes a couple of steps toward it, bends over and smells one of the roses. Then she touches the petals of the rose and notes its soft, silk-like texture. She now has three quite distinct sensations relating to the rosebush— visual, olfactory, and tactual. Joan’s imagination is at work as she looks at, smells, and touches the rosebush, because she is going to remember this experience later, and perhaps tell people about it. But her memory is active at this very moment, and that explains how Joan can recognize this rosebush as the very same one she was standing in front of several months before, when it was not blooming. The pleasure that Joan derives from her various sensations indicates the positive response o f her estim ative sense to the rosebush. Each of those distinct sensations that Joan is experiencing can be called an image. As noted earlier, when we speak of images we most commonly think of visual im ages, and perhaps that is because visual images seem to leave the deepest imprints on our minds. But all of the five senses produce distinct mental images, so that, besides visual images, there are auditory, olfactory, taste, and touch images as well. The proof o f that is the fact that, while we can bring before our m in d ’s eye an object we have seen som etim e in the past— say, M ount Rushm ore— we can also remember, and therefore recognize, the sound of a jet plane, the smell of burnt toast, the taste of chocolate, the feel of sandpaper when we run our fingers across it. In some people, certain sense images m ight be

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considerably more potent than others. It would seem, for example, that musicians have especially strong auditory images. Standing next to Joan is her dog Rover. He is also looking at the rosebush, perhaps not with the same degree o f interest as is Joan, but he is nonetheless looking at it. Does Rover have a sense image of the rosebush? He does. He can have the full panoply o f external sensations relating to that instance of floral existence. Besides seeing the rosebush, he can hear its leaves rustling in the wind; he can smell it; he can taste it, if he were to start chewing its leaves; and he can feel it, should he brush up against it and be pricked by one of its thorns. Not only do all the higher animals have the same external senses as do we, but often certain of their senses may be far superior to ours. Joan’s sense of smell and o f hearing are no match for Rover’s, but the sense of sight of neither of them could measure up to an eagle’s. But how about the internal senses, is Rover equipped with those? He is. Dogs like Rover, and all of the higher animals, have the common sense, which is shown by the fact that they can fix their attention on a particular object and clearly associate any num ber o f particular sensations with that object, as dem onstrated by Rover when he spots a rabbit and chases it across the yard. T hat dogs have im agination and m emory is demonstrated by their ability to retain im ages o f objects which are not being sensed here and now, and to recognize them when they reappear. W hen Joan goes off to school in the morning, Rover goes into a blue funk and remains in it the entire day. His canine sadness would seem to be best explained by his ability to retain an image of his absent m istress (im agination). W hen Joan returns from school he of course immediately recognizes her (memory), and practically wags his tail off in sheer doggy delight in response to her presence (estimative sense). T he D istinction B etween S ense I mages

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I ntellectual Images

We have called attention to the two basic kinds of human knowledge, sense knowledge (which we share with the higher animals) and intellectual knowledge, which is peculiar to humans. We said that sense images belong in the realm of sense knowledge— they could be called the basic building blocks o f that kind o f knowledge— and that ideas belong in the realm o f intellectual knowledge. It is very im portant to stress the real distinction between a sense image and an intellectual image, or an idea. But first of all, let us be reminded of what they have in common: they are both mental entities, and, as such, do not subm it them selves to any kind of empirical measurement. The presence of a sense image might be announced by synaptic activity in a particular part of the brain, but the synaptic activity is not the sense image. To get at the heart o f the distinction between a sense image and an intellectual image— which from now on we will refer to as an idea, for they are one and the same— we need to recall the definition of an idea which was provided above: It is a mental image that reflects the nature o f its object. Both

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a sense image and an idea have an object, e.g., the thing in the external world they represent. The rosebush is the object of the sense image possessed by both Joan and R over, but Joan has som ething that Rover doesn’t, and that is a knowledge o f the rosebush precisely as a rosebush. She knows not only that she is sensing in various ways (seeing, smelling, feeling) a real, concrete object in front o f her, but she knows what she is sensing. She grasps the nature of that real, concrete object, and she does so through the medium of an idea. The most obvious indication that Joan has an idea of what she is sensing is the fact that the term “rosebush” is m eaningful to her, and that is the term she uses later in the day when she is describing to her father the experiences she had earlier in her grandm other’s backyard. A very common experience brings home the real distinction between a sense im age and an idea. W henever we find ourselves confronting an object of whatever kind and we ask the question, What is that? we are disclosing our state o f m ind to be such that: (a) we definitely have a sense image; (b) but we do not have an idea. You are standing before an enclosure in a zoo peering with no little am azem ent at a duck-billed platypus, the likes o f which you have never seen before. And you ask your companion, “What is that?” Your companion replies, not very helpfully but quite revealingly for our purposes here, “I have no idea.” That is precisely it. Neither of you have an idea of what you are sensing because you lack know ledge o f its nature, knowledge of the kind of thing it is. So you both take note o f the plaque attached to the enclosure and learn that the object before you is a duck-billed platypus. You have both learned something, added to your store o f ideas. Should you later happen to find yourself in Australia or Tasmania and see there one o f those memorable mammals, you can readily identify it. We fairly com m only run into things whose nature we cannot precisely identify, and therefore have no precise name for. It is not that we are ever completely in the dark. In the most general sense, we know that we are confronting a real “thing,” som ething that actually exists in the external world. In other words, we know that we are not suffering from illusions. Less generally, we know that we are dealing with a machine of some sort, or an animal, or a bird, but we do not know w hat kind o f m achine it is (W hat does it do?), or the kind of animal, the kind of bird. W hen we come to know that, then we have an idea of the thing. We have both sense knowledge of it, and intellectual knowledge as well. T he R elation B etween S ense K nowledge Intellectual K nowledge

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T he nature o f the relation betw een sense knowledge and intellectual know ledge is this: intellectual knowledge depends on sense knowledge. To bring the m atter into sharper focus we put it this way: the intellectual image (the idea) is dependent on the sense image. The sense image necessarily precedes the idea, and if we w ere incapable o f form ing sense images, then we would be

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incapable o f having ideas. A sense image is, as it were, transformed into an idea by the process o f abstraction, whereby the m ind discovers the nature o f the object whose presence is being registered by the senses. We have already said that the nature o f any object is simply what it is— a dog, a cat, a rosebush. The most distinctive feature of what we call the nature of an object is that it is som ething which is shared by that object and all objects o f the same kind. Y ou share the sam e nature with all other hum an beings, and that is what gives m eaning to the term “human nature.” O nce we know, through ideas, the natures o f various objects, then we im m ediately recognize them for what they are, the particular kind o f objects they are. You are out w alking in the park and you see a dog which, just as that dog, you have never seen before. But you have no trouble at all recognizing it as a dog. You have the “right idea” about that object. The inestim able value of ideas, then, is that they provide us with a very precise and specific kind of knowledge o f the world in which we live. Because intellectual knowledge relies on sense knowledge, ideas on sense images, the quality o f our ideas depends on the quality of our sense images, and the quality o f our sense images, in turn, depends, ultimately, on the reliability of the data provided to us by the external senses. If Joel’s eyesight is not as good as it could be, or, say that there is nothing wrong with his eyes but he is in a situation where visibility is very poor, he could squint off into the distance and identify as a Shetland pony what is as a matter o f fact a St. Bernard. He has the wrong idea about the world to which he is responding, and that wrong idea— Joel know s the difference betw een a Shetland pony and a St. Bernard— is explained by the imperfect sense image on which it is based. Our external sense organs, though they may be in tip-top working order, are limited in the range of things they are able to register (our sense o f hearing is not as acute as a dog’s), but we can enhance the pow er o f our senses by giving them technological assists. W e did not know o f the four new moons o f Jupiter until Galileo came along with his telescope and trained it on that planet. Enhanced sensation rem ains sensation. If you are seeing stars through a telescope, you are seeing stars. (See Appendix B for a discussion o f differences in the sense powers.) T he I dea A s M eans T he object o f an idea, as we noted, is sim ply what the idea is about. The object o f Jo an ’s idea o f a rosebush was the rosebush in her grandm other’s backyard; that’s what her idea was about. But notice this: though her attention was focused on a particular rosebush at a particular place at a particular time, the very fact that she knew that it was a rosebush she was reacting to shows that she had a know ledge o f rosebushes in general. T hat’s what it means to say that an idea provides us with knowledge of the nature of an object. The idea of rosebush tells Joan that this particular plant before which she is now standing is not unique, but is one instance of a specific kind.

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Is the idea o f rosebush in Joan’s mind the same thing as the rosebush itself, the physical object she is looking at, and sensing in other ways? Obviously not. Her idea o f rosebush, unlike the rosebush, is not material. It really exists— who can deny the reality o f ideas?— but it exists immaterially, as a purely intellectual entity, a “mental thing.” The idea of rosebush is the means by which Joan knows the rosebush. The object of Joan’s knowledge is the rosebush itself, that is what she is actually thinking about, but she could have no knowledge of the rosebush were it not for her idea o f rosebush. The idea o f rosebush— the intellectual image which she holds in her mind— is the one and only way that she can make contact with the object that exists outside o f her mind and is independent of it. Real, concrete objects in the external world, then, can be the objects of ideas, and it is ju st those ideas which “connect” us with those objects. But it would seem that we can also have ideas of things for which there are no corresponding real, concrete objects existing in the world outside the mind. The mathematician can have an idea of a triangle, a very precise idea, rich with nuance, the likes of which is not to be found in the real world. His idea is of a triangle whose internal angles add up to exactly 180 degrees, not the minutest fraction of a degree more, not the m inutest fraction less. But it is safe to surmise that there is not to be found anywhere in the universe a real, concrete triangle, a physical object, that m easures up to those exacting standards. If this is so, does it not take the wind out o f our principle, stated above, that all our intellectual knowledge is dependent on sense knowledge, for sense knowledge is nothing else than the know ledge o f real, concrete things, sensible things? No, it doesn’t. Even the m ost abstract o f mathematical ideas are ultimately traceable back to sensible objects. Granted, there is no one-to-one equivalent between the mathematician’s idea o f triangle and any physical object to be found in the external world, but the m athem atician’s perfect triangle is an abstraction from the admittedly imperfect but nonetheless distinctly triangular shaped things to be found in that world. The proto-mathematician who first started thinking about circularity in m athem atical term s was possibly inspired one evening when he was sitting outside his cave, gazing wonderingly at a full moon as it rose luminously over the distant hills. Ideas themselves can be the object of ideas, and this is what happens when we think reflectively. We focus our attention on an idea just as an idea, and put it under close examination, perhaps for the purpose of determining its quality. Take as an exam ple the idea o f justice. The proper object o f this idea is som ething that can be identified as actually existing in the real world— a particular way in which people behave toward one another, which we would describe as “ju st.” It is to that reality that my idea o f justice is related, though perhaps not very directly. One day I begin to think seriously about justice, not about how it may or may not exist in the external world, but about my idea of justice. I have some doubts about it, and wonder if it is in fact a sound idea. In our ordinary language we often make the distinction between good ideas and

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bad ideas. That is an entirely legitimate distinction, and later we will be looking into it with some detail. But the point to be made here is that even when we are involved in highly abstract reflective thinking, where ideas themselves become the immediate objects of our thought, ideas do not cease to be the principle means of thought, for we think about ideas through the medium of ideas. In the ordinary course of mental events, we do not think about our ideas just as ideas; in fact, we are almost always completely unconscious of them as such. It is as if the ideas were not really there. What is very much there, at the forefront of our consciousness, is the content of our ideas, what the ideas are about. Imagine gazing down at a little basket of luscious, freshly picked strawberries. Chances are you would be completely oblivious of the little basket, totally concentrated as you are on the strawberries. Let the strawberries stand for the object of the idea and the little basket the idea itself. It’s far from a perfect comparison, as we shall see later, but at least it serves to illustrate the relative degrees of awareness we usually give to ideas and to their objects. In logic, as in mathematics, we deal with many ideas that do not have a direct, one-to-one correspondence with objects in the external world, but it is precisely because all of our ideas are rooted in the external world, because they have their ultimate source there, that they can have practical application to that world. There may not be any perfect triangles out there, but we can do some very useful things with trigonometry. T he S econd A ct

of the Intellect:

J udgment

The first act of the intellect gives rise to ideas, and it is through ideas that we are put in contact with all the fascinating particulars of the world in which we live. The second act of the intellect, judgment, is the mental operation by which we put ideas together in order to determine what is true and what is false in that world. Judgment is that intellectual act, that mental operation, by which real, i.e., extra-mental, existence is ascertained. Through the first act of the intellect we come to have, through the medium of ideas, knowledge of individual things, and when we know the natures of things we can assign names to them, and thus confirm their distinctness. W hen the mind entertains the idea “chicken,” or “table,” or “tree” it thereby shows that it has at least a primitive knowledge of what makes a chicken a chicken, a table a table, and a tree a tree, and it is not likely to confuse them, mistaking one for another. But there may be instances where we might have clear and confident knowledge of a particular nature without knowing whether there is any actually existing entity that embodies that nature. In other words, we can have a very clear idea of something, but the mere fact of the existence of the idea in the mind does not mean that the referent of the idea, its object, really exists outside the mind. For example, we can have a clear idea of what a centaur is, but there is nothing in the real world that corresponds to it. Ideas, then, clear and vivid though they may be, do not, just as ideas, tell us anything about real, that is, extra-mental, existence. It is the mental

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operation called judgm ent which ascertains whether or not a particular idea refers to a real existent. We can have a very clear idea which bears the name, “World Trade Center,” and we owe that idea to the fact that it refers to something which once really existed. But judgment tells us that there is now no actually existing thing to which that particular idea corresponds. C omposition

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D ivision

The second act of the intellect, or judgment, has traditionally been referred to as composition and division, a fitting way of describing it for it calls attention to what the mind is actually doing— composing ideas (connecting one with another), or dividing them (recognizing that, in terms of what obtains in the real world, they simply do not go together). The subject of composition and division, then, is the specific ideas which are born out of simple apprehension. Just as the results of the first act of the intellect are expressed in words, the results of the second act of the intellect are expressed in sentences, more exactly, in that type of sentence which grammarians call declarative. A declarative sentence, recall, is one that states, without ambiguity, that something is actually the case. “Joan is in the second grade” is a declarative sentence. In logic the term we use to identify declarative sentences is proposition. The following two propositions reflect the process of composition, where two ideas are conjoined. The table is in the corner. The tree is diseased. What is being composed, or brought together, in the first proposition is the idea of table and the idea of being placed in a comer. In the second proposition, a union is being forged between the idea of tree and the idea of being in a diseased state. Now, these two propositions are reflective of, stand as the linguistic expressions of, the second act of the intellect, which ascertains real existence. We could, in each case, express real existence in a much more blunt way, as follows: The table is. The tree exists. We seldom talk that way, however, nor is there much need to, for whenever we make any statement, whenever we attribute anything to a particular subject, we are thereby implying, for both subject and what is being attributed to it, actual, extra-mental existence. We could not meaningfully say of “table” that it is “in the com er” if the table did not actually exist and if there were not a real comer in which it could be situated. In like manner, our saying “is diseased” of “tree” is intelligible only if there is a real tree in the external world which really has the quality of being in a diseased state. Our propositions thus stand as the linguistic expressions of the second act of the intellect, the act by which the mind acknowledges real existence.

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N o w le t u s c o n s i d e r tw o p r o p o s i t i o n s th a t a r e e x a m p le s o f th e p r o c e s s o f d iv isio n .

The chicken is not in the bam. Samantha is not happy. We immediately recognize that what distinguishes division propositions is the fact that they are negative, whereas composition propositions are affirmative. The division, or separation, which is taking place is between the subjects and the predicates o f the propositions. In the first, the idea of “chicken’* is being separated off from the idea of being “in the bam.” The two ideas are associated with one another negatively. In the second proposition, the idea of “Samantha” is being separated off from the idea of being “happy.” In both cases it is real existence, an actual state of affairs, that is being addressed. Negative propositions reflect the second act of the intellect just as much as do affirmative propositions, for, after all, division is as much an act of judgment as is composition. When we say “The chicken is not in the bam ” we are making a statem ent about what is actually the case, and so are we when we say “Samantha is not happy.” It would make no sense to assert that the chicken is in the bam , or that Sam antha is happy, if we were not referring to real chickens, real bam s, a real Samantha, and a real state of unhappiness. A note, to contribute to the building up of our logic vocabulary. Every declarative sentence (i.e., proposition) is composed of a subject and predicate. The predicate is what is being said of, or attributed to, the subject. In logic we refer to the move by which something is attributed to a subject as predication. So, in the proposition, “Jerome plays the clarinet,” the idea o f playing the clarinet is being predicated of Jerome. P ropositions

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Propositions are the linguistic expressions o f the psychological reality we call the second act of the intellect. The very im portant role that propositions play in logic lies in the fact that they are the principal conveyors of truth. It is only propositions which can be said to be, in the strictest sense, either true or false. We can readily see how this is so. If someone were to say to you, “keys,” and then ask you whether that is true or false, you would understandably be baffled, and would probably respond with som ething like, “W hat about the keys?” Something has to be said about the keys, som ething needs to be predicated of them, in order for there to be an existential situation to which we can rationally respond. If we are told, “The keys are on the desk,” we now have something we can work with, for a statem ent has been made about the keys which either conforms to the way things really are, or it does not. If it does so conform (the keys are in fact on the desk), then the proposition is true; if it does not, the statement is false. An act of judgment is sound if the existential claims (claims about real existence) which it makes reflect what is actually the case.

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Sound judgments are expressed in propositions which are true. We can never determine whether any particular proposition is true or false simply by studying the proposition itself. We must go beyond the proposition, and decide whether or not the claim it is making squares with the way things really are. Every proposition must be tested against objective criteria. T he T hird A ct

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Intellect: R easoning

By the first act of the intellect we form ideas. By the second act of the intellect we put ideas together, or separate them from one another, to form judgments, in order to mirror what is actually the case in the external world. By the third act of the intellect, the process of reasoning, we move from one judgment to another for the purpose of discovering new truths. The operative unit of the proposition is the idea, and the operative unit of reasoning is the proposition; thus, in reasoning, we move mentally from proposition to proposition. Reasoning, which is also called discursive thinking, is a process, a controlled and carefully ordered mode of thought, which is directed toward a definite purpose— the discovery of truth. It is the type of thinking which the study of logic is intended to perfect, and in its most accomplished form it is one and the same with what we call logical thinking. Inference Inference is the pulsing heart of the reasoning process. It is the movement by which the mind, beginning with a proposition which it knows to be true, proceeds to a second proposition which it takes to be true on the basis of the truth of the first proposition. So, the truth of the second proposition depends on the truth of the first. Take Proposition A and Proposition B. If I hold Proposition B to be true on the basis of my conviction that Proposition A is true, I can be said to infer the truth of Proposition B from the truth of Proposition A. If my thinking is correct about how the two propositions relate to one another, then we can say that the truth of Proposition A necessarily implies the truth of Proposition B, or, in logical language, we say that Proposition A entails Proposition B. The two propositions are so related to one another that it would not be possible for Proposition A to be true without Proposition B also being true. The truth of Proposition B flows out of, as it were, the truth of Proposition A. Consider the following: Proposition A : Mysterious Person X is a mother, from which it can be inferred that... Proposition B : Mysterious Person X is a woman. If all I know about Mysterious Person X is that she is a mother—something I know with certainty— then it necessarily follows that she is a woman. I can infer that with the greatest confidence. Being a mother entails being a woman. But

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what if the only thing I know about Mysterious Person X is that she is a woman. That is all the information about the person I have at hand. From that can I infer that she is a mother? I cannot. While being a mother necessarily implies being a woman, being a woman does not necessarily imply being a mother. In logic we make a distinction between immediate inference and mediate inference. The example given just above is a case of immediate inference. This is where we move directly from one proposition to another, with no intervening propositions. Concluding that “Giovanni is Italian” on the basis of the true proposition that “Giovanni is a Rom an” would be another example of immediate inference. Being a Roman necessarily entails being Italian. Mediate inference is the kind of discursive thinking that takes place when we begin with a proposition which we know to be true, and end with a second proposition which we take to be true, but we arrive at that second proposition through the medium of a third proposition. The following is an example of mediate inference. All lions are carnivorous. Leo is a lion. Therefore, Leo is carnivorous. The argument begins with the true proposition that all lions are carnivorous. But from that truth we cannot directly conclude to the truth that Leo is carnivorous. We need more information about Leo. Once it has been established that Leo is in fact a lion— information provided by the middle proposition above— then we can conclude that Leo is carnivorous. The truth of the final proposition is established through the mediation of the truth of the middle proposition. R easoning

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Although reasoning and argument are very closely allied, they are not the same thing. Recall what we have said about words, that they are the linguistic expression o f ideas; and about propositions, that they are the linguistic expressions of judgm ents. The aesthetically pleasant picture can now be completed with the announcement that arguments are the linguistic expressions of reasoning. Argum ent is, if you will, the public display o f the reasoning process, which itself is a very private matter indeed. The reasoning process can get rather complicated, and so, therefore, can the arguments which express it. But please take careful note of this: no matter how lengthy an argument might be, no matter how complex and convoluted, if it is in fact an argument, its basic structure is the very soul of simplicity, made up as it is of but two basic elements. And those two basic elements are the premiss and the conclusion. The premiss o f an argument is a proposition which serves as its foundation; its function is to support. The conclusion is a proposition which rests upon the premiss and is supported by it. The conclusion is the “point” of the argument;

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it is what the argument is asking us to accept as true on the basis o f the truth of the premiss. The examples of immediate inference given above both represent the simplest form of argument, where there is only a single premiss. In the first example, “Mysterious Person X is a mother” is the premiss, and “Mysterious Person X is a woman” is the conclusion. In the second, “Giovanni is a Roman” is the premiss, and “Giovanni is Italian” is the conclusion. In the example of mediate inference, the first two propositions in the argument are the premisses, and the third is the conclusion. That the third proposition is the conclusion is clearly indicated by the fact that it begins with “therefore.”

Review Items 1. Briefly describe the three acts of the intellect: simple apprehension, judgment, reason. 2. Give a definition of “idea.” 3. W hat is the “object” of an idea? 4. What is the difference between sense knowledge and intellectual knowledge? 5. Describe the function of the four internal senses: the common sense, imagination, memory, the estimative sense. 6. What does it mean to say that an idea captures the nature of its object? 7. Explain the importance of the proposition for logic. 8. What is predication? 9. What is inference? 10. Describe the basic structure of an argument.

Exercises A. In the following propositions, indicate what is being predicated of what. 1. Simon is a sophomore at Syracuse University. 2. Democracy is a form of government. 3. Susan sings. B. Identify the following as referring to either sense images or ideas. 1. The sound of a horn. 2. Horn. 3. The color blue. 4. Salty. 5. Hammer.

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C. In the following pairs of propositions, indicate which one is an inference from the other. 1. There must be somebody home. All the lights are on. 2. Gerald won three Olympic gold medals. Gerald is a very good athlete. 3. There are puddles in the street. It rained last night. 4. Pamela is a citizen of Chicago. Pamela is an Illinoisan. 5. Y ou’re blushing. There’s nothing to be embarrassed about.

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Chapter Two Ideas and Their Expression D istinctions Distinctions are very important in logic, as they are in life. You have already been presented with a fair number of distinctions in this book, and by the time you reach the last chapter you will have been introduced to many more. The French philosopher Jacques Maritain took as his motto, distinguer pour unir, “distinguish in order to unite.’’6The human mind, marvelous instrument though it is, is limited in its capacities, and cannot achieve an adequate understanding of any large, complex subject in a single, voracious gulp as it were. It must go about mastering the subject in a piecemeal manner, studying it part by part. That is where making distinctions comes in, which is simply the accurate identification of the various parts or elements of the subject. It is by carefully distinguishing the parts, and by studiously observing how they relate to one another, that one learns how they all go together to constitute the unity of the subject in its entirety. The ultimate purpose of making distinctions, then, is to gain a holistic view of whatever subject it is one is studying. No one becomes an expert in human physiology at a glance, but must proceed methodically, organ by organ, system by system, relation by relation, until eventually one arrives at a comprehensive understanding of the integrated whole— the human body and how it functions. It is very much to our advantage as aspiring logical thinkers that we foster an appreciation for the critical importance of distinctions, for clear thinking is impossible without them. And we must especially guard against an all too common tendency to become impatient with them. If bitten with that bug, we can even reach the point where we look upon them as if they were little more than a form of unnecessary nit-picking. Not that a tendency to be impatient with distinctions can never be justified. Important though the process of making distinctions is, it can be overdone, and sometimes logicians are the worst offenders in this regard. A surfeit of distinctions serves to confuse rather than clarify, creating a verbal maze in which one can easily get lost. There are good distinctions and bad ones. The basic test of a good distinction is that it performs

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the practical function o f helping us better to understand the subject to which it is being applied. It clarifies rather than confuses, is revealing rather than concealing. Perhaps the most basic distinction of all, at least from a logical point of view, pertains to distinctions themselves. It is the distinction between real distinctions and logical distinctions. Real distinctions, to describe them in the broadest terms, are those which are to be found, as their name indicates, in the real world. They are part of the objective order of things. They do not have their genesis in the mind; rather, they are discovered by the mind. The clearest example of a real distinction is to be found in the phenomenon of separation. If two things are physically separate, they are obviously distinct from one another. Susie and Sally are identical twins, and for that reason we can sometimes mistake one for the other, but there can be no confusion about the fact that they are really distinct. As a matter of fact, if they were not really distinct we could not mistake one for the other. So, we can confidently conclude that things that are separate are necessarily distinct. May we then make the further conclusion that distinction and separation are one and the same thing? No, we may not, for it is possible for things to be quite distinct but not at all separate. The right side of the face is distinct from the left side, but there is no separation between the two. Another example: there can be no dispute over the fact that the “heads” side of a coin is quite distinct from the “tails” side, yet they are not separate from one another. They could not be. If one were to attempt to separate them, the only result would be the destruction of the coin. Again, a real distinction is “out there,” a fixed feature of the order to be found in the external world. We may decide that one side of a coin will be called “heads” and the opposite side “tails,” but we do not determine that a coin will have two sides. That comes with being a coin. A logical distinction, in contrast to a real distinction, is a product o f the mind. We do not discover it in the external world, but apply it to that world to give system to our thoughts about it. A logical distinction is an organizing tool, a means employed by the mind for the purpose of bringing structure and order to our knowledge. Most of the distinctions we make in the science of logic— no surprise here— are logical distinctions. Take, for example, the distinction between the subject and the predicate of a proposition, a distinction to which we have already alluded and to which, in pages ahead, we will be devoting a considerable amount of attention. The subject of a proposition is clearly distinct from its predicate, but we do not call the distinction between the two a real one. W hy not? Because there is not to be discovered, in the real world, any real subject or predicate. That claim might strike you as rather odd. Surely we are dealing with something out there. Indeed we are, but what we are dealing with is simply words. There is no given word, or group of words, which by their very natures are to be identified as either subjects or predicates. It is we who designate them as such, in order to indicate the peculiar functions they perform

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in a proposition. There are words that execute different operations when we bring them together to form propositions, and to indicate those different operations we assign different names to the words, calling them respectively “subject” and “predicate.” We thus make a logical distinction, one which, in this case, is intended to clarify the structure of a proposition, and to throw light on how the parts of the proposition work. Consider an example taken from grammar, which, like logic, makes liberal use of logical distinctions. We are all familiar with the grammatical terms, “noun,” “verb,” and “adjective.” As in the case of subject and predicate, there are no words which, by nature, are any one of these three. If any particular word were a noun by nature, then that word could not function as anything else but a noun, and likewise with verbs and adjectives, if there were words that were such by nature. But that this is not the case is demonstrated by the fact that we can have the very same word serving as a noun, or a verb, or an adjective, depending on the function it performs in a particular sentence. And we assign a particular name to a word— thus making a logical distinction— according to the particular function it performs. Take the word “running.” In the three sentences to follow it functions, first as a noun, then as a verb, finally as an adjective. Running is good exercise. Robert is running. The running dog caught up with the Frisbee. Logical distinctions, we said, rather than being discovered in the world, are applied to it. But not in a whimsical or arbitrary way. If a logical distinction is to have any practical usefulness, it must have its roots in the objective realities of the situation to which it is being applied. The distinction itself might not be real, but it must be founded on real differences in the external world. There is of course the obvious reality o f the words themselves, with which logical distinctions deal directly. But there is also, and more relevantly, the real differences in the functions that words play within a proposition. The function performed by the subject is not to be confused with that performed by the predicate, and vice versa. It is in realities of this kind in which logical distinctions are grounded. T he T hing We will use the very capacious, all-purpose word “thing” to indicate in a general way the ultimate source of all of our ideas. A thing is that which exists external to and independent of the human mind. It is not beholden to the human mind for its existence. Our thinking does not make things so; they are so before we think about them. And, in fact, it is their being so— i.e., the fact that they actually exist— which makes our thinking possible. In other words, we can have ideas only because there are, in the first instance, things about which ideas can be conceived. The general idea underlying this particular relation is expressed

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by the principle that the human mind is measured by things. Things in the world are the necessary antecedents to ideas in the mind. This can be put in a more general way by saying that the subjective order is dependent upon the objective order. T he I dea As we have seen, an idea is an intellectual image which is the product of the m ind’s active response to an extra-mental thing. It is the effect of the m ind’s capacity to capture the basic essence or nature of a thing— its “what-ness” if you will. The idea and the thing grasped by the idea are not identical, but, though distinct, they are inseparable, because of the peculiar kind of fusion that takes place between them. The idea becomes the perfect medium for the thing, the means by which the human mind achieves real knowledge of the thing. The act by which the mind grasps the basic essence or nature o f the thing is called abstraction. All of our most primitive ideas are of material things; the human mind, on the other hand, is immaterial. Therefore, in order for the mind to be able to grasp the nature of a material thing, a psychological transformation must take place which renders the thing compatible to the mind. This is what abstraction accomplishes. It is through the process of abstraction that the immaterial essence or nature o f the thing is introduced to the mind, leaving behind its material aspects. As I look out the window at a partridge in a pear tree and think about both of those objects, I am entertaining ideas of both of them. In a very real sense, the partridge and the pear tree are now in my mind, but certainly not as material objects. The contact that has been established between myself, as a material being, and those two material beings outside my window, takes place on an entirely immaterial plane, and is attributable to the abstracting powers of the mind. (See Appendix A for further discussion of abstraction.) T he W ord The only way the human mind can grasp the nature of a thing is through the medium of an idea. The only way one human mind can communicate an idea to another human mind is through the medium of the word. If we regard abstraction as something like an unclothing process, whereby a material object is divested of its materiality so that its essential nature is exposed, thus making the thing accessible to the mind, the process of attaching words to ideas may be regarded as something like a clothing process, whereby the idea is invested in a form o f materiality (i.e., language) so that it is thus rendered accessible to another mind. W ords thus build the bridges from one mind to another. To see more clearly how “thing” and “idea” and “word” are related to one another, try imagining the following: first picture the thing as enclosed within the idea, and then picture the idea as enclosed within the word, so that we have

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an object placed in a container, and then that container in a larger container. The word comes to us pregnant with its idea, which is in turn pregnant with its object.

T he I dea A s U niversal “By the term ‘universal’,” Aristotle writes, “ I mean that which is of such a nature as to be predicated of many subjects.” {On Interpretation, 17a, 3 5 )7 When the mind, by abstraction, grasps the nature of a thing, it is grasping, in that nature, something which is shared by many things. And this is clearly shown by the language we use. Every common noun represents a universal concept— table, chair, bird, rainbow, pencil, soup, sink, satellite, etc., etc. When we think and speak “table” we need not necessarily have this or that particular table in mind, but only table in general. We are thinking of any object, past, present, or future, that shares a common nature, which we might call table-ness. But we can also universalize other parts of speech as well, most usually verbs and adjectives. We say, “Paula is swim m ing,” but we can also speak about “swim m ing” as a distinct kind o f activity, which, because it has certain characteristics peculiar to itself, can be said to have a “nature,” and as such can be applied broadly. “Swimming” thus becomes a universal concept. We say, “The pencil is yellow.” But we are able to make such a statement only because we understand yellow (or yellowness) as a universal concept which can be applied to pencils, but also to canaries, taxi cabs, dandelions, and any number of other things which have the quality of being yellow. Some philosophers have denied that there are true universals. W hat lay behind their denial was the conviction that the human mind is not really capable o f grasping the essences or natures of things, which is precisely what identifying ideas as universals necessarily implies. These philosophers— they have been given the name “nominalists”— argued that common names such as “table” and “chair,” and “dog” are mere labels of convenience by which the human mind classifies things on the basis of their having common external characteristics. So, we give the name “dog” to certain animals because we recognize that they share a number of characteristics, and not because the mind is capable somehow of “seeing into” these animals and therein discerning a common nature or essence. What we have in this point of view is the effective denial of the existence o f common natures. But to deny the existence of common natures is to remove any feasible explanation for common

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characteristics, the reality o f which the nominalists readily acknowledged. If there is no one nature which is common to all those animals we call dogs— i.e., caninity— how are we to account for all those common dog-like characteristics? There is only one explanation for them: a common nature. The basic idea here is that what is common extrinsically is an inevitable manifestation, the external and observable proof, of what is common intrinsically. Common characteristics thus publicly announce a common nature. In W hat S ense A re U niversals R eal? On the opposite side of the fence from the nom inalist philosopher is the realist philosopher, who takes the position that natures really exist and that they are really known by the human mind. Furthermore, he maintains, if we were not capable o f knowing natures we would not be able to form ideas, and without ideas there would be no words, thus no language. We would have nothing to think about, and nothing to say to one another. But words do in fact exist, and there is a particular type o f word we call a common noun, which shows that there are certain ideas which deal with universals, which simply means that certain ideas refer to common natures. The common noun “dog” does not refer ju st to this dog or to that one, but to all animals now living, which ever have lived, or which ever will live, that share the same nature— canine nature. We go a step further, and claim that universals— i.e., common natures— are real. But if so, precisely in what way can they be said to be real? In what does their reality consist? In answering this important question, we begin by noting that universals exist principally as concepts, as ideas in the mind. But our ideas, as we have seen, are not self-generating; all of our ideas are ultimately traceable to things in the world. A universal, then, though it exists in the mind alone, just insofar as it is an idea, can enjoy that real mental existence only because there is something outside the mind to which it is related and on which it depends, for this is true of all ideas. We use abstract terms like caninity, felinity, equinity, and humanity to identify the common nature which is found respectively in dogs, cats, horses, and human beings. Those terms designate the universal, and we are claiming that the universal is real, which, once again, is simply to claim that common natures are real. But consider the term “humanity.” Surely that does not refer to some concrete thing in the external world. Who could point to “humanity” and say, “Ah, there it is!” And yet who would doubt the reality of humanity? Who would doubt, in other words, that there is such a thing as human nature? Humanity is real, then, but we want to know in what sense it can be considered to be real. The universal “humanity” is real because it is rooted in the reality of all those actually existing creatures we call human beings. Humanity, as an idea, would be utterly empty, meaningless, if there were not real beings such as Tom, Dick, and Harry, such as Tessie, Dottie, and Harriet who share a common human nature. A universal is not something arbitrarily foisted upon

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things by the human mind, as the nominalists would want us to believe. It represents the recognition, on the part of the human mind, that common essences or natures are real, as real as the creatures that possess them. S igns We have seen that the idea represents the thing, and the word represents the idea. We need now to be more specific about the nature of that representation. It is the representation, specifically, of signs. The idea is a sign of the thing, and the word is a sign of the idea. Before we discuss the specific natures of ideas and words as signs, we must first examine the nature of signs in general. Doing so will help us better appreciate the special ways in which ideas and words signify. A sign is anything that conveys meaning. We note the distinction between the sign itself, and the signified, the signified being the meaning of the sign. You are driving along a city street and, as you approach an intersection, you see that there is a policeman standing in the middle of the intersection. He is facing you, his feet apart, his right arm is upraised, and the palm o f his hand is open, fingers spread. Registering this visual image, you apply the brakes and bring your car to a halt. You did that because you interpreted the stance and gesture of the policeman to mean “stop.” You were presented with a sign, and you read it correctly. (See Appendix B for further discussion of universals.) N atural S igns

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There is more than one way the category o f signs can be analyzed. The procedure we follow here is first to make a broad distinction between natural signs and conventional signs. A natural sign, as the name indicates, is simply a sign which is given by nature. It is part of the natural order of things. Listed below is a set of natural signs, along with the things which they signify. Sign smoke heavy, dark clouds fever shivering laughter leaves changing color blushing

Signified fire possiblerain illness being cold happiness autumn season shame, embarrassment

A natural sign has its meaning built right into it, so to speak, but a conventional sign, because made up by man, has its meaning assigned to it by man. It is a product of human invention. The most elaborate and complex set of conventional signs is a language. We might be inclined to think that the words that compose any language are natural signs, but when we stop to consider the matter we readily see that such is not the ca se. If any word in any language were

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a natural sign, then its meaning would be fixed and invariable, and it would be intelligible to any human being. But could we say this about the verbal sign “dog,” which is to be found in the English language? Would it be immediately interpreted in the same way by all human beings, as denominating a certain kind of animal, in the same way they would immediately interpret smoke as a sign of fire? For someone who doesn’t understand English, “dog,” as spoken, would be a meaningless sound; as written, it would be unintelligible marks upon a page. If “dog”were the n a tu r a l verbal sign signifying a certain kind of animal, then how could we explain the existence of verbal signs such as the following: c a m s, c h ie n , p e r r o , h u n d , c a n e , c d o , s k y la x . These words are all quite different from “dog,” both in sound and in spelling, and yet they mean exactly the same thing as the English word in each of the seven separate languages from which they come: Latin, French. Spanish, German, Italian, Portuguese, and Greek. A sure indication that one is dealing with conventional signs, such as words in a language, is that the signs themselves can be quite different as you move from one sign system to another, but, as in the example given above, a set of widely varying signs may all signify the same thing. We can become so used to conventional signs, especially when they take the form of words in our mother tongue, that they come to seem “natural” to us. But this is true of non-linguistic signs as well. We might find it difficult to imagine that a red light, as a traffic signal, could mean anything but “stop,” and that green could mean anything but “go,” but there is nothing in the natural order of things that says it must be so. It is quite conceivable that a different convention could have developed, according to which a red signal would mean “go,” and a green one would mean “stop.” Then the phrase, “to be given the green light,” would mean something entirely different from what it means now. Following are some examples of conventional signs. Sim

waving the hand handshake a yard stick triangular orange placard picture of burning cigarette, circled in red, with red slash through it

Signified farewell, goodbye fri endship, agree ment measure of length caution no smoking

three, three things is equal to $ dollars (See Appendix C for a discussion of language and conventional signs, and Appendix D for further comments on the distinction between natural signs and conventional signs.) 3

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F o r m a l S ig n s

We have made the distinction between natural signs and conventional signs. Now we need to make another, between in stru m e n ta l sig n s and fo r m a l sig n s. All of the signs that we have discussed thus far, natural and conventional, are in s tr u m e n ta l s ig n s . An instrumental sign is one in which there is not an inseparable bond between the sign itself and what it signifies. The thing which is acting as a sign enjoys an independent existence in relation to its signification, and it would be recognized as a real existent even by someone who did not know that it functioned as a sign and therefore could not interpret it. Someone may not be able to interpret certain natural signs, but that person would nonetheless be aware of the physical phenomena which function as signs. For example, Magua, recently moved from the tropical zone to the Upper Midwest of the United States, may not at first be aware that the changing colors of the leaves of deciduous trees signals the approach of winter, but even so he is quite cognizant of the phenomenon itself, and is quite enamored of it. Certain conventional instrumental signs could have their meaning deliberately changed, or they could completely lose their status as signs, but they would not cease to be the things they were before their significance was changed, or even before they functioned as signs at all. A code word that has its meaning changed remains the same word after the change as it was before. The flag which preceded Canada’s present one may still be seen in museums, but it has lost its significance as that country’s national ensign. The handshake is conventionally understood to be a sign of friendship, but if someone were habitually to use it only as a cynical means of ingratiating himself with people whom he actually despises and wants to take advantage of. we would say that, for such a person, the handshake is an empty gesture. It is still a handshake, but for him it no longer signifies what it is intended to signify. However, he is only able to employ it for cynical purposes because most people readily accept its commonly understood meaning. The salient feature of instrumental signs is that they are things in themselves, apart from the fact that they function as signs. Fire is the cause of smoke, but smoke, as a sign of fire, can continue to exist after the fire that caused it is extinguished. Trembling is a sign of fear, but it is not the same thing as fear, and it may exist apart from that which it can truly signify, such as when an actor, who feels no fear, trembles on stage to give the illusion that he is fearful. Most of the signs we encounter on a day to day basis are instrumental signs, which is to say, again, that they are the kind of signs whose existence is not entirely summed up in their signifying functions. They could lose their signifying value tomorrow, but they would not vanish into thin air. With fo r m a l s ig n s , things are quite different. The whole being of a formal sign is summed up in its act of signifying. The formal sign has no other purpose than to function as a sign. A formal sign is, we may say, a pure sign. There are only two kinds of formal signs, sense images and intellectual images or ideas.

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The idea is a formal sign. This means that it has no other function than to signify; its whole reason for being is to convey meaning. And what the idea signifies, what it stands for, is of course the thing, an existent in the external world. In the practical order, the distinction between an instrumental sign and a formal sign is brought home to us by the fact that we can know an instrumental sign im m ediately and directly, and even before we know what it signifies. A nyone who has studied a foreign language is very fam iliar with that experience. W e can know that we are dealing with a Latin, or Greek, or German word, but we may not know what it means. We know without a doubt that it is a sign, but we do not know what it signifies. This is precisely what does not happen with respect to formal signs. When we know an idea, we never know it first as a sign, that is, as something that represents something other than itself. We see right through the idea, so to speak, to the thing which it is signifying. And the same is true, and perhaps more emphatically so, with respect to sense images. When we smell a freshly baked mince pie at Thanksgiving, it is not the olfactory sensation itself o f which we are principally conscious, but the mince pie. It is only through reflection that we come to recognize formal signs as signs at all. W hen I am thinking of my dear Aunt Flossie (i.e., I have an idea of Aunt Flossie in my mind), my thought is concentrated on Aunt Flossie herself. It is only through reflection, the process by which we review our own thinking, that I become aware of the fact that Aunt Flossie and my idea of Aunt Flossie are not the same thing. There is a real distinction between the two that must be recognized. Distinction, but not separation. There is no way I could somehow skirt my idea of Aunt Flossie and still have knowledge o f her. Because the object o f an idea is enclosed within the idea itself, the only way I can have knowledge o f Aunt Flossie is through the medium of my idea of her. There is no separation between idea and thing, but there is a real distinction. The idea is not the thing, nor is the thing the idea. By the very fact that formal signs are indeed signs, the distinction between the sign itself (e.g., an idea) and the signified (its object) is part and parcel of its descriptive contents. But in the case of an idea and that which it signifies, the two are so closely fused together that, in marked contrast to what could happen with respect to instrumental signs, there can never be real separation between the two. A discarded “stop sign,” stashed away in a corner of a highway department warehouse, no longer functions as a sign, but it still exists as a physical artifact. But it is impossible that there could exist a non-signifying idea, an idea without meaning, an idea that does not serve some representational function. The same holds true of sense images. There are no content-less, non-representative sense images. T he Interpretation

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example, the various physiological conditions which serve as the symptoms for disease. Correctly reading these signs requires a great deal of expertise, and even the experts can sometimes seriously misinterpret them, which is why diagnosis is commonly recognized as one of medicine’s most difficult tasks. The most basic requisite for the correct interpretation of signs is knowledge. First of all, we have to be aware of the fact that the object that we are dealing with is a sign, that it is more than simply the particular kind of object it is, that it bears a meaning which points beyond itself. Obviously, if I do not know that an object functions as a sign, the question of my interpreting it does not even arise. When you are attempting to learn a foreign language you are engaged with an elaborate and complex sign system, and the essence of the learning process is your coming to know how to interpret all the individual signs (i.e., words) of which it is composed. You know that each particular sign/word is in fact interpretable, that it bears a definite meaning, and your job is to discern the right meaning for each sign and commit it to memory. We can be completely oblivious to the fact that a particular object has a sign function. On the other hand, we can be confident that it does have such a function, but despair of the possibility of ever being able to figure out what it is. An archeologist digs up an artifact belonging to an ancient civilization; he knows enough about that civilization to be certain that the artifact had, in its day, a definite sign value, but recovering its one-time meaning as a sign is judged to be permanently beyond reach. Breaking a code can prove to be an extremely difficult task for interpretation. The would-be code breakers know for a fact that the coded items can have meaning, but the system has been constructed with the express purpose in mind of making it virtually impossible for anyone not possessing the key to the code to interpret that meaning. Physical gestures or postures— what might generally be described as “body language”— that serve as conventional signs can offer special problems for interpretation, especially when it involves cross cultural interaction. A posture which might be considered totally innocuous in one culture can be interpreted as offensive in another culture. Odd though it may be, energetic efforts are sometimes devoted to the interpretation, not of a sign, but the absence of a sign. On occasion an historian, writing about Famous Person X ’s possible attitude toward an important issue of his day, reports that on that issue Famous Person X was completely silent. And then the historian goes about trying to interpret that silence. Does it mean that Famous Person X had a positive or a negative attitude toward the issue? Interpreting silence is rather chancy business, but some people seem to enjoy doing it. In logic, the focus of our interpretative concerns is the word. In order correctly to interpret a word we must, in the first instance, be aware of the meanings conventionally assigned to it; these would be its standard dictionary definitions. We should be especially sensitive to ambiguous words, those with multiple meanings. In logic, words are always interpreted in context, that is,

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with regard to how they relate to and operate within larger linguistic structures, either the proposition or the argument. It is o f param ount importance to determine the intended meaning of a word. This does not mean that we involve ourselves in any attempt to read the mind of the one using the word. That would be as futile as it is unnecessary. Usually we can tell without too much trouble, from the context of the linguistic discourse in which a word is being used, the meaning that is intended for it. The most common cause of the misinterpretation of words is paying insufficient attention to how they fit into a larger linguistic context. T erms “Term,” though roughly synonymous with “word,” is broader in scope, and because it is both more precise and more versatile in its practical applications, it is preferable to “word” in logical usage. A term may be defined as a linguistic utterance which signifies an idea. What is meant by “linguistic utterance” in the definition is simply a word, or words. It might seem, then, that word and term are perfect synonyms, but in fact they are not. What we call a term is that which signifies an idea, a single concept. But it is possible to have one word which can convey more than a single idea; it would therefore be one word with multiple terms. There is to be found in every language a num ber o f words, called homonyms, which, though they sound the same and may have the same spelling, have more than a single meaning, which is to say, they can embody more than one term. Not only can one word have m ore than one m eaning, the various meanings it can convey could bear little or no relation to one another. Take the English word “bark.” W hat does it mean? It can mean at least five distinct things. As a noun, it can refer to the covering on the trunk or branches of a tree, or to the sound a dog makes, or to a small sailing vessel; used as a verb, it can refer to the action of a dog barking, or to the act of removing the bark from a tree. In this case, then, we have one word with five distinct terms, or meanings. In logic, we give our principal attention to terms, for what we need to know is the meaning that is being attached to a particular word in any given context. The correct interpretation of a word, then, tells us its term. Another reason why word and term are not to be considered equivalent is that in some cases a single term (idea) is conveyed by more than one word. The three word phrase, “winning at poker,” conveys but one idea. In many propositions, the subjects and predicates can be composed o f more than one word, yet each bears a single basic meaning. T he C omprehension

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Once we have successfully identified a particular term, we have no problems with ambiguity, for, remember, a term is a word with a single meaning. “Bark,” referring to the covering on the trunk o f a tree, has that meaning and that

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meaning only, a meaning which we determine by the linguistic context in which the word is used. In analyzing any particular term, we distinguish between its comprehension and its extension. By the comprehension of a term we simply refer to its meaning. But the comprehensions or meanings of terms can differ in the respect that some can be richer, more ample and interesting, than others. Consider two terms, “ball bearing” and “chimpanzee.” Both have meanings, but they vary greatly in breadth and depth. It would not take long to exhaust the m eaning of a ball bearing; there are only so many things that one could say about it. On the other hand, one could go on and on talking about a chimpanzee. In describing the quality of the comprehension of any term, we refer to its “notes.” A note is a particular attribute or feature of a term. Because a term signifies a single idea, when we say that a term’s comprehension contains many notes we are referring to the capaciousness of the idea which it signifies; the idea contains much that can be thought about and talked about. “Ball bearing” would have but a few notes, whereas “chimpanzee” would have many. In sum, the comprehension of a term is simply that which it signifies. So, for example, if the term in question is “dog,” its comprehension would be all those essential characteristics that represent canine nature. The extension of a term refers to the actual number of individuals to which the comprehension of the term applies. A term’s extension is constituted by all the members of the class which is identified by its comprehension. Thus, if the term in question is “human being,” then, unless otherwise indicated, its extension would be every individual human being, past, present, and future. The extension of “chair” would be all those pieces of furniture which qualify as chairs, and the extension of “rosebush” would be all the individual rosebushes of the world. There is an interesting inverse relation that exists between the comprehension of a term and its extension, in this respect: the larger the comprehension of a term (i.e., the more notes it contains), the smaller its extension (i.e., the lesser the number of individuals to which it applies); conversely, the smaller the comprehension of a term, the greater its extension. Take the two terms “animal” and “man.” Man has a larger comprehension than animal, in that it contains the note “rational.” Accordingly, the term “man” can be applied to fewer individuals than can the term “animal” ; that is, it can be applied only to those animals possessed of reason. The more notes added to a term, the greater its comprehension, and the smaller its extension. So, for example, if the note “female” were to be added to “human,” its extension would be smaller, and with the addition of “mother” its extension would be smaller still. Moving in the other direction, consider a term like “thing” which contains very few notes, and accordingly its extension, the objects to which it can be applied, is huge. Notice how we apply “thing” to, well, just about everything.

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T he P redicables A predicable, understood in the broadest sense, is anything that can be predicated o f som ething else. To predicate sim ple m eans to say som ething about, or attribute som ething to, som ething else. In the statem ent, “Jim is running,” the act o f running is being predicated of the subject, Jim. But logic attaches a specialized m eaning to the term “predicable,” and we m ust now fam iliarize ourselves with that meaning. “Predicable” refers to one of the five very foundational things that can be said of any subject. The five predicables are: genus, species, specific difference, property, and accident. Genus. “A ‘genus’,” Aristotle tells us, “is what is predicated in the category o f essence of a number of things exhibiting differences in kind.” ( Topics, 102a, 3 0 ) 8 W hat is especially to be noted in this definition is that the predication of a genus (i.e., attributing a genus to a particular subject) has to do with the “category o f essence.” This means that w henever we predicate genus o f a subject, we are attem pting, through the predication, to get at its essential identity, its basic nature. To predicate genus, or any of the other predicables, of a subject is a m eans by which we seek to gain the m ost foundational kind of knowledge possible of that subject. We are placing that subject as accurately as we can. W hat is a genus? It is a large class o f things whose m em bers have certain elementary traits in common. “Animal” is an example o f a genus, a large class which is made up of all those li ving creatures which, besides the powers of nutrition, growth, and reproduction, have appetitive powers (e.g., desire, aversion), powers o f sensation, and the power o f locom otion. To predicate genus o f man is simply to say, “Man is an anim al,” which is to convey a great deal o f information about the nature of the creature we are dealing with. W hat is especially valuable about this information is that it is not peripheral, but essential. It informs us as to the basic nature o f man. When we say that man is an animal, we mean that everything included in the notion “animal” (listed just above) applies to him. Consider a different kind of large class, which is not in the least bit as informative as “anim al,” the class of, say, “blue things.” There are any num ber of particular objects that could be put in this class— marbles, autom obiles, tablecloths, shirts, walls, books, and on and on— but by identifying them as being blue we do not reveal what is essential to them. A book may have a blue cover, but it is not of the very essence of a book to be blue, and what does a blue book, considered as a book, have in common with a blue Corvette, or a blue tablecloth? However, when we identify man as an animal, i.e., predicate genus of him, we reveal what is essential to human nature, and we call attention to what human beings have in common with other members of the genus to which they belong. Species. A second key feature of a genus, besides the fact that it is a large class of things which identifies something essential about its membership, is the fact that it embraces within itself a number of smaller classes. This is what

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Aristotle is referring to, in his definition, when he speaks of a genus as being made up o f “a number o f things exhibiting differences in kind.” So, the genus “animal” is composed of different sub-classes, or kinds of animals, to which we give the name “species.” There are giraffes, and bears, and sheep, and that rather peculiar animal we call man. W hen we say, “Man is an animal,” we are predicating the predicable genus of man. The subject here, “man,” is one of the sub-classes of the larger, generic, class. Genus is most accurately predicated of species, which is precisely what we are doing when we say, “Man is an animal,” by which we mean that every human being is an animal. The larger class is being predicated of the smaller class. But for obvious reasons we cannot go the other way. We cannot predicate the sm aller class o f the larger one, saying, “Every animal is a man,” for we thereby end up making a false statement. We can say, “Sally Mae is an anim al,” and this is a true statement. It identifies the subject accurately, but not very precisely. The most precise predication we can make o f a subject is one which would give us tht fullest account o f the nature o f the subject. And this is done by placing the subject in a class to which it is immediately subordinate. An example of this is, “Man is an animal,” for the sub-class “man,” as a species, is immediately subordinate to the genus “animal.” We call animal the proximate genus of man. If we were to say, “Man is a living being,” man would not be immediately subordinate to that genus, because it is divisible into the sub-classes of plants and animals, and man does not belong to the first at all. The subordination would be even less immediate were we to say, “Man is a physical substance.” Again, the statement is true enough, but not very informative. Rocky is a physical substance, but so is a rock. Back to Sally Mae. When we predicate “animal” of “Sally Mae” there is no immediacy in the predication, and that is because something stands between the subject, Sally Mae, and the predicate, animal, and that is the species, “man.” When we say, “man is an animal,” we are predicating a class to a member of the class (in this case the “m em ber” is itself a class), and thus the predication is immediate. When we say, “Sally Mae is an animal,” we are predicating a class o f som eone who is m em ber o f a class, which in turn in a member of a larger class, and we are thus skipping over her “home” class, human beings, the one in which she properly belongs, and to which she is immediately subordinate. So, in order to identify her in the fullest, most proper way, we say, “Sally Mae is a human being.” Species, or kind, is the immediate sub-class of genus. The human species is one of the various kinds which are to be found within the genus animal. The individual human being is immediately subordinate to the species identified as “m an,” or “hum an being.” There are no sub-species of human beings, no “kinds” of men, in the strict sense of that term. What this means is that all human beings, as human beings, are essentially the same. There are, to be sure, many differences to be found among human beings, but none of them are essential. In

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common speech we do in fact group human beings into various classes. We say, for example: “The French are human beings,” “Eskimos are human beings,” “The East Timorese are human beings.” But “French,” “Eskimos,” “East Timorese” do not represent different species. Specific Difference. We have noted that a genus is a class which is made up of various sub-classes called species, or kinds. But how is any one species identified as a species, and how is it set apart from other species within a genus? This is done through specific difference. The specific difference is an intrinsic, deep-set mark or characteristic which identifies a certain class within a genus as essentially unique, and therefore not to be confused with any other class within the genus. That which serves to set apart “man” from all the other species to be found in the genus “animal” is the specific difference “rationality.” The specific difference is that which constitutes a species, and it can be precisely applied to any member of the species which it constitutes. Thus we can say, “Sally Mae is rational,” or “Sally Mae is possessed of rationality.” But what is the justification for our making these predications of Sally Mae? It is not simply because she is Sally Mae, that is to say, a particular person who is individualized by reason of her physical separateness from other human beings, but because she is a member of a species whose specific difference is rationality. The first three predicables, genus, species, specific difference, are called the essential predicables because they all have to do with the very essence, or nature, of the subject of which they are predicated. It is of the very essence of Sally Mae that she is an animal, that she is a human being, that she is rational. These first three predicables, as we shall learn in due course, play a very important role in logical definition. Property. The predicables “property” and “accident” are called nonessential because they do not make up the very essence of the subject of which they are predicated. Calling them non-essential does not mean that they are not informative of the subject of which they are predicated, but simply that they do not reveal the very nature of the subject. That has already been done by the essential predicables. If someone were to tell me that a certain book has a maroon cover, that information, though perhaps mildly interesting, does not tell me much about the book itself. Generally described, properties and accidents are characteristics of a thing. Nothing could be a real characteristic of a thing, be genuinely applicable to it in terms of the kind of thing it is, if it were not ultimately dependent upon the essence, or basic nature, of the thing. If there were no clearly identifiable object— something with a definite nature— we could not intelligibly speak of its characteristics. What would “it” be? In other words, there first has to be a book before there could be any sense in talking about the color of its cover. The property of a thing is not its essence but it is a natural corollary of its essence. It is of the very essence of human beings that they are rational. There are any number of things that would follow from that fact, and one of them is the

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ability to learn language. So we say that the capacity to learn language is a property o f man. The peculiar feature of a property, which distinguishes it from an accident, is that it is inseparable from the subject which possesses it, and that is because it flows right out o f the essence, or basic nature, of the subject. To suppose that a property could be separated from a subject would imply that the subject could be separated from its very nature, which is absurd. Human beings are unique for the fact that they possess rationality, and they are also unique with respect to everything that necessarily follows from rationality, such as the property which is the capacity to learn language. Accident. An accident, like a property, can be generally described as a characteristic of a thing. The key difference between accident and property is that, as mentioned just above, a property is inseparable from the subject which possesses it, whereas an accident is not. To try to separate a property from its subject would change the very meaning o f the subject. We would be talking about someone other than Sally Mae, as a human being, if we were do deny that she has the natural capacity to know language. But an accident, on the other hand, can be conceived as separated from the subject in which it inheres, without the basic nature of the subject being in the least bit altered. Sally Mae is six-foot-two (she played basketball in college), has brown eyes, and auburn hair. All of these are accidents, or non-essential features of Sally Mae, as a human being. Now, imagine that things were different, that Sally Mae was fivefoot-two, that she had blue eyes, that she had blonde hair. W ould the fact that those accidents were changed serve to change the essential nature of Sally Mae, the fact that she is a human being? Clearly not. There are any number of accidental characteristics of a person that are gained and lost over the course of a lifetime, but the person remains essentially the same.

Review Items 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Describe the relations among thing, idea, and word. W hat is a universal? W hat is a sign? W hat is the difference between a natural sign and a conventional sign? W hat is the difference between an instrumental sign and a formal sign? How does “term” differ from “word”? W hat is meant by the comprehension o f a term? W hat is meant by the extension o f a term? Explain what it means to predicate. Describe the five predicables: genus, species, specific difference, property, accident.

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Exercises A. Identify the follow ing item s as natural signs or conventional signs, and indicate what they signify. 1. frost 2. across 3. “bandage” 4. a wink 5. a wedding band 6. a growl 7. a pat on the back 8. a smile 9. thunder 10. 6 x 6 11. 12. a rash 13. a kiss 14. the thumbs-down gesture B. In the following pairs of terms, how does the first relate to the second, with regard to the predicables of genus, species, and specific difference? 1. anim al,m an 2. rationality, man 3. George, animal 4. mosquito, insect 5. vehicle, automobile

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Chapter Three The Varieties of Ideas C omplexity

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There is an element of the invariable with any idea, if it is indeed a bonafide idea, which would be the case if in fact it serves as a sign for a discernible object. There is an unmistakable link between every idea and that to which it refers. An idea is not a self-enclosed, self-referential entity; it always points beyond itself, is always “about” something, and that something is of course the object of the idea. But ideas can be highly variable in terms of their comparative depth and richness, the practical result of which is that some ideas carry with them more content than do others. They are more challenging, more interesting, in the way they can stir up and stimulate the mind. Such ideas are well endowed with what in logic we call “notes.” A note is a particular attribute or feature of an idea. Ideas vary in complexity by reason of the number of notes they possess. But how does it come about that some ideas have more notes than others? The explanation for this is to be found in the things to which the ideas refer. This stands to reason. The more complex the object to which an idea refers, the more complex the idea itself, that is, if the idea is faithfully reflecting its object. Because the very purpose of an idea is to act as a sign for its object, that to which, as a sign, it refers, then the complexity of any idea depends on the complexity of its referent. The less complex the referent, the less complex the idea; the more complex the referent, the more complex the idea. The comparison here would be between an idea with fewer notes and one with more. The idea of the ballpoint pen I am now holding in my hand is relatively simple because of the relative simplicity of the ballpoint pen itself. I would not have to think too long or laboriously about this humble instrument before I ran out of things to think about. But now contrast that idea with the idea of a human person, cousin Toby, let us say. The object, or referent, of the idea of Toby is of course Toby himself, who, as it happens, is a rather complex fellow. The idea of Toby contains many notes, and the more you get to know him the more they seem to multiply. What can be said about Toby can be said about almost every

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adult human being. In each o f them we find a depth which no outsider’s knowledge can ever completely plumb. How often does it happen that we are quite surprised to discover something entirely new (another “note”) about a person whom we knew, or thought we knew, very well. In the idea of another person, then, we have an idea which can be called complex by reason of its many notes, and its complexity is accounted for by the complexity of its object. C oncrete

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A concrete idea is one whose referent is a specific object or some specific feature of an object. In more cases than not, the object in question is a physical object. The idea I have of my ball point pen is a concrete idea, for its referent, the pen itself, is something very definite and directly perceivable, and thus easily grasped by the mind. Indeed, for that matter, it is easily grasped by the hand. I can pick it up and chew on the end of it while I am thinking about what I should write next. My pen is tri-colored, the barrel is white and black, and its writing nib is a brownish-yellowish color. Each o f those colors can be the object of a concrete idea, because they are specific and definite. A concrete idea is a sharply focused idea. Imagine it as a picture of something, the linear edges of which are drawn very cleanly and boldly, with no blurring. An abstract idea is one which does not have a specific “thing,” a clearly detectably individual entity, to which it refers. A concrete term refers to a thing itself, whereas an abstract term refers to the essence or the nature of the thing, or a particular aspect of the thing, as separated off, by abstraction, from the thing or one of its aspects, and considered in isolation from the thing. The term “white,” as descriptively applied to my ballpoint pen, expresses a concrete idea; “whiteness,” on the other hand, expresses an abstract idea. When I think about whiteness, I think about it as abstracted from my pen, or any other particular white object in the world. I am concerned with whiteness just in itself. True to its name, an abstract idea abstracts from the concrete particular, separates itself from it, soars above it as it were, and, in the case of an idea like “whiteness,” is capable of being applied to each and every thing which, in whole or in part, we would correctly identify as white. But notice this important thing about abstract ideas: they may soar to stratospheric heights, but they all have their beginnings in the rich, warm loam of mother earth. The abstract idea of “whiteness,” in other words, owes its existence, its very intelligibility, to all those actually existing white things, concrete realities, which are to be found in the external world. An abstract term is quickly recognized as such by the fact that it refers to an object that cannot be pointed to, and that is because its referent can claim mental existence only. No matter how assiduously you might search for it, you will never find whiteness anywhere in the world. White things, yes, but whiteness, no. Abstract ideas fulfill a most important function in our thought and in our language. Without them, our ability to communicate with one another would be

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severely hampered, if not entirely crippled. We can cover a great deal of referential territory with a single abstract term. If Senator Smith tells us that he is unswervingly dedicated to democracy, we know, at the very least, that he is referring to a specific form o f government. Contrast “democracy” with “blueness.” I know that blue is Belinda’s favorite color, because she reminds me of the fact at least twice a week, not that those reminders would be necessary, for most of her clothes, herpurse, her car, andjust about every other thing she owns, is blue. Belinda is completely enamored of blueness, wherever, in whatever thing, it might manifest itself. Because blueness, though an abstract idea, is a simple idea for which most of us have a clear and ready referent, we would have no difficulty in understanding just what it is that Belinda is so enamored of. But with “democracy” things are different, for that is a highly complex idea, and therefore we would request of Senator Smith that he explain to us as precisely as possible what he means by the term. “If you please, Senator, just what is your understanding of democracy?” But for all the beneficial uses abstract terminology can have in language, it can also be problematic, and that is because o f its lack o f clarity, and in logic clarity in expression is of the utmost importance. Often, when we respond to a public statement, or to an article or book, by saying that it is too abstract, what we usually mean is that it is lacking in clarity. We may get the message in a vague sort of way, but we are beset with uncertainty because we are unable to form in our own minds any clear ideas as to the precise contents of the message. There is only one remedy for the kind of mental obscurity that an overuse, or perhaps deliberate misuse, of abstract terminology can cause, and that is an appeal to the concrete. If Senator Smith is in fact as passionately dedicated to democracy as he says he is, and if he wants to persuade us of the soundness of his position, he should give us some specific examples of what he means by that abstract term, then we will be in a better position to assess his political philosophy and to decide to what degree we agree or disagree with it. While engaging in formal argument, it is a good rule of thumb studiously to avoid the use of abstract terminology. But if one thinks it necessary to employ abstract terms at times, the next rule of thumb to follow is: always take care to give as precise a definition as possible to abstract terms. If you are holding forth on the subject of democracy, it should not be left to your audience to try to figure out what you mean by democracy. That is something you should make perfectly clear to them right at the outset. (See Appendix A for further commentary on the nature o f an idea, and Appendix B for commentary on Descartes’ “Clear and Distinct Ideas,” and Appendix C for a discussion of philosophical idealism.) S ingular T erms

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A singular term is one whose idea refers to something that is unique, of which there is only one. All proper names—John Adams, Florence Nightingale, M ortimer Adler— are singular terms, as are the names of things such as the

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Brooklyn Bridge, the Sears Tower, and Chartres Cathedral. The grammatical name assigned to singular terms is “proper noun.” But a singular idea can also be expressed by the use of demonstrative adjectives, as when we say, “That car was going over 60 mph in a 40 mph zone,” or “This chair was given to us by Grandma Casey.” A general term expresses an idea which is a universal, the kind o f idea, remember, that is applicable to many things. Grammar identifies general terms with the name “common noun,” an altogether fitting designation, for it reminds us that the idea we are dealing with here is a common one, in that it refers commonly to a multitude of things. The explanation for this lies in the fact that the idea signifies a nature, and a nature is, by definition, something which is shared by many. The term “dog” is applied to all those animals that possess a canine nature, and not just to Spot or Snoopy. If we could not think in generalities, and express ourselves in general terms, we would be incapable of having a genuinely scientific knowledge of the world. The dedicated purpose of all serious science is to arrive at reliable general ideas, ideas that have the widest possible application to the subject m atter which is under study. If all I know, or care to know, is that if I drop my car keys they will surely and inevitably fall to the ground, my knowledge o f how the physical world works remains at a very primitive level, and it would not at all deserve to be called scientific knowledge. But if I put in the effort to gain access to a set of general ideas which inform me that all material bodies, not just car keys and the earth, influence one another by reason o f their respective m asses and their distance from one another, then I am able to think in more global fashion, and can get beyond mere facts to the explanations of facts. The trivial experience of dropping my car keys in the driveway suddenly puts me in mind of how it is that the whole physical universe is in fact a universe, that is, an ordered whole. General ideas expand our horizons and introduce us to an endless succession of new and interesting realms. However, it would not be wise to rely too exclusively on general ideas. The purpose and em inent usefulness of general ideas is that they can be applied informatively to concrete particulars. General ideas are especially valuable when they take the form of those principles— we call them first principles— which found and give guidance to every science. A principle is a fundamental truth having to do with the main subject matter of a science, and it is meant to be applied to specific cases in order to make them more intelligible. The importance of this application of principles to particular cases— applying the general to the particular—is especially evident in practical sciences like logic and ethics. It would do little good, in the case of logic, were one to master all the basic principles that pertain to correct and effective thinking, and yet never get around to giving them practical application. The theory has to be brought down out o f the clouds and put to earthy uses. General ideas, which emerge out of concrete particulars, must be returned to concrete particulars.

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A nalogous T erms

A uni vocal term is one that expresses a single meaning, which is to say that it is the sign of an idea whose comprehension is clear and invariable. “Animal” is an example of a uni vocal term. W hat do we mean, clearly and invariably, when we use that term, as when we predicate it correctly of subjects like “man” and “gopher”? We refer to an organic creature which is sensitive (i.e., is possessed of at least the most basic of the five senses, touch), has at least the minimal appetitive powers o f attraction and aversion, and is capable of locomotion. Thus, when we assert that “Man is an animal” and “A gopher is an anim al,” we are predicating precisely the same idea of those two subjects. Perhaps the best examples of univocal terms are scientific and technical terms, for many of these were invented for the express purpose of referring to one thing and one thing only. “Electron” and “positron” are intended to signify particular kinds of subatomic particles and nothing else. Computer technology has given rise to a whole array of new uni vocal terms. Every profession and trade has its store of uni vocal terms, as do the various athletic sports and parlor games. In baseball, “double play” has but a single meaning, and so does “checkmate” in chess. The beauty and usefulness of uni vocal terms lies precisely in their clarity and reliable steadiness of meaning. As such, they are a potent antidote against ambiguity in language. (See Appendix D for more on univocal terms.) An equivocal term is a homonym, that is, a single world that does service as designating more than a single thing. We have already used the example of the English word “bark,” which has at least five distinct meanings. Every language has its share of equivocal terms— or ambiguous words, as the grammarian would be inclined to call them— and usually they cause few problems when it comes to interpretation because of the context in which they are used. If we read, “The sailor leaped out o f the bark and swam vigorously to shore, using the butterfly stroke,” we would have no trouble in discerning that the “bark” which figures in the sentence refers to a small sailing vessel. One of the more interesting equivocal terms in English is “secretary,” which can signify a clerical worker, or an officer of a company or organization, or a peculiar type of desk, or a large bird of prey which makes its home in Africa— all with the same spelling and pronunciation. Words like “bark” and “secretary” are obviously equivocal in that in each case we have one word which can convey at least two quite distinct meanings. As far as logic is concerned, there is potential for problems when abstract terms are used without being carefully defined, especially in argument, for they

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lend themselves easily to equivocation. The word “love,” for exam ple, can convey a multitude of meanings. Consider the following statements. Estelle was once president of the Free Love Society o f Nadir County. I just love popcorn. W e are told that we should love our neighbor as ourselves. In proposing marriage to Betty, Bert avowed that he was hopelessly in love with her. “Love it or leave it,” the sign read. In no two o f those five statements does “love” mean exactly the same thing. A word like “love” can be used twice in a single argument, conveying two distinct m eanings, with the result that the reasoning of the argum ent is rendered fallacious. This can come about as the result of carelessness on the part of the one who constructed the argument, or it can be done quite deliberately, but in either case the result is fallacious reasoning. More about this later in the book. There are not a few national governments around the globe which boldly claim to be democracies, and where the word “dem ocratic” m ight figure prominently in a nation’s official title, but we might be hard-pressed to find in some of those nations apolitical system in which we could find serious traces of what we would be prepared to call a democratic government. T wo people can use a word like “dem ocratic,” and can mean appreciably, perhaps even radically, different things by it. A uni vocal term has one m eaning; an equivocal term has more than one meaning. So, with those two terms we have a distinction between sameness and difference in meaning, same meaning with univocal terms, different meanings with equivocal terms. W ith an analogical term we have, in a sense, a combination of the univocal and the equivocal, for an analogical term conveys at once sameness and difference of meaning. In order rightly to understand what is going on in an analogical term, we need first to step back and reflect briefly on the nature of analogy in general. When we employ analogy in language we are giving public expression to analogical thinking, and the essence of analogical thinking is comparative thinking. Thus, an analogical term always refers to at least two things about which a comparison is being made. As applied to those two things, the term is conveying the idea that in one way they are the same, and in another way they are different. It is presenting us with a cognitive package containing both similarity and dissimilarity. There are a great many terms that can be used analogously, for the simple reason that very often, in our everyday affairs, when we are comparing any two things, we see that they have both similarities and dissimilarities. Seldom are any two things perfectly identical, but suppose that we were to come across a couple of objects which are pretty close to being identical, or so they appear to us. In that case we would naturally give more stress to what they have in common, but in the interest of providing the most complete and accurate account of them, we would want also to point out how they differ. Philosophers

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have argued that perhaps the single most basic verb in any language— “to be,” in English— must necessarily be used analogously. Here is how they reason on the matter. The verb “to be” conveys the idea of actual existence, as when we say, “The pebble is,” or “The president of MIT is.” The term “is” should be regarded as analogous in those two statements, or in any other pair of statements that have that term as its predicate, and whatever might be their subjects, because it implies both sameness and difference on the level of existence itself. W hat both the pebble and the president of MIT have in common is the foundational fact that they both actually exist. They are both firmly established within the realm of real being. But we would not for a moment think that the pebble and the president exist in precisely the same way. Indeed, there is a dizzying span of difference between the mode of existence of an inanimate thing like a pebble and a rational creature like a human being, be he the president of MJT or not. Analogous terminology attempts to make us aware of the kind of balance which is in play, with respect to sameness and difference, between any two things. Analogous thinking, which, once again, is in its most elementary form simply comparative thinking, is something that comes quite naturally to us. It is, among other things, an integral part of the learning process. Whenever we come into possession of genuinely new knowledge, we are involving ourselves in a process whereby, more or less consciously as the case may be, we compare the unfamiliar (the new knowledge) with the familiar (knowledge which we already possess), and then we integrate the new with the old. It is just to the degree that we see how the new knowledge fits into what we already know that we are able fully to assimilate it and make it securely our own. The ability to make solid evaluative judgments is dependent upon our success in thinking analogously. Whenever we evaluate two or more things in order to determine which is better or which is the best, we are not only comparing them with one another but we are comparing them with a standard of some sort. And whenever we are called upon to evaluate a single item—say, an essay or a book— we compare the essay or book with what we take to be the proper criteria for a good essay or a good book. At least that is what we do if we are making a responsible judgment, and not just acting on whim. In a situation in which we are comparing any two things, whatever they might be, and however markedly different they might be, they are necessarily going to have something in common, if nothing else than the most rudimentary of facts that they both exist, they are both real entities. O f course, even the most widely differing things will have more in common than the bare fact that they both exist. When we consciously engage in analogical thinking, there are two things which we need to pay special attention to. First, and generally, we have to take note of the overall proportion between the similarities and the dissimilarities which are evident in any two things we are comparing. Are there appreciably more similarities, or vice versa? Or do

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similarities and dissimilarities pretty much balance one another out in the two things? Second, and more importantly, we need carefully to register thequality of the similarities and dissimilarities. Are they essential to the natures of the two things being compared, or of only peripheral importance to them? If I am asked to evaluate the worth of two men for their competence in performing a task other than playing professional basketball, when one man stands 7 feet 2 inches and the other 5 feet 2 inches, and I judge the taller man to be superior solely on the basis of his greater height, then my judgm ent would be seriously flawed because of the irrelevant criterion on which it was based. So, once again, we m ust be attentive not only to the comparative num ber of sim ilarities and dissimilarities, but we must heed their quality as well. Later in the book we will come to see how important these considerations are when we meet a form of argument called the argument from analogy. T he A nalogy

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A ttribution

There is a very basic type of analogical reasoning which has been given the name o f the analogy of attribution. The governing idea behind this mode of reasoning can be briefly described as follows. Because it is analogical reasoning, it involves the comparison of at least two things. In comparing them, it is noticed that the two things relate to one another by the fact that one o f them possesses a certain quality by reason of its very nature, simply because it is the kind of thing it is— we will call it Quality X— while the other thing, though not possessing Quality X by nature, is closely linked to it on account o f its being either (a) a cause o f Quality X, or (b) an effect o f Quality X. An exam ple o f the analogy o f attribution would be helpful. To represent Quality X, I will use the classical instance o f health. W hat is health? After reflecting a moment, we would readily see that health is a quality which is properly attributed only to living organisms, be they plants or anim als. We would call a hibiscus tree or a heifer healthy, but not a wrench or a windmill. Using logical terminology, we say that health is intrinsic to living organisms. But consider the various other things, inorganic things, which without hesitancy we also call healthy, and in doing so we do not at all seem to be speaking nonsense. We say such things as: this is a healthy climate, exercise is healthy, 98.6° is a healthy temperature, a balanced diet is healthy, Joyce has a healthy attitude toward life, Boppo Plus is healthy m edicine. And on and on. But isn’t this usage rather odd? Why do we call climate, exercise, temperature, a balanced diet, attitude, and m edicine healthy, when clearly none o f these things is a living organism? What is the connection between the health of a non­ living thing and the health o f living things? It is the connection created by a cause/effect relation, moving either from the inorganic to the organic, or in the opposite direction. To be specific, a climate, exercise, a balanced diet are called healthy, not because they them selves have health in the literal sense, but because they can cause and preserve health in living organisms. A temperature

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of 98.6 ° is healthy because it is the effect of a healthy human organism; it is a sign of health, understood in the strict sense. And Joyce’s attitude is healthy because we read it as a sign of her personal health—her mental health, to be more precise about it. Her attitude is the effect of her sound mental health. In denominating as healthy things that either cause health in living organisms or are the effects of that health, we understand health, as attributed to those things, to be extrinsic to them. They are not healthy in the strict sense, but only after a manner of speaking— that is, analogously. Finally, we will make mention of a few technical terms which apply to the analogy of attribution, to add more precision to our description of it. The term analogates is assigned to the things that are being compared. Among the analogates, a distinction is made between the primary analogate and the secondary analogates. In the example used above, a living organism would be the primary analogate, because that is what the analogon—i.e., the basis for the comparison, in this case health— is intrinsic to. Things like exercise or a 98.6° temperature would be secondary analogates, in relation to which the analogon, health, would be an extrinsic quality, something to which they relate respectively as cause and as effect. M etaphor M etaphor is a particular form of analogy. It plays a very important role in literature, as a rich and, if artfully employed, provocatively suggestive figure of speech. But one does not have to be a Dante or a Shakespeare to advert to metaphor, and we all make ample use of it in our everyday speech. When we call little Henrietta an angel, or our neighbor to the north a donkey, we are using metaphor. But metaphorical language has a special bearing on logic because it often intrudes itself into argument, and more often than not with negative results. Metaphor is an implicit way of making a comparison. Little Henrietta is of course not literally an angel, but a human being like the rest of us. We are quite aware of this fact, but the idea we are attempting to communicate, impressed as we are by her celestial mien, is an implicit version of the explicit claim that Henrietta is like an angel. And when, rather unkindly, I refer to my neighbor to the north as a donkey, I am not speaking literally, but only making the suggestion that Mr. X bears not a few resemblances to what the dictionary describes as a “long-eared equine quadruped otherwise known as an ass.” Because it is a comparison, there is minimally two components to a metaphor. There is the subject, that to which the metaphor is principally calling our attention, and its predicate, that to which the subject is implicitly being compared. In the example referring to little Henrietta, she would be the subject of the metaphor, and angel would be that to which she is being compared. From a purely logical point of view, a metaphor would be considered to be aptly

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employed if it provides us with a greater understanding of the nature or character of its subject. If used judiciously, not to say with artistic sensitivity, it can be much more effective in revealing a subject to us than what we might have to say about it in straightforward, literal terms. If used carelessly, or even maliciously, we are left with a distorted understanding of its subject. In the final analysis, the value of metaphor— and this can be said of any linguistic device we employ in logic— is determined by the degree to which it is in the service of the truth. T he O pposition

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T erms

Ideas relate to one another in a wide variety of interesting ways, as when their respective contents are such that we say, in logical parlance, that they are opposed to one another. Speaking generally, two terms are regarded as being opposed when (a) the comprehension of the first term, in one way or another, is directly at odds with the comprehension of the second, or (b) the comprehension of the first term necessarily implies that of the second. Ideas can be opposed to one another in at least four distinct ways: as contradictories; by reason of privation; as contraries; and by reason of relation. Contradictory Opposition. This represents the most emphatic and definite kind of opposition between two ideas. It is based upon the most fundamental kind of opposition there is, that between being and non-being, between that which is clearly the case and that which cannot possibly be the case. Contradictory opposition is expressed simply by negating any particular term. Thus, the contradictories of “tree,” “faith,” and“flying” would be “non-tree,” “non-faith,” and “non-flying.” But there are certain words whose ideas are unquestionably contradictory in that there is no way that they could both be true at the same time; their respective comprehensions are mutually exclusive, and such words do not have to make use of the prefix “-non.” Two words of this kind are “life” and “death.” Another two words, and rather significant ones, that relate to one another as contradictories are “truth” and “falsity.” That these latter terms are flatly contradictory may be something which may not be immediately evident to us, but so they are. But do we not on occasion use expressions like “partially true,” or “half true,” which suggest that truth and falsity are not mutually exclusive and that there is a middle ground of sorts which can be found between them, a twilight zone as it were, where a proposition is neither true nor false but a hybrid of the two? Notwithstanding linguistic usages of that sort, truth and falsity are in fact contradictories. A proposition has to be either one or the other; there is no third alternative. This is a point which we shall examine more closely in a later chapter. The key feature of contradictory ideas is that they allow for no middle ground between them; if they refer to the objective order at all, one or other of them must be true, with no opening left for another possibility. An organism is

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either alive or dead. We employ phrases like “half alive” and “almost dead ,” but these are simply figurative ways of speaking, and do not imply areal state which is situated between being alive and not being alive. Someone who is “half alive” lives, however tenuously, and one who is “almost dead” is in fact not dead, any more than som eone who alm ost had an auto accident in fact had an auto accident. Near misses are still misses. There are words in the English language which carry negative prefixes with them, such as “insane” and “unhealthy,” and these might suggest a contradictory relation, so that, supposedly, insane is to be taken as the contradictory of sane, and unhealthy as the contradictory of healthy. But the two pairs just cited, and those like them, do not represent true contradictories. The test of this is to ask ourselves, regarding both examples, if it necessarily has to be either one or the other, with no third possibility. And we see that such is not the case. A person could be in a certain mental condition where one would not, on the one hand, identify him as being insane, but neither, on the other hand, would one want to say that he enjoys perfect mental health. Let us say that he is beset by some serious mental problems, but they are of the sort that can be effectively treated, and are therefore not significantly debilitating. In other words, there is a rather large stretch of territory lying between the extremes of insanity and perfect mental health. And the same can be said of healthy and unhealthy, in this case with respect specifically to physical health. People could be in a state where they are not perfectly healthy, and yet we would be reluctant to describe their condition as positively unhealthy. They are bothered by periodic aches and pains, but that does not keep them in bed in the morning. Their health, we might say, is so-so; it could be better, but it could also be much worse. It should be obvious that in dealing with terms of the kind we have been reflecting on, there are some pressing problems o f definition which have to be squarely met if our logical analysis of them is to be fruitful. Right at the outset we have to be perfectly clear as to exactly what we mean by terms like sanity and insanity, healthy and unhealthy. Privative Opposition. A privation is the lack of a quality in a subject which, given the very nature of the subject, it should possess. A privation is to be contrasted with a pure negation, which would refer to a situation where a subject lacks a particular quality which, given its nature, one would not expect to find in the subject in the first place. The lack of sight in a tree would be an example of pure negation, for it is not of the nature of a tree, even a tree as formidable as a giant sequoia, to possess the power of vision. However, blindness in a horse would represent a privation for the reason that horses are, by nature, meant to have sight. Two terms relate to one another privatively, then, when the idea borne by one term refers to a natural quality in a subject—i.e., something which belongs to the subject by nature— and the other term, the privative term, refers to the absence o f that quality. Blindness, deafness, and muteness would be examples of privative terms as applied to a human subject, for all three indicate

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the lack of a quality, or power, which is natural to the human animal: sight, hearing, and the ability to speak. Blindness, deafness, and muteness, and like privations, can be consequences of circumstances which are quite beyond human control. But this is not so with all the privative terms we could think of. Consider the following pairings: seaworthy— unseaworthy; humaneness— inhumaneness; virtue— vice. A ship, if it is to withstand the blasts and bufferings of a winter passage across the North Atlantic and make its way safely to its intended port, must be seaworthy. The unseaworthy condition of a ship would count as a definite privation, but it could be the result of human neglect, a failure on the part of the captain and crew to keep the ship ship-shape. In some cases, then, moral considerations could enter into our analysis of a privation. Humane activity is what we would expect to be natural to human beings, and we would accordingly consider its absence— inhumaneness— to be a privation, but a privation which carries moral culpability along with it. Perhaps the most poignant pair of pri vatively opposite terms is virtue and vice. Vice is, by definition, the absence of virtue, and vice, by definition, necessarily involves conscious and deliberate choices on the part of a person. Vice is not something that might just happen to us, as could blindness and deafness; we make it happen by our free choices. Contrary Opposition. In both contradictory opposition and privative opposition, one of the terms is positive, the other negative: square— nonsquare, as contradictories; prudent— imprudent, as privatives. The negative quality of the terms is clearly indicated by prefixes like non-, un-, in-, im-, and by suffixes like -less. A mindless person is one who is considered to be, rightly or wrongly, not as intellectually adept as he should be. In the case of the contrary opposition of terms, both of the opposing terms are positive, so their opposition does not rest in the fact that the comprehension of one idea negates, in whole or in part, the comprehension of the other idea, but they represent the extremes of a single genus or a class. So, for example, black and white are both contained within the genus “color” (each can be considered to be a species o f color), but they are the polar opposites o f that genus. Black and white are the extrem es when it comes to color, but between those two extremes are to be found an array of other colors which are neither black nor white. But there is at least one example of contraries where they are snug up against one another, with nothing between them, and that is the case of odd and even numbers. Between two and three there is no integer or whole num ber which separates them. This state of affairs calls for a distinction to be made regarding contraries. The contrary opposition that exists between all odd and even numbers is called immediate, because there is no intermediary entity or entities between the two opposites. However, in the case o f black and white we have mediate opposites because there are other colors that stand between them. Other examples of contrary opposition would be largest— smallest, hottest— coldest, and loudest—softest.

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The salient difference between contradictory ideas and contrary ideas is that in the case of contradictories it is either one or the other, no further choice is available (except, of course, the choice of rejecting both of them), whereas with mediate contraries several choices are available to us. We can choose any one of the ideas that lie between the two extremes. In dealing with ideas, however, we must be careful to distinguish between contradictories and contraries, for the ability to do so can have significant practical consequences for us. Sometimes we are presented with two ideas as if they were contradictories when in fact they are only contraries. What is often happening in such a situation is that we are being led to believe that we have but two choices, whereas in truth we might have several available to us. We will look at this particular problem more closely when we study fallacious reasoning. Relative Opposition. When two ideas are related to one another in such a way that the meaning of each is dependent on the meaning of the other, we say that they are in relative opposition to one another. For example, the term “uncle” is meaningful only if the person to whom it is applied has a niece or nephew. And the term “nephew” is meaningful only if the person who is designated as being such has an uncle or aunt. The nature of relative opposition precludes the possibility of either of the terms in a pairing to have any meaning while standing alone. It would make no sense to call a woman a mother, in the literal sense, if she had no children. In an instance like that there could be, in the person of an unmarried woman, the potential subject for the predication of a term in relative opposition. If she were one day to have children, then the mother/child relation would be established. Or the aunt/niece or nephew relation could be established without her ever marrying or having children. There are common situations where the very existence of the subject necessitates that a certain kind of relation is in place. One cannot be a daughter without having a mother and a father; the very meaning of “daughter” implies the child/parent relation. However, there is nothing in the comprehension of “woman” that demands a mother/child relation. There are innumerable terms whose meaning entirely depends upon their correlatives. If “right” is to be meaningful, it must be contrasted with “left” or with “wrong” ; there cannot be an “up” without a “down,” and if we point to an object and say that it is “larger,” there must be another object in relation to it which is called “smaller.” Ideas that are related to one another in relative opposition are richly informative for the way they show how the multitude of individual things, or concepts, are knit together to form a large, intricate, wonderfully integrated system. S ound

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U nsound I deas

We remind ourselves of a basic epistemological principle regarding all ideas— that their ultimate origins are to be found in our experiences with the external world. Put another way, and a bit more precisely, all intellectual

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knowledge is dependent upon sense knowledge. Ideas (intellectual images) are bom out of sense images. It is to this principle we appeal when we endeavor to make the altogether critical distinction between sound ideas and unsound ideas. Might we not ju st as well speak o f true and false ideas, rather than sound and unsound ones, and be m eaning the sam e thing? In ordinary language we do commonly refer to ideas as being either true or false, and that usage seem s to serve us quite well. However, for all the functional usefulness ordinary language brings with it, it does not always have the kind of clarity and precision we are continuously trying to achieve in logic, and this is a case in point. An idea, no matter how brilliant it might be, cannot, in itself, be either true or false. It is only when idea is m arried to idea to form a proposition that there is established the kind o f factual situation to which we are able to respond with a “true” or “false.” If someone says “cardinal” to me, clearly referring to a species o f bird, and not to a cleric from Rome or a ballplayer from St. Louis, I understand well enough the idea he intends to communicate to me, but he has to predicate something of “cardinal” before I can m eaningfully think in terms of truth or falsity. If my informant says, “There is a cardinal at the bird feeder,” and I look out the window and discover that to be the case, I assent to the truth of the statement. But if that same informant were to assert, ‘T h e cardinal has black and blue feathers, a long slender beak, and is about the size of a wild turkey,” I would not even have to look out the window to know that I was face-to-face with a false statement. W ell, then, if isolated ideas cannot correctly be called either true or false, what does it mean to say that they are either sound or unsound, or, to use more homey language, what does it mean to say that they are either good or bad, just as ideas? Let us recall the tripartite relation existing among word, idea, and thing; the word is the sign o f the idea, and the idea is the sign o f the thing, that is, o f the object to which it refers. An idea reflects, represents, in a sense embodies, the object to which it refers. An idea is sound or good, then, precisely to the extent to which it faithfully and accurately fulfills these functions. An idea creates a bond between its object and the mind which cradles the idea. If the idea represents a faithful and accurate image o f its object— the thing as it actually is in itself—then the m ind is possessed o f a sound idea, one which is putting the m ind in touch with the objective order o f things, the way things really are in the external world. An unsound idea, on the other hand, is an idea which to one degree or another is not faithfully representative of its object. It is presenting a defective picture o f its object, and therefore a mind which is possessed of—or rather, burdened by— an unsound idea is not fully connected with the extra-m ental world, a situation which can be more or less serious, depending on the importance of the idea in question. Can we do anything about unsound ideas? Not only can we, we must, for to continue to harbor unsound ideas is to do nothing less than to distance ourselves from the objective order of things, and this is the kind of situation in which none

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of us can afford to remain for any extended period of time. Unfortunately, it is quite possible, and not especially unusual, for us to harbor unsound ideas, perhaps for years, while being only dimly aware, if at all, that they are unsound. Often it takes a shock of sorts to make us realize that an idea is unsound, the kind o f shock that follows upon a head-on collision between the idea and the object of which it is purportedly the faithful representative. This usually happens as a result o f our encountering the object itself with a new, especially alert, eyeswide-open attitude which, for some reason or another, had not accompanied any of our previous encounters with it. And we are set back on our heels to discover that there is a discrepancy, perhaps a glaring one, between our idea of the object and the object itself. As an illustration of the kind of circumstance to which I just gave a general description, I invite you to consider how it is that, if we are at all concerned with having honest estimates of other people, we are constantly needing to adjust our ideas of them as we become better acquainted with them. It is all too easy to formulate wrong ideas of others, and the plainest explanation for those wrong ideas— i.e., unsound ideas— is lack of sufficient knowledge on our part of the subjects to whom those ideas refer. As a general rule, the less we know of other people, the more likely that our ideas about them will be unsound. And, folk wisdom to the contrary, seldom are first impressions to be relied on. When Kevin first met Kerry he thought of her as a greedy and avaricious person, for she was always talking about making money and how she could make more of it. As he got to know her better he came to find out, much to his surprise, that although she did in fact put much time and energy into making money, at which she was very successful, she gave most of that money away to the poor, and she herself lived in very modest, almost impoverished, circumstances. Kevin quickly changed his mind about Kerry. Whereas he initially had an idea of her as a selfish materialist, he now thought of her as a virtual paragon of selfless altruism. The difference between his earlier and latter idea of Kerry is that the first was unsound and the second was sound, sound because it reflected the real Kerry. Our ideas, even about the simplest of things, can never be perfectly flawless, for were they to be such we would have, through them, comprehensively exhaustive knowledge of any given object, and the human intellect is simply not capable of that. But there is a difference to be recognized, with respect to ideas, between the essentially faithful and the flatly unfaithful. We must be continuously checking up on our ideas, in order to ensure that they are reliably representing their objects, and we must make whatever adjustments to them which are necessary to bring them into line with their objects. On occasion we might find that a particular idea is so totally bad, because its representational quality is just about nil, that it is beyond repair, and the only logical thing to do is simply to get rid of it. Really bad ideas are like an organism which is terminally ill with a deadly communicable disease. They have to be put in quarantine in order to preserve the overall health of the mind.

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There is only one way effectively to test ideas in order to determ ine their soundness, and that is to return to their sources, the objects which account for their being birthed in our minds. If I have any questions as to the soundness of my ideas regarding the Pythagorean Theorem, for example, my only recourse, if I seriously want to m eet those questions, is to go back to the theorem itself, study it more intensely, wrestle with it if needs be, read about it, talk to the friendly neighborhood geometrician about it, meditate on it as I take my daily walk in the park. C reative I deas The claim that all of our ideas have their ultimate source in our experiences with the external world is not to be interpreted as meaning that there is a neat, clean one-to-one relation between any particular idea that m ight be bouncing around in our heads and a particular object which is to be found in the external world, for that is patently not the case. We have all sorts o f ideas, and perhaps the m ost interesting and provocative o f them are those for which there is no single object in the extra-m ental world that directly corresponds to each o f them. How then are we to explain those ideas, in light o f our epistem ological principle? Invariably those ideas are complex, in that they contain many notes. Now, while there may be no single thing in the external world to which a particular com plex idea, taken as a whole, corresponds, nevertheless, with respect to its parts, that is, the multiple notes of which it is composed, each o f those particular notes, taken separately, will be found to have a specific extra­ mental source; there is som ething out there to which the note directly corresponds. Very early in our careers as rational creatures we began to store up an abundance o f ideas which had direct referents in the external world, and throughout the course of our lives, as our experience broadens and deepens, we are continuously adding to that store. Because of the creative capacity o f the human mind, it is not too long before we learn how to com bine certain o f our ideas and come up with something which is entirely new, in the sense that the resulting idea, again, taken as a whole, does not have anything in the external world that directly corresponds to it. And for that reason ideas o f this kind can be called original. I will make use o f the m ythical horse Pegasus to do service as an example. Pegasus is a rather rem arkable horse because he has wings and he can fly. Now, there are obviously no w inged horses out there in the real world, flying over our patios on sw eet sum m er days as we barbecue the hamburgers, for which we can be grateful, considering how inconvenient bird droppings can som etim es prove to be. W hoever was the creative genius who first came up with the idea of a flying horse did not, in doing so, start with nothing. W hat that anonymous ancient did was to take the idea of wings, which he got from observing birds and bats and maybe insects as well, and joined that idea in his mind with the idea of horse, and thus came up with a novel idea— a

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winged horse, for which there is no corresponding object in the real world. But notice, in a case like that, how the mind depends upon its experience with the external world in order to come up with a novel idea, and thus we can say that the idea of Pegasus has its ultimate source in sense experience. And what is said of the idea of Pegasus can be said of any other idea, no matter how intricate or complex, no matter how abstractly distant and indirect, just as formulated, is its relation to the external world. Once we have a store of ideas in our minds, we can combine them in a countless variety of ways so as to come up with novel ideas which may have little to do directly with the external world, but nonetheless they all trace their origins to that world. Creative ideas can be either good or bad, and the way we determine whether they are one or the other is comparable to the way we distinguish between sound and unsound ideas of any kind. The definitive standard we must appeal to is the objective order of things. How a creative idea measures up to the external world will tell us whether it is a good or a bad idea. I can concoct all sorts of novel ideas which represent a grossly distorted picture of reality, and then, if they become the prism through which I view the external world, I will not be seeing that world as it truly is but how I erroneously conceive it to be. I become a captive of my bad creative ideas. On the other hand, creative ideas can be wondrously positive, and immensely fruitful. All the great inventions and technological advances that human history has borne witness to are explained by the fact that creative minds put ideas together to come up with new ideas for things, things which did not actually exist but had the possibility of existing, and it was just that possibility which provided the incentive that fueled the labors of the inventors and eventually led them to the point where they could transform a mere idea into a reality. Before there was the flying machine there was the idea of the flying machine. And when we consider the realms of literature, the fine arts, architecture, we can become fairly overwhelmed by the power and the beauty of creative ideas.

Review Items 1. W hat is the “note” o f an idea? 2. Describe the difference between a concrete idea and an abstract idea. 3. What problems could follow from an overuse of abstract ideas? 4. Describe the function that general ideas play in scientific inquiry. 5. Describe univocal, equivocal, and analogical terms. 6. Give a general account of analogical thinking. 7. Cite the benefits and the drawbacks of metaphorical language.

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8. Give examples o f terms that are opposed to one another as contradictories and as contraries. 9. Explain the difference between sound and unsound ideas. 10. Is there a simple one-to-one correspondence between an idea in the mind and an object in the external world?

Exercises A. W ith the analogy of attribution in mind, for each o f the items listed below, (1) identify the term either as a primary analogate or a secondary analogate, and (2) if it is a secondary analogate, specify it as related to the primary analogate either as cause or as effect. The analogon is “held.” 1. a golden retriever 2. the glossy coat of a golden retriever 3. dog food 4. pills to prevent worms 5. the clear eyes of the dog 6. taking the dog out for a walk B. For each of the pairs o f term s listed below, indicate w hether they are contradictory, contrary, privative, or relative in their opposition to one another. 1. teach er-pupil 2. 32 degrees F - 212 degrees F 3. Jimmy physically in Paris right n o w -Jim m y physically in St. Petersburg right now 4. forw ard-backw ard 5. ju s t-u n ju s t 6. elated-depressed 7. honest-dishonest 8. d o n o r-recipient 9. north magnetic pole - south magnetic pole 10. generous-ungenerous

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Chapter Four The Categories W hat A re

the

C ategories?

In ordinary language we use “category” to refer to a class or group of things. And when we “categorize” something we arrange it into a number of distinct parts. So, if we were to categorize a subject like literature, one method we could use in doing so would be to parcel it out according to its different types, and come up with classifications, among others, like: prose fiction, prose non­ fiction, poetry, and drama. To categorize, in this sense, is to break down a subject into its constituent parts, and this can prove to be a beneficial exercise because it allows us to gain a better knowledge of any subject, as a whole, by making us vividly aware of the parts that compose it. There are some similarities between how the idea of category is understood and used in ordinary language and how it is understood and used in logic. For one thing, the employment of the logical categories has very much to do with increasing our knowledge of any given subject. Even so, logic’s understanding of category is quite specialized, and when we refer to the Categories, what we have in mind is a set of very basic concepts which, taken together, exhaust all the possible things that can be predicated of any particular subject. It was Aristotle who first formulated the Categories, and subjected them to close analysis, in one of the six books on logic he wrote, which is called, fittingly enough, Categories. What can generally be said of the ten categories is that each of them, by being predicated of a subject, provides us with some salient information about that subject. (See Appendix A. Are the Categories exhaustive?) W e have already acquainted ourselves with the predicables—genus, species, specific difference, property, and accident. By predicating the first of these three elementary ideas to a particular subject, we are giving it precise meaning and intelligibility through the simple process of classification. Let us say that it is Albert that we want better to understand, from a logical or scientific point of view. We begin by noting that Albert is an animal, thus placing him in a large class called a genus. Then, regarding our subject a bit more closely, we

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see that there is something specifically different about Albert that sets him apart from the greatest portion o f the m em bers in the large and copious class o f animals: i.e., he is possessed o f reason. That justifies our placing him in a sub­ class, or species, o f the genus anim al, which is labeled “hum an.” We thus conclude that A lbertis a rational animal, or human being. Once we have Albert properly “located” in that most basic way, we can then go on to predicate any number of other particular things of him, in the form of properties and accidents. W e may say, for exam ple, that A lbert has the capacity for laughter, which is called a property, because it can be accounted for only by adverting to A lbert’s essential nature as a rational creature. Only a rational creature, we would argue, can “get” ajoke, for such a creature is able, through reason, to see and appreciate the element o f incongruity— a surprise departure from what is accepted as the proper order of things— which is the basis of all humor. We then might go on to remark about Albert that he has red hair and green eyes, which are identified as accidents because they are not essential to his nature as a human being. Though he really does have red hair and green eyes, he would be no less Albert (i .e., his essential nature would not be changed) if he were to have black hair and black eyes. The Categories are much like the predicables in that they represent very rudimentary ideas, and they are predicated o f a subject in order to provide us with important information about the subject. The similarity between the two is accentuated by the fact that the Categories are also known as the predicaments, orthe predicamentals. There is, however, a significant difference between the Categories and the predicables, in that the predicables are concerned prim arily with the logical order, i.e., with how ideas can be employed to organize our knowledge o f the phenom ena of the external world. The Categories, for their part, address directly the actualities o f the external world, and hence we say that they have principally to do with the existential order. Put another way, we may say that while the predicables tell us about the workings o f the world of the mind, the Categories tell us about the workings of the world outside the mind. Consider the predicable “genus.” This is called a logical concept because there is nothing in the external world to which it directly refers. There are no genera to be found out there. W hat is to be found are any num ber of real entities which, in order better to understand them, the irrepressibly classifying human mind gathers together into large groups on the basis of broad shared characteristics, and thus are created the genera. “Genus,” then, and all the rest o f the predicables, are essentially mental constructs which are brought to the external world as organizing tools. As for the Categories, they are what the mind recognizes as the basic realities of the external world. W ith these prelim inary observations having been made, we can now introduce the Categories. They are ten in number, and are divided unevenly between substance, which stands alone, and the nine categories of accident, which are: quantity, quality, relation, action, passivity, time, place, position, and habit. The distinction between substance and accident is of the utmost

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importance, for each represents two radically different ways of existing. To put it in the briefest terms: a substance is a thing; an accident is a feature o f a thing. An apple is a substance ; the redness and roundness of the apple are accidents. A substance exists independently, is separate from other substances, has an identity which is uniquely its own, and therefore has a name which is peculiar to itself, informing us just what kind of substance it is. We can easily distinguish one apple from another, and we are not likely to confuse an apple and an orange. P rimary S ubstance

and

S econdary S ubstance

Aristotle defines substance as “that which is neither predicable of a subject nor present in a subject."(Categories, 2a, 10)9 How is that to be interpreted? A substance is not predicable of a subject because it is precisely a substance which is the subject about which something is predicated. To predicate, remember, is simply to attribute something to a subject, as when we say, “Roger is running,” where we attribute the act o f running to Roger, so Roger here is the substance who is the subject o f predication. If, in this case, we were to predicate a substance o f a subject/substance, in disrespectful defiance of Aristotle’s definition, we would end up with the statement, “Roger is Roger,” which, while incontestably true, is not terribly informative, for, having been long acquainted with Roger, we already know that he is who he is. A statement like “Roger is Roger” is a tautology, which means that its predicate simply repeats the idea represented by the subject, and therefore is not, in the strict sense, a predicate at all, although the structure of the statement might lead us to believe otherwise. True predication provides us with some additional information about its subject, as in, “Roger is running”; it does not simply repeat the subject. In sum, then, a substance is that which is not predicable o f a subject because you cannot, without being tautological, force into the role of predication that whose proper role is to be the subject of predication. The second part o f A ristotle’s definition tells us that a substance is not present in a subject. W hy is that? In briefly stating the distinction between substance and accident, ju st above, we said that a substance is a thing and an accident is a feature o f a thing. A thing is an independently existing entity, whereas an accident, as a feature of such an entity, is something which can only exist dependently. The redness of an apple is a feature of the apple; we say that it has accidental being because, though it is real enough, its existence depends upon the existence o f the apple: no apple, no redness. When Aristotle tells us that a substance is not present in a subject, he is simply making the plain point that a substance is not an accident. It is accident, as exemplified by the quality of redness, that is “in” a subject, for that is the only way an accident can exist. A substance, on the other hand, is just that in which accidents are to be found. Very well. At this stage we should be clear about the fact that a substance is something which cannot be predicated of a subject, or, to put it differently, a substance cannot be predicated o f a substance, which is to say the same thing.

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The Roger of whom running was predicated is a substance. Y ou are a substance; I am a substance; every human being is a substance. This being the case, I can confidently say that, “Roger is a human being.” But if every human being is a substance, am I not in that statem ent predicating substance o f substance, and therefore doing violence to A ristotle’s definition? As a m atter o f fact, I am predicating substance of substance in that statem ent, but in an entirely perm issible way. To see how that is so we m ust now look at the im portant distinction between primary substance and secondary substance. Prim ary substance is sim ply what we have been talking about up to this point— an actually existing entity, apart from and quite independent o f any mind that might be thinking about it. In our example, Roger him self is a primary substance. When I make the claim that Roger is a human being, I am not merely mouthing a tautology, and that is because I am making a genuine predication. The predicate here, “human being,” is an example of a secondary substance. A secondary substance is the result of the mental process by which we look upon any primary substance— an actually existing thing “out there”— and abstract from it its essential nature, and then, with the very special knowledge we have as a result o f that process, we place the prim ary substance in the class or category in which it properly belongs. Thus, secondary substance is the abstracted nature of a primary substance, and it can be legitim ately predicated of a primary substance, for by doing so we are not merely repeating the subject of a proposition, but revealing the essential nature o f that subject, which is to communicate very important information indeed. The ten Categories, as noted, are divided between the category of substance and the nine categories of accident, that distinction being based on the fact that the two, substance and accident, represent two radically different ways of existing: independently, in the case of substance; dependently, in the case of accident. But it is important to be aware of the fact that substance, as it figures in the Categories, is secondary substance, which allows it to be predicated of a subject in the same way that the nine categories of accident can be predicated of a subject. A secondary substance is simply a universal idea, one, that is, which can be applied to many things, specifically, to primary substances, by reason of the fact that they share a common nature. The term “chair” incorporates the universal idea o f chair; as such, it is not the same term as “that chair,” referring to a particular piece of furniture which is placed near the window on the other side o f the room. “That chair” designates a primary substance; “chair,” the general term , is an instance of secondary substance. Given the resiliency and wide applicability o f “chair,” understood as a universal, I can say, pointing to the aforementioned piece of furniture which is placed near the window on the other side of the room , “That is a chair.” In doing so, I am not predicating primary substance of primary substance (if I were to be doing so, as I point to the object in question, the result would be, “That chair is that chair,” a tedious tautology),

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but I am predicating secondary substance (a universal idea) of primary substance. When I unhesitantly claim that “Roger is a human being,” and when I made the same claim about Albert earlier, I am predicating the concept “human being,” designating a nature, as abstracted from individual, actually existing human beings, and here, once again, secondary substance is being predicated of primary substance. T he G eneral N ature

of

A ccident

A few more words need to be said about the general nature of accident. Apropos of the nature of primary substance, we have seen that (a) it cannot be predicated of a subject, and (b) it cannot be present, or contained, in a subject. Now, primary substance and accident are so related to one another that to have an understanding o f one is at the same time to have an understanding of the other, for they represent correlative ways of existing. In other words, to know what it means to exist independently, as does a substance, entails a knowledge of what it means to exist dependently, as does an accident. An accident is just that which, like secondary substance, (a) is predicated of a subject, and(b) is present, or contained, in a subject. So, then, if substance can be said to be that which exists in itself, then an accident is that which exists, can only exist, in another, that “other” being nothing else but a substance. Only a little reflection shows how it must be that accidents depend upon substances. Obviously, there first must be an actually existing thing, a primary substance, before we can intelligently talk about the ways in which it exists, that is, its various modes of existing, as black or blue, as running or sitting. And the nine categories of accident represent the various ways in which a substance can exist. In fact, they exhaust all the possibilities in that respect. Once we have predicated all of the nine categories of accident of a substance, we have attached to it all the fundamental ideas that can be attributed to any physical entity, and thus our knowledge o f that entity is as complete as we can ever expect it to be. But initially there must be an actual existent, a real being, before the act of predication can take place. There must be a real chair before it can be said of it that it is brown, or standing in the corner. If there were no real Roger, there would be no subject to receive the predication “human being.” T he A ccident

of

Q uantity

The order in which the nine categories of accident were listed above (quantity, quality, relation, action, passivity, time, place, position, habit) is a fairly common way of ordering them, but, apart from the first three—quantity, quality, and relation— there is nothing especially sacrosanct about that order, taking it as a whole. But as for those first three, we are justified in regarding them as the most import of the accidents, in the order listed, with quantity being the most fundamental of the three, then quality, then relation. Of all of the

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categories of accident, quantity is essential to any material entity. And for this reason we call quantity a property of any physical thing, because it is impossible that one could ever have a physical thing, whatever might be the precise nature o f the matter o f which it is composed, which does not have the inherent feature o f quantity, and which therefore can always be analyzed in quantitative terms. Q uantity expresses itself in two basic ways, as continuous quantity and discrete quantity. Continuous quantity manifests itself in the spatial extension o f things. Every physical thing has dim ensions to it— length, breadth, and depth. It has a place; it takes up space, large or sm all, depending upon its dim ensions. Even the sm allest subatom ic particle, if it is an actual physical thing and not simply a theoretical construct, m ust necessarily have a place, a definite position in relation to other physical things, even though we m ight be hard pressed to determ ine with any kind o f accuracy the exact location o f that position at any given time. The continuous quantity o f those physical things we know through the m eans o f ordinary, unaided sense experience is som ething which is im m ediately evident to us. The top o f the desk on which I am now w riting is extended over a given space. But no physical thing is extended interminably; if it were to be, we would not be able to recognize it as a thing, an individual entity possessing an intelligible identity. All physical things have borders, in other words, the limits of their extension. The top of this desk starts over there to my left, and it ends over there to my right. W e can describe extended things with vague term s like “long” or “short,” “wide” or “narrow ,” but by availing ourselves o f established standards o f m easurement, we can be more exact about the matter. So, tape measure in hand, I discover that the top of my desk has a length o f 64 inches, a width of 32 inches, and is3/»of an inch thick. A nother characteristic o f continuous quantity, then, is the fact that it is measurable; it can be analyzed quantitatively. Yet another characteristic o f continuous quantity is the fact that it is divisible; its extension can be systematically reduced. Though I would not be at all inclined to do so, I could remove the top of my desk and cut it in two, so that instead o f having a single slab o f wood m easuring 32 inches by 64 inches, I would end up with two, each measuring 32 inches by 32 inches. Every physical substance is divisible, but ju st as there are lim its to its extension, so too there would have to be lim its to its divisibility. It would be possible, with the right kind of tools and instruments, and with plenty of patience, to divide the top of my desk again and again until the point is reached where one would be working with bits o f wood the size o f sawdust grains, and where any further division would be practically impossible. For along time it was thought that what we call an atom should have its name taken with strict literalness, and that it could not be divided (our word “atom ” comes from a Greek word meaning, “cannot be cut”), but then it was discovered, with enormous consequences, that in fact the atom could be divided. We will leave it up to the theoretical physicists to determine if there is an ultimate bit of matter which defies all attempts to divide

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it. A unit of matter with a precise identity can only be said to be divided if the two units resulting from the division have the same identity (share the same nature) as the original unit. When an electron and a positron bang into one another to produce photons, neither the electron nor the positron has been divided, but both have been destroyed. Even though a bit of matter might be so minuscule that we do not have access to it by direct observation, if it is in fact a bit of matter, a physical entity, then it has continuous quantity— extension. And all physical things which are known to us through ordinary sense experience, and which are subject to ordinary manipulation by us, can be divided. Discrete quantity, sometimes called discontinuous quantity, is expressed by number. When we think in terms of continuous quantity, we are considering one physical thing, and, with respect to its extension, noting how it begins over there and ends over here. When we think in terms of discrete quantity, we are considering more than one physical thing, and, noting how they are separate from one another, we distinguish them quantitatively, using number. “There’s one, there’s another, and there’s yet another,” and out of primitive experiences like that, numerical counting began. Of the two kinds of quantity, continuous and discrete, continuous quantity is the more foundational, in that discrete quantity depends on it, is intelligible only in terms of it. If there were not actually existing physical things to be counted, there would be no counting. Number, ethereal though it can sometimes be, has it roots in material reality. Of the two great subject areas of mathematics, geometry and arithmetic, geometry concerns itself principally with continuous quantity, whereas arithmetic is mainly occupied with discrete quantity. T he A ccident

of

Q uality

Quality is one of the most capacious and varied of the categories of accident; it contains much. Aristotle identifies quality as that by which things are said to be “such and such,” a phrase which is not, it must be admitted, particularly informative. Though it would be quite helpful if he were to have presented us with a precise definition of quality, Aristotle is not to be faulted for his failure to do so, for quality, as well as all the other accidents, will not submit themselves to definition in the strict sense. They can be defined, but only in a loose way, by description, and Aristotle provides us with plenty of descriptions of the various accidents. The reason that accidents cannot be strictly defined has to do with the fact that they represent the most primitive kind of ideas, a point which will be clarified in the following chapter when we deal with definition. A quality is a feature, a trait, a characteristic of some subject. Think of someone whom you know very well, and think of all the non-quantitative things you can say about that person. You would soon discover, if you really set your mind seriously to the project, that you will have drawn up a very long list, for any adult human being has a virtually countless number of qualities. Luella is

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pretty, very smart, knows French, plays the piccolo, has a sense o f humor, is a M innesota Twins fan, tends to get a bit im patient at tim es, sm okes surreptitiously, dislikes peanut butter, has shoulder length auburn hair— and on and on and on. Aristotle does not stop with his “such and such.” He goes on to spell out for us four distinct kinds o f quality, w hich, save one, he groups in pairs: disposition/habit; capacity/incapacity; sense qualities; figure/form . A ttend­ ing to what he has to say about each of these, we can come up with a reasonably com prehensive grasp of what the accident o f quality is all about. D isposition/Habit. A disposition is a certain natural bent or proclivity, a basic personality trait, a feature o f tem peram ent. C onsider Terrence. If we rem ark (more likely than not in his absence) that he has a tem per and is easily given to anger, we are identifying a disposition. W ith a disposition o f that sort, we would be most likely to classify it as negative. As an exam ple o f a positive disposition we might cite a natural tendency in a person to be thoughtful of and generous toward others. We do not choose our dispositions. We are bom with them; they are the rudim entary “givens” that are part and parcel o f our basic personality and with which we have to deal, either as burdens or benefits, throughout the course o f our lives. To be sure, we are responsible for how we deal with our dispositions, but not for the dispositions themselves. The big difference between dispositions and habits, then, is that the latter are under our control. Habits do not ju st happen to us; we m ake them happen, set them in place, establish them as fixed features o f our personality, through consciously chosen repeated acts. The professional football player performs in the consistently skillful way he does because he has form ed a num ber o f good physical habits through constant practice. But he cannot dispense with the practice once the habits have been established, for the perm anency o f a habit depends upon the continuity o f practice. The peculiar benefit o f a good habit, as compared to a disposition— and this is no small benefit— is that it is reliable and readily available, whereas a disposition tends to be fickle and overly dependent upon m ood. People who are generous by disposition rather than by habit are inclined to be generous only when they feel like it. Habits have been described as constituting a kind o f second nature, m eaning that they becom e so deeply ingrained a part of our persons that we act according to them with a natural-like ease and sm oothness. Professional m usicians do not have to stop and think about every move they make when they are perform ing. The notes flow forth effortlessly and flawlessly. The practiced fingers o f the concert pianist seem to fly over the keys on their own, as they bring to vibrant life the music o f Mozart or B eethoven. “C larissa is moody,” and “Clarence is a nervous type” give us exam ples o f dispositions; and “Sir Thomas M ore was a ju st man” indicates a habit, in this case the good habit, or virtue, of justice. C apacity/incapacity. For a person to have the capacity to do som ething, either as a result of an inborn talent, or as the result of training and practice is,

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for that person, an important identifying quality. And to know what any particular person is capable of is to have significant knowledge of the person. A good athletic coach can exact maximum effort from his team because he has a keen sense of the peculiar strengths of each of his players, and matches those strengths to the demands of the positions he assigns to the players. And each one of us, if we set a value upon living a balanced, effective life, must have a reasonably accurate and reliable sense of our own capacities. This might seem to be the kind of self-knowledge that comes automatically, but in fact in doesn’t, not in all cases in any event, and it is not only in the pages of fiction that we come across people who do not seem to know what they are really capable of. It is as if, in this respect at least, they are strangers to themselves. Oftentimes, this kind of ignorance of a capacity on the part of a person who actually possesses the capacity is explained by the fact that the person, for one reason or another, never had occasion to exercise that capacity. There is no little truth in the folk wisdom which has it that sometimes we don’t know what we can do until we actually have to do it. If capacities provide us with very useful information about a subject, so too do incapacities— what a subject is not capable of doing, or at least not capable of doing well. Surely, to know one’s limitations, and to govern one’s actions accordingly, translates into a decidedly positive kind of knowledge. With regard to both capacities and incapacities, we have to be careful to avoid succumbing to the extreme of either overestimation or underestimation. To overestimate one’s capacities can not only prove to be embarrassing for oneself but perhaps even dangerous for others. Someone whose piloting abilities are marginal should not offer to take some friends up for a flight, especially if the weather is uncertain. On the other extreme, we can so grossly underestimate our capacities that we never get around to giving them a fair test. The atrophying of genuine talent in a person because that talent was never properly exercised makes for a rather sad situation, if not, indeed, a tragic one. The qualities of capacity and incapacity apply to any substance whatever, and not just to that substance which seems mostly to command our interest, the human person. Tools, for example. They of course have to be well designed and well made, so that they will do the job for which they are intended. A skilled craftsman knows both the strengths and limitations of his tools, and therefore knows ju st the right tool to use for any particular task. Virginia the virtuoso violinist can tease out exquisite tones from the Stradivarius because of her intimate familiarity with what that famed instrument is capable of. But she knows its limitations as well, and she will never demand of a violin what no violin, not even a Stradivarius, is capable of delivering. Sense qualities. Our five senses are passive in the respect that, though each may be organically in perfect health, no sensation will be registered by any particular organ unless it is properly stimulated. Without light waves, the eye sees not; without sound waves, the ear hears not. And so it is with the other

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senses as well: sensation follows stimulation. The sources of the stimulation are the objects in the external world that possess those qualities which activate each o f the particular sense organs. C onsider the follow ing cluster o f sensations: seeing something as bright and blue; hearing something as loud and discordant; sm elling som ething as rem iniscent o f burning rubber; tasting som ething as cloyingly sweet; feeling something as hard and cold. In each case the particular sensation was caused by an object which is said to possess the qualities corresponding to the sensation. So, it was the sky that had the quality of being bright and blue; the am ateur band was loud and discordant; it was Uncle Sigm und’s cigar that smelt like burning rubber; the icing on the carrot cake was cloyingly sweet; and it was the chisel left outdoors on a night in January that was hard and cold. Sense qualities are in substances as the direct causes of qualitative changes in us, in the form of specific sensations of one kind or another. Though sensation itself is obviously a subjective experience, it is a subjective experience which is firm ly rooted in the objective order. I can only feel hardness and coldness by being in touch with an object which is hard and cold. (See A ppendix B for a discussion o f John L ocke’s distinction betw een prim ary and secondary qualities.) Figure a n d fo rm . Figure and form (or shape), the fourth o f A ristotle’s sub­ categories o f the accident o f quality, is rather straightforw ard and uncom plicated, and refers to the surface qualities o f a m aterial object. Every m aterial object m anifests continuous quantity or extension, but no material object can be extended indefinitely; each must have boundaries, or limits to its extension. And those boundaries give to the object a definite configuration. We may call certain things shapeless, but strictly speaking no material thing can be devoid o f shape, for the shape o f a thing is determined by the boundaries of its extension, and there is no material thing that is not bounded. Usually what we m ean when we call an object shapeless is that its shape is very irregular, and therefore it does not lend itself easily to description, nor to precise m easurem ent. It m ight be thought that the inform ation provided to us by the shape of a thing is of no great consequence, but actually it is very often the shape of a thing, its defining contours, which gives us the first clue as to what kind of thing we are dealing with. And som etim es that kind o f information m ight turn out to be quite important. It makes a considerable amount of difference whether that vague creature com ing down the path tow ard us in the early m orning fog eventually reveals itself in the shape o f a lion or o f a lamb. Relation. The idea o f relation— how one thing stands with respect to another— is one o f the m ost sem inal and fertile ideas with which the hum an m ind has the privilege to contend. W henever there is a m ultiplicity of things, there is necessarily relation. B ut there is m ultiplicity everywhere. Therefore, there is relation everyw here. In any situation w here we have to deal with a m inim um o f tw o things, A and B le t’s label them , relation com es into play,

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albeit perhaps a relation of no great moment, such as the fact that A is to the left of B. Typically, what is initially most obvious to us are external relations, that is, relations between things, rather than relations among the parts of a thing. As to internal relations, we may speak of those that obtain among the various organs of the human body, which relate to one another not simply in terms of their respective physical placement, but with respect to their specific functions as well, so that they all work together harmoniously to give rise to a healthy organism. Because relation is an integral and inseparable concomitant of the multitude of entities existing in the world, our knowledge of those entities will be importantly advanced to the degree that we know how they are related to one another, and, with regard to any individual entity, how its parts are related to one another so as to compose a unified and coherent whole. There are innumerable ways in which things can be related to one another, one of the most basic of which is the relation of place to place, whereby we say, for example, that Pitfall Junction is twenty-five miles due east of Pimpleville. It is a quantitative relation which prompts the observation that this package is larger than that one, or, using more precise terms, that this package measures 12" x 16" x 8" and that one measures6" x 8" x4". Dealingpurely with numbers, we note that 4 is related to 2 as its double, and, looking at it from the other direction, that 2 is related to 4 as its half. In that example, ideas of double and half are correlatives, meaning that each is intelligible only in reference to the other: you cannot have a double without a half, and vice versa. The ideas of right and left are correlatives, as are up and down, forward and backward, big and small, and good and bad. Human beings are related to one another biologically because they share progenitors, proximate or remote— hence the common term “relative.” Bill and Bob are related to one another as brothers because they have the same father and mother, and Beatrice and Beverly are first cousins because they have one set of grandparents in common. Knowledge is a relative term, though at first it might not strike us a being such. Knowledge involves the relation between the knowing subject and the object which is known. The knowing subject is dependent upon the object known in a very rudimentary way, for of course if there were no object to be known there could be no knowing. There is complete interdependency between correlatives, because their respective meanings depend on one another. One of the most significant of relations is that between cause and effect. To know raw facts is to know something of foundational importance, for knowledge of the facts is where we must begin. But we would have at our disposal a knowledge far superior to that of the mere facts if we knew as well how those facts are to be explained, how they came to be precisely the facts that they are. We have that superior kind of knowledge when we know the causes of things. Sense knowledge can be sufficient to provide us with reliable knowledge of the facts, just as facts, but it takes intellectual knowledge, the workings of reason, to ferret out the causal explanations of the facts. One thing,

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A, relates to another, B, as cause to effect if A accounts for the existence o f B, either absolutely, as having brought B into existence (as parents are the cause of a child), or relatively, as having brought about an accidental change in B (such as change in position, e.g., when the cue ball strikes the eight ball and causes it to move in a trice from the center o f the table to the com er pocket). Close analysis o f any particular relation shows that it is com posed o f three basic elements: its subject, its term, and its foundation. The subject of a relation is that to which it refers, as the principal focus o f our attention; linguistically considered, it is simply the subject o f the proposition in which the relation is expressed. In the proposition, “Joel is the father of Andrew,” Joel is the subject of the relation. The term o f a relation is that toward which its subject is directed, which, in the case o f the proposition ju st cited, would be Andrew. The foundation o f a relation explains the nature o f the connection between subject and term, so we would say that consanguinity is the foundation o f the relation between brother and sister. The relation between Joel and Andrew can be stated in more specific terms by saying that Joel is A ndrew ’s generative cause, or, to put it in plainer terms, we say paternity is the foundation o f the relation between the two. The relation between Joel and Andrew is a mutual relation, in that Joel is just as much related to Andrew as Andrew is related to Joel, but because they are not related to one another in the sam e way, we say that the relation is asymmetrical. W ith a m utual relation, one can switch the subject and the term , but if the relation is asym m etrical, as that betw een Joel and Andrew, one has also to provide a new foundation for the relation. The result would be an entirely new proposition. Performing those two operations on our original proposition, we end up with: “Andrew is the son o f Joel.” Here Andrew is the subject o f the relation, and Joel its term. And we would identify the foundation of this relation as filiation, in that Andrew is the generative effect o f Joel. A sym m etrical mutual relation is one in which we can switch subject and term without altering the foundation, for the foundation is the same whichever of the two elements of the relation serves as the subject. I can say, “M ary M argaret is the sister o f Theresa,” or, “Theresa is the sister o f M ary M argaret,” for both are the daughters of the same parents. A non-m utual relation is one that can proceed only in one direction, from subject to term; the subject and term cannot be switched, given the nature of the foundation of the relation. The know ledge o f inanim ate m atter would be an exam ple o f a non-m utual relation. “The paleontologist knows the skeletal fossils.” In that proposition the paleontologist is the subject of the knowledge relation, and the skeletal fossils its term. The foundation of the relation is the act of knowing, which, as a conscious process, cannot be attributed to inanimate matter. Thus, while we can meaningfully say that the paleontologist knows the skeletal bones, it would make no sense to say that the skeletal fossils know the paleontologist. W e can say, “The skeletal fossils are the object o f the

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paleontologist’s knowledge,” which is true enough, but this only expresses the m eaning o f the original proposition in different words; the act o f knowing remains with the paleontologist, and cannot be transferred to the skeletal fossils. (See Appendix C for further discussion on mutual and non-mutual relations.) A ction

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How any subject behaves, the actions it performs, tells us much about the nature of that substance; in fact, it is through the behavior of a substance that we are able to identify its nature in the first place. All things being equal, if an animal walks, quacks, flies, and generally behaves in a manner we would expect a duck to behave, we can be reasonably sure that we are dealing with a duck. On the most fundamental level, the actions of a particular substance inform us of what it is capable o f doing, for the proof positive that a substance possesses a certain capacity is the public and observable exercise of that capacity. If the substance in question is a human person, then the revelations that follow upon the actions performed by that person take on a special interest for us. Knowing that Eddie has participated in four marathons per year over the past four years tells us much about the m an’s physical stamina and endurance, not to say his will power and discipline as well. These and other moral qualities of a person are manifested by the actions he performs. The old saw that tells us that actions speak louder than words is relevant here. Horatio might protest loudly and often that he is a just and fair fellow in all his business dealings, but his words are belied by his actual behavior, and it is his behavior which is the conclusive determinant o f his moral status. The grammarians dub a verb “transitive” when it describes action on the part o f one object which is transmitted to another object, so that we have an agent, the source o f the action, and a patient, something on the receiving end of the action. “Push” is an example o f a transitive verb. It is impossible to have the action of pushing without there being a recipient of that action. Whenever there is pushing and shoving going on, there is something, or someone, who is being pushed and shoved. Transitive action necessarily entails passivity. Just as it is informative of the nature of any substance to know what actions it performs, it is also inform ative— and in some cases no less so— to know what actions a substance is capable of receiving. W hat is the character and extent of its passivity, its ability to accept transitive action without any damage to itself (that would be the purely negative side of it), but in ways that may prove to be positively beneficial? In constructing a house on the Gulf coast, it is imperative to know how much stress and strain can be borne by the materials that go into its construction, if the house is to make it safely through the next hurricane season. Every physical object, at one time or another, is passive with respect to another physical object; that is, it is the recipient of the transitive action of another object. But no object is ever completely passive with respect to an

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another, which is sim ply to say that, for every action on the part o f the agent, there is a reaction on the part o f the recipient o f that action, and a close study of that reaction can tell us much about the nature of the recipient. For the smooth running o f hum an affairs, there is considerable practical benefit in know ing how a certain person is likely to receive a particular kind o f action, in the form, say, o f some well-meaning corrective advice. And it is also helpful to know how much people can be expected to put up with, when special demands are made of them , or when they have to bear unusually heavy burdens. Are action and passivity correlatives? If we were to start with passivity we might be led to think so, for the idea of passivity is intelligible only as related to action. To advert to the exam ple used above, it w ould not be m eaningful to describe an object being pushed and shoved without an implicit reference being made to an agent which is responsible for those actions. So, the idea of passivity is correlative with respect to action. And if the action in question is transitive, then here too any reference to such action necessarily im plies that there is a recipient o f the action. Again, we cannot have a pusher and shover without a pushed and shoved. But besides transitive action there is also immanent action, which is action that takes place within an agent, and has no external expression. The various m etabolic activities which take place w ithin a living organism would be exam ples o f im m anent action. T ime

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In the world in which we live we are constantly “locating” things in terms of tim e and place. W hen did it happen? W here did it happen? Som etim es information of this sort can be vitally important. “I know for a fact,” I patiently explain to Mr. Holmes, “that Cindy was at the La Mange Restaurant at 2:00 p .m . on Thursday, July 14, because I happened to be there with her. Therefore, she could not have committed the murder.” W hat is time? It was St. Augustine who fam ously quipped that he knew perfectly well w hat tim e was, until som eone asked him to explain it. Then the difficulties began. There have been some great intellects, people like Galileo and Isaac Newton for example, who conceived of time as if it were something along the lines o f a substance, which is to say, a free­ standing reality w hich apparently exists blithely independent o f the physical universal. But then along cam e A lbert Einstein, who rejected the ideas of Galileo and Newton, and brought us back to what is essentially an Aristotelian understanding of time, by recognizing it as being inextricably bound up with m atter in m otion in space. M atter in m otion, and a conscious agent calculating the motion— that, for A ristotle, was w hat tim e is basically all about. Tim e can be said to be fully realized when the m otion o f material objects is systematically kept track o f by observing subjects, nam ely, hum an beings. It is the registering of successive motion— one thing following another so as to establish the distinction between

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before and after— that constitutes the essence of time. If we were to consider our common units of time, we can readily see how they are founded upon matter in motion, specifically, upon the relative motion between planet earth and the sun. What we call a year is a single trip of the earth on its orbit around the sun. What we call a day is the marking o f a single revolution of the earth on its axis. We have conventionally divided that day into twenty-four equal segments, which we call hours. The hours are divided into sixty equal segments called minutes, and the minutes, in turn, into sixty equal segments to which we give the name seconds. And perhaps for fine work we might choose to divide the second into milliseconds, each segment representing one thousandth of a second. Let’s stop at that tiny temporal unit called the millisecond. What is it, basically? It is a sub­ division of what we calculate as transpiring when the earth revolves once on its axis. All time comes down to the phenomenon of matter in motion. If matter in motion necessarily involves time, it necessarily involves space as well, for in order for matter to move it needs room to do so. In order to get a correct understanding of the nature of space, we need to begin with place. We cannot meaningfully think about place unless we first think about the physical object that is in place. Each physical object has a place which is proper to itself, and which is established by the external boundaries of the object. Every physical object is essentially characterized by its extension, which we may regard as the “internal space” which is to be found within the boundaries of the object. The primary principle of place, that which can be said to constitute it in the strict sense, is the extension of a physical object; the secondary principle is the relation of the object and its place (the two are inseparable, though distinct) to other objects and their places. Thus, just as matter in motion is the foundation of time, so the extension o f a physical object is the foundation of place. But just as matter in motion is not time itself, because we have to add a conscious agent who is keeping track of the m otion, so it is not simply extension of a physical object that constitutes place, because we have to take into account its relation to all the physical objects around it. We can say then that what fully establishes place is the relation o f a physical object to other physical objects. The principle of the impermeability of matter tells us that no two physical objects can occupy the same place at the same time, and the place of any given physical object is defined by the boundaries of its own extension, in association with the extensions o f the other physical objects in its neighborhood. What then is space? It can be understood as the sum total of all the places, which in turn are established by all the physical entities in the universe. If we can imagine that there were no such physical entities, there would then be no places and therefore no space, just as, if there were no matter in motion, there would be no time. We are regularly measuring space, and the standards of measurement by which we do so are based on the extension of physical objects. We estimate that the sun is some 93,000,000 miles from the earth. What is a mile? It is 5,280 feet. What is a foot? It is a unit o f measurement taken from the length of a rather big-footed

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adult human being. Physical objects, with their extension, provide us with the wherewithal by which we measure the length o f the dining room, or project our imaginations into the far distances o f the cosmos. P osition

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The last two of the nine categories of accident are position and habit. When we predicate position of a subject we are indicating how its parts are arranged in relation to one another, or how the subject is related to objects external to itself. A person is standing with arms akimbo, or with arms folded, or slouching, or stooping, or kneeling, or leaning against a tree with hands in pockets— all these would be exam ples o f position. The accident o f habit has to do with one substance being in continuing contiguous relation to another. The shirt on one’s back would be an example o f habit, as would any kind of vesture or protective covering, but so too would be egg on the face, dew on the grass, frost on the roof, and rust on the saw blade. Position and habit are perhaps the least inform ative o f the accidents, but there are situations in which the know ledge they provide can take on real importance. Jeannie makes no secret of the fact that what first attracted her to her husband Greg was his noble bearing, the way he held his head, those broad, squared shoulders, and that ram-rod straight back. And, to cite a quite different instance, the police did not consider it irrelevant inform ation to learn that the fellow who robbed the Misers and M erchants State Bank on 14th and Main was w earing a red ski mask, a green trench coat, yellow rubber gloves, and beige show er clogs. There are, then, situations where the accidents o f position and habit can provide valuable information. S ummary C omments

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A ccidents

The accidents are dependent upon substance, for it is precisely in substance that they m anifest them selves. If there were no substances, there would be no accidents. By the same token, it would not be possible to imagine a substance completely lacking in accidents. That would be to imagine an actually existing entity w ith no features w hatsoever. W e would be in a world where there are supposedly real things, but they would not act, nor would they be acted upon; they w ouldbe no place, at no time, in no position, naked as jaybirds, and without a single relative to call their own; they would not be able to be seen, heard, tasted, touched, or smelt, and they would defy any attempts to subject them to quantitative analysis. It is just because accidents are inseparably bound up with substances that they are able to reveal the nature of substances to us. It is through the accidents, and only through the accidents, that we come to know substances. Very rarely is our know ledge of substances anything like complete, but it is genuine knowledge nonetheless. W e may not know everything we would want to know about a particular substance, but the knowledge which we do have of

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it would be sound and reliable so long as our knowledge of its accidents is sound and reliable. In review ing the nine accidents, for the sake of clarity of exposition we treated each o f them separately, but in real life any two accidents, though quite distinct, are never separate, and there is much overlapping among them. Seldom is it the case that we can refer to one accident without making at least implicit reference to another. For exam ple, we cannot speak of a given substance being “in place” without simultaneously acknowledging the accident of relation, for, as we saw, a substance, a physical object of any sort, can be meaningfully said to be in place only insofar as it stands in relation to other substances. Relation, in fact, is an accident which is operative in the predication of all the other accidents, for what else are we doing, on the most basic level, when we predicate som ething o f a subject but expressing a relation between the subject and the predicate? Beyond that most basic kind o f relation, there is that which is to be found within the category o f discrete quantity, between any two numbers. In the accident o f quality, there is the relation between disposition and habit. Action and passivity necessarily involves the relation between the agent and the patient— the source o f the action and its recipient. Time has to do with the relation betw een before and after in successive motion, or, looked at from a different angle, the relation between motion and the measuring of motion. The accident o f position entails the relation o f one part to another, as evidenced in the statement, “He sits bolt upright with his legs crossed.” And the observation that “She wore a stocking cap” (an example o f the accident of habit) suggests an unavoidable relation between the stocking cap and the head o f the wearer.

Review Items 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

W hat is the difference between a substance and an accident? Distinguish between primary substance and secondary substance. W hat is the difference between continuous quantity and discrete quantity? Name the three basic elements in any relation. Give an example o f a mutual asymmetrical relation. Give an example o f a mutual symmetrical relation. Compose a sentence representing the accidents of action and passivity. W hat is the essence o f time? Give an account o f the nature o f space. Compose a sentence representing the accidents of position and habit.

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Exercises Indicate what accidents are predicated in the following statements. Be alert to the possibility that there may be m ore than one accident being predicated in a given statement. 1. The convertible was fire-engine red. 2. She was twenty m inutes late. 3. The pugilist was knocked out in the first round. 4. Joe wrote the letter quickly. 5. He was a surly, foul-m outhed character. 6. There were only tw o cherry pies left. 7. The cat was crouched in a com er o f the room. 8. The box m easured 20" x 12" x 6". 9. Nancy is N elson’s niece. 10. The um brella was propped against the coat rack. 11. M elinda wore an ankle-length mink coat. 12. The parakeet was in its cage. 13. The Civil W ar ended in 1865. 14. Georgine is taller than Marianne. 15. The jacket was covered with mud.

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Chapter Five Definition and Division T he N eed

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It is through the first act o f the intellect that the mind produces ideas, and ideas are the elementary stuff of human knowledge. But human knowledge is not infallible— a som ber truth which it would be helpful to recall on occa­ sion— and the root explanation for our disconcerting epistemological fallibility is to be found in ideas themselves, ideas which are either frankly bad, or which, though basically sound, are not as clear as they should be. Our ideas, especially the most important o f them, almost always stand in need of periodic clarifica­ tion, and the longer they have been a part of our mental repertoire, usually the greater this need. We naturally grow used to ideas we have been living with for a long time, and begin to take them for granted in such a way that eventually we do not see that they could use some serious reexamination. Ideas that are not regularly reexamined grow blurry to the m ind’s eye, and if they are impor­ tant ideas the result is that our general knowledge of things thus becomes tenuous and uncertain. It was Socrates who made the memorable claim that the unexam ined life is not worth living. W hat is an unexamined life? It is one made up o f unexamined ideas. If we are not trying continuously to clarify our thoughts, we eventually find ourselves in the predicam ent where many things which we may confidently think we know, we in fact do not know, or at least we do not know them as well as we think we know them. There may be certain ideas to which we are firmly comm itted, the idea, say, that liberal democracy is the best form of govern­ ment, and yet it could be embarrassing for us if we were asked to defend that commitment in public. We might disconcertingly discover that, though we have often bandied the term about freely, we are not at all clear as to just what we mean by liberal democracy. There are two important logical processes by which we can bring greater clarity to our ideas: definition and division, and the treat­ ment of these will be the subject of this chapter.

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Definition and division involve different processes, as we shall see, but they both serve essentially the same purpose: the clarification o f our ideas, giving them cleaner and sharper configuration. Our word “define” derives from the Latin definere, which means to set limits or bounds to. When we define a term, or subject it to the process o f division, we mark out its boundaries in very explicit fashion. By definition, we give as full and accurate an account as we can of the comprehension, or meaning, o f a term; by division, we endeavor to map out its extension, or the scope of its meaning. The two modes of analysis are very closely associated, for an integral part of the knowledge of the meaning of any term, with which definition provides us, is a knowledge of the conceptual spread of that meaning, i.e., everything implied by it, which division seeks to make clear. A good definition inform s us o f the essential nature of an object being defined; a division of an object shows the different specific manifestations o f that nature, the various specific ways in which it is realized. So, we might define a college student as a person who is enrolled in a third level educational institution with the primary purpose of becoming accomplished in a particular field of study. There are any number of ways we could divide the term “college student.” For example, we could simply divide according to class, and come up with the traditional quartet: freshm an, sophom ore, junior, senior. More interestingly, we could make divisions according to college students’ major fields of study, or their econom ic backgrounds, or their religious affiliations, or their political penchants or preferences, or according to how they would respond to the question, W hat is the purpose of a college education? W hatever the basis of the division, so long as it is non-trivial— and the division according to class is admittedly rather trivial— it should serve to broaden our understanding of what it means to be a college student. An exhaustive set o f divisions of any term, if we can imagine such, would draw out everything that is reasonably implied by it. E ssential D efinition All definition should have as its goal the revelation o f the essential nature of that which is being defined. W hat is the essential nature of a thing? It is its core identity, what, at its most fundamental level, it is. The kind o f definition whose very purpose it is to reveal the essential nature of what is being defined is known, appropriately enough, as essential definition. It also goes by the nam es o f logical definition, and scientific definition. The process by which we arrive at an essential definition of a term is very sim ple, consisting as it does o f but two steps. In the first step, what we want to define, which is known as the definition, is placed in its proximate genus. Step number two: we differ­ entiate the definitum from other members of that genus. Now to explain those two steps.

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A genus is simply a large class of things, so in the first step of the defining process we are putting what we want to define (the definitum) into the class into which, on the basis of the knowledge we already have of the definitum, we see that it naturally belongs. The definitum relates to the proximate genus as a class which is im m ediately subordinate to a larger class. To make it clear how this works, we will consider A ristotle’s classic definition of man as a rational animal, imagining the mental process Aristotle himself went through on the way tow ard arriving at that definition. We start with an item, a human being, a creature which we certainly know but whose exact nature is perhaps a bit of a puzzle for our minds, and we want to clarify our ideas about the creature. Just what is, precisely, a human being? The first thing we want to do in answering that question is to “place” or “locate” the definitum in a general sort of way. This is done by incorporating “human being” into a class whose members, we see, have many fundam ental features in com m on with human beings. That w ould be the class o f animals. Thus, the completion of the first step of the definition allows us to propose with confidence the proposition, “Man is an animal.” We call the class of animals the proximate genus of human beings because, again, that is the class to which hum an beings, as a class, are immediately subordinate. It is well to stress here that all essential definitions pertain to classes, not to individuals. For convenience sake, we make use of terms like “man” and “human being,” but they are to be understood as standing for an entire class. (The fact that individuals cannot be defined is a point we will return to later.) So then, the class of human beings comes right under the class of animals, and that is how we know that we have correctly taken the first step in the defining process. How might we have made a mis-step in the process? In other words, what would count as a non-proximate, or remote, genus for our definitum, human being? The genus “animal” is a member of a hierarchy of genera, or classes, which has as its apex the supreme genus, a class so large and all-encompassing that there is no larger class into which it can be placed. This is the genus of substance. A substance is simply anything that actually exists. Now, imagine w hat would happen if, in taking the first step in attempting to define man, I were to place my definitum in the genus of substance, and thus declare, “Man is a substance.” That is a true enough statement, but it is not very informative, for I have my definitum rattling around in this huge category along with literally everything else that exists. I need my first step to be more focused, meaning that I need a smaller class for my definitum. If I were to remain content with leaving “man” in the genus “substance,” I would then be making the next step in the defining process— distinguishing the definitum from other members in that genus—an extremely complicated and laborious task. And in fact I could not be successful at all in performing the task without eventually recognizing smaller genera within the suprem e genus o f substance, and eventually responding appropriately

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to them. Thus, to make the task easier for m yself right at the outset, 1 need to go directly to a smaller, less diversified, genus, one which is closer to home for the definitum. A definitum should relate to a genus as a fam ily relates to a neighborhood, rather than how it relates to a city, or to a state, or to an entire country. By working our way down the hierarchy of genera, we will be better able to see the rightness of the move we made in putting man in the genus of animal. Next under the supreme genus o f substance com es material substance, then living material substance, then sensitive living material substance, otherwise known as animal. Man is, to be sure, a material substance, but so is the moon, Mount Everest, the leaves now being blown about the yard, the teaspoon in the teacup (along with the teacup), and the shoes under the bed (along with the bed). The class is much too large to be useful to us. Descending to the genus of living material substances, we are closer to where we want to be, for excluded from this class are all inanimate things in the universe, which, from all reports, constitute the bulk o f it. And yet this class too is too large to be useful because it includes all plant life, with which human beings cannot be directly associ­ ated because, though we share with them that precious and m ysterious commodity called life, our life is radically different from theirs for the fact that it comes accompanied with sensation, appetition, and locom otion. We need then to drop down to a lower level yet, which will land us precisely where we w ant to be, at the genus o f sensitive living m aterial substances, or anim als. And in that genus we put our definitum. In the second step o f the defining process we m ust differentiate man, the peculiar anim al we are attem pting to define, from all the other m em bers o f what remains, still a very large class indeed. W hat we are specifically looking for here is what are referred to in logical term inology as the specific differ­ ences, the differences that serve to identify a species. W hat particular features are unique to this animal, man, which would set it apart from all the other types that are to be found in the genus? Aristotle was satisfied that there was but a single characteristic which, because so radical in nature, sharply differentiated human beings from all the other animals, and that was the fact that they pos­ sessed powers o f reasoning. Human beings were creatures with wide-open, inquisitive minds who had the remarkable capacity of thinking their way across the far stretches of the cosmos, and back again. They were creatures who could think about anything, even thinking, and thus find positive enjoyment in, of all things, taking a course in logic. A ristotle’s definition o f man, then, reduces itself to the succinct two-word expression, “rational anim al,” where “anim al” is the proxim ate genus, and “rational” is the specific difference. Because the specific difference is precisely that which identifies a species, we recognize man as a species o f anim al. There have been m any other attempts to provide an essential definition of man— such as M ark Tw ain’s, “Man is the only animal that blushes.. .or needs

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to”— but A ristotle’s has stood the test of time. If someone like Twain could take exception to the Aristotelian definition it was perhaps because he missed the ancient Greek philosopher’s point. Aristotle said that what essentially dis­ tinguishes human beings is the fact that they possess reason, not that they are always reasonable. They have reasoning powers, but how they make use of those powers is a separate question, and there is no doubt that many of the uses to which reason is put would be cause for much blushing. Substance, as we saw, is the highest genus, for it is the class that contains everything that actually exists. Is there a lowest genus? There is, and, from our perspective, it is the one to which we belong— animal. The class immediately below that one, which would be the species to which we belong, is human beings. A species is simply a sub-class of a larger class. Thus, if we were to relate the class of animals (which is a genus from the point of view of the class of human beings) to the one immediately above it, living material substances, animals would then stand to that class as a species to a genus. In other words, in this case living material substances would be the larger class or genus, and animal would be a sub-class or species. And within the genus of living material substances there would be another species besides animals, and of course that would be plants. But what are we to say of that species of the genus animals to which we give the name human beings? Can we proceed downward from that class, regarding it now as a genus, and thus discover beneath it sub-classes or species? We cannot. There is no species below that which we occupy as human beings. Consider what would happen if the case were otherwise? Within the large genus of animals there are many species besides man, and, by any number of standards we m ight want to choose, we would not put them on exactly the same level with one another. The species to which the bald eagle belongs could be considered superior to that in which one would find fleas, with no prejudice to the fleas o f the world. If the class o f human beings were to be considered a genus, that would mean that there were sub-classes or species of human beings, different kinds of human beings, who differed from one another in significantly essential ways. But this is not the truth of the matter. However, once people begin thinking along those lines, then the doors are opened to any number of very serious problems, not the least o f which would be racism. A racist is one who fails to see that all human beings are essentially the same, sharing an identical nature, and who effectively regards the class of human beings as a genus which is divided into several species, some superior to others. And, conveniently enough for the racist, he usually ends up placing himself in the highest species of human beings. That was the thinking of Adolph Hider. (See Appendix A for further discussion of “genus” and “species.”)

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E ssential D efinition

Logic provides us with a set of rules, or guidelines, which, if followed faith­ fully, will be o f great help to us when we are trying to form ulate reliable and illuminating definitions. And they also serve as a useful set o f standards against which we can test the reliability o f definitions form ulated by others. Rule One. The definition must be com posed o f a genus and a specific difference. The successful execution o f this rule is what ensures that the definition will be essential, for it is just the correct identification o f a definitum 's genus and specific difference which reveals its essence. All the rule is doing is sim ply directing us to take the two critical steps that constitute the defining process. It is the genus, or, m ore precisely, the relation o f the definitum to the genus, which tells us what, in term s o f its nature, the definitum has in com m on with other things. And it is the specific difference that calls attention to how the defintum differs from other things. Thus, in taking the first step toward arriv­ ing at a definition o f man, “m an” is placed in the genus “anim al,” whereby we show that, like other species in that genus, man has the pow ers o f sensation, appetition, and locomotion. Then, in taking the second step, whereby we iden­ tify “rational” as what specifically differentiates the definitum , we set “m an” apart from all the other species in the genus “animal.” Rule Two. The definition and the definitum must be convertible. If, in the proposition that expresses the definition— the subject term of which is the definitum (the thing being defined) and the predicate is the definition itself—the two terms can be switched around without the meaning of the origi­ nal proposition being in the least bit altered, we then have in that circumstance the sure sign o f a sound definition. Our essential definition of man is: “Man is a rational animal.” W hen the subject and predicate terms o f the proposition are converted, or sw itched, we end up with: “A rational anim al is m an,” which conveys the same meaning as the original, albeit in a rather clumsy way from a stylistic point of view. Consider the following glaringly inept attem pt to pro­ vide an essential definition of a human being. Man is a two-eyed animal. If we were to convert this proposition we would have: Every two-eyed animal is man. The inadequacy o f the second proposition as an essential definition speaks for itself, for although it is undeniably the case that human beings are possessed of two eyes, that feature is not essential to their nature as human animals, for most other kinds o f anim als also have two eyes. The possession o f two eyes is not sufficient to differentiate man from a mongoose, for example. W hat the con­ vertibility o f term s in a sound definition tells us is that such a definition has

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some similarities to a mathematical equation. One can say 7 + 3 = 10, or 10=7 + 3. Either way the statement is true. Rule Three. The definition must be clearer than the definitum. This is a more important rule than it might appear to be at first glance. The whole purpose behind expending the effort to define our terms, in logic or in life at large, is to bring greater clarity to our thoughts regarding ideas that we consider important enough to deserve serious commitment on our part. But the effort is for nought if a definition throws no real light on a term that is troublesomely murky. Very often the causes of unclear definitions are linguistic in nature. Either the definition is badly expressed, as the result of sloppy speaking or writing, or it uses words the meaning o f which one is either uncertain or com pletely ignorant. There is the often cited— and worth citing again— definition of the word “net” which the inimitable Dr. Samuel Johnson included in his famous dictionary. A net, he informed his readers, is “a reticulated fabric decussated at regular intervals.” This entry would, I suspect, send most readers right back to the dictionary, Dr. Johnson’s or another’s, to find out what “reticulated” and “decussated” mean. Normally, a good definition should not make that kind o f work necessary. It should be stated in simple, accessible language, and, whenever possible, expressed in positive rather than in negative terms. A good definition should be simple, but not simplistic. Perfectly clear and understandable words are not worth much if they fail to disclose the essential nature of the definitum. The definition o f freedom as “the capacity to do what­ ever one pleases” has the virtue of being clear, but it does not provide us with a very serious account of one of the most important of our possessions. Apropos of the Dr. Johnson definition of a net, cited above, a definition might be quite clear even though we may not have an immediate familiarity with some of the terms it contains, which could often prove to be the case with technical terms that we are confronting for the first time, terms like “insulin” and “exocarp,” for example. Rule Four. The definition must not be circular. A definition is circular when the key idea in the definition is the same idea which is found in the definitum. Circular definitions can be easy to spot when they make use o f the very same words that are used to express the definitum. “A democratic government is one which is based on democratic principles,” and “C ancer is a disease characterized by the fact that tissue is adversely af­ fected by cancer cells,” would be examples of circular definitions. If you were unclear about the meaning of “democratic” or “cancer” before being presented with those would-be definitions, you would not be much enlightened by them. Expressed symbolically, a circular definition amounts to little more than: X is X. Some circular definitions may not appear to be such at first hearing, as could be the case with som ething like, “Anger is an emotion in which are typically to be found displays o f choler and ire, and, in its more extreme forms,

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o f fury, rage, or w rath.” Though superficially inform ative, this attem pt at definition does not really tell us much at all about the definitum, for, as it turns out, “choler,” “ire,” “fury,” “rage,” and “w rath” are so m any synonym s for “anger.” Thus, in effect, we are being told that anger is anger, something which presum ably we already knew. C onsider this effort at defining “choice” : “a conscious human act whereby we pick, elect, or opt for a particular alternative.” In response to which we m ight properly ask, W hat is the difference between choosing, picking, electing, and opting for? And the answer would be, virtually none. And with that we would realize that we have been served up a circular definition. Only a cursory review o f a circular definition would alm ost always reveal that it lacks what is essential to an essential definition— a clearly stated proxi­ m ate genus and specific difference (Rule #1). And very likely the same large problem would account for a definition’s not being as clear as it should be (Rule #3). A circular definition m ay m eet the dem ands o f Rule #2, in that it would be cleanly convertible— but only as a tautology. It is the combined in­ form ation provided by the genus and the specific difference which identifies the species o f the thing we are attem pting to define, and it is the species that fully discloses the essential nature o f the thing T he D ifficulties

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E ssential D efinition

A prominent logician once aptly quipped that it is much easier to critique a definition than to construct one. Through definition, we are endeavoring to get at the very essence, the innerm ost identity, o f a thing, and that can prove to be one o f the more dem anding challenges with which the hum an mind is faced. Apropos o f the particular requirements that have to be met in order to arrive at a good definition, we often run into the difficulty o f not being able precisely to identify the specific difference, or differences (there are usually more than one), which is just what we must know if we are to succeed in clearly and unambigu­ ously setting apart what we are attempting to define from the other members of the class to which it belongs. Quite often it is fairly easy to make the first step in the defining process: placing the definitum in its proximate genus. Thus, in attempting to define something like anger, we take the first step by identifying it as a hum an emotion, which seems nicely to qualify as its proximate genus, the class in which it properly belongs. But where do we go from there? There is a whole slew o f hum an em otions, and what is it that makes this human em o­ tion, anger, different from all the rest? How does anger differ from fear, for exam ple, or from desire, or from pleasure, or from despair? We have to iden­ tify som ething which is peculiar to the em otion o f anger, and which sets it apart from all the other emotions. Surely there is such a differentiating factor, for we all know , sim ply on the basis o f our own em otive experiences, that feeling anger is the not the same thing as feeling fear, or desire, or pleasure, or

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despair. But what’s the difference, a difference that can be put into words which will serve to shed some beneficial light on the subject? Consider the following as a candidate for a definition of anger: it is a human emotion (proximate genus) by which we respond to a perceived offence by taking action which is intended to redress that offence (specific difference). The following would describe the typical structure of a situation which would commonly call forth the emotion of anger. Somebody says something or does something which we regard as a personal affront, and by their doing so we feel that the proper order of things has been disrupted in a way that is distinctly to our disadvantage. The situation, we feel, has to be corrected, so we retaliate, by saying som ething or doing som ething which is meant to counterbalance the offence done to us and thus restore the proper order of the universe. More con­ cretely: Carl, who clearly has the right of way, is almost clipped by a speeding vehicle that makes a left-hand turn right in front of him (the offence); Carl swears, slams on his brakes, leans heavily on the horn, and makes an ostenta­ tious obscene gesture for the benefit of the offending driver (the redress of the offence). We might try our hand at correcting the circularity of the definition of de­ mocracy cited above, wherein we were unhelpfully informed that a democratic government is one which is based on democratic principles. “Democracy” is our definitum. W hat is dem ocracy? Step one of the defining process would seem to be successfully taken by asserting that democracy is a form of govern­ ment. With that move we have our definitum safely placed within its proximate genus. Now to complete the process by identifying the specific difference. We would have a reputable definition of democracy if we were to propose the fol­ lowing: “Democracy is a form of government whereby the governing process itself, either directly or indirectly, is essentially under the control of those who are governed.” T he L imitations

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E ssential D efinition

Essential definition is a powerful logical tool for the kind of critically important knowledge it can provide us, but it has its limitations. Not every idea will docilely subm it itself to its penetrating process, and some of the more reluctant ideas in this respect are very important ideas indeed. Take the term “being,” for example. We would all agree that the idea, or set of ideas, which that term signifies are o f the weightiest sort. But “being” defies definition, according to the process to be followed in formulating an essential definition. In order to see how that is so, it is only necessary that we consider the first step which is to be taken in that process: placing the definitum in its proximate genus. W hat are we normally doing when we take that step? We are placing what we intend to define, which is always a class of things, in a larger class. Thus, in the Aristotelian definition of man, the class of human beings is inserted

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into the larger class of live material substances possessed of the powers of sensation, appetition, and locomotion, otherwise known as animals. Now, if we were to try to take that first step with “being," we would discover, much to our chagrin, that it cannot be done. There is simply no class into which we could put being, for being is simply all that really is, everything that actually exists, the only alternative to which is non-being, nothing. An effort to take the first step toward achieving an essential definition of being would result in something like, “Being is being,” which is a tautological statement and therefore, though completely true, is completely uninformative. There are any number of ideas—often just those ideas to which we attach the most importance—that cannot be logically defined. And there are any num­ ber of other things besides ideas, such as primary feelings—e.g., pain, thirst, longing—which frustrate any attempt precisely to define. How would we handle a primary feeling like pain? We could perhaps start confidently enough by classifying it as a feeling, but then what? How would we precisely differenti­ ate, verbally, the feeling of pain from the feeling of pleasure? And can we even be all that confident in the first step we took, by which we identified pain as a feeling, for there does not seem to be universal agreement on what is meant by that term. What if we were asked to define feeling? We couldn't do it. And we would likewise run into insurmountable definitional problems with sensations, visual or otherwise, and their objects. What is whiteness? We could take a stab at defining it by saying that it is a color (proximate genus), but then we would be stymied in attempting to express in words how the color white differs from, say, blue or yellow. Our only recourse would be to let our index finger do the talking. We would point at a patch of white and say, “Look, do you see that? That’s white!” Moral virtues, such as duty or honor or trustworthiness, cannot be defined in the strict sense, nor, as we mentioned earlier, can individuals, either individual persons or individual objects. Why is it that individual persons cannot be defined? Let us say that we would like to come up with a logical definition ot Oscar. In attempting to do so we would be taking a reasonable first step in the defining process by saying, “Oscar is a human being?' for we would be placing him in the class in which he properly belongs. But then we immediately run into problems. Recall what happened when, in attempting to define “human being,” we ascertained that rationality was the specific difference that set human beings apart from all other species in the genus “animal.” We rightly recognized that there is something essentially different about that animal we call man, in comparison with all the other animals. Now, if we were to suppose that we could formulate a logical definition of Oscar, or of any other individual person, that would involve the possibility of being able to cite something about Oscar that would make him essentially different from other human beings, but that is precisely what we cannot do, for all human beings are essentially the same in that they share the same nature. We would confront the same difficulties in

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trying to define individual objects that we meet in a trying to define individual persons. We cannot define St. Peter's Basilica, the Washington Monument, or Wrigley Field. Does the fact that some of the most important and familiar ideas in our lives cannot be logically defined mean that we have no real knowledge of those ideas? Not at all. Let’s go back to that very big idea to which we assign the term “being.” We may not be able to define being, but we certainly know it, in an immediate experiential way. Being is the most comprehensive of ideas be­ cause, again, it takes in everything that actually exists, the sum total of reality. We are very much a part of that reality, indeed altogether at home within its allencompassing embrace. We know what being is simply because we know ourselves as beings. At the core of every existent, such as ourselves, is the act of existing by which the existent is an existent. We have no need whatever to define being, the act of existing; we just do it. While acknowledging the limitations of essential definition, we must none­ theless be sensitive to the fact that it remains a very useful tool, even when it cannot be employed with complete success. If we are confronted with a par­ ticular term our knowledge of which is not as clear as we would want it to be, and if we have the praiseworthy incentive of wanting to remedy that situation, it is highly recommended that we begin by trying to come up with an essential definition of the term. Our efforts to do so might fail, but here is a case where failure can be positively instructive, for to discover that a particular term can­ not be strictly defined tells us much about the nature of the idea that lies behind the term, as well as about the limitations of logical analysis itself. In dealing with a great many terms, we would most likely be able to take the first step in the defining process, putting the definitum in the class in which it properly belongs, as we did when we correctly identified Oscar as a human being. Even if we can get no farther than the first step in essential definition, we have, in taking that step, provided ourselves with very important information about the object of our concern. Our knowledge has been significantly advanced. D e scriptiv e D e f i n i t i o n

That a particular term is not amenable to essential definition does not mean that we have to abandon all hope of defining it, and that is because there is another form of definition besides essential definition, and it is called descrip­ tive definition. The singular merit of essential definition is that, if done correctly, it reveals the very nature of the definitum, opening up for our inquisitive minds its foundational identity. But, as we have seen, essential definition is not al­ ways possible. In such cases we do the next best thing, adverting to an alternative means of definition. Through the various forms of descriptive definition we get as close to the essential nature of the definitum as we can. Descriptive definition can be described, in the most general of ways, as anything less than

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an essential definition. M ore precisely, we recognize five distinct types o f de­ scriptive definition: definition by property, definition by accident, definition by cause, definition by nam e, and definition by narration. D escriptive D efinition

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P roperty

A property, or proper accident, is a trait or feature o f a thing which, though not the very essence o f the thing, is inseparable from its essence. So, with re­ spect to a hum an person, w hose essence w ould be succinctly declared by the defining phrase, “rational animal,” we would cite the capacity of language (gram­ m aticalness), or the capacity for hum or (risibility), as properties o f a hum an person because, while neither of those exactly specifies the essence of a human person (i.e., rationality), they are inseparable from that essence and can only be explained in term s o f it. Though citing a property o f a thing does not directly identify its essence, it does so indirectly. If, then, I want to define “man” by the property o f gram m aticalness, I would say, “Man is a gram m atical anim al,” or “M an is an animal which is capable o f language.” And if I want to define man by the property o f risibility, I would say, “Man is the animal possessing risibil­ ity.” I could also say, by the way, “M an is a risible anim al,” which would not be to define him by property, but it would nonetheless be to say something true of him, for we often show ourselves to be rather laughable creatures. W e would not be able to define anything by singling out one o f its proper­ ties if we did not already have som e understanding o f w hat constituted its essential nature, for correctly to identify a property o f a thing implies our know­ ing that what we have identified is inseparable from the thing’s essence. To know that quantity is a property o f any material object is to know beforehand that it is not possible to have a material object which does not have measurable extension, i.e., quantity. The question then arises: Why would one want to settle for descriptive definition by property when one could presumably provide an essential definition in its stead? Answer: Because often properties have a con­ creteness and imm ediacy to them which can give us a more accessible avenue to the “what-ness” o f the thing we are dealing with than can a formal essential definition. To identify human beings as the animals that laugh provides us with a less abstract, a more vivid and dynamic, picture of them them to identify them as rational animals. Man is the laughing animal because he is a rational animal, and by putting stress on the form er perhaps we can be led to a deeper under­ standing o f the latter. D escriptive D efinition

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A ccident

In the previous chapter we acquainted ourselves with the nine categories of accident— quantity, quality, relation, action, passivity, place, time, position, and habit. To define something by accident is simply to cite one or more of the accidents that actually pertain to it, as I would do if I were to describe a robin as

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“a medium size bird with dark, brown-black feathers and a reddish breast, that hops rather than walks, lays pale blue eggs, feeds on earth worms, cocks its head fetchingly when searching for them, and goes south for the winter.” In considering the strength of any descriptive definition by accident, it is helpful to bear the following considerations in mind: (1) Because it is of the very nature of an accident (unless it is that special kind of accident we call a property) that it is not necessary to the substance to which it pertains (and therefore can be conceived as separable from it), we are not, in citing the accident of a substance, getting to the very heart o f its identity. (2) However, because it is also of the very nature o f an accident to inhere in a substance, we cannot know any accidental feature of a substance without knowing something of its essence, though that knowledge might be quite remote and superficial. (3) Not all accidents are on the same plane with respect to how they relate to the essence of a substance, in that some o f them are more closely related to that essence than others and therefore more revealing o f it. In the majority of cases, the accident of quality will tell us more about a substance’s essence than would the accidents o f position or habit. The fact that Frances knows French (quality) tells us more about her essential self than the fact that she is now sitting down (position), and wearing a beige cashmere sweater (habit). But certain qualities (like various bodily features) might supply us with only slight information about a substance. All in all, the fact that Vincent is now building a twenty-two foot boat (the accident of action) tells us more about him than the fact that he has red hair (quality). If we are even to come close to getting at the essence of the definitum through descriptive definition by accident, we must concentrate our attention on com­ mon accidents. These are accidents which are not peculiar to this or that particular member of a class but which are shared by all of its members. Con­ sidering the class of human beings, three accidents which are common to us all are our tool-m aking ability, our penchant for organized gregariousness (the fact that we are, as Aristotle observed, political animals), and the interesting habit we have of cooking our food. W ith just these three common accidents at hand, we could construct a reputable descriptive definition of man along the following lines: “Man is a tool-m aking and tool-using animal who fries his eggs and routinely associates with others in organized social units.” Auburn hair, blue eyes, and skill at playing chess would be examples of accidents which are not common to human beings as such. D escriptive D efinition

by

C ause

In his analysis of causation, Aristotle, thoroughgoing thinker that he was, identifies four distinct causes: the material cause, the formal cause, the effi­ cient cause, and the final cause.10The first two, the material and formal cause, are intrinsic to the thing which is being explained in terms of causality, whereas the second two, the efficient and the final cause, are extrinsic to it. Normally

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when we think about a cause it is the efficient cause we have in m ind. The efficient cause accounts for (a) the very existence o f a thing, or (b) the fact that it is existing in a particular way. The cabinetm aker is the cause o f the cabinet (its very existence), for he made it, and he’s also the cause o f the peculiar ways it exists, i.e., its various features, for he gave it an oak stain and three coats o f polyurethane. Someone could come along later and be the cause o f a change in the w ay the cabinet exists, by painting it a vivid purple. In any cause/effect relation, where the cause is an efficient cause, knowledge of the cause provides us with the fullest possible explanation we would want for the existence o f the effect. And because every cause usually leaves a deep and indelible stamp on w hatever it effects, we can, by closely exam ining the effect, arrive at varying degrees o f reliable knowledge o f the cause, even though the cause may no longer be present. By the distinctive tracks it left in the fresh snow, I can tell that there was a deer in the backyard last night, and have a fair idea o f its size and weight. On a much more interesting level, a Beethoven piano concerto gives us insight into the person and personality o f the com poser who was its cause. We can arrive at a fairly com plete picture o f any object we are attem pting better to understand if we are able to analyze it in terms o f all o f the four causes. To illustrate this, I will take as an exam ple something rather ordinary, a dormi­ tory building. T he m aterial cause o f the building is all o f the m aterials that w ent into its construction, which o f course would be many and varied. Its for­ mal cause would the peculiar arrangement and configuration of those materials so that the end result o f the construction process clearly declares itself as a college dormitory, an edifice which is not to be mistaken for a domestic dwell­ ing, an office building, a bus depot, or a chicken coop. The formal cause is the identifying cause; it explains why something is precisely what it is, and distin­ guishes it from what it clearly is not. The efficient cause o f the dormitory would be the sum total o f all those workers who were responsible for bringing it into being in the state in which we now find it. Among these efficient causes would be the architect w ho designed the building, the m echanical engineers who planned the heating, air-conditioning and plumbing systems, the electrical en­ gineers who planned the electrical lay-out, and all the construction personnel, skilled and unskilled, who put the building together and gave it all its finishing touches. The final cause o f the dormitory is the purpose it is intended to serve, which is to house resident students at Catfish College. D escriptive D efinition

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N ame

Descriptive definition by name, also called nominal or verbal definition, is the least penetrating kind of definition, though it does have its value. It is the kind of definition upon which most dictionaries are founded. The most common type of nominal definition is a synonym ; a word, one which is, ideally, more fam iliar than the term w hich is being defined, is offered as a substitute for it, as when “irate” is defined as “angry,” and “pertinacious” is defin ed as “stubborn.”

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Nominal definition endeavors to explain the usage of a term, the manner in which it is em ployed in ordinary discourse, rather than attempt to get at the essence o f the idea which the term represents. Another fairly common way in which a term is defined nominally, which can often be quite instructive, is by giving its etym ological background. So, “philosophy” is defined etymologi­ cally by noting the fact that it is a compound made up of two Greek words, philos (“one who loves”), and sophia (“wisdom”). From that we can say that philosophy, at least as originally understood, is the love of wisdom, and that a philosopher is a lover o f wisdom. Digging into the root meaning of words can be interesting, but the results do not always reliably inform us as to how they are to be understood in the contemporary setting. Much can happen, in terms of basic meaning, between the distant origin of a word and how it is being used today. And the word “philosophy” could be cited as a case in point. D escriptive D efinition

by

N arration

There are certain terms, certain concepts, and often those which carry spe­ cial weight for us, whose meaning can be best conveyed through the medium of story. The story o f the Good Samaritan, for example, one of the most famous tales ever told, came in response to a question, Who is my neighbor? I think we would all agree that even the best attem pt at a formal, logical definition of “neighbor” would be a very poor substitute for the story of the traveler who, in a gesture of rem arkable selflessness, goes out o f his way to aid a complete stranger who had been robbed and beaten and left for dead at the side of the road, a stranger— and this gives an especially poignant twist to the story— who, according to the social conventions of the day, would have been considered the sworn enemy of the helping traveler. We might be able to work up a crisp, formal definition of “war,” but if we really want to understand the meaning of that gruesom e phenomenon, short o f experiencing it firsthand, we could do worse than to sit down with novels like War and Peace, The Red Badge o f Courage, A ll Quiet on the Western Front, and The Naked and the Dead. J1 D ivision Division is an analytic process by which we break up a complex idea into its constituent parts. So, if I were to take “the United States government” as the whole to be divided, and divide it according to its principal branches, the result can be schematized as follows: United States Government Executive Branch

Legislative Branch

Judicial Branch

The complex idea which represents the whole which we are dividing into its various parts— the United States government—could be divided in any

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num ber o f other w ays, som e o f w hich w ould yield a great m any parts. The division we have done here is very basic and reveals the largest parts into which the w hole in question can be divided. If we were to select as the whole to be divided a more general concept, such as “Forms o f Political Government,” then each o f the parts o f the division would represent a distinct form o f government. In his book called Politics, Aristotle tried his hand at making a division o f this idea, and he came up with six specific forms o f government, which he evidently thought exhausted all the possibilities. They are: M onarchy, A ristocracy, Constitutional Government, Tyranny, Oligarchy, and Extreme Democracy. O f these six, he considered the first three to be good, and the second three bad forms of governm ent.12 In defining a term, our principal concern is with its comprehension or mean­ ing, which is precisely what a good definition is intended to bring out into the open. In dividing a term, our principal concern is with its extension: the spread or coverage o f the m eaning o f the term. W hen we focus on the extension o f a term (which o f course means that we are focusing on the idea which the term represents) we are interested in its particular contents. W hat is the full panoply o f its m eaning? A com plex idea is such because it is made up o f multiple sub­ ideas, or w hat we have called “notes.” The task o f division is to spell out all those sub-ideas in explicit form. W hat is the extent o f the application o f this or that idea?— such can be taken as our guiding question in doing a division. The way we go about answering that question is simply to account for all that is implied in the full meaning of the idea. A definition, especially if it is an essential definition, will reveal the heart o f an idea’s meaning. And because definition and division are very closely allied to one another, as modes o f logi­ cal analysis, division, if carefully and competently done, serves to enrich our understanding o f any term to which it is applied, as is the case with definition. Division is a means by which we clarify our ideas by making ourselves aware o f the specifics o f their complexity. The philosopher Plato is comm only con­ sidered to be the creator o f the method o f division, and he made much use o f it, confidently regarding it as a very effective means o f clarifying our ideas by a close exam ination of their contents.13 P hysical D ivision

or

P artition

W hen the object of our division is a single entity, the process by which we discern its various parts is called physical division or partition. Dividing the United States government into its principal branches is an example of physical division, as would be the division of a living organism into the various organs and system s o f which it is com posed. In the latter case we would be dealing with a physical body, in the former, with a legal one. Aristotle, taking a literary work as the thing to be divided (a play or a long narrative poem were the par­ ticular cases he had in m ind), saw it as a com position which is made up of a beginning, a middle, and an end.14 That too would be an example of partition. It

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is a way o f analyzing any literary work which can be helpful to both the con­ sumer and the producer. We can achieve a deeper appreciation of a good novel, say, if we are sensitive to how it is structured. If it is a good novel, the early chapters introduce us to the special “world” that the novel deals with; the brunt of the book is given over to the development of the story line and of the charac­ ters that people the novel; then things are brought to an aesthetically satisfying resolution in the novel’s final chapters. Aristotle’s division of a literary work can also be helpful to those who pro­ duce them. Take the case o f Lisa, for example, who has to write a paper for a history course she is taking. At the very outset, she thinks in terms of a whole that will be composed o f a beginning, a middle, and an end. Accordingly, she leads o ff with an introduction in which she informs the reader of her main thesis and how she intends to develop it; in the main body of the paper she does that developing, then she follows that “m iddle” with a conclusion of one or two paragraphs in which she provides the reader with a brief summary of what she has done. One way quickly to identify a physical division, and to distinguish it from a logical division (to which we will be turning next), is by the fact that the whole that is being divided cannot be predicated of any of its parts. In the case of Lisa’s paper, I cannot say that the introduction of the paper is the paper itself. Take another example, a tree. I can divide a tree into roots, trunk, branches, leaves, and (assuming it to be an apple tree), fruit. That done, I cannot mean­ ingfully say that roots are a tree (thereby claiming than a part is the same as the whole), and it would be equally silly for me to say that a tree is its roots (thus ruthlessly reducing the whole to but one of its parts). L ogical D ivision The distinctive feature o f a logical division is that the whole which is di­ vided is a genus, and the parts into which it is divided are species, so what we have then is a situation where a larger class is divided up according to smaller classes which naturally compose it. Our definition of a human being as a ratio­ nal animal could be said to represent the beginning of a logical division of the genus animal. A human being is a species, or sub-class, of the genus, or class, of animals. If we were to complete the logical division of the genus “animal”— a m onumental task— we would need to name every other bonafide species, besides the human species, that together make up the genus. The test of a logical division is the fact that, unlike the case with physical division, the genus can be meaningfully predicated of the species— i.e., the whole can be said of the part— but not vice versa. I can say truly that a human being is an animal, but I can’t turn that around and say that an animal, just as such, is a human being. The reason I can truly make the first statement is because animality is of the essence of humanness; you cannot be human without being an animal. And the reason I cannot make the second statement is because, while

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anim ality is o f the essence o f hum anness, it is the not the whole essence; som ething o f radical im port has been left out o f the picture— rationality. A creature can be an anim al without being a hum an being. To say that an animal is a hum an being w ould be effectively to equate a w hole w ith only one o f its parts, such as we would be doing if we were to claim that a tree is its roots. T he R ules

for

L ogical D ivision

In order to effect a successful logical division, one that could make a real contribution to our know ledge, there are three basic rules that need to be fol­ lowed. Rule #1 — There m ust be a single, consistent basis fo r the division. W e cannot expect to produce a useful division o f a class o f things if we attem pt to break it down into sm aller classes in a haphazard or arbitrary way. Division is a mode o f analysis, and analysis must be rational and systematic; it can be such only if it is guided by a clearly defined principle. Before I begin any division I must ask myself, W hat is the specific criterion according to which the division is to be m ade? W hat is the foundation for the division? Let us consider the plane three-sided figure known as a triangle. A triangle is a class of geometric figures which can be divided into sub-classes. Using as the basis of my division the length o f the sides o f a triangle, I can logically divide tri­ angles into (1) equilateral triangles (where all three sides are equal), (2) isosceles triangles (where two sides are equal), and (3) scalene triangles (where each of the sides has a different length). A lternatively, I could make another logical division of triangle by employing a different basis, which in this case would be the respective size of the internal angles of a triangle. By this criterion I could divide triangles into (1) obtuse triangles (where one of the angles is larger than ninety degrees), (2) right-angled triangles (where one angle is exactly ninety degrees), and (3) acute triangles (where all o f the angles are less than ninety degrees). As can be seen by those examples, a single class of things can be divided in more than one way, the different divisions being founded on different bases. Im agine the many ways a large and diverse class like “Europeans” could be divided. One division that immediately suggests itself is to divide Europeans according to nationality, but a division could be made according to any number of other criteria, such as (to name only a few) religious, economic, ethnic, lin­ guistic, educational, and political. But the point to be kept clear is that once a particular basis for a division has been chosen, it has to be consistently main­ tained throughout the division. If one were to change the basis o f a division while engaged in the process of dividing, the inevitable result would be a botched division. Care should be taken that what is chosen as the basis for a division is sufficiently interesting so as to yield a result which is genuinely informative. The division of Europeans according to nationality would not tell us much

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beyond what we already know, but a division based on differences of opinion regarding subjects like abortion and euthanasia could turn out to be quite inter­ esting and informative. W ith regard to the basis of a division, a distinction is made between a natural division and an artificial division. A natural division, as the name suggests, is one whose divided parts are natural or intrinsic to what is being divided, and in such a case the division can be said to be scientific in the special sense that it is a process of discovering what actually obtains in the objective order o f things. An ornithologist would be making a natural division if he were to divide the class of birds according to the different migratory pat­ terns they follow, or according to their mating habits, or nest-building practices. Dividing evergreens (non-deciduous trees) into their various species would be a natural division, as would dividing plants according to the different struc­ tures o f their flowers. An artificial division is one whose basis is arbitrarily established by the one m aking the division, usually with a specific practical purpose in mind. It is not something which is discovered by a close examina­ tion o f the object to be divided. D ividing a certain population, such as the residents of Cucumber County, according to the types of charities they would be most likely to contribute to, or according to the political issues they tend to feel most strongly about, or according to the colors they most prefer—these would be examples of artificial division. Rule #2 — The division must be exhaustive. In the division o f triangles according to the length of their sides, were I to have om itted scalene triangles from the division, it would not have been ex­ haustive because one o f the parts o f the whole had been left out. A successful division is one in which all of the divided parts have been accounted for, and in which the sum total o f those parts equal the whole which they compose. In order to m eet the dem ands o f this rule, one w ould need to have a sufficient general acquaintance with the object to be divided in order to be able to sense that something was missing were the division in fact to be incomplete. One has to know enough about a baseball team to realize that any division of it, on the basis o f player positions, and which omits the outfielders, would be an inad­ equate division. But som etim es it may take a while before we realize that a division is incomplete, and that is because o f the insufficiency of our knowl­ edge of the object being divided, an insufficiency which need not necessarily be due to carelessness on our part. Take the case of an ornithologist again, who has made a division of birds according to, say, nest-building practices. In pur­ suing his research he roam ed the wide world, and identified the various distinctive types of ways birds build their nests. As far as he knew, his division was exhaustive. But then, while on vacation in Borneo, he happens upon a rare avian species that builds its nest in a way that does not fit any o f the types of nest he has identified— a kind of split-level affair with a sun deck and a twoport garage. Good scientist that he is, he immediately expands his division to include this new type of nest. The point to be made here is that the process of

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division can often be a means by which we discover new things about the class being divided, because of the peculiar kind o f attention to the class the process demands of us. We embark upon a division guided by our best available knowl­ edge of a class, but sometimes that knowledge can be increased, thanks to the dividing process itself. Natural division especially can be a very productive means of discovery. Even though an initial division may be defective by reason of the fact that it is not exhaustive, it nonetheless provides the conceptual framework wherein you are most likely to discover how the division is defective. The very fact that you took the trouble to make the division in the first place, though it turned out to be less than perfect, gave a focus to your attention that it otherwise would not have had, and attention creates the atmosphere within which discoveries are made. Any systematic analytic process— and that’s what division is— in­ evitably results in a higher degree of potentially productive mental alertness. Rule #3 — The parts o f the division must be mutually exclusive. The purpose of division is to bring greater clarity to our ideas. That purpose would be defeated if the parts of a division were to be blurred, if one part were not distinctly separate from another. There must not be any obvious overlapping among the parts o f a division. The principal cause of such overlapping is the failure to maintain a consistent basis for a division from first to last. Consider the following division. Members o f the U.S. Congress Democrats

Representatives

Republicans

Senators

This is an obviously flawed attempt at division in that it is made according to two distinct criteria— party affiliation, on the one hand, and the chamber to which members o f the U. S. Congress belong, on the other, with the result that there is significant overlapping. A member of Congress can be in the House of Representatives and be either a Democrat or a Republican, and the same holds true for the Senate, so the four classes are not distinct. Another thing we need to tend to in order to ensure that our divisions are as clear as possible is the need for a part to be immediately inferior to the whole which is being divided. Recall the attention we had to give, in formulating an essential definition, to the importance o f placing a definitum in its proximate genus, as the first step in the defining process. Logical division, remember, is essentially a m atter o f breaking down a genus into its proper species. In doing this we m ust take care that we do not identify as a part of a genus what is in fact a part o f a species o f that genus. This is what I would be doing if, in intending to divide the genus Living Substances, I come up with a tripartite division of Plants, Anim als, and Hum an Beings. Plants and Animals are species o f the genus Living Substances, but Human Beings constitute a species of Animals. That m akes Human Beings an illegitim ate part o f the division because they

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belong to a class which is not immediately inferior to the class o f Living Substances. To correct a mistake o f that sort, one only has to create a subdivision of the original division, in this particular case moving the class of Human Beings down one level, placing it under Animals, and then taking on the enormous project of adding all the remaining species of animals. Please note, in this regard, that a subdivision must be ju st as exhaustive as the division to which it is subordinate. It is best to maintain the same basis for both a division and a subdivision, though there is no hard and fast rule on the matter. It would not be unforgivably wrong to make a division according to one criterion, and then to subdivide that division according to a new criterion, so long as the end result is reasonably clear. Consider the following division and subdivision: Naval Ranks Ordinary Seaman

Non-Commissioned Officers

Commissioned Officers

U.S. Naval Academy

NROTC

OCS

The basis for the original division is announced by its title: distinction according to types o f rank. Now, sub-divisions could be made for each of the listed types, by naming all the specific ranks within each (e.g., Ensign, Lieutenant Junior Grade, Lieutenant, etc. under “Commissioned Officers”), and the sub­ divisions would thus maintain the same basis as the original division. But the basis for the single subdivision that is made in the model above, under Commissioned Officers, is the training program that led to commissioning. D ichotomy A foolproof way to make a technically flawless division is to set down a particular class and then to negate it. W hat results is called a dichotomy. So, I could divide the entire human race into residents of Morton, Minnesota and non-residents of Morton, Minnesota. The division covers everyone on the face o f the globe; it is exhaustive, and there is no overlapping of parts. But it is pronouncedly uninform ative, and that is because o f the basis on which the division is made. The division might have the effect of raising the self-esteem of the residents of Morton, Minnesota, but it will not do much for the rest of us by way of advancing our knowledge of the rich particulars of the class which is being divided. One part o f the division is fairly precise and focused, but the other part, the sum total o f humanity not residents of Morton, Minnesota, is a huge undifferentiated blob. We know intuitively that there is a staggering amount of diversity in that part of the division, but the division itself gives us no hint of that fact. The above example should not lead us to believe that there are not serious, non-trivial ways in which dichotomy can be employed. W hether or not a

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dichotomy is genuinely inform ative all depends on the significance o f the term which is negated. D ividing the genus animal into two sub-classes, rational and non-rational, w ould be a genuinely inform ative dichotom y because o f the weightiness o f the specific difference, rationality, which founds the division. A legislator w ho is sponsoring a bill m ay, as a practical m atter, divide all the other legislators into possible backers and possible non-backers o f the bill, and then co n cen trate his persuasive energies on the form er. D ichotom y can be effectively used as a process o f elim ination in various kinds o f investigation, such as that devoted to the solution o f a crim e. Sidney Sleuth, called upon to investigate the sudden dem ise o f M alcolm M alodorous, begins his analysis with the sim ple m urdered/not-m urdered division. W as M alodorous a victim of hom icide, or did he die o f natural causes? On the basis o f the fact that there was a butcher knife securely implanted between Mr. M alodorous’s shoulder blades, Sidney, keen-w itted detective that he is, decides that the “not-m urdered” part o f the dichotom y can be elim inated. The pattern o f the rem ainder o f his investigation can be illustrated by the following series o f dichotomies. M alodorous m urdered by outsider or by insider by fam ily m em ber

not by fam ily m em ber

by the gardener by the maid

not by the gardener not by the maid the butler

C lassification The process o f classification is broadly similar to the process o f division in that, like division, it is a m eans by which we clarify our ideas, but it differs from division in that, instead o f proceeding from genus to species, it moves in the opposite direction; it begins with a species, or sub-class, and then determines the genus, or larger class, in which the species properly belongs. Or classification can begin with individuals, and then place them in their proper species. W hat is the basis for classification? According to what principle would an individual, for example, be placed in one class rather than in another? It would be so placed on the basis o f certain sim ilarities, structural or otherw ise, between that individual and the individuals which are already snugly incorporated within a particular class. Let us say that a biologist discovers a new species o f animal. In closely exam ining the creature, he sees that it com es equipped with a backbone, and on the force o f that knowledge he places the creature in the class o f vertebrates. One could classify the words o f the English language according to their linguistic origins— Anglo-Saxon, Celtic, French, Latin, Greek, etc.—

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or one could classify books, as libraries do, according to their subject matter. (See Appendix B for additional commentary on classification.)

Review Items 1. How do definition and division fulfill their basic purpose of helping us to clarify our ideas? 2. W hy is an essential definition called essential? 3. W hat are the two steps to be taken in an essential definition? 4. W hat are the rules for an essential definition? 5. Give an example of a circular definition. 6. Name and briefly describe the five types of descriptive definition. 7. Explain what it means to say that definition has to do with the comprehension of a term and division has to do with its extension. 8. W hat are the rules for logical division? 9. Give an example of a division whose parts overlap. 10. W hat is the difference between division and classification?

Exercises A. Provide a definition for the following terms. In each case try constructing an essential definition (placing the term to be defined in its proximate genus and then finding a specific difference for it), but if that fails make use of descriptive definition. 1. freedom 2. criminal 3. justice 4. orphan 5. fear 6. terrorist 7. virtue 8. prejudice B. Make a division of each of the following terms, then make a sub-division of at least one of the parts of the original division. 1. athletes 2. works of literature 3. music 4. American history 5. trees

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C. Critique the follow ing divisions. Specify w hatever weaknesses you might find in them. 1. the human race: into male and female 2. college professors: into chemistry, history, emeritus, Hungarian 3. poetry: into epic and non-epic 4. employee: into clerical, unskilled, manual laborer 5. games: into indoor and outdoor 6. mathem atics: into pure and applied 7. W ar and Peace: into its chapters 8. solids: into length, depth, thickness 9. history: into ancient, medieval, m odem 10. basic colors: into red, orange, yellow, green, blue, violet

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Chapter Six Judgment T he S econd A ct

of the

I ntellect

We remind ourselves at this point that our course in logic is structured around the three foundational acts of the intellect: simple apprehension, judgment, and reasoning. We have already examined the various ramifications of simple ap­ prehension, that act of the intellect whereby we generate ideas in response to the information which is provided to us by our five senses. Now we turn our attention to the second act o f the intellect, judgment, which involves the kind of thinking which regards ideas specifically in terms of how they are related to one another. To give it a more specific identification: judgment is the act of the intellect by which we either compose or divide ideas, according to their respec­ tive compatibility or incompatibility. Composition and division, then, are the two basic functions of judgment, which is the mental act itself. The linguistic expression of that mental act is called a proposition. The result of the composi­ tion process, where we associate two ideas positively, is an affirmative proposition (“The wine is from Australia”); the result of the division process, where we separate one idea from another, is a negative proposition (“Dominic is not a Mason”). The two ideas which we either separate or unite in judgment, and then ex­ press in a proposition, need not necessarily relate to actually existing things in the extra-mental world. For example, they may relate to a fictional world. None­ theless, they may still involve either composition or division in that they either are or are not correctly responding to the fictional world to which they refer. If I claim, “Huckleberry Finn was the brother of Tom Sawyer,” I would be assert­ ing something which does not reflect a particular fictional world created by Mr. Mark Twain, and therefore it would stand as an erroneous example of com­ position. I brought two ideas together which do not belong together. The general rule is this: the composition or division of ideas must be consistent with what­ ever world they refer to.

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udgm ent

In logic, the principal world with which we are concerned is the real world, the extra-mental realm constituted by the objective order of things. The most important judgments we make are about that world, and it will be what actually obtains in that world which serves as the ultimate determinant whether or not we are composing and dividing correctly in our judgments. A sound judgment reflects what is actually the case: the ideas that we are uniting or separating in our minds faithfully represent the extra-mental situation. “Ruth is running” is a sound judgm ent because that is precisely what she is doing at the moment, whereas, given that reality, “Ruth is in bed with the m easles” would be an unsound judgment; we might call it a rash judgment. It is because judgment is most importantly concerned with the objective order of things that we call it “existential.” It is the human intellect’s response to real existence, to what is actually going on in the extra-mental world. A proposition, the linguistic expression of judgment— the common means by which the second act of the intellect “goes public”— is true or false to the extent that it either succeeds or fails faithfully to reflect the world to which it refers. Thus, the proper response to any proposition is either to affirm it, if we deem it to be true, or to deny it, if we deem it to be false. And the only way a proposition can be reasonably affirmed or denied, under most circumstances, is by looking beyond the proposition itself, to that to which it is referring in the public domain. Again, the basic structure of the relationships involved here are quite simple. If there is a correspondence between what the proposition avers and what is actually the case, then we confidently pronounce that proposition to be true. However, if we detect a fundamental discrepancy between the assertion made by the propositionand the facts to which it is referring, then we withhold our assent to the proposition and boldly call it false. We thus stand in judgment o f judgments, determining whether or not they are deserving of our assent. It is hard to imagine a more important occupation with which the human mind can concern itself. On it depends the degree to which we are in touch with the real world. P redication Given the critical role that the proposition plays in logic, as the expression of judgment, it behooves us to become very familiar with this peculiar mode of linguistic discourse. The proposition is all about predication, and predication, in the plainest terms (the terms used by Aristotle, by the way), is simply “say­ ing something about something.” It is bringing together two ideas in such a way that one idea is, or is not, attributed to another. When one idea is positively associated with another, the result is an affirmative proposition; and when one idea is dissociated from another, the result is a negative proposition. One idea can be associated with another in whole or in part, and the same holds true for the dissociation of ideas. This points to another way propositions can be distin­ guished, which we shall be looking at presently.

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All propositions are composed of two elements, the subject term and the predicate term. The subject term is that about which something is said, and the predicate term is that which is said. So, in an affirmative proposition, the predi­ cate term represents the idea which is being attributed; the subject term is the receptor of the attribution. In the language of logic, when one idea is attributed to another, we say that it is predicated of that idea. Consider the following propositions: (1) The grass is green. (2) Some guns are not loaded. (3) No males are mothers. In the first proposition the idea of “green” is positively associated with the idea of “grass.” Green is being predicated of grass. In the second proposition there is a partial dissociation established between the idea of “being loaded” and the idea of “guns,” and we can say that here the predication is negative but applied partially. In the third proposition, the predication is negative and complete. We are being told that there is no association at all between the idea “male” and the idea “mother.” T he F irst P rinciples

of

A ll H uman R easoning

A proposition is true if it reflects what is; that is what we mean when we refer to the existential import of the judgment which a proposition represents. If a proposition expresses just the opposite of what we know to be the facts of the matter, then it is false. The relation between a true proposition and the real world situation to which it refers is called logical truth. Logical truth is founded upon, and totally dependent on, ontological truth, alternatively known as “the truth of things.” or “the truth of being.” The word “ontological” has its roots in the Greek onta, which means “existing things,” or, more comprehensively, “reality.” A thing is said to be ontologically true if it actually exists. The Wash­ ington Monument is ontologically true because it is really there; it is not simply a figment of my imagination. Having spelled out the difference between logical truth and ontological truth, we can readily see how the first necessarily depends on the second. Unless something actually exists in the extra-mental world, there would be nothing to which the idea in my mind could be said to correspond. There would be no existential basis for my judgment, and therefore no way by which the proposi­ tion, through which I express the judgment, could be determined to be either true or false. All the salient aspects of ontological truth, the truth of being, are incorporated within four truths that are absolutely foundational to thought, and which are known as the first principles of all human reasoning. Without them, human reasoning is impossible. There is something redundant about the phrase “first principle,” because it is of the very nature of any principle to be first. (The word comes from the

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Latin princips, which means “first.”) A principle is a starting point, an elemen­ tary truth with which one must begin, otherwise there is no moving forward. Every science, as noted earlier, is based upon first principles— elementary truths pertaining to the science— and these constitute the foundation on which the science is built. Logic, like every other science, has its set of first principles, and they are what we are calling the first principles of all human reasoning. T hat way o f identifying them suggests that there is som ething very special about the first principles of logic, and that is indeed the case. Logic, as a sci­ ence, is foundational to all other sciences. W hatever other particular science you may pursue— physics, chemistry, biology— you must use logic if you are to have any success at all in your endeavors. You must think clearly and co­ gently; your ultimate aim must be the attainment of truth. Given the fact, then, that logic is foundational to all other sciences, it follows that the first principles upon which it is based would also be the very first principles of every science, the most general truths which constitute the basis for any scientific inquiry, and that is why they are appropriately called the first principles of all human reasoning. It is with these principles that all sound thinking must start. They are thus “first” in the most unqualified and emphatic of ways, for there are no truths antecedent to them. With them we are at rock bottom. Another important feature of the first principles of all human reasoning needs to be called attention to, and that is the fact that they are self-evidently true, and this has to do with their rock-bottom status. Something is self-evidently true if you do not have to look to anything beside or beyond it to see that it is true. We say that it is true prima fa c ie , on its very face. Another way of putting it is to say that these principles do not have to be proved. We can be even stronger than that: they cannot be proved. How so? As we shall see more clearly later on, to prove any proposition to be true, we must rest it upon a proposition that can serve as supporting evidence because it is self-evidently true, and the truth it expresses is more basic than the truth o f the proposition which we are at­ tempting to prove. But because, as noted, these principles are absolutely first, unqualifiedly basic, there are no truths more basic than the ones they represent. There are no more primitive truths upon which we could rely in order to prove them to be true. The process of counting whole numbers begins with one. But what comes before one, on what is it based? Nothing. Unless you accept one, as your one and only starting point, you are never going to arrive at two, and you may as well completely forget about ever reaching seventeen. Unless we accept the self-evident truth of the first principles of all human reasoning, nothing worthy of being called reasoning ever takes place. However, there is no real difficulty involved here for, among other things, common sense immediately recognizes the transparent veracity of these principles. We see them as the very cornerstones of how we correctly think about reality.

J udgm ent

T he P rinciple

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I dentity

The very first of the first principles, the principle of identity, is the most elementary of them all. It can be stated as follows: “A thing is what it is.” Now, that is patently obvious, but let us not be deceived by the utter plainness of the statement into thinking that it isn’t telling us anything significant about the nature of reality. It is telling us something very significant indeed. The prin­ ciple informs us, negatively, that reality is not one big homogeneous, undifferentiated blob. Reality is immensely complex by reason of the fact that it is composed of myriads of individual things, and any individual thing, how­ ever we might precisely identify it, is not to be confused with any other individual thing. To say that a thing is what it is (and nothing else than what it is) is to acknowledge its uniqueness, and not to mistake it for something other than itself. If a thing actually exists, then necessarily it can exist only as in fact it does, and in no other way, and it is just that which allows us to recognize it for what it is and to identify it properly. Applying the principle to the human realm, we see that there is no mistak­ ing one person for another, even though they may be identical twins. The principle of identity explains individuality. It is what makes counting possible, and what justifies our giving different names to different things; it is what leads us to use demonstrative adjectives to distinguish things which bear the same general name. “No, not that chair, this one!” T he P rinciple

of

C ontradiction

If a thing is what it is and cannot be other than what it is (principle of iden­ tity), then any attempt to claim otherwise would constitute a false claim. It is the principle of contradiction which stands in the way of such a claim. The principle is stated as follows: “It is impossible for something both to be and not be at the same time and in the same respect.” Thus stated, the principle refers to ontological truth. It is not possible for Henry to be, right now, physically in San Antonio and to be, right now, physically in San Luis Obispo. But what is the purport of the qualifying phrase, “in the same respect”? That tells us that there would be no contradiction involved if two different modes of existing were in play regarding the same subject. For example, Henry could be physically in San Antonio right now, but his mind could be elsewhere, specifically, in San Luis Obispo, where he had left his heart. If the principle of contradiction were to refer to logical truth, it would be stated in the following manner: “It is im­ possible to affirm and deny the same predicate of the same subject atthe same time and in the same respect.” We may symbolically express the principle of identity as “A is A.” It would then be a flat contradiction to assert that “A is not-A.” I cannot concurrently claim, on the one hand, along with Gertrude Stein, that, “A rose is a rose,” then turn around and say, “A rose is not a rose.” Reality refuses to be trifled with in

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so blatant a manner. However, I would not be guilty o f violating the principle of contradiction were I to say, first, “The bird is in the bush,” then, “The bird is notin the bush,” if the first statement was made at 3:05 p .m ., when the bird was in fact in the bush, and the second statement was uttered at 3: 10 p .m ., when the bird was in fact in hand. A man may be said to be laughing and not laughing at the same time, but not in the same respect, in the sense that while he is display­ ing all the commonly recognized signs of merriment, he is not, psychologically speaking, really merry at all. Thus Liam is now, as we say, laughing on the outside but crying on the inside. Given this state o f affairs, it would not be contradictory both to affirm and deny laughter of Liam, with the understanding that his physical behavior does not signal the state of mind we normally asso­ ciate with it. T he P rinciple

of

Excluded M iddle

The principle of identity states the m ost rudim entary of facts, the fact of existence. A thing either exists or it does not. Between those two possibilities there is no middle ground, and that is the truth which is expressed by the prin­ ciple o f excluded middle. The “m iddle” that is being excluded here is any supposed state between being and non-being. There can be no such state. When it comes to the matter of sheer existence, it’s all or nothing. There is no halfway house on the way to, or on the way back from, being. There have been philosophers who have argued that the principle o f ex­ cluded middle does not apply. There is, they claimed, a middle state between being and non-being, and the name of that state is “becom ing.” According to this theory, a thing which is in a state o f becom ing is neither being nor nonbeing. It has emerged out of the murky precincts o f non-being and is heading hopefully in the direction of being; it is thus becoming being. Or perhaps it is heading in the opposite direction, toward non-being, in which case it might be appropriately labeled unbecoming being. W hat are we to make of this way of thinking? Notice that in order to lend any kind of intelligibility to this point of view, it was necessary to imply the presence of a “thing” which is in a state of becoming. This serves to emphasize a very elementary fact about the phenom­ enon of change (“becoming” is just another word for change) which was pointed out by Aristotle centuries ago— perhaps with a bit of em barrassm ent on his part, given the brute obviousness of the fact— to wit: in order for there to be change, there has to be a subject of change, that which changes. So, if there is to be any becoming, there must necessarily be something which is becoming. To imagine pure becoming, or becoming just as such, airily detached from a sub­ ject of becoming, is to imagine what can never have any real existential status. It is, in other words, to imagine a purely fantastic entity, an idea without a referent, like “unicorn,” or “griffin.” Those who claim that there is a third state between being and non-being are in effect hypostatizing becoming, which is to

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say, they are gratuitously conferring substantial existence upon what has only accidental existence. They are making a “thing” out of becoming or change, rather than acknowledging that becoming or change can only be what happens to a thing. This would be like claiming that “blue” or “humor” exist as inde­ pendent realities; they don’t, and they can’t. There must be a substance in which those qualities inhere, such as blue blouses and humorous people. Are we denying the reality of becoming or change? Of course not. We are simply emphasizing what kind of reality, what kind of existence, becoming represents— accidental existence. Change exists only as a feature of a substan­ tial existent which is in the process of undergoing change. Change or becoming, then, can only take place fully within the realm of being. When we talk about real change we are in the same breath talking about the real thing that is chang­ ing. T he P rinciple

of

S ufficient R eason

A thing is what it is (principle of identity); it cannot not be what it is and remain itself (principle of contradiction); and it is a matter of absolute either.. .or with respect to its existence (principle of excluded middle). The fourth of the first principles of all human reasoning is the principle of sufficient reason, which tells us that for everything that exists, there must be an adequate explanation for its existence. In other words, things don’t just happen. The existence of any actually existing things is not self-explanatory. Common sense readily attests to this foundational truth. A thing cannot bring itself into existence. Supposing that to be possible would involve the absurd situation where a thing would have to exist before it exists in order to bring itself into existence— quite a trick, if it could ever be pulled off. Everything that has existence, then, needs an explanation, outside itself, for its existence. What is the explanation for the existence of that Poodle puppy now cavorting about on the front lawn? Mr. and Mrs. Poodle. When we think in terms of the principle of sufficient reason we think about causes. Genuine scientific knowledge is a knowledge of causes. The principle of causality is a more limited expression of the principle of suffi­ cient reason. (See Appendix A for further discussion of the first principles of all human reasoning.) T he C ategorical P roposition A proposition is a linguistic construct, specifically, a grammatical sentence, which says something (the predicate) about something (the subject). A cat­ egorical proposition is the most important kind of proposition for logic because it asserts that something is definitely the case, without ambiguity or any quali­ fication. A categorical proposition expresses perfect clarity and certainty about what is being said on the part of the person who is saying it. The surest way to identify a categorical proposition is to ask yourself if it makes sense to respond

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to it by saying either “True” or “False.” In the term inology o f grammar, a cat­ egorical proposition is called a declarative sentence. Such a sentence unequivocally “declares” something to be the case, with regard to how the predi­ cate term relates to the subject term. A further gram m atical qualification: a declarative sentence is said to be in the indicative mood. It “indicates” a real state o f affairs, and does not sim ply suggest a possible or probable state o f affairs. The following sentences are categorical propositions. The turkey is in the oven. President McKinley died on Septem ber 14,1901. The following sentences are not categorical propositions. The book may be in the library. Calvin Carp could have graduated from Colgate. Notice the conjectural nature of the non-categorical propositions. They do not take a definite stand concerning the matters about which they speak, and thus they leave us in doubt as to what, in each case, the exact situation is. Is the book in the library or isn’t it? Did Calvin Carp graduate from Colgate or didn’t he? Because they do not tell us anything definite, we cannot designate either of them as true or false. Logic is principally concerned with categorical proposition. We can respond directly and confidently only to sentences that invite affirmation or denial, even though the state of our knowledge may not perm it us to do one or the other immediately. In our own discourse we should alw ays m ake it a point of expressing ourselves categorically, insofar as the real-life situation to which we are referring allows us to do so. Needless to say, a categorical proposition is empty if it does not reflect what is actually the case in the objective order of things. T he A natomy

of a

P roposition

A proposition, which is the expression o f a psychological judgm ent (the second act of the intellect), is a linguistic structure that is com posed, as we have seen, of two basic elements— subject and predicate, the recipient of an attribution and the attribution itself. Propositions have the property of convey­ ing a “complete” thought, in the sense that they relate two ideas in such a way as to describe an existential state of affairs, the truth of which m ust be either affirmed or denied. Suppose a friend of yours comes up to you and says “Louis.” You could respond to that one word with some degree of comprehension. You might safely enough surmise, at the least, that the term refers to a male member of the human race. You may actually know someone by the name of Louis, and wonder if that is the person being referred to. W hat if your friend, after saying, “Louis,” then asked, “W ell, do you think that’s true or false?” You would at this point understandably be quite puzzled, and would m ost likely respond,

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ill

“Who is this Louis you’re referring to, and what about him?” In order to affirm or deny something about a subject we need more than just the subject; some­ thing has to be said of that subject, predicated of it. We need more than a single idea, in other words; idea must be linked to idea to form a categorical proposi­ tion. At last your friend comes through with: Louis L ’Amour wrote Westerns. Now you have something you can sink your teeth into. “Louis” has been precisely identified; it is the inimitable Louis L’Amour. He is the subject of the proposition. And what is being predicated of him is the fact that he wrote Western novels. So, we have a proposition, and a proposition has the effect of bringing about a determined resolution of our thought. It tells us something definite, and we can respond to it in definite terms. If what it tells us squares with what we know for sure about the world, then we give our assent to the proposition; we dub it true. In this case, knowing of Louis L’Amour, knowing that he did in fact write Western novels, in abundance, we know that “Louis L ’Amour wrote W esterns” is a true statement. Every proposition, we know, is made up of two basic elements, subject and predicate. Sometimes it takes only two words to construct a bonafide proposi­ tion, as in, “Susan sings.” Singing is predicated of Susan, and she either is or she isn’t; the proposition is either true or false. In a proposition like that, there is no problem at all in distinguishing between subject and predicate. There are other propositions, however, before which we have to pause and consider be­ fore we can correctly identify subject and predicate, and then, within each, we may find some interesting complications. Long, word-laden propositions can give us wheels within wheels. Consider the following example: Jeannie, bored with her job, thoroughly disgusted with and disoriented by the decadent culture in which she was living, homesick for her native land, // finally decided to write to Uncle Petrov and ask him for money to pay for her passage back to Upper Utopia. Like every proposition, this one has but two elements, subject arid predicate, but both are rich in descriptive qualifications. The double bar serves to sepa­ rate the principal subject and predicate of the proposition. We can quickly enough identify its precise subject by citing a single word, “Jeannie”; all the other words in the proposition relate to her. We read that, “Jeannie, bored with her job, thoroughly disgusted with and disoriented by the decadent culture in which she was living, homesick for her native land...” That segment is actu­ ally quite complex, and if we analyze it closely we discover that it has tucked within it no fewer that four distinct propositions, which can be stated explicitly as follows: “Jeannie was bored with her job”; “Jeannie was thoroughly dis­ gusted with the decadent culture in which she.was living”; “Jeannie was disoriented by the decadent culture in which she was living”; “Jeannie was

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homesick for her native land.” The principal predicate of the proposition is also complex in that it is saying two things of Jeannie: that she decided to write a letter to Uncle Petrov, and that she decided to ask him for money. T he L ogical F orm

of

P ropositions

In terms o f its basic structural make-up, every proposition consists mini­ mally o f the conjoining of two distinct ideas. The linguistic link between those two ideas (represented respectively by the subject and the predicate) is called the copula, which always takes the form of the third person, present indicative active, of the verb “to be,” either singular or plural, depending on the number o f the subject. In other words, the copula, either implicit or explicit, is always “is” or “are.” We say that a proposition is in proper logical form if the copula is stated explicitly, as in, “Henrietta is in the third grade,” and, “The Barbarians are on the borders.” However, in eveiyday speech we commonly mouth propo­ sitions in which the copula is only implied: “Victor voted for Smith for president”; “The Korean caucus refrained from revealing their position on the issue” ; “Gilbert gave all his money to the poor.” To put those three proposi­ tions in logicalform we would rewrite them in such a way that in each case the copula is stated explicitly. Thus: Victor is the one who voted for Smith for president. The members of the Korean caucus are the ones who refrained from revealing their position. Gilbert is the one who gave all his money to the poor. In those three propositions, it is respectively the “is,” “are,” and “is” which clearly demarcates the distinction between subject and predicate term. Propo­ sitions in logical form would seldom win any awards for stylistic felicity. However, as logicians our primary concern is not to win Pulitzer Prizes in lit­ erature, but to gain as clear an idea as we can of the distinction, within any proposition, between subject term and predicate term, the importance of which distinction will become increasingly evident as we proceed. Usually we have no difficulty in distinguishing between subject and predicate, but whenever we have any doubts about the matter, that is when we should advert to putting a proposition in logical form, with the result that all ambiguities are then re­ moved: whatever comes before the copula is the subject; whatever comes after the copula is the predicate. Consider the following proposition. “Death to tyrants!” Booth cried, after jumping onto the stage. Some propositions behave themselves very regularly: first comes the sub­ ject, then the copula, then the predicate, as in, “Gary is the team s’s leading scorer.” But this is clearly not the case with the above proposition, so some sorting out needs to be done. A little reflection shows us that “Booth” is the proposition’s subject. A closer look at it reveals that two separate ideas are

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being predicated of Booth. So, in order to make things as explicit as possible, we come up with two propositions put in logical form. Booth is the one who jumped onto the stage. Booth is the one who then shouted, “Death to tyrants!” T he Q uantity

of

P ropositions

We recall the distinction that is made between the comprehension and the extension of a term. A term’s comprehension is simply the meaning of the idea which it signifies. So, if our term is “man” we could easily identify the mean­ ing behind it by citing the classical definition of the term: “rational animal.” And the term’s extension? That would be all those entities to which that defini­ tion applies; in other words, in this case, all human beings now living on the face of the earth, and, for that m atter, all human beings past and future. The entire class of human beings, then, would exhaust the extension of the term “m an.” If we want to make clear, in our language, that we have in mind the exhausted extension of a particular idea with which we are concerned, we use words like “all” or “every.” If we are referring to less than an entire class, not concerned with the full extension of a term, then “some,” or variants thereof, is the proper word of choice. W ords like “all,” “every” and “some” have to do with the quantity of the terms they modify. They tell us how much of the term’s extension is being referred to. Regarded from the point of view o f what is called their quantity, there are two basic types of proposition, general and singular. General propositions, in turn, are divided into universal and particular propositions. Thus, in sum, there are three distinct types of propositions, when regarded from the point of view of their quantity: universal, particular, and singular. The quantity of a proposi­ tion is determined by the quantity of its subject term, that is, by the limits of that term’s extension. A universal proposition is one whose subject term refers to each and every member of the class which it signifies. “Every triangle has three sides” is a universal proposition, as is, “All Marines are in the Depart­ ment of the Navy.” A particular proposition is one whose subject term refers to anything less than the entire membership of the class which it signifies. “Some birds can’t fly,” and “One-third o f the delegation walked out of the conven­ tion,” are particular propositions. A singular proposition is one whose subject term is not a class but an individual, and is most commonly signified by a proper noun rather than by a common noun. Examples: “Aristotle was the stu­ dent of Plato”; “The Mona Lisa is in the Louvre Museum.” Words such as “every,” “all,” and “some” are called logical indicators, and they explicitly inform us o f the quantity of the subject term of a proposition, and hence of the quantity o f the proposition itself. “All” and “every” are the most commonly used logical indicators for universal affirmative propositions, and “no” for universal negative propositions. The most frequently used logical

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indicator to signal a particular proposition, affirmative or negative, is “some,” although there are any number of linguistic expressions that can tell us that the subject term o f a proposition is less than universal in its extension, such as, “a part of,” “m ost,” “m any,” “the m ajority of,” “a few ,” “half of,” “thirteen and three-quarters percent of,” and the like. We should be aware that the word “some” is very versatile, and refers to anything less than the full membership o f a par­ ticular class. Thus, to say “ninety-nine point nine percent” is to say “some.” As mentioned, in most cases a singular proposition is easily recognized by the fact that its subject term is a proper noun. However, a singular demonstra­ tive adjective, qualifying a common noun serving as a propositions’s subject term , identifies the propositions as singular. “This knife is dull,” and “That sonata was written by M ozart,” are singular propositions. The salient charac­ teristic o f a singular proposition is that its subject signifies an individual thing or person— a “one” rather than “many.” By way o f contrast, the subject terms o f a general proposition, universal and particular, alw ays refer to more than one, even though it be only one more than one. A peculiarity regarding singular propositions needs to be noted here. Looked at from a purely grammatical point o f view, there is a clear distinction between singular and general propositions. From the point of view o f logic, however, a singular proposition is treated as a universal proposition. W hat is the rationale behind that? The quantity o f a term, as we have seen, has to do with its exten­ sion. In the proposition, “All canines are vertebrates,” the subject term “all canines” clearly indicates that the extension o f that term is being exhausted; each and every m em ber of the class “canines” is being referred to. Now, in a singular proposition like, “Juanita Carmen Perez lives in Toledo,” essentially the same thing is taking place, with respect to the proposition’s subject term. “Juanita Carmen Perez” refers to one person and one person only, and there­ fore the extension o f the term can be said to be exhausted by that person, in that it does not go beyond that person. Or, it may be explained this way: Because each person, just as a person, is unique, it could be said that each person consti­ tutes a category unto itself, a category in which there is but one m ember, the person in question. Again, we seldom find it hard to determine the quantity o f any proposition. All we need do is look at the logical indicators that qualify the subject term. In a few instances, how ever, we m ust be careful, so that we don’t jum p to the wrong conclusions. For exam ple, in a proposition like, “N ot all canaries are yellow,” one might, first noting the “all” in the proposition (a logical indicator announcing the universal), and then picking up on the “not,” too quickly sup­ pose that what we have here is a universal negative proposition. But a second, keener look at the proposition would tell us that actually it is a particular nega­ tive proposition we are dealing with. The syntactic peculiarities o f the English language are such that the “not all” construction is to be interpreted as “some are not.” “N ot all those who try hard succeed” does not mean, “No one who

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tries hard succeeds,” but “Some of those who try hard do not succeed.” Perhaps they’re in the wrong business. What are we to make of propositions whose subject terms are not graced by logical indicators? Consider the following propositions: The Irish are belligerent. Americans are decadent. What is the quantity of these two propositions? Because they both lack logical indicators, there is no way we can tell. Does the first proposition refer to all Irish or to some; does the second refer to all Americans, or to some? And if both are to be interpreted as “some” propositions, what, in each case, is the precise extent of that “some”? Are we supposed to be thinking of many Irish or only a few, many Americans or only a few? These are questions which, given the actual language of the propositions, we can only guess at. But in logic our ambition is to eliminate guessing. Propositions which lack logical indicators are called indefinite propositions. Here is a general rule of thumb which I propose as the proper way to respond to any indefinite proposition: Treat it as a universal proposition. After doing that, then ask yourself: Can this universal proposition reasonably be assumed to be true? Apropos of the two propositions cited above, our first concern should be to seek some clarification regarding two key terms they make use of, “belliger­ ent” and “decadent.” What precisely is the meaning which is being attached to those terms? Having satisfied ourselves on that score, we next turn to the prin­ cipal issue at hand. Are “All Irish are belligerent,” and “All Americans are decadent” true statements? In any effort to show that they are, the burden of proof would rest heavily on those making the statements. I think most of us would balk at accepting the statements as true, however one might define “bel­ ligerent” and “decadent.” It sometimes happens, in the heat of argument, that people will deliberately use indefinite propositions with the conscious idea in mind that their auditors will in fact take them to be universal propositions. Dick the demagogue de­ clares boldly from the podium, “Lithuanians are lazy!” Then, later, during the question and answer period, when he is called to task for making that reckless statement, he has a Plan B he can fall back on. In plaintive tones of offended innocence he says, “I didn’t say ‘all’, did I?” No, Dick, you didn’t say “all,” but knowing you as we do, we are quite confident that that is what you meant. Let us say that the two propositions cited above were specifically expressed as particulars: “Some Irishmen are belligerent,” and “Some Americans are deca­ dent.” Thus stated, we would not be justified in rejecting them out of hand as false. O f course, we would want to be informed, in each case, of the precise extension of “some,” knowing that it is possible the speakers might be thinking in terms of ninety-nine percent.

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Diagram Summary: The Quantity o f Propositions Propositions General Universal (Every S is P.) T he Q uality

of

Singular (This S is P.) Particular (Some S are P.)

P ropositions

The quality o f a proposition refers to the fact that it is either affirmative or negative. A proposition is either one or the other, with respect to how the copula o f the proposition is being m odified, either affirm atively or negatively. And that points to the need at times, if there is any ambiguity regarding the quality o f a proposition, of putting it in logical form, so that the copula (“is” or “are”) is stated explicitly. Any difficulty that we might run into in determining the quality o f a proposition would almost invariably have to do with negatives. A proposition is negative only when the verb that connects subject and predicate is negative. Some confusion may arise in cases where the predicate terms, but not the copula, is negated, such as in, “Lucille is a non-sm oker.” Despite the negation of the predicate term, that is an affirmative proposition— a universal affirm ative proposition, to give it its precise identification. “Lucille is not a sm oker” is a negative proposition, for in this case we see that it is clearly the copula, “is,” which is being negated. The two propositions mean exactly the sam e thing, but from a logical point o f view they are im portantly different because o f their difference in quality. As we shall see in due course, a lot rides on the quality of a proposition when it comes to determining the extension of its predicate term. M odal P ropositions Any bonafide proposition tells how its subject term relates to its predicate term. A modal proposition tells us, explicitly, just how they relate to one another. There are four distinct ways in which a subject can be related to a predicate in a proposition: necessarily, impossibly, possibly, and contingently. The specific m anner in which the two relate to one another would depend on the peculiar natures of subject and predicate themselves; that is, given the natures of each, how they relate to one another in real life. In other words, the relations that modal propositions express are not merely formal, having only to do with the structure o f the proposition and with no reference to anything external to the proposition. To make that point clearer, suppose that we are presented with a proposition which is expressed symbolically, such as, “S is P.” Then suppose we are asked to identify the mode of that proposition, that is, we are asked to explain just how subject and predicate term are related to one another, according

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to one o f the four categories listed above. We would be stymied. We would have to know what “S” and “P’ stand for before we could tell how they relate to one another. Now let us say that the proposition is so altered to be expressed as follows: “S is necessarily P.” We would now know that, according to its form, it is a modal proposition, for it is explicitly stated as such. But because we still do not know what “S” and “P” stand for, we have to assume that whatever they might refer to in the real world would in fact be related to one another necessarily. Let us continue this little investigation by supposing we are told that “S is necessarily P” stands for “Michelangelo’s Pietti is necessarily in Rome.” At that we would be obligated to balk, for although it is indeed a fact that Michelangelo’s great sculpture is in Rome, it is not a matter of necessity that it be there. The nature o f the Pieta does not demand that it be in Rome, and it would not cease to be just what it is if it were somewhere else. There is no necessary connection between subject and predicate in the proposition. The only way we can be certain that a symbolically expressed modal proposition is what it claims to be is to know the referents for the subject and predicate terms and ascertain precisely how they relate to one another in real life. The proposition which puts the Pieta necessarily in Rome must be declared false. But “S is necessarily P” would be quite true were it to represent the English language statement that, “Man is necessarily mortal.” Once again, there are four ways in which subject can relate to predicate— necessarily, impossibly, possibly, and contingently. We need now to acquaint ourselves with each of those modes of relationship. The subject and predicate o f a proposition are related necessarily if, given the meanings of each, they cannot be separated from one another. Consider the proposition cited just above, “Man is necessarily mortal.” Given the very nature of human beings, the melancholy fact o f mortality is part and parcel of what they are; any right understanding o f them must necessarily include the fact of their being mortal. A less immediately obvious example would be, “Man is grammatical.” Here too subject and predicate terms bear a necessary relation to one another, although it is not stated explicitly. This is the case because the predicate is a property of the subject. A human being is by essence a rational anim al. A m ong other things that ratio n ality necessarily entails is grammaticalness, the capacity for language; thus grammaticalness is recognized as a property because, you may recall, it is something which is inseparable from essence. Where you have a human being you have necessarily a rational creature, and where you have a rational creature you have someone who necessarily has the capacity for language. To make explicit the nature of the relation between the subject and predicate in the proposition, we restate it as follows: “Man is necessarily grammatical.” “Man cannot be immortal.” This proposition asserts that it is impossible that immortality be predicated of human beings. Because it is of the very nature of human beings that they are mortal, it would be a clear contradiction to claim

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the opposite. To put the truth o f the matter in explicit modal language, we say: “It is impossible that man is immortal.” There are any number o f things in real life that are com pletely incom patible with one another and which therefore block the possibility of their ever being conjoined. “It is impossible that a circle be a square.” “It is im possible that a seal can learn Old Slovanic.” “It is impossible that light travels faster than 186,000 miles per second.” Consider this proposition: “Cyril knows Greek.” The proposition refers to an actual matter of fact, and therefore it is true. Cyril does indeed know Greek, and rather impressively so. But what is the nature of the relation between Cyril and his knowledge of Greek? We could not call it a necessary relation, for if that were the case it w ould be o f his very nature, as a human being, that he would know Greek. But we know that not to be the case, for at one time Cyril did not know Greek, and it was only through years o f assiduous study and application that he came to master the language. But before Cyril knew Greek, he was not one whit the less a human being. Could we say that there is an im possible relation between Cyril and his knowledge of Greek? Obviously not. Nothing more emphatically proves possibility than actuality. The fact that Cyril actually knows Greek right now incontestably demonstrates that it was once possible for him to learn the language, and he realized that possibility. Making all this modally explicit, we say: “It is possible for Cyril to know Greek.” This seems like a rather anemic way of putting it, given the fact that Cyril actually does know Greek, but the modal proposition simply aims to make explicit the nature of the relation between subject and predicate, to explain an actual relation by the fact that it was antecedently a possible one. The nature of a possible relation is clearly grasped by thinking o f it as just the opposite of an impossible relation. “Man is musical” expresses a contingent relation between the subject and predicate. Human beings vary as to the quality of their musicalness. Some people are very musical, others scarcely at all, but the latter group are no less human for their lack o f m usicalness. M arvin, as it happens, is one o f those who is very m usical. His im pressive m usicalness is a m atter o f fact, but we say that it is a contingent matter of fact because it need not to have been so, and there is no contradiction in supposing that it could have been otherwise. “It is contingent that Marvin is musical” is what we say by way of expressing the situation in modal form. Just as the possible relation is most clearly seen as opposite to an impossible relation, so, comparably, a contingent relation is best seen as the opposite to a necessary relation. Necessary relations are those which are so and must be so; contingent relations are those which are so but not nec­ essarily so. They could be otherwise. A salient difference between propositions that involve possible relations and those involving contingent ones lies in ac­ centuation. Possible propositions accent the positive, and can be expressed as “S may be P”; contingent propositions accent the negative, and can be expressed as, “S need not be P.”

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Necessary and impossible relations provide us with certainty concerning the subject and predicates which they govern, for in the case of the former we know for sure, given the respective natures of each, that a particular predicate must be attributed to a particular subject (e.g., “A trilateral plane figure is trian­ gular”), and in the case of the latter it is as clear as day to us that there is no way in the world that a particular predicate can be attributed to a particular subject, and this is spelled out in a proposition like, “It is impossible for a triangle to have more than three sides.” Possible and contingent relations, on the other hand, can provide us with probable knowledge only, in the sense that, even though a given proposition be true as stated, and therefore faithfully reflects reality, the nature of reality is such that there would be no contradiction if things in the real world would be otherwise than as the proposition says they are. It would not be an impossible situation if Cyril did not know Greek, nor is it necessary that Marvin should be musical. In ordinary usage we seldom feel the need to express in explicit terms how the subject and predicate terms of our propositions relate to one another. The fact that human beings are mortal creatures is generally understood, and we don’t have to rub it in by saying, “Man is necessarily mortal.” But we have to be careful that we do not apply modality incorrectly in our language, and thus distort an actual situation. In my frustration over his lack of application to his studies, I might say, “There is no way that Jason is going to pass the final exam,” suggesting that failing the exam must necessarily be predicated of him. But in fact there is no necessary relation between the two; the relation is con­ tingent. Jason may indeed flunk the final. On the other hand, he might experience a transforming epiphany two weeks before the event, put in days and nights of dedicated cramming, and end up passing the exam after all, my foreboding conjectures to the contrary notwithstanding. It is also possible for us to get careless about the distinction between possible and impossible relations, and in our exuberance declare certain things to be possible which, if we were to stop and give them some sober thought, we would have to admit that they are in fact well out of the realm of possibility. T he D istribution

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When we speak of the distribution of a term we sire referring to the extent of the application of the term to the members of the class it signifies. A distributed term is one that applies to each and every member of the class it signifies; this m eans that a distributed term is the same thing as a universal term. An undistributed term is one that applies to any quantity of a class which is less than its full membership; from that we can see that an undistributed term is the sam e thing as a particular term. “All antelopes” and “no nannies” are distributed terms; “some snowballs” is an undistributed term. The distribution o f a term tells us, with m ore or less precision, how many individuals the term is referring to.

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In our treatment o f the quantity o f propositions, we saw that it is the quan­ tity o f the subject terms— its distribution— which determines the quantity of the proposition as a whole. W e also saw, apart from the possibly problematic nature of indefinite propositions, that it is quite an easy matter to determine the distribution o f subject terms: all we need do is look to the logical indicators that govern them. Those logical indicators do our work for us, clearly identify­ ing the term s they m odify. But how are we to determ ine the extension or distribution of predicate terms, for here we have no logical indicators to help us out. (Logical indicators could be inserted in a proposition to indicate the distribution of predicate terms, but it would make for rather clumsy language, and not reflect the way we normally think and speak.) Logic provides us with two sim ple rules which allow us unerringly to determine the distribution o f predicate terms. Rule One: The predicate terms of negative propositions are always distributed. Rule Two: The predicate terms o f affirmative propositions are always undistributed. The reasoning behind the first rule, governing negative propositions, is easy enough to grasp. Consider the proposition, “No insects are m am m als.” The idea being communicated by this proposition is that the entire class o f insects is separate from the entire class of mammals. “M am mals,” then, the predicate term, is distributed. Each and every member of the class of mammals is being taken into account here. A handy way by which we can prove the distributed nature of a predicate terms in universal negative propositions is by reversing the subject and predicate terms; by doing so we discover that the new proposi­ tion, with reversed subject and predicate terms, means the same thing as the original proposition. There is no difference in meaning between, “No insects are mammals,” and, “No mammals are insects.” The first rule applies equally to particular negative propositions as it does to universal negative propositions. In the proposition, “Some women are not mothers,” the logical indicator “some” makes it clear that the subject term is undistributed. And because “mothers” is the predicate term of a negative propo­ sition, we know that its is distributed, or universal. The entire class o f mothers is separated off from a part of the class of women. The second rule tells us that the predicate terms of affirmative propositions are always undistributed, or something less than universal. For an example of a universal affirmative proposition we will consider, “All felines are carnivo­ rous,” the subject o f which, the logical indicator infallibly informs us, is distributed. And because this is an affirmative proposition, its predicate term, “carnivorous anim als” (to fill the term out a bit), is undistributed. In every universal affirmative, it should be noted, the subject term relates to the predi­ cate term as a smaller class to a larger one. This being so, what is happening in such a proposition, regarded logically, is that a smaller class, here “felines,” is

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being located within a larger class, “carnivorous animals.” But notice this as well: the first class is not coterminous with the second; it does not cover it completely, does not exhaust it. In other words, what the proposition is telling us, to make explicit the extension of the predicate term, is that all felines are some carnivorous animals. Thus the predicate term is undistributed. This is made quite clear if we were to reverse the subject and predicate term, with the supposition, in doing so, that the predicate term is to be regarded as distributed. We would end up with the proposition, “All carnivorous animals are felines,” which is a false statement— against which all the crows and vultures of the world would cry out in lusty protest. That the predicate terms of particular affirmative propositions are undis­ tributed is perhaps more immediately obvious to us than is the case with universal affirmatives. When we aver that “Some girls are Vietnamese,” we are not making reference, in that predicate term, to the entire class of Vietnamese, but to only a part of it, to that part of it which is in fact made up only of girls. We can clearly see how this is so if we reverse the subject and predicate terms of the proposition, understanding the predicate to be— what in fact it is— un­ distributed. We would come up with, “Some Vietnamese are girls,” which is as true as the original proposition. D iagraming P ropositions By using some very simple diagrams we can produce a visual image that can help us better to see how, in each of the four general propositions, subject term relates to predicate term. A universal affirmative proposition can be sym­ bolically expressed as, “All S are P.” That proposition can be diagramed as follows.

The diagram tells us that the class designated by “S” is completely enclosed within the larger class designated by “P.” It says that there are no “S’s” which are not “P’s,” or, to put it in another way, it shows that all “S’s”. are some “P’s.” A universal negative proposition may be symbolically expressed as, “No S are P.” Its diagram would take this form: S

P

The diagram leaves no ambiguity about the fact that the class “S” is completely separated from the class “P.” They have nothing to do with one another. The diagram also makes clear that each class, because presented whole and entire, is distributed.

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“Some S are P” serves as a symbolic expression of a particular affirmative proposition, and it is diagramed thus:

The diagram informs us that there is a definite overlapping relation between class “S” and class “P,” in that, as a matter of fact, there are at least some S that are P. To indicate this positive comm unication between the two classes, we place an “X” in the space where the two rectangles overlap, as shown in the diagram. The fourth type of general proposition is the particular negative, symboli­ cally expressed as, “Some S are not P,” and diagramed as:

S X

P

As is the case with the particular affirmative, this proposition is asserting some­ thing about part of “S,” but here the emphasis is negative, and we are being told that it is definitely the case that there are at least some “S” that are not “P.” To indicate that emphasis, we place an “X” in the “S” rectangle that is outside the “P” rectangle. Whether or not there may be some “S” that are also a part of “P” remains an open question. All that the proposition explicitly claims, and which is shown by the diagram, is that it is an undisputed matter o f fact that some “S ’s” are to be found outside of the realm of the “P’s.” (See Appendix B for a brief note on diagraming propositions.) P ropositions A re E ither T rue

or

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We have seen that ideas cannot correctly be identified as either true or false. It is only when idea is conjoined to idea, to form a proposition, that “true” or “false” becomes a proper response. “Racoon” is neither true nor false, but “There is a racoon in the backyard” must be one or the other. It is either a real fact, or it isn’t. W hen a proposition is expressed symbolically, as in, “All S are P,” where “S” and “P” can respectively signify anything at all, I may assume, for logical purposes, that that represents a true proposition, but it is only when a proposition is stated in ordinary language, where the subject and predicate terms refer to real objects in the objective order, that I am able to ascertain with full confidence the truth or falsity of a proposition. Let’s say “S” stands for “Queen Elizabeth I,” and “P” for “was the daughter o f King James II.” Because that assertion does not square with the actual historical facts o f the matter, we unhesitantly declare the proposition to be false. There are some propositions that can be seen to be either true or false at a glance, simply by reason of knowing the comprehension (i.e., the meaning) of

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subject and predicate, and how they relate to one another. Such would be the case, for example, with propositions that express definitions, as with, “Man is a rational anim al,” or, “A triangle is a plane, three-sided figure the sum of whose internal angles equals 180 degrees.” In propositions of this kind, the predicate term, before it is explicitly stated, could be said to be contained within the subject term. And the two terms are equivalent in the sense that you could reverse the subject/predicate order of the two propositions above and not alter the meanings of the originals. In sum, with propositions of this kind one does not need to appeal to anything beyond the proposition itself in order to deter­ mine its truth or falsity. Again, you simply have to understand the meanings of the subject and predicate terms. It is rare, however, in our ordinary everyday language, that we make state­ ments in which the predicate is the definition of the subject. And this means that in the vast majority of instances we have to go beyond the statement itself, and appeal to its referents, in order to tell whether it is true or false. Let’s re­ view some basic facts pertaining to how we come to have knowledge of our world. An idea is a sign, a formal sign, of an existing entity, a thing in the extra­ mental world. A term, or word, is a sign of an idea. A term, then, is an indirect (i.e., working through the medium of an idea) linguistic representation of the real-world object to which it refers. When, by the second act of the intellect, judgment, we compose or divide ideas, and express the results of those opera­ tions in the form of propositions, we are working within the realm of logical truth. Propositions, we have learned, are the linguistic vehicles by which logi­ cal truth is expressed, so that any proposition must be either true or false. We have also learned that logical truth is dependent on ontological truth, which stands to reason, for the truth o f what we say must necessarily rely on the truth of what actually is. T he C orrespondence C riterion

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What does it mean, in more specific terms, to say that logical truth depends on ontological truth? Simply that there is a clear, reliable connection between the mental world and the extra-mental world, between what we say and what is actually the case. And that describes the correspondence criterion fo r truth. According to this criterion, which is absolutely foundational for logic, any par­ ticular proposition is true if there is a correspondence between what the proposition asserts and that to which, in the objective order, it refers. And given the fact that the words in a proposition are signs of ideas, the more elementary correspondence is one between ideas in the mind and facts in the world. “The cat is in the kitchen” is true if there is a real cat, a real kitchen, and the real cat is really in the real kitchen. If there is a discrepancy between what a proposi­ tion asserts and what is actually the case, if, that is, the relevant observable facts do not corroborate its assertion, the proposition is false. There is a break­ down between the proposition and reality.

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If any given proposition is compatible with, fits coherently into, an already accepted set o f ideas— such as a particular philosophy, or economic system, or scientific theory— then that proposition is considered to be true according to the coherence criterion o f truth. For example, a physicist comes up with a new theory relating to a certain aspect of gravitational force. After several other physicists carefully study the theory, they accept it as very probably true be­ cause it is consonant with Einstein’s General Theory of Relativity, which these physicists regard as being in the main a sound and reliable account of physical reality. In sum, the theory is taken to be true because it jibes with an already established theory which is regarded to be true. Another example: Professor Ernst Popover proposes a novel thesis pertaining to human history which, after being minutely examined by a select committee o f Hegelian philosophers, is declared to be true by them because it nicely conforms to the Hegelian theory of history. O f the two criteria for truth, the correspondence criterion is the more basic, and the coherence criterion is ultimately reliant upon it. Appeal to the coher­ ence criterion can serve as a handy first step in determining the truth or falsity of any proposition, but it is inadequate as the final determinant. Whether or not we are justified, in any particular case, in identifying a proposition as true be­ cause it is harmoniously compatible with an already accepted set of ideas would, in the final analysis, depend altogether on the reliability of that set of ideas. It is safe enough to say that Proposition X is true because it agrees with Theory Y, but that way of thinking is trustworthy only to the extent that Theory Y is itself trustworthy. Sooner or later the correspondence criterion has to be called upon, and applied to Theory Y. We have to ask ourselves: Does Theory Y itself faith­ fully reflect the real world? Does it correspond to the way things really are? P ropositional T ruth I s A bsolute T ruth If a proposition is true, it is absolutely true. There is no other way for it to be true. That might come as a shock to people who are inclined to attach too much weight to the word “absolute,” and are unaware o f how we use it in logic. To say that a proposition is absolutely true is simply to say that it admits of no exceptions, and that it is immutable as stated. The m athematical statement, 3 + 4 = 7, is absolutely true, for it admits of no exceptions; it was true yester­ day, it is true today, and it will be true tomorrow. We may make bold to say that it will be true forever. And the same thing can be said of statements like, “George Washington was the first president of the United States,” and, “Babe Ruth hit sixty home runs in 1927.” The principle of excluded middle applies in an especially pertinent way to the matter of logical truth, the truth of propositions. There is no middle ground, no intermediate possibility, between True and False. With respect to proposi­

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tions, there are no degrees of truth or falsity; it is either one or the other. No proposition, precisely as stated, can be more or less true, or more or less false. It faithfully reflects the circumstance to which it refers, or it does not. All this does not mean, of course, that from the point of view of our knowl­ edge of any given circumstance, we cannot be hesitant about a proposition that is referring to it, uncertain as to whether the proposition is true or false. This is, in fact, a rather common experience for us. But it reflects more on the quality o f our knowledge, not on the quality of the proposition itself, as being either true or false. Objectively considered, it is, as stated, exclusively one or the other. A proposition takes an existential stand with respect to the objective order to which it refers. It asserts, say, “All S are P.” Now, the principle of excluded middle tells us that S is either in fact P, or it is not; there is no other alternative. And the principle of contradiction comes along to assure us that, if S is in fact P, then it cannot at the same time and in the same respect be P and not-P. So, the assertion that “All S are P” must be either unqualifiedly true or unquali­ fiedly false. But m ight not the claim that every proposition, if it is true, is always and only absolutely true, be a bit too strong? Consider this situation. I hear it said of Vincent, whom I happen to know rather well, “Vincent is a vacillating char­ acter.” I thoughtfully respond to this assertion by saying, “Well, that’s somewhat true.” And isn’t that response, or something like it, a fairly common way we react to many of the assertions we hear on a more or less regular basis? We don’t reject them as being altogether false, but neither do we accept them as being altogether true. We often use phrases like “more or less true,” “half right,” and “partially true” in responding to propositions, and in doing so are not un­ der the impression that we are acting in a wantonly illogical way. And in fact we aren’t. But doesn’t that then undermine the notion that every statement is unqualifiedly either true or false? No, it doesn’t. Let us consider the matter more closely. Going back to what I said in my response to what was asserted about Vincent, if I were to stop and reflect on what I was attempting to convey by it, I would see that what I meant to say in describing the statement as “somewhat true” is that I could not accept the statement as true precisely as stated. Knowing Vincent as well as I do, I am aware that, yes, sometimes he behaves in a vacillating fashion, but I am also aware that there are times when he can be anything but vacillating, can be in fact impressively decisive. Therefore I consider it to be a distorting exaggeration to describe Vincent as a vacillating character. What this comes down to, after I stop to think about it, is that I regard the statement, “Vincent is a vacillating character,” to be J u s t as stated, a false statement. It does not accurately report the actual state of affairs regarding Vincent. When­ ever we respond ambivalently to propositions by calling them “partially true,” or the like, we are really saying that, as stated, they are not true at all. The

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remedy? The propositions have to be rephrased so that they faithfully reflect reality. To what I heard said about Vincent I could offer, as a corrective, “Vincent is sometimes vacillating, and sometimes not.” But are there not some statements that can rightly be said to be neither true nor false? Consider this example: “The dog is in the living room.” Now, as I check on the exact state of affairs at the moment, I discover that the dog, the ever faithful Rover, is lying in the doorway that separates the living room from the library, fast asleep. Does not that circum stance allow us to say that the claim that the dog is in the living room is neither unqualifiedly true nor false, and that we might be justified in saying that it is half true? No. The statement, “The dog is in the living room ,” given what is actually the case, can only be false, for by any reasonable understanding of normal usage, when we say that a thing is “in” a room , we mean that the thing is clearly and unambiguously within the physical confines of the room. If that is not the case we should say otherwise. Given the indisputable fact that Rover’s canine carcass is half in the living room and half in the library, then only a proposition that faithfully re­ ports that circumstance can be true. Two possibilities: “The dog is half in, half out of, the living room .” “The dog is lying in the doorway between the living room and the library.” We must make our propositions as precise as possible; only then can they be indisputably true.

Review Items 1. W hat is a first principle? 2. W hat is a categorical proposition? 3. What does the quantity of a propositions refer to, and how is it determined? 4. W hat do we mean by the quality of a proposition? 5. What is a modal proposition? 6. What is the difference between a distributed term and an undistributed term? 7. W hat is the distribution of predicate terms of affirmative propositions, and of negative propositions? 8. What is the correspondence criterion of truth? 9. W hat is the coherence criterion of truth? 10. What is meant by saying that every true proposition is absolutely true?

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Exercises A. Identify the quantity and the quality of the following propositions. 1. All that glitters is not gold. 2. A majority of the electorate went to the polls. 3. Most Texans eat hamburgers. 4. Sylvester did not hesitate. 5. Every effort failed. 6. Each of the nuns of the Carmelite community was executed. 7. The greater part of the class disagreed with the teacher. 8. This is a non-starter. 9. Ninety-nine percent of the eggs were rotten. 10. Some people do not pray. B. Identify the distribution of the subject term and the predicate term of each of the following propositions. 1. No contracts are non-negotiable. 2. Celia was not a member. 3. Few Minnesotans were socialists. 4. Every participant at the conference was a citizen of Germany. 5. Some judges are not elected. 6. Only a handful of the diners were not vegetarians. 7. St. Louis of France did not die in France. 8. None of the resignations was accepted. 9. Every man is mortal. 10. Sixteen percent of the applicants were Hispanic.

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Chapter Seven The Varieties o f Propositions C omplex P ropositions A simple proposition is one which predicates a single predicate of a single subject. “John is a sophomore” and “Nancy plays the flute” would be examples. A complex proposition is one that has more than a single subject, or more than a single predicate. The following would be examples of complex propositions: Curly, Moe, and Larry got a job at the golf course. Lydia went to Paris, met Pierre there, and married him in June. The first proposition is complex by reason o f its subject; it in fact contains three subjects. The second proposition is com plex by reason of its predicate, for three separate things are being predicated o f Lydia. Propositions o f this kind are called exponibles, which means that they tire propositions which, just as they stand, need further explanation in order to make as clear as possible the ideas that are being communicated through them. Though at first glance these propositions might look as if they are simple, in fact they are not. Their com­ plexity consists in the fact that they are m ade up o f more than one simple proposition. To bring this fully into the open, to make explicit the implicit, we restate complex propositions by breaking them down and spelling out the indi­ vidual simple propositions of which they are composed. Thus, the first of the above com plex propositions would yield the three following simple propositions. Curly got a job at the golf course. Moe got a job at the golf course. Larry got a job at the golf course. The second complex proposition would also yield three simple propositions, this time because of the complexity of its predicate. Lydia went to Paris. Lydia met Pierre in Paris. Lydia married Pierre in June.

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There is nothing to preclude a proposition’s being complex by reason both of its subject and its predicate. Consider this proposition: “Jack and Jill went up the hill and fetched a pail of water.” In this proposition there are four separate simple propositions, which are spelled out explicitly as follows: Jack went up the hill. Jack fetched a pail of water. Jill went up the hill Jill fetched a pail of water. Reducing complex propositions to simple ones is not merely an idle exer­ cise to wile away the time on rainy afternoons. It is a means by which we make fully intelligible propositions which, as presented, may not be such. And we do this by making explicit just what specific idea is being associated (or dissoci­ ated, in the case of negative propositions) with just what specific idea. The common mental process we are engaging in when we do this is called catalysis, whereby we break down complex entities into the simpler components of which they are made. A principal advantage of dealing with simple propositions is that it is much easier to determine their truth value, because they have but a single subject and a single predicate. When we think logically, what we are most concerned about in any proposition is whether it is true or false. That should be regarded as the “bottom line” with respect to any proposition. A not unusual problem we can run into with complex propositions is that they may not be true in all their complexity, and it is only when we break them down into their constituent simple propositions, then check each of those simple propositions against their referents in the objective realm, that we make this discovery. Consider one of the examples cited above, concerning Curly, Moe, and Larry getting a job at the golf course. Let us say that, after we reduce that complex proposition into its three simple propositions, then measure each of those against the real-world situation, we find out that, though Curly and Moe did indeed get a job at the golf course, Larry did not, his application having been rejected because he made a very bad impression in his interview. The original complex proposition was therefore false as stated, and it was only by submitting it to closer analysis that this was brought to light. C ompound P ropositions A compound proposition is one which is composed of at least two simple propositions, and this composition is made explicit by the language of the propo­ sition itself. No analysis is necessary. The chief difference between a complex proposition and a compound proposition is the difference between the implicit and the explicit. Complex propositions are implicitly compound propositions, whereas compound propositions are explicitly so. There are three basic types of compound propositions: conjunctive propositions, disjunctive propositions, and conditional propositions. A conjunctive proposition is one whose simple

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propositions are conjoined by “and.” Disjunctive propositions are “either.. .or” propositions; they offer us alternatives. A conditional proposition is o f the “i f .. .then” variety, where a condition is placed upon the possibility of som e­ thing being true. In this chapter we will concentrate our attention on conjunctive and disjunctive propositions, and on the kind o f thought processes which they embody. The treatment o f conditional propositions, and the interesting form of reasoning they involve, will be saved for a later chapter. Inference , A gain At this point in the course we need to jo g our memories a bit regarding one o f the key concepts o f logic, introduced in the first chapter, and that is the concept o f inference. Inference is that mental move whereby we conclude to a new truth on the basis o f another truth we are already certain about. I begin with som ething which I know for sure is true, call it A, and from that I see that B m ust also be true. The two are associated in such a way that A could not be true without B also being true. So, it is said that I infer B from A. And I am able legitimately to do that because A entails B. The nature o f the relation between A and B is such that the truth o f B is implied by the truth o f A, and the function o f inference— w hat we might call the “inferential move”— is to make explicit, to draw out o f A and bring into the full light o f day, the truth o f B, which is, as it were, tucked away neatly inside A. W e are justified in having the greatest confidence in any inference we make w hen we can clearly see that there is a necessary bond betw een the inferred truth and the truth from which it is inferred, so that, given the truth o f A, it is inescapably the case that B is also true. Given the tight connection that exists between being a citizen o f Peoria and a citizen o f Illinois, in that you cannot be the first w ithout also being the second, then, if I know for a fact that Paul is a home-owning, tax-paying citizen of Peoria, with supreme assurance I can con­ clude that Paul is a citizen of Illinois. Being a Peorian entails being an Illinoisan. Likewise, from the fact that mysterious Person X gave birth to a baby, I have no hesitancy in inferring that m ysterious Person X is a woman. Granted, nei­ ther o f these inferences is particularly earth-shaking, but, modest though they be, inferences they are. C o n ju n ctive P ropositions By a conjunctive proposition we m ean a com pound proposition whose sim ple propositions are linked together by the conjunction “and.” The follow­ ing is an exam ple o f a conjunctive proposition: C harlie is a student at the University of Oklahoma and is majoring in history. T hat innocent looking little “and” that connects the two sim ple proposi­ tions carries a good deal o f logical weight. It means that the proposition must

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be considered in its entirety in determining whether it is true or false. In other words, in order for a conjunctive proposition to be able to pass as true, all o f its conjuncts (the simple propositions which compose it) must be true. If any one conjunct is false, then that renders false the proposition as a whole. And as we saw in the previous chapter, we cannot get away with saying that such a propo­ sition is partially true, or something like that. In the case of the above proposition, it can only be true if it is a fact that Charlie is actually a student at the Univer­ sity of Oklahoma, and he is actually majoring in history. If it should be revealed, upon judicious investigation, that though Charlie is indeed a student at Okla­ homa, but that his major field is chemistry, then the entire proposition goes down in flames. That is the nature of conjunctive propositions. And it goes without saying that if both of the conjuncts are false (Charlie is really enrolled at the University of Wisconsin, where he majors in German), the conjunctive proposition that tells us otherwise would be totally fraudulent. With conjunc­ tive propositions, then, it is a matter of all or nothing: each and every conjunct must be true in order for the proposition itself to be true. Now, one might be tempted to think that if confronted with a conjunctive proposition containing a great many conjuncts— let’s say ten—we would be justified, if nine of those ten conjuncts are true, in letting the proposition as a whole pass as true. After all, getting ninety percent of something right is pretty good. But that kind of thinking does not apply here. Once again, it is a matter of all or nothing. One bad apple is cause for rejecting the entire barrel. Con­ sider the following proposition: “Ulysses S. Grant was bom in Point Pleasant, Ohio and graduated from West Point and served in the Mexican War and was commander of the Union armies and received Lee’s surrender at Appomattox and was the nineteenth president of the United States.” That’s a rather impres­ sive statement, despite the stuttering effect produced by all those “and’s,” and every item in it is true except the last. Grant was the eighteenth, not the nine­ teenth, president of the United States. That one false item poisons the entire proposition. Only a little reflection is needed to appreciate the basic logic of a conjunc­ tive proposition. Put yourself in a situation in which someone makes a statement to you in the form, “A and B and C,” where each of the three letters stands for a simple proposition. When presented with a statement of that kind, do we not naturally assume that each of its component parts is true? And would we not feel that we were the victim of willful deception if we found out later that one or another of the statement’s components was false? We understand the force of “and” to be such that the import of the statement is, “A is true and B is true and C is true.” A conjunctive proposition stands or falls as a whole, on the basis of the integrity of each of its parts.

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D isjunctive P ropositions A disjunctive proposition is a compound proposition whose simple propo­ sitions, which in this case are known as disjuncts, are conjoined by the word “or.” Disjunctive propositions reflect a very common mode of thought, wherein we consider alternatives— “either.. .or” type thinking. Disjunctive thinking is a response to those real-life situations in which there is more than one possibil­ ity that has to be considered. A conjunctive proposition, if true, presents us w ith a set o f ideas all o f which are true. A disjunctive proposition is more flexible in that respect. Like a conjunctive proposition, which must have at least two conjuncts, a disjunctive proposition must have at least two disjuncts. And as is also the case with conjunctives, it is possible to have, with a disjunc­ tive proposition, an indefinite num ber o f disjuncts, as in a proposition of the form, “A or B or C or D or E.” But to overload either type of proposition would be self-defeating, for the human mind can handle only so much information in a single serving, and an excess o f “and’s” or “o r’s” would discom bobulate even the m ost alert and attentive o f audiences. In exam ining the disjunctive proposition here, we will be using its simplest expression, where there are but two disjuncts, the fam iliar “either this or that” formulation. W hereas in a conjunctive proposition each o f its elements must be true if the proposition as a w hole is to be true, the condition that must be met in a disjunctive proposition, if it is to be true, is that at least one o f its elements must be true. Common sense quickly recognizes the logic that is at work here. Imagine that a friend comes up to you, extends toward you two closed hands, and tells you that in one o f them there is a silver dollar. If you pick the correct hand, you get the silver dollar. You are faced with a classic e ith er.. .or type situation. You point to your friend’s right hand. He opens it. No silver dollar. Ah well, so it goes; you win some, you lose some. But then your friend opens up his left hand. No silver dollar there either. You would not be amused; you would very likely feel that you had been deceived, perhaps even have the vague sense, now that you are studying logic, that some seminal principle of reason­ ing had been violated. And on that last point you would have been quite correct. W hen we pause to consider it carefully, we recognize that the very intelligibil­ ity of an either.. .or situation depends upon the fact that one of the alternatives m ust be a real alternative. If, in the proposition “A or B,” neither A nor B is true, if neither is a live possibility, then the proposition is false. It represents a fraudulent use o f a particular linguistic structure and the logic upon which it depends. So, then, in a disjunctive proposition at least one of the disjuncts must be true; it must offer a genuine option. But there is nothing to preclude the possi­ bility o f both o f them being true; that would represent a legitim ate state of affairs for a disjunctive proposition, which is reflected in what is called an inclusive disjunctive. It is called inclusive because it includes the possibility that both disjuncts, A and B, can be true. Imagine a different outcome in the

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example I used above. You point to your friend’s right hand, he opens it, and voila! there’s the silver dollar. As you are contentedly pocketing the coin, your friend opens his left hand, and there’s a silver dollar in that one too. You doubt­ less would be a bit puzzled by that turn of events, for when your friend extended his two closed hands and asked you to take your pick, you were naturally under the assumption that a silver dollar was going to be in one or the other hand, but not in both. That is what we would all normally expect. But the basic structure of a disjunctive state of affairs, an either.. .or situation, which demands that at least one of the options offers a real possibility, does not preclude both of them from doing such, depending on the nature of the options being presented and how they relate to one another. By reason o f the fact that your friend had a silver dollar enclosed in both of his hands, he was graciously presenting you with a no-lose situation. Life should always be that nice to us. Consider the following proposition: Either Paul will go to law school next fall or he will get married to Pauline. This is an inclusive disjunctive proposition, for it can readily be seen that, though Paul may go to law school next fall and not get married to Pauline, or though he may marry Pauline and forget about law school for next fall, there is nothing in the nature of either option, and how they relate to one another, to prevent him from doing both. His doing either one does not automatically rule out the possibility of his doing the other as well. But now consider this proposition: Benjamin either died of pneumonia in 1999 or he is now living incognito in Argentina. Here we have an example of an exclusive disjunctive, called such because it excludes the possibility that both of the disjuncts could be true, by reason of the fact that they are totally incompatible with one another. They cannot possi­ bly both be true, nor, for that matter, can they both be false, for as we saw with inclusive disjunctives, that would do violence to the basic logic of a disjunc-. tive proposition. In an exclusive disjunctive, the disjuncts relate to one another as contradictories. If one is true, the other must be false; if one is false, the other must be true. We can more clearly see how this is so if we focus on the key idea in each of the disjuncts of the proposition cited above: death, in the first; life, in the second. Those two, life and death, are strictly exclusive, for perforce of necessity it must be one or the other; it can never be both. Here are some further examples of exclusive disjunctive propositions. Either the entire orchestra went on tour or some of its members did not. Viola either stole the money or she didn’t. Either the rocket reached the height o f50,000 feet or it fell short of that altitude.

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In formulating disjunctive propositions we need to take care that we have a sufficient grasp o f the ideas we are dealing with in them , so that we do not propose as an exclusive disjunctive what is in fact an inclusive one, or vice versa. Politicians are easily given to the habit o f proposing as exclusive disjunctives what, if closely examined, are discovered not to be so. “Either this bill m ust pass,” Senator Bluster declaim s, “or the country will be faced with imminent economic collapse.” Really? Does that accurately describe the situa­ tion at hand? Giving the m atter our full attention, we first subm it the bill in question to careful scrutiny, then we reflect carefully on general economic con­ ditions. Having done that, we m ight be prepared to admit that it would not be o u t-an d -o u t irrational to give some credence to the senator’s disjunctive as­ sertion. But weighing all things judiciously, we simply cannot see that we are faced with a strict, mutually exclusive choice: we choose to pass the bill, and thus avoid economic collapse; or, alternatively, we effectively choose economic collapse by refraining from passing the bill. Reason tells us that there are other possibilities which the senator’s way of stating the case does not encourage us to consider. One possibility is that the bill could pass, and economic collapse ensues anyway, demonstrating that the bill did not have the saving effects which had been claim ed for it. A nother possibility is that the bill could fail to pass, and yet economic collapse does not come about after all. To these, in fairness, we add the two possibilities proposed by the senator: a passed bill followed by economic recovery, a rejected bill followed by economic collapse. Taking the situation all in all, we see that it is more complex than the senator would have us believe, and that there are more possible outcom es than he is willing to propose. Recommendation: he should tame his use of exclusive disjunctives. There is another factor that has to be considered in situations such as the one just described, which makes all the more risky the careless use of exclusive disjunctives, and that is the factor of future contingencies. When one puts an exclusive disjunctive in the future tense— “Either A will happen or B will hap­ pen”— the precariousness o f the claim is made obvious by the fact that no one can say with certainty today how things are going to play out tomorrow. To be able to determine the truth or falsity o f an exclusive disjunctive proposition, we have to be able to see, here and now, whether or not its disjuncts are mutu­ ally exclusive, which is precisely what we are unable to do if they are projected into the future. Inferences T o B e D rawn D isjunctive P ropositions

from

C onjunctive

and

B ecause we know that for a conjunctive proposition to be true all of its elements m ust be true, we can therefore with serene confidence assume any single one o f those elements to be true. This a very modest inferential move, and not terribly enlightening, but in certain cases it can prove to be practically

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helpful. If we are certain that all the apples in a barrel are sound, then we do not have to fret and fuss over choosing any one of them. The simplest conjunctive proposition can be put in symbolic form as follows: A • B. “A” would represent one conjunct, “B,” the other. That inconspicuous looking dot that separates them also has symbolic significance: it stands for “and.” Two inferences can be drawn from the proposition. A B A B Therefore, A. Therefore, B. A disjunctive proposition is expressed symbolically as, A v B, where “A” and “B” represent the disjuncts, and the “v” between them is the symbol for the inclusive “or,” meaning, “one or the other, and possibly both.” What can we infer from an inclusive disjunctive proposition? First of all, we can take it for granted that both A and B cannot be false, for if that were the case we would not have a legitimate disjunctive. Given that much, then, if we know for sure that one disjunct is false, then we know that the other must be true. If A is false, B is true, and if B is false, then A is true, for they both cannot be false. But what can we infer if we know that one or the other disjunct is true, and that is all we know? Let us assume that we know for sure that A is true. What can we say with certainty, on the basis of that knowledge alone, about the truth or falsity of B? Nothing. B could very well be false, but given the fact that this is an inclu­ sive disjunctive, which allows for the possibility of both disjuncts being true, B could just as well be true. We could always hazard a guess as to the truth or falsity of B, but logically we could arrive at no firm conclusion as to its being one or the other. Apropos of an example used above, if I know for a fact that Paul enrolled in law school last fall, and that’s all I know, that knowledge does not permit me to say that he either did or did not marry Pauline. “A v B” is a standard way by which an exclusive disjunctive proposition is symbolically expressed. The only difference to be noted between this expres­ sion and that for inclusive disjunctives is the “v” that separates the “A” and the “B,” which is to be interpreted as having the proposition say, “It’s either A or B, but it can’t be both.” What possible inferences are open to us with regard to exclu­ sive disjunctive propositions? As with inclusive disjunctives, we begin with the assumption that it is impossible that both A and B can be false. But what peculiarly characterizes an exclusive disjunctive is that it does not allow both of them to be true. This being the case, if we know A to be true, B must be false, and if we know B to be true, A must be false. And because exclusive disjuncts relate to one another as contradictories, knowledge of the falsity of A allows us to conclude that B is true, and certainty about the falsity of B permits us the inference that A is true. Consider the proposition, “Either Edgar is an Eagle Scout or he is not.” If it is true that he is, then it is false that he is not; but if it is true that he is not, then any claim that he is must be branded as false. But if I know it to be a blatant falsehood that Edgar is an Eagle Scout (he never made it beyond Tenderfoot), then the denial that he ist>is true; and if it is false to deny

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that he is an Eagle Scout, then he must necessarily be one. We will have more to say about the interesting subject o f contradictory propositions in the next chapter. T ruth T ables Logicians have devised a handy device for quickly determining the truth or falsity o f compound propositions on the basis o f the truth or falsity o f each of its component parts— the simple propositions o f which it is constituted— and it is called a truth table. Truth tables can become quite complex, depending on the complexity of the propositions which they are analyzing, but those which I present here are very sim ple, reflecting as they do very sim ple propositions, and are intended only to give you a taste o f how they work. A truth table gives us a succinct visual summary o f all o f the inferences that can be drawn from any given proposition. We will start by providing the truth table for the simplest possible conjunctive proposition, symbolized as, A • B. • B A T T T (1) F F T (2) F T F (3) F F F (4) The “T ’s” and “F ’s” placed under the conjuncts, A, B, indicate whether or not they are true or false. Those placed under the dot which separates A and B, the middle column, indicate whether or not the proposition as a whole is true or false. The information we are given in (1) tells us that both A and B are true, in which case the proposition as a whole, A • B, is true, for here the necessary condition for the truth o f conjunctive propositions has been met. In line (2) we see that A is false, and line (3) informs us that B is false; in both cases, then, the proposition as a whole m ust be false. Line (4) declares both conjuncts to be false, which of course spells instant doom for the proposition as a whole; there is no way in the world that it could be true. In sum, the table shows us that the only situation in which a conjunctive proposition can be true is one in which all of its constituent parts are true. Now let us look at truth tables for disjunctive propositions, beginning with exclusive disjunctives. A T T F F

v F T T F

B T (i) (2) F (3) T (4) F In line (1) we are provided with the information that both disjuncts, A and B, are true, but given the nature o f an exclusive disjunctive, that would be a

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contradiction, and therefore the proposition as a whole is false. An exclusive disjunctive proposition excludes the possibility that both of its disjuncts could be true; they are mutually exclusive. If contradictory propositions are both claimed to be true, and if the claim is cast in the guise of an exclusive disjunctive, it is in fact no more than a logical aberration, and not a genuine exclusive disjunctive. Line (2) tells us that A is true and B is false, whereas the situation is reversed according to the information contained in line (3), with A being false and B being true. Both situations are ju st what we would expect in an exclusive disjunctive, and therefore in both cases the proposition as a whole is to be considered as true. Because line (4) identifies both A and B as false, the proposition as a whole must necessarily be false, otherwise the very intelligibility o f a disjunctive proposition would be rendered nugatory. In sum, the table instructs us to the effect that there are only two circumstances in which an exclusive disjunctive proposition can be judged to be true, and that is when one of its disjuncts is true and the other false. The truth table for inclusive disjunctive propositions takes the following form. V B A T T T (1) F T T (2) T T F (3) F F F (4) Because it is of the very nature of an inclusive disjunctive proposition to include the possibility that both disjuncts can be true, as line (1) informs us is the case with this proposition, then it must be judged as true. But because an inclusive disjunctive is a genuine disjunctive in that it posits a real either.. .or situation with regard to the truth or falsity of its disjuncts, then the information provided us in line (2), where A is true and B is false, and in line (3), where A is false and B is true, allows us to declare, in each case, the proposition as a whole to be true. Line (4) presents us with the same situation we ran into in line (4) of the truth table for exclusive disjunctives: if both disjuncts are false, the proposition as a whole cannot be anything but false. In sum, this table apprises us of the fact that, with respect to inclusive disjunctive propositions, the only way they can be false is when all their elements are false. Let us consider once again the possibility of multiple disjuncts in a disjunctive proposition. We must first note that this would not be a possibility with exclusive disjunctives, by reason of the fact that here the disjuncts are mutually exclusive, relating to one another as they do as contradictories. Imagine that we would start with this proposition, “The deer is either alive or dead” (A v B). Where could we go from there, by way of offering further possible alternatives? Either one or the other of those disjuncts is true, and its truth automatically makes the other false, and there the matter ends. But the case is

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different with regard to inclusive disjunctives. Here, theoretically at least, one could have an indefinite num ber o f disjuncts, ju st so long as no one o f them excludes the possibility of any of the others. Consider the following proposition: “Lucretia will marry Tom or she will marry Dick or she will marry Harry or she will marry Mortimer. (Symbolically expressed: A v B v C v D.) How would we go about trying to determine the truth or falsity o f a proposition like that, taking it as a whole? The first observation to be made is that, unless Lucretia lives in a very perm issive society, it is hard to imagine that A, B, C, and D could all be true at one and the same time. Circumstances could be such, in a society which does not perm it polyandry, that she could marry Tom, Dick, Harry, and M ortimer sequentially, divorcing one to marry the next, until she finally gets to M ortimer. If we admit such a possibility, then the proposition could be regarded as true because each o f its disjuncts is true. Less bizarrely, the proposition could also be counted true if at least one of its alternatives is true, say by the fact that Lucretia decides to marry Harry. The only way the proposition as a whole could be false is if Lucretia turned down all of her ardent suitors and entered a convent. A brief comment on a proposition of the following sort: “Clem neither so­ licited any advice on the matter, nor did he accept any when it was offered.” At first blush we might be inclined to identify that as a disjunctive proposition, but in fact it is not. Remember, a bonafide disjunctive proposition must offer us at least one real possibility; one o f its disjuncts must be true. But it is the very nature of a “neither.. .nor” proposition that it slams the door on both alter­ natives to which it refers. The above statement about Clem is a straight categorical proposition. T he O bversion

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P ropositions

Logic has devised a number o f ways of altering the forms o f propositions for the purpose of making evident the intricacies of their structure, and showing what im plications, in the form o f new propositions, can be drawn from an original proposition. T he general nam e given to this process is eduction, which is the mental act whereby, starting with a given judgm ent, we infer from it a second judgm ent. And because all judgm ents are expressed by propositions, this means that we infer a new proposition from a given proposition, the intelligibility o f the new proposition reflecting, and expressing in a different way, the intelligibility of the original proposition. By m eans o f this conscious reworking o f the structures of propositions, in which one proposition is transformed into another—and sometimes that one into yet another—we come to see more clearly how different propositions have an underlying relation to one another in terms of their basic meanings. One of the form s this process takes is called obversion. When we obvert a proposition we significantly change its form , but the alteredform carries

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the same meaning as the original proposition. There are two steps to be followed in obverting a proposition. Step One: Change the quality of the proposition. Step Two: Negate the predicate term of the proposition. We begin with the proposition, “Pierre is a plumber.” Following step one, chang­ ing the quality of the proposition, which is affirmative, gives us: “Pierre is not a plumber.” Hastening on to step two, which directs us to negate the proposition’s predicate term, provides us with the finished product of the process of obversion: “Pierre is not a non-plumber.” That is admittedly an awkward way of express­ ing the matter, and unless we purposefully want to make life difficult for people, we do not go around speaking in that way. But please note that the obverted proposition, clumsy though it be, means precisely the same thing as the origi­ nal proposition. The reason that is so, from a grammatical point of view, has to do with a peculiar feature of the English language by which two negatives in a proposition cancel one another out and produce an affirmative proposition.15 A proposition in the form, “S is not non-P,” is but a convoluted way of saying, “S is P.” Not much advantage, if any, is ever gained for the cause of clear communi­ cation by obverting a simple affirmative proposition into a negative one with a negated predicate term, but this is not the case if we are moving in the opposite direction; that is, obverting a negative proposition with a negated predicate term into a simple affirmative proposition. Here obversion does commendable service for the cause of clarity. The use of double negatives in a sentence in­ variably has the effect of beclouding the ideas which the sentence is attempting to communicate. Granted, double negatives are often used quite deliberately, for they serve as a sly, indirect way o f communication, which can have the effect of softening the impact of certain information, which, if stated directly, might come across as a bit too harsh. “Willie, you know, is not exactly incul­ pable” is a roundabout way of saying, “Willie is guilty.” Consider the following proposition. Nanette is not a non-smoker. We may have to pause a second before we fully register the message which that proposition is communicating. However subdy, double negatives can have an ob­ fuscating effect on the mind. But there is a ready remedy for that at hand in obversion, to which we quickly submit the above proposition. We change its quality, negate its predicate term, and suddenly everything becomes clear as day: Nanette is a smoker. A note on the second step we took in effecting that obversion. The predicate term of the original proposition was already negated; by negating that term we produce, “non-non-smoker,” and because two negatives cancel one another to make an affirmative, the final result is “smoker.” A “non-non-nun” is a nun, and a “non-non-gnat” is a gnat. But we have to be careful to distinguish what is

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a direct negation or contradiction of a term from what is contrary to it. The difference between the two is this: there is no middle ground between contradictories (A and not-A); there is middle ground between contraries (A and B). “Polite” and “non-polite” are contradictories; “polite” and “impolite” are contraries, as are “good and bad,” and “black and white.” “Impolite” may seem just a alternate way of saying “non-polite,” but it isn’t. If we negate “nonpolite” we get “polite,” but the negation of “impolite” does not yield the same results. Isidore may not be actively impolite; he may not go out of his way to be impolite to people, but that does not necessarily mean that he is actively polite to them. He may simply be indifferent in his treatment of others, being neither distinctly impolite nor polite to them. There can be a whole range of intermedi­ ate possibilities between being polite, at one extreme, and being impolite, at the other. And so it is with other contraries such as good and bad, and black and white. Som eone who is not bad is not necessarily good; between those two there is the broad area of moral mediocrity. And if something is not white, that certainly does not allow us to conclude that it is black; there is always gray to consider, among other chromatic possibilities. T he C onversion

of

P ropositions

Another way in which we rework propositions for analytic purposes— and one which, taken just in itself, is more interesting and immediately productive than obversion— is called conversion. The basic operation of the conversion of propositions is a very simple process, and consists in exchanging the subject and predicate terms, so that the subject term becomes the predicate term, and the predicate term becomes the subject term. Unlike what happens in obversion, here the quality o f the proposition is left untouched: affirmatives remain affirmatives, negatives stand pat as negatives. The critical test for a successful obversion, as we saw, is that the obverted proposition, though it takes on a new form, means the same thing as the original proposition. And if the original proposition is true, this would o f course entail that the obverted proposition is also true. Now, in the case of conversion, the key test of its success lies in the fact that the converted proposition, like its original, must be true. However, because of the exchange o f subject and predicate terms that takes place, the converted proposition cannot have precisely the same meaning as the original, by reason of the fact that there is a different predication at work in the con­ verted proposition, with the difference in emphasis this would necessarily involve. To say, “S is P” is not to say exactly the same thing as, “P is S,” though we are dealing with the same terms in both propositions. Given the key test of a successful conversion, we would automatically know that som ething has gone wrong in the process if we end up with a converted proposition which is false. But if the rules for the conversion of propositions are faithfully followed, there is no danger that the process could ever lead us

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astray, presenting us with a false proposition. Needless to say, however, this assumes that the proposition with which we begin, and which we intend to convert, is a true proposition. We can best show how conversion works by beginning with a singular proposition of a peculiar kind. Consider the following: Jerome Jones is the Master of Ceremonies. In this proposition, what is s tructurally doing service as a predicate is simply an alternate way of naming the subject. The sentence is thus roughly equiva­ lent to a m athem atical equation, where what is to the right of the equals sign is ju st another way of expressing what is to its left. This being so, we can say, 2 + 2 = 4, or 4 = 2 + 2. That’s an example of conversion. We find the same kind of relation in the proposition above, which allows us to convert it, and the converted proposition, besides being true, conveys the same meaning as the original. But didn’t we say that in a converted proposition the meaning is altered, because in it we have different predication? We did, but what is pecu­ liar about the kind of proposition we are considering here is that what looks like a predicate is not really a predicate. Why not? Because a true predicate attributes some new information to the subject, but, as noted above, what stands in the place of the predicate in this proposition is simply a different way of identifying the subject. That being the case, we can convert the proposition, as we did with the mathematical statement, and there is not, from a logical point of view, any alternation in meaning. Thus, to say: The Master of Ceremonies is Jerome Jones is to say essentially the same thing as, “Jerome Jones is the Master of Ceremo­ nies.” Granted, though these two statements are the same from a logical point of view, they do carry a difference in linguistic emphasis, and we can imagine them to be the responses to two different questions. “The Master of Ceremo­ nies is Jerome Jones” would be the response to the question, “Who is the Master of Ceremonies?” while, “Jerome Jones is the Master of Ceremonies” might serve as the expected response to, “Who is Jerome Jones?” Every proposition which provides us with a definition of its subject is of the same type as we have been discussing here, and thus can be converted without any alteration in mean­ ing. “Man is a rational animal” converts to, “A rational animal is man.” “A square is a quadrilateral all of whose sides are equal and each of whose internal angles is a right angle” converts to, “A quadrilateral all of whose sides are equal and each of whose internal angles is a right angle is a square.” But it is general propositions with which conversion is principally concerned, and to which it is most productively applied. There are two basic types of conversion, simple conversion and accidental conversion. The first is applied to two kinds of general propositions, universal negatives and particular affirmatives, and the second to but one kind, universal affirmatives. Simple conversion is the process by which subject and predicate are exchanged with no change in the quantity pf the proposition. (Parenthetical note: There is never

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a change m ade in the quality o f a proposition in conversion.) Accidental conversion is the process by which subject and predicate terms are exchanged and the quantity of the proposition is changed. What are the procedures to follow to effect a successful conversion o f a proposition?

Rules for the Conversion of Propositions Rule #1 —U n iversal n eg a tive p ro p o sitio n s co n vert sim p ly . No birds are fish, converts to No fish are birds. In the previous chapter we saw that the predicate terms o f negative propositions are always distributed, i.e., universal. Thus, in a universal negative proposition both the predicate and the subject terms are distributed. In the case of the first proposition above, reference is being made to each and every member o f the class o f birds, and to each and every m em ber of the class of fish. This allows us to convert the subject and predicate terms without altering the quantity o f the proposition, and this is the essence o f simple conversion. In the above exam ple, the first proposition is universal, and it rem ains universal in the converted proposition.

Rule #2 - P a rtic u la r a ffirm a tive p ro p o sitio n s co n vert sim p ly . Some Italians are teachers. converts to Some teachers are Italians. W e know that, just as the predicate terms of negative propositions are always distributed, so the predicate terms o f affirm ative propositions are always undistributed, i.e., anything less than universal. In the first proposition above, the predicate term does not refer to each and every teacher, but only to those who are Italian. This allows us to convert the proposition, switching the subject and predicated terms, without altering the quantity of the proposition: both the original and the converted propositions are particular affirmatives, and the quantities o f both the subject and predicate terms in the converted proposition remain the same as they were in the original proposition, i.e., undistributed.

Rule #3 —U n iversal a ffirm ative p ro p o sitio n s con vert accid en ta lly . All dogs are mammals, converts to Some mammals are dogs. Again, simple conversion means that the subject and predicate terms are exchanged without altering the quantity of the proposition. The signal feature o f accidental conversion, which applies only to universal affirmatives, is that in this case, besides the exchange of subject and predicate terms, the quantity of the proposition is changed, specifically, from universal to particular. We can easily see why this m ust necessarily be done if we recall that the predicate term s o f all affirm ative propositions, whatever their quantity, are always undistributed. In the first proposition above, the subject term clearly refers to each and every member of the class of dogs, but the predicate term is referring only to some mammals— those that are dogs. This is precisely what has to be

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kept in mind in converting universal affirmative propositions. If we were to forget that, in converting “All dogs are mammals,” we would end up with, “All mammals are dogs,” which is a false statement. We know then that we have gone wrong, for, again, the key test for a successful conversion is that the converted proposition, like the original proposition, must be true. In sum, a successfully converted universal affirmative proposition always results in a particular affirmative proposition.

Rule #4 - P a rticu la r n egative p ro p o sitio n s do not convert . Particular negative propositions do not convert? Why is that? To repeat, the test o f a successful conversion is a converted proposition which is true. All right. But then what are we to make of the following pair of particular negative propositions, the second being proposed as the conversion of the first. Some farmers are not Nebraskans. Some Nebraskans are not farmers. Surely the first proposition is true, and just as surely is the second. And couldn’t the second be considered to be a legitimate conversion of the first? No. In fact, what we witness there is an illegitimate conversion, for it fails to give due recognition to the fact that the predicate terms of negative propositions are always distributed. The predicate term of the first proposition above is distributed, but it is incorrectly made the subject term of die second proposition as undistributed. Therefore, the correct way of exchanging subject and predicate terms in the first proposition would yield a proposition which reads, “No Nebraskans are farmers,” which is clearly false. But notice something else that invariably goes wrong in any attempt to convert particular negative propositions. Besides the fact that a converted proposition, like its original, must be true, it is also necessary that the distributions of both subject and predicate terms undergo no alteration as the result of the conversion. If both are distributed in the original, both must be distributed in the converted proposition (as is the case with a successfully converted universal negative proposition); and if both are undistributed in the original, both must be distributed in the converted proposition (as is the case with a successfully converted particular affirmative proposition). In the case of a properly converted universal affirmative proposition, the distribution of the original subject and predicate terms is nicely preserved. In the movement form “All dogs are mammals” to “Some mammals are dogs,” we are rightly recognizing that “mammals” in the original proposition was undistributed. And in the converted proposition, “dogs,” as the predicate o f an affirmative proposition, now becomes undistributed. But is this not a bit odd, for now we are saying, to put it in strict logical terms, “Some mammals are some dogs.” This sounds odd because we normally do not talk that way, but perhaps we can better see, by stating the proposition in that ungainly way, what is being suggested regarding how the two terms relate to one another: the entire class of dogs is to be found within the larger class of mammals. So, if all dogs are

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mammals, which is the case, then it is necessarily so that some are. (See Appendix A for further discussion o f particular affirmative and particular negative propositions.) Now let us see what happens to the quantity of the subject and predicate terms when we attempt to convert particular negative propositions. We already know that if we honor the proper quantity of the predicate term we end up with a proposition which is false, as was the case with the above proposition when an attempt to convert it produced, “No Nebraskans are farmers.” But take note also that there is something else wrong with that proposition, when we compare it to the original, besides the fact that it is false. The subject term of the original proposition is “some farmers.” When “farmers” is made the predicate term of a negative proposition, it becomes distributed, as the predicate term of a negative proposition, so we have here an alteration in the quantity of a term, which is precisely what is not permitted in conversion. (See Appendix B for a discussion o f the additional forms of eduction.)

Review Items 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

W hat is a complex proposition? W hat is a compound proposition? Describe what is happening in an act of inference. W hat do we mean when we say that the truth of A entails the truth of B? W hat condition has to be met in order for a conjunctive proposition to be true? Explain the character of an inclusive disjunctive proposition. Explain the character of an exclusive disjunctive proposition. How does a universal negative proposition convert? How does a particular affirmative proposition convert? How does a universal affirmative proposition convert?

Exercises A. Reduce the following complex propositions to the simple propositions of which they are composed. 1. Julius Caesar came, saw, and conquered. 2. After carefully assessing the situation, the coach decided to fire all his assistants. 3. Gerald and Joanne were married and lived happily ever after. 4. Grace and Frances scored highest in the exam. 5. Leopold, faltering badly in the last lap, crossed the finish line in fourth place.

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B. Identify the following conjunctive propositions as either true or false. 1. At the beginning of World War Two, Adolf Hitler was the political leader in Germany, Benito Mussolini in Italy, and Harry S. Truman was president of the United States. 2. Three plus three makes six, and three plus four makes nine. 3. In order to qualify to be elected as president of the United States, one has to be a native-born citizen, at least thirty-five years old, and a college graduate. 4. An equilateral triangle is a plane three-sided figure, all of whose sides are equal, and has three internal angles, and each of those angles equals ninety degrees. 5. Herman Melville was a nineteenth-century American novelist, who was born in New York City, and who wrott Moby Dick and Billy Budd. C. Determine whether the following disjunctive propositions are either inclusive or exclusive. Keep in mind that an exclusive disjunctive proposition is composed of two elements that are contradictory, so that there is no middle ground between them. 1. Spencer will marry Tessie or Tricia. 2. In this life it’s a matter of all or nothing as far as success is concerned. 3. Tomorrow it will either rain or shine. 4. The flight either arrived at 3:45 p . m . or it did not. 5. A work of art is either beautiful or ugly.

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Chapter Eight Further Explorations in Immediate Inference T he I nterrelations A

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G eneral P ropositions

Singular propositions are the linguistic m eans we em ploy to express our engagem ent with individual things, unique entities. (“Mount Vernon is in Vir­ ginia.”) But when we are dealing with m ultitudes o f things, we have recourse to one or another o f the four general propositions for the proper linguistic ex­ pression o f our ideas. W e can either affirm or deny something of an entire class o f things (universal affirm ative and universal negative propositions), and we can either affirm or deny som ething o f a part o f a class o f things (particular affirmative and particular negative propositions). O f all the possible assertions we can m ake about things in the world around us, clearly the strongest would take the form o f a universal affirmative proposition. Such a proposition, if true, would be founded on the most solid kind of scientific knowledge. If you know for a fact that all cats are carnivorous, and if a stray and starving member of that species should show up at your door one day, you could be morally certain that the creature would be receptive to, say, a couple of chicken wings. But every general proposition, if true, and not only universal affirmatives, provides us with important, sometimes invaluable, information which can have a direct practical bearing on our day to day lives. If I know that, in Euclidean geometry, no parallel lines meet, it will prevent me from wasting time trying to extend two such lines ad infinitum into imaginary space in the vain hope that somewhere out there they just might converge and eventually merge. The knowl­ edge that som e prize w alleyed pike have recently been taken from Lake W ishy washy is enough to compel Herbert regularly to visit that body of water, jum p into a boat with rod and reel as soon as he arrives on the scene, and go out after them with hope springing eternal in his angler’s breast. And it is precisely because Joan know s that som e o f her colleagues are not teetotalers that she m akes a p oint o f having som e beer and wine on hand when she invites the whole crew over to her place for an evening of conviviality and philosophical dialogue.

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When we investigate how general propositions logically relate to one an­ other, we discover the possibilities that are open to us as far as inference is concerned. One pair of propositions will allow us to make the inferential move, another pair will prohibit it. In this chapter we will be looking at: (a) how general propositions relate to general propositions that differ in quality; (b) how general propositions relate to particular propositions with the same and with a different quality; (c) how particular propositions relate to particular propo­ sitions that differ in quality; and, (d) how particular propositions relate to general propositions with the same and with a different quality. We will thus exhaust all the possibilities for immediate inference among the general propositions. S horthand W ays

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Logic makes use of any number of ways of expressing ideas through sym­ bols, which is especially handy when dealing with propositions. Each general proposition has been assigned its special symbol, as follows: A for universal affirmative; E for universal negative; I for particular affirmative; O for particu­ lar negative. Why, you might wonder, the choice of those four letters? The answer goes back to the days when Latin was the common tongue of most logicians. The letters A and I, representing the affirmative propositions, are the first two vowels in the Latin affinno, “I affirm,” and the letters E and O, repre­ senting the negative propositions, are the two vowels in the Latin nego, which means, “I deny.” Instead of having cumbersomely to repeat “universal affirma­ tive propositions” or “universal negative propositions” every time we want to refer to one or the other, we can simply say “A propositions” or “E proposi­ tions,” and that will be my prevalent practice henceforth. Earlier I introduced a standard way of symbolizing a complete proposition, as in: “All S are P.” This would of course represent an A proposition, a universal affirmative. Needless to say, but I will say it any way just to make sure we are clear about the matter, “S” represents the proposition’s subject term, and “P” its predicate term. Here is the complete list o f symbolic forms that we will be using for the general propositions. All S are P. — Universal Affirmative (A) No S are P. — Universal Negative (E) Some S are P. — Particular Affirmative (I) Some S are not P. — Particular Negative (O) Besides the general usefulness of any shorthand method of notation, put­ ting propositions in symbolic form has the added advantage of accentuating their structural makeup. We put aside for the moment any consideration of a proposition’s conceptual contents, its “matter,” and concentrate on its form. “All S are P,” as a universal affirmative proposition, is so structured that its subject term relates to its predicate term as a smaller class to a larger one, so we are presented with a logical arrangement with respect to S and P such that S is

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completely contained within P. And this is so whatever in the objective order S and P might be representing. “All chipmunks are vertebrates” tells us that the class o f chipm unks is em braced in its entirety in the more capacious class of vertebrates. In dealing with a “No S are P” proposition, we are not able to tell, simply in terms o f the structure o f the proposition itself, how S relates to P with respect to their relative extensions. But it doesn’t matter. All we know, all we need to know, is that the two classes, S and P, have nothing to do with one another. The case is comparable with both I and O propositions, in that the structure of these propositions provides us with no information as to how the two classes, S and P, m ight stand to one another with regard to relative size or extension. But again, the information is irrelevant in that it does not affect our ability to know the kind o f logical relation which is established between the two terms in each o f these propositions. “Some S are P” tells us that, of the two classes, S and P, there is some positive interaction between them: a certain number of the mem­ bership o f class S, at least one, is to be found within the class P. “Some S are not P,” on the other hand, accentuates the negative, and tells us that, however it m ight be that some o f the m em bers o f class S are in class P (that, at any rate, would be simply a m atter o f conjecture), it is definitely the case that a number of them, at least one, is not to be found in that class. (See Appendix A for more on the symbolic expression of propositions.) T he O pposition

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P ropositions

You would doubtless recall that in a previous chapter we introduced the four ways in which terms can be said to be in opposition: as contradictories; as contraries; as privatives; and, as relatives. (If this information puzzles you, go back and check the relevant section in Chapter Three.) Now we want to con­ sider the important matter of the opposition of propositions. Two propositions are said to be opposed to one another when: (a) they have the same subject and the same predicate; and (b), they differ with respect to quality, one being affir­ mative, the other being negative. The following two singular propositions would be in opposition to one another. Charles Lindbergh flew the Atlantic solo in 1927. Charles Lindbergh did not fly the Atlantic solo in 1927. By way o f contrast, the following propositions would not be in opposition. Buffaloes are mammals. Bees are not mammals. T hey m eet one o f the criteria for opposition, in that they differ in quality, but they do not have the sam e subject, albeit they do share the same predicate. Accordingly, the next pair of propositions also fails to qualify as logical oppo-

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sites because in this case, though they manage to share subjects, they have different predicates. Sidney is in Australia. Sidney is not in Slovakia. Because the key criterion for opposition is the fact that two propositions with the same subject and predicate differ in quality, we have a problem on our hands regarding truth, for one proposition is affirming something of the sub­ ject, while the other is denying it. This demands resolution. When the terms of any two propositions are signifying in a clear, uni vocal fashion— that is, they are not being used ambiguously—we encounter no diffi­ culties in determining whether or not they are logically opposed. However, the case is different with propositions whose terms are ambiguous. Then we have to pause and consider the precise meaning which seems to be assigned to the terms. In doing this, it is often helpful to consult the context in which the prob­ lematical propositions are to be found. Consider the following propositions: Barking is permitted in the park. Barking is not permitted in the park. At first blush it would seem that we have here two logically opposed propositions, for they clearly differ in quality, and, apparently, they also have the same subjects and predicates. Or do they? Two terms are considered to be the same not simply because we have in them two instances of the same word, but rather when those two identical words bear identical meanings. In this case, the two subject terms are problematical, and should raise our suspicions. “Barking” most usually refers to the peculiar kind of noise which comes forth from the mouths of dogs, though, not to be carelessly exclusive here, it can be said that seals too do bark. But “barking” has another and quite different meaning, referring to the action by which the bark is removed from a tree. Now, let us suppose, for the purposes of illustration, that the “barking” in the first proposition refers to the sounds made by canines, while the same word in the second proposition refers to stripping a tree of its bark. In that case the two propositions would not be in opposition, for they have different subject terms. Perry, the park manager, in composing his signs, has not in this case succumbed to blatant contradiction. He wants to inform the park’s patrons that their pet pooches may yap away in complete abandon, but there will be no denuding of trees. Even so, he should be urged to enroll in Sign Composition 101 at the earliest opportunity. C ontradictory O pposition The most complete and definitive way in which two propositions can be opposed to one another is as contradictories. The specific characteristic of contradictory opposition is that the two propositions differ both in quantity and in quality. (It is understood of course that they have the same subject and

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predicate terms.) Thus, one of the propositions is universal affirmative (A), while the other is particular negative (O); or, one is universal negative (E), and the other is particular affirm ative (I). Given the logical relation that obtains between contradictory propositions, what kind of inferences from one to another is possible? That is, given the four possible starting points, an A, E, I, or O proposition, and being supplied with the knowledge that the starting proposition is either true or false, what can we infer as to the truth or falsity of its contradictory? Here is the general rule: if a proposition is true, then its contradictory must be false; if a proposition is false, its contradictory must be true. Such is the nature of contradictory opposition. Let us consider some ordinary language propositions so as better to see the logic which is at work here. We will start with an A proposition. All fish are aquatic animals. W e can, I think, safely assume that to be a true statement. Because it is an A proposition, we know that its contradictory is an O proposition, a particular negative: Some fish are not aquatic animals. W e can immediately recognize the radical and unresolvable conflict set up by those two claims. One or the other of them has to give way, for it is impossible that they can both be true. Actually, however, the conflict in this case is easily enough resolved, for we know the first statement to be true. On the basis of that knowledge, we infer the necessary falsity of the second. The truth of any A proposition absolutely precludes the truth of an O proposition with common subject and predicate terms. In an A proposition, something is being predicated of each and every member of a given class; no exceptions whatever admitted. The O proposition then comes along and claims that there is an exception to that predication, and this renders the two propositions completely incompatible. Now we start with an O proposition which we know to be true, “Some rab­ bits are not turtles.” Particular negative propositions of that sort can strike us as a little odd, because they are saying something about a part of a class which we otherwise know to be true of the entire class: no rabbits are turtles. But as we shall see more clearly presently— what, after all, common sense tells us is the case— if something is true of an entire class, it is obviously true of part of that class, however awkward it might be to state as much in explicit terms. So, then, we know “Some rabbits are not turtles” to be a true statement; from that we can infer that its contradictory A proposition, “All rabbits are turtles,” cannot be anything but false. If it is true that something cannot be predicated of a part of a class, then any attempt to predicate that same thing of the entire class is an exercise in logical futility. The truth of “Some S are not P” guarantees the falsity o f “All S are P.” Precisely the same principles that apply to A and O propositions apply to E and I propositions as well. If “No dragons are real” (E) is true, then its I

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proposition contradictory, “Some dragons are real,” is false. That is the only correct inference to be made. If “Some horses are thoroughbreds” (I) is true, then its E proposition denial, “No horses are thoroughbreds” is clearly false. If “Some horses have wings” (I) is false, and we would have no hesitancy in recognizing it as such, then we are forced to admit that “No horses have wings” is true, for if the assertion that there is at least some connection between two classes (in this case, between horses and winged creatures) is a false assertion, then there can be no connection between the classes. Consider another example. Because we know “Some men are mothers” is false, we can infer that none of them are. That particular contradictory relation might require a little reflection before the logic behind it becomes clear to us, for we might wonder: how is it that, if we know something cannot be predicated of a part of a class, this demands the inference that there is a complete separation between the class in question and the something being predicated of it? Let us look at what is being said in the I proposition with which we begin and which we know to be false. Two classes are being introduced, the class of men and the class of mothers. The claim is made that there is a relation, some sort of overlapping, between these two classes. But that is a false claim. If it is false to claim that there is any relation between any two classes, then that must mean there is no relation at all between them. If two classes do not overlap, they must be separate. As noted earlier, a universal affirmative proposition, if true, is the most powerful kind of proposition we have at our disposal. If we can say with confidence that each and every member of class X has characteristic Y, especially if X happens to be a large and diverse class (such as, for example, college students, or lawyers, or Minnesota Twins fans), then our position is an especially strong one, and people are apt to pay close attention to what we have to say about the subject of class X and its relation to characteristic Y. But one only has to think of any class which is both large in size and diverse in its membership to be aware of just how difficult it is to make a true universal statement about the class which could be confidently relied on. And yet universal propositions, affirmative or negative, are bandied about rather freely in ordinary discourse, and we are all treated to a steady diet of them. Sometimes we can allow ourselves to be cowed by them, simply by reason of the sweeping comprehensiveness they lay claim to, and especially if we are not all that conversant, in terms of our own first-hand knowledge, of just how the subject and the predicate in those propositions relate to one another, that is, in terms of their real world references. “All Catholics are superstitious,” and “No Jews are generous” might strike us as proclaiming indisputable truths if, say, we tend to be gullible and have no Catholic or Jewish acquaintances. It is precisely when we are on the receiving end of reckless generalizations such as the above that we can make useful appeal to logical contradiction. It proves to be a very potent defensive weapon. All universal propositions that present themselves as true—and not just manifestly goofy ones such as those just cited—

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live a rather precarious existence, and that is because it takes but a single opposite instance to what they are claiming to be true in order to collapse their sails. An assertion of the form, “All X are Y” will be able to hold its own and remain credible among thinking people only so long as no enterprising soul comes along one day and finds but a single X which, as a matter of fact, is not Y. You need only to refer to your long acquaintance with Noreen, who is (a) a nurse, and (b) decidedly nice, to brush aside as nonsense the claim, “No nurses are nice.” For a long time, at least among Europeans, it was thought that, “All swans are white,” was as true as “All water is wet,” until word was heard from Australia that there are black swans in the world, making “Some swans are not white” a true statement. Now logicians are banking on the stability of, “All crows are black.” C ontrary O pposition Contrary propositions are those which differ in quality (this being the key feature of every kind of opposition), but which have the same quantity, that quantity being universal. This means, to be precise about the matter, that A and E propositions are contraries— universal affirmatives and universal negatives. The nature of the logical relation between contrary propositions is such that, though they cannot both be true, it is possible that they can both be false. It is not difficult to think of an A and an E proposition both of which are false, such as the following pair: Every man is wicked. No man is wicked. There may come certain days when our estimate o f the human race is at low ebb, and we might be tempted to assent to the first statement, but our clearerminded selves would quickly check the impulse. As to the second statement, no assiduous research would be required to ascertain its falsity. There are many large classes of things, such as the class of human beings, which are so com ­ plex and varied in their membership that— unless we are addressing what is essential to that membership, such as rationality in human beings— seldom can we either predicate a particular quality, or deny it, to each and every mem­ ber of the class. Mixed bags must simply be acknowledge to be mixed bags. But consider the following contraries: Every man is mortal. No man is mortal. In this case the first statement is clearly true, while the second is clearly false. They are quite incompatible, indeed mutually exclusive, given the fact that both refer to each and every member of the class of human beings. The truth of one precludes the truth of the other.

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What kind of inferences can we make with regard to contrary propositions? One line of implication has already been suggested. Given the fact that both contraries cannot be true, knowing one of them to be true allows us to infer that the other one is false. If we know the A proposition to be true, then the E proposition must be false; conversely, if we have certainty concerning the truth of the E proposition, that means the A proposition must be false. The world is not big enough to hold two true contraries. So, then, apropos of the proposi­ tions cited above, because “Every man is m ortar’ is true, the claim that “No man is mortal” must be rejected as false. If we are confident that a particular attribute, in this case mortality, applies universally to the class of human be­ ings, then it is quite clear that any claim to the contrary is prima facie false. “No whales are fish” is a true E proposition, on the basis of which we can infer that the A proposition which is contrary to it, “All whales are fish,” is a false statement. What if the only certain knowledge we have of contraries is that one of them is false? Is any inference possible with respect to the other? No. Let us say that we know for sure that “All swans are white” is a false statement, which indeed it is. On the basis of that knowledge, and on that basis alone, we are not entitled to say anything certain about the proposition, “No swans are white.” It is important to keep in mind that, in immediate inference, we cannot go beyond the knowledge which is provided to us by the proposition with which we be­ gin. We cannot appeal to knowledge that comes to us from sources other than that proposition. No doubt most of us would, on an intuitive basis, be reluctant to accept “No swans are white” as a true statement; that’s interesting, but it has nothing to do with logical inference. All we have to work with is the certainty that “All swans are white” is a false statement. We are presented with a class, swans, and we know that a particular quality, whiteness, cannot be predicated of each and every member of that class. But if we cannot say something truth­ fully about each and every member of a class, that does not allow us to maintain that it must then be denied of each and every member of the class. It simply doesn’t follow. Now, clearly, “No swans are white” is a false statement, but its falsity is not inferred from the falsity of “All swans are white.” Because, as we saw above, both contraries can be false, if we know one to be false, the other could be true or false. And the same process is in play if we move in the opposite direction, from an E proposition to an A proposition. If I know for sure that “No medical doc­ tors know chemistry” is false, I cannot on the basis of that knowledge say anything for sure about, “All medical doctors know chemistry.” My certain knowledge of the falsity of the E proposition assures me that the claim that there is complete severance between the class of medical doctors and the class of those who know chemistry has no basis in fact. So, I can reasonably infer that there is then some kind of association between those classes (I know the contradictory of the E proposition to be true, “Some medical doctors know

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chemistry”), but the exact nature of that association is beyond my ken. And I certainly cannot conclude that, because the two classes are not separated from one another, one of them is completely contained within the other, which is precisely what I would be doing if I were to infer the truth of the A proposition. When a proposition like, “All S are P,” is false, we know with certainty that the attempt to predicate P of S universally fails. It is not true that each and every member of the class S has the quality P. But that leaves two possibilities open regarding the contrary, “No S are P.” It may be true, as when we move from the false “All horses have wings” to “No horses have wings.” On the other hand, when we begin with an A proposition like, “No men are wicked,” which is false, we discover that its contrary, “All men are wicked,” is also false. In sum, because the contrary of a false A or E proposition may be either true or false, no inference is possible. Contrary propositions represent extreme positions on a continuum of ideas. If we know, of two extremes, that one of them is true, then that automatically precludes the possibility of the other extreme being true. If something is definitely black, there is no way it can also be white. But if all I know for sure is that something is not black, I cannot on that basis alone conclude that it is white. Ruling out one extreme neither rules in nor rules out the opposite extreme. If something definitely is not black, it may or may not be white; it may be gray. And it is just that intermediate possibility that points to a salient feature of contrary propositions which radically differentiates them from contradictories. With contradictories there is no middle ground between them; with contraries there is. Both contraries can be false precisely because between them there can be a whole array of intermediate possibilities. “All men are wicked” and “No men are wicked” are both false, but from that we do not conclude that there is no wickedness to be found within the human race, nor, on the other hand, that the race contains no instances of goodness. In order to prove an A or an E proposition false, the most efficient way to do so is to cite its contradictory, not its contrary. If I attempt to prove the falsity of “All horses have wings” by demonstrating the truth of “No horses have wings,” the only way I could do this would be to survey the entire membership of the class to determine the plan facts of the matter—a monumentally laborious, if indeed not practically impossible, task. But if I proceed by way of contradictories, all I need do to prove “All horses have wings” to be false is to find a single non-winged horse, which would then allow me to declare that “Some horses are wingless.” (Reminder: “some” means “at least one.”) So too, the falsity of “No men are saints” is proved by the presence of a single saint in the world.

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S ubcontrary O pposition Two propositions are opposed to one another as subcontraries when, while differing in quality, they share the same quantity, and in that they are like contraries; but in this case, unlike contraries, the shared quantity is particular, not universal. That means that we are talking about the opposition between I and O propositions, between particular affirmatives and particular negatives. Consider the following sets of subcontraries. Some New Yorkers know Spanish. Some New Yorkers do not know Spanish. Some mothers are women. Some mothers are not women. We know that both propositions in the first set are true, and this is just what the subcontrary relation allows. The first proposition in the second set naturally strikes us as odd, for we know that in fact all mothers are women—it’s understood that we are referring here to human mothers. But if all mothers are women, there is no escaping the fact that some of them are, so the proposition, for all its oddness, is true. But the second proposition is clearly false. And this is the second possibility that is allowed for between subcontraries: one of them can be true and the other false. What is not allowed by the relation is that both propositions can be false. What prevents that possibility is the principle of contradiction. If I were first to claim that “Some S are P” is false, and then go on to claim that “Some S are not P” is false as well, I would be contradicting myself. To speak in ordinary language, if I contend that “Some St. Paulites like Minneapolis” is false, that must mean that “Some St. Paulites do not like Minneapolis” is necessarily true, otherwise I ’m talking nonsense. Unlike contraries, but like contradictories, there is no middle ground between subcontraries. Why is that? We cannot suppose both subcontraries to be false, for by that, once again, we would fall into contradiction. But we can suppose them both to be true. In that situation we have in place something like an inclusive disjunctive, expressible as: I v O. There are only two possibilities presented to us, I and O, and if both of those possibilities are met, then there is nothing remaining, either between them or outside them. In what we have said so far, we have already alluded to certain possibilities for inference between subcontrary propositions, but for clarity’s sake we now need to spell them out in explicit terms. Because both subcontraries cannot be false, if we know one to be false, we infer the other to be true. The falsity of “Some Europeans are not German” makes “Some Europeans are German” a true statement. However, no inference can be made about the other subcontrary if I know one of them to be true, for that other one may be either true or false, depending upon the contents of the propositions themselves. “Some teenagers smoke” is true, and so is “Some teenagers do not smoke.” “Some Secret Service

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agents are employed by the government” is true, but “Some Secret Service agents are not employed by the government” is false. S ubalternation Strictly speaking, propositions that we identify as subalterns are not in opposition to one another, for they do not differ in terms o f their quality. They do differ with respect to quantity, however, and the relation which is established between them on that account sets the stage for some very interesting and important inferences. It is for this reason that logic includes subalterns— along with contradictories, contraries, and subcontraries— in its treatment of immediate inference. O f the four general propositions, the two pairs that relate to one another as subalterns are universal affirmatives and particular affirmatives (A and I propositions), on the one hand, and universal negatives and particular negatives (E and O propositions), on the other. The universal propositions are called subaltemands, and the particular propositions are known as subaltemates. There are four specific inferences that can be made with respect to subaltern propositions, and the one which is the most obvious, the surest, and arguably the most important, involves the move from the universal to the particular, as when, for example, we move from an A proposition to an I proposition. Nothing could be more patent than the fact that, if I know “All S are P” to be true, it must be true that “Some S are P.” This move provides the clearest example of the idea that what lies at the heart o f inference— its principal effect— is the making explicit, in the inferred proposition, what is implicit in the proposition with which we begin. If “All men are m ortal” is true, and every indication leads us to believe that it is, then our being told that “Some men are mortal” would not strike us as earth-shaking news. What has been asserted there, we say, “goes without saying,” so obvious an inference does it represent. The second statement is simply drawing out and exposing to full view what is already contained in the first statement. The logic which is at work here, though not at all complex, is commanding. If Y can be truly predicated of each and every member of class X, it can clearly be predicated of any portion of that class. But let us say that we know for a fact that a particular A proposition is false. Then what? What can we infer concerning the I proposition to which it is related by subaltemation? We can make no firm determination about the I proposition, one way or the other. Consider the logic that is involved in this case. Something can be falsely said of an entire class, but that does not mean that it cannot be truly said of a part of that class. I may not be able legitimately to predicate Y of each and every member of class X, but maybe I can do so of some of the members of that class. And then again, maybe I can’t. The point to be made here is that if all I know for sure is that I cannot predicate something of an entire class, that knowledge alone will not permit me to infer anything definite about the possibility of its being predicated of a part of the class.

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My knowing for certain that “All S are P” is a false statement provides no basis for any inference regarding the status of “Some S are P.” “All women are geniuses” is a false statement; “Some women are geniuses” is true. “All Wisconsinites have wings” is a false statement, and so is,“Some Wisconsinites have wings.” When those kinds of alternatives are possible in the relation between false A propositions and their respective subaltemates, we can see why inference is ruled out. It is of the essence of inference, as it operates within the realm of deductive reasoning, that it must yield a proposition which is necessarily true or false, given the very structure of the logical relation which is set up by any two subaltern propositions, and given the truth value of the proposition with which we begin, and irrespective of the conceptual content of the propositions themselves. Whatever “S” and “P” might stand for in the real world, if all we know is that “All S are P” is false, we can say nothing for sure about the truth or the falsity of “Some S are P.” It could be one way or the other, and—here is the key point—it need not necessarily be one way rather than the other. We begin now with an I proposition which we know to be true. With that knowledge in hand, what inference is possible with regard to its related A proposition? None. The logic that supports this judgment is clear, and is easily grasped. If I know for sure—I have my facts as straight as they can possibly be concerning the matter—that “Some S are P,” that provides no warrant for my saying anything for sure about the possibility of P being predicable of the entire class of S. Maybe so, maybe not so. But inference does not deal in “maybe’s.” Certainty alone is acceptable. One of the most flagrant, and common, mistakes made in reasoning is to conclude that because a “some” assertion is true, so is its related “all” statement, but, as the old Latin phrase has it, non sequitur, “it doesn’t follow.” It may be a firm and incontestable matter of fact, supported by a superabundance of incontrovertible evidence, that “Some Lilliputians are lazy,” but from that I am not entitled to conclude that they all are. This is the “that’s the way they all are” fallacy, whose egregiousness is matched only by the facility with which we can so frequently succumb to it. Now let’s consider a false I proposition as our starting point, and ask what we can infer about its related A proposition. We can infer that it too must be false. Think about it. If I cannot truthfully attribute a particular quality to a part of a class, on what grounds could I ever suppose that I could do so with respect to the class as a whole? The falsity of an I proposition automatically renders false its related A proposition. If I cannot truthfully say that “Some reptiles are birds,” much less could I ever truthfully say that “All reptiles are birds.” Everything that has been said about how A and I propositions relate to one another in terms of the inferences that are possible between them, applies equally to the relation of E and O propositions. So, because it is true that “No insects are vertebrates,” the truth of “Some insects are not vertebrates” follows with rigid necessity. But if the E proposition is false, no conclusion is possible

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regarding the truth or falsity of the O proposition; it could be either, depending on the material contents of the propositions. Correspondingly, a true O proposition offers no possibility for an inference regarding the E proposition. “Some Chicagoans have no sense of humor” may be true, but that provides no basis for the predication of humorlessness of the entire class of Windy City residents, or for refraining from doing so. But if an O proposition is false, then we know that its related E proposition must also be false, for what is false for a part is a fortiori false for the whole. S ummary

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Possible Inferences A mong G eneral P ropositions

Contradictories If “All S are P” is true, “Some S are not P” is false. If “All S are P” is false, “Some S are not P” is true. If “Some S are not P” is true, we infer that “All S are P” is false. If “Some S are not P” is false, we infer that “All S are P” is true. If “No S are P” is true, then “Some S are P” is false. If “No S are P” is false, we correctly infer the truth of “Some S are P.” If “Some S are P” is true, then “No S are P” is false. Finally, if “Some S are P” is false, then we may infer the truth of “No S are P.”

Contraries If “All S are P” is true, we may infer that “No S are P” is false. If “All S are P” is false, no inference can be made regarding the truth or falsity of “No S are P.” If “No S are P” is true, the inference that “All S are P” is false is justified. If “No S are P” is false, no inference regarding the truth or falsity of “All S are P” is possible.

Subcontraries If “Some S are P” is true, no inference can be made regarding the truth or falsity of “Some S are not P.” If “Some S are P” is false, we may infer the truth of “Some S are not P.” If “Some S are not P” is true, the truth or falsity of “Some S are P” cannot be determined. If “Some S are not P” is false, then “Some S are P” must be true.

Subalterns If “All S are P” is true, so also is “Some S are P.” If “All S are P” is false, no inference can be made regarding the truth value of “Some S are P ” If “Some S are P” is true, no inference can be made regarding the truth value of “All S are P.” If “Some S are P” is false, then we can confidently infer that “All S are P” is false. If “No S are P” is true, “Some S are not P” is also true. If “No S are P” is false, no inference can be drawn regarding “Some S are not P.” If “Some S are not P” is true, no inference can be made with regard to “No S are P.” But if we know that “Some S are not P” is false, then we can safely infer the falsity of “No SareP.”

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O pposition

The square of opposition is a device, a logical visual aid, which allows us to see at a glance how the four types of general propositions relate to one another in terms of the logical inferences that can be made among them, starting with any given proposition whose truth or falsity is known. And here it is. All men are mortal.

A

E No men are mortal.

Some men are mortal.

I

O Some men are not mortal.

Studying the figure, we see that contrary propositions (A and E propositions) occupy the top of the square, and subcontraries (I and O propositions) reside at the bottom. The left side of the square represents the affirmative subalterns (A and I propositions), while the right side belongs to the negative ones (E and O propositions). The contradictory relations (A and O; E and I) are shown by the diagonal lines that connect the square’s four comers. When we have actual propositions to work with, such as those given above, we can immediately see how the four general propositions are logically related to one another in the various ways we have just discussed. Beginning with the A proposition, we know that because it is true that “All men are mortal,” its contradictory, “Some men are not mortal,” must be false. Given the nature of the contradictory relation— which is such that if one of the propositions is true the other must be false, and vice versa— we could just as easily have begun with the O proposition, “Some men are not mortal.” Knowing that to be false, we infer the necessary truth of “All men are mortal.” Focusing on that proposition now, we consider its contrary, the E proposi­ tion, “No men are mortal,” and we infer it to be false because we know that both contraries cannot be true, and the truth of the A proposition is already known. If we were to have started with the E proposition, knowing it to be false, we could not from that knowledge alone have made a direct inference about the truth of the A proposition. The only inferential move we could have made in that case would have resulted in the assurance that the I proposition, the contradictory of the E proposition, is true. Next, we drop down to the bottom of the square of opposition and consider the relation of subcontraries. The nature of this relation is such that both of them may be true, and at least one of them must be true; they both cannot be false. In this case we know the I proposition to be true and the O proposition to be false. Note, however, that if my only knowledge was of the truth of the I proposition, I could make no inference concerning the truth value of the O proposition. But if my only knowledge was of the falsity of the O proposition, then I would know that the I proposition must be true, for, again, both subcontraries cannot be false.

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Finally, there is the relation of the subalterns. We start with the A proposi­ tion, about whose truth we harbor not the least bit of doubt. That permits me to infer the truth o f the I proposition, for it stands to reason that if the whole class of human beings is mortal, any part of that class is also mortal, and necessarily so. But imagine that we did not know it to be true that all men are mortal, but we did know it to be a fact that some o f them were. If that were the only sure knowledge we had at our disposal, we could draw no sure conclusion as to the status of “All men are mortal.” What we could do with full assurance, though, is infer the falsity of “No men are mortal.” But from there we could make no further inference. Why not? We have correctly inferred the falsity o f the E proposition on the basis of our knowing the I proposition to be true. Keep in mind now, we are assuming that our knowledge does not extend beyond that provided us by the truth of the I proposition, that some men are mortal. That gives us the additional knowl­ edge that “No men are mortal” is false. With that, can I infer anything about its contrary, the A proposition? I cannot, for it is possible for both contraries to be false, and if all I know for sure is that one of them is false, as is the case here, then I must remain doubtful about the truth or falsity of the other, for it could be either one. So, I am thwarted in making any inference between contraries. Would I have better success if, on the basis of knowing the E proposition to be false, I were to attempt an inference regarding its O proposition subaltemate? Here too I would be met with frustration, for in this case I would run into essentially the same problem. Knowing that something is false universally— i.e., as applying to an entire class—does not preclude the possibility o f its being true for part of the same class, nor does it necessarily include that possibility. Something may be false on the universal level and either true or false on the particular level, and this means that no certain conclusions can be drawn re­ garding the particular level. But we know for a fact, from independent sources, that “Some men are not mortal” is a false statement. If we were then to start with that O proposition, we could infer the falsity of “No men are mortal,” for, once again, if something cannot be truthfully predicated of a part, the door is unceremoniously slammed shut against any attem pt at predicating it of the whole. Given the contents of the four general propositions which accompany the diagram of the square of opposition above, we of course know beforehand, by common experience, the truth value of each of them. W e know that “All men are mortal” is true, that “No men are mortal” is false, that “Some men are mor­ tal” is true, and that “Some men are not mortal” is false. But the peculiar virtue of the kind of analysis we can do with the square of opposition is due to the fact that the various propositions are being considered from a purely formal point of view, and that provides us with immediate insight into the possible ways in which any one proposition can logically relate to any other. In other words, we are regarding the propositions first and foremost from the point of view of their

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intrinsic structure—abstracting from their conceptual content—and taking note of how a particular proposition, given its structure, relates to the structure of another proposition, and what inferences that relation allows us to make. Pro­ ceeding from this purely formal point of view, all we need to know is that we are dealing with, for example, an A proposition of the form “All S are P,” and that it is a true proposition, to be able to know with certainty that its contradic­ tory, “Some S are not P” is a false proposition. And this is the case no matter what “S” or “P” might be referring to in the real world. It is simply the respec­ tive structures of these two kinds of propositions (A and O) that warrants the various inferences we can make with regard to them. Knowing (a) the type of proposition (A, E, I, O), and (b) whether it is true or false, we have the information we need to make all possible inferences be­ tween any two propositions. There is a simple exercise which can be performed with the square of opposition, to which I give the name “solving the square,” which helps us to get a quick sense of how the general propositions relate to one another. The exercise begins after we have been given the truth or falsity of any one of the four propositions. Equipped with that information, we then de­ termine what inferences are possible with regard to the remaining three propositions. Consider the following examples.

In solving the square of opposition, the first move to make is the surest one, which is to infer the truth or falsity of the contradictory of the proposition with which we begin. This is easy enough to do, for whatever the truth value of our beginning proposition, the truth value of its contradictory is just the opposite. Thus, it is always possible to make an inference between contradictory propo­ sitions. If the given proposition is true, its contradictory is false; if the given proposition is false, its contradictory is true. And this is the case with whatever proposition we start, A, E, I, or O. In the square on the left, above, we are told that the universal negative proposition, the E proposition, is true. Given that information, I can immediately conclude that its contradictory, the I proposi­ tion, is false. What move can I make from there? Actually, I have two options open to me, following the line of either subcontraries or subalterns. If I opt for the first, I can, on the basis of knowing the I proposition to be false, infer the truth of the O proposition, for both subcontraries cannot be false. And that would be fully compatible with the truth of the E proposition with which we began. Or, alternatively, I could go the subaltern route, and on the basis of the falsity of the I proposition infer the falsity of the A proposition, for if some­ thing is false for a part, it is emphatically so for the whole. And now, knowing

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the A proposition to be false, we would expect its contradictory to be true, and that is precisely the case. So, in sum, the solution to the square reads as fol­ lows: E is true (given); I is false; O is true; A is false. The square on the right, above, provides us with the initial information that the I proposition is true. From that I immediately infer that its contradictory, the E proposition, is false. Then what? If I try to solve for the A proposition along the line of contraries, I discover that I cannot, for contraries can both be false, and if one is false— which I know to be the case here— the other can be true or false. So, I enter a question mark within the parentheses next to “A.” My next move is to see if I can determine the truth or the falsity of the O proposi­ tion, on the basis of my knowing the E proposition to be false. But I find that I am blocked there as well, for again we have a situation where the proposition could be either true or false: something may be false for a whole, though not for a part of the whole. I place a question mark within the parentheses next to “O.” There is another possibility for trying to solve for A, which, if I am suc­ cessful, I would also have the solution for O, its contradictory, and that is by following the subaltern line. I know the I proposition to be true. Does that allow me to make an inference regarding the A proposition? It does not, for while something can be truly predicated of a part, that will not permit me to say with assurance that the same thing can be predicated of the whole, or, for that matter, that it cannot be. Thus, the final tally for this square: I is true (given); E is false; A is unknown; O is unknown. (See Appendix B for further discussion of the square of opposition.) What possible real world, or near real world, lesson might be drawn from the situation illustrated in the second square of opposition we have just analyzed, where we begin with the knowledge that an I proposition, a particular affirmative, is true? Imagine that you are an internationally famous researcher and you have determined to settle once and for all the question whether or not all the crows in the world are black. To do so, you map out an exhaustive empirical study, the purpose of which will be to check out every single crow now living on the face of the earth. You write a scintillating proposal describing the project, on the force of which you are awarded a multi-billion dollar grant from the famed Bernard B. Boondoggle Foundation, which will allow you to meet the heavy costs of the project. With that money you hire thousands of assistants and work begins; they fan out across the entire globe, assiduously counting crows. Now, let us say we are six months into the project, and to date some one hundred and sixty-two million crows have been caught, banded, and released. So far, each and every one of them has been black. Now, you had previously estimated the total number of crows now residing in the world, and so you know that there is still much counting that needs to be done before you can claim complete success. But we want to stop and consider where things stand right at the moment. Millions of crows have been counted, all o f which have been black, and that

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allows you and your research team to say with the utmost confidence, and to present it to the public as an infrangible scientific fact, that “Some crows are black.” That much you know with absolute certainty. Knowing that much, you can, also with the utmost confidence, make a logi­ cal inference, and dutifully inform the public that, because it is a matter of scientific fact that some crows are black, anyone who would dare to claim that no crows are black would have to be taken as a fool, a madman, or someone who is, for reasons you are not interested in investigating, in a severe state of denial. In an interview on national TV, you are asked if, on the basis of the research results thus far in hand, you thought that all of the crows in the world were black. Without the least bit of hesitancy, good scientist that you are, you re­ spond that this is something about which you have no definite knowledge. You explain to the interviewer that the question he asks is precisely the one for which you are attempting to find a definitive answer. That is the whole purpose of the monumental research project which you have launched. You go on to say that at the moment things look promising for the possibility of there being nothing but black crows in the world, for so far not a single non-black crow has been discovered. But you remind the interviewer that it just might happen— tomorrow, next week, two months from now—that a dedicated researcher in northern Borneo, or southwestern Minnesota, or who knows where, could pos­ sibly stumble across a snow white crow, or maybe even a pink one. The interviewer then wants to know, given that it is an established fact that some crows are black, if we could then reasonably suppose that some are not. You heave a deep sigh, then say, quietly, no, it is not at all reasonable to sup­ pose that, if by reasonably supposing one means arriving at a conclusion that is certainly true. Our knowing for a certainty that some crows are black only allows us to conjecture about the probability of some of them not being black, but we can say nothing for sure about the matter. However, you explain, given the results of our research to this point, the possibility of some crows not being black does not suggest itself as a particularly strong probability. Furthermore, you go on, if the project has the success you intend for it, and that having checked out every crow on the face of the earth you discover each and every one of them to be black—no exceptions—then “All crows are black” becomes a true statement, which means that its contradictory, “Some crows are not black” is false. You reach for your clipboard and are about to sketch for him the square of opposition to illustrate the logic behind that point, but he nervously throws up his hands and informs you that, unfortunately, the airtime allotted for the interview has just run out. Perhaps at a future date we could get into the square of opposition.

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I mmediate Inference

There are a couple o f other forms o f immediate inference which deserve mentioning, the first of which is called inference by added determinants. This involves adding the same qualification to the subject and predicate of a propo­ sition, thereby giving a narrower scope to the ideas it expresses. Some examples will best illustrate the process. Original: Music is entertainment. Inference: Good music is good entertainment. Original: Dishonesty corrupts human relationships. Inference: Systemic dishonesty systemically corrupts human relationships. Original: Teachers influence their students. Inference: Bad teachers adversely influence their students. By these examples we can see that inference by added determinants, despite that rather formidable label that logic attaches to it, is really a quite common way of thinking. We begin with a proposition which predicates something of an entire class, and then, in the inferred proposition, we qualify both the subject and the predicate in the same way. So, in the first exam ple above, we begin talking about music as entertainm ent; if that is so, then a qualified kind o f music (“good music”) represents a like qualified kind o f entertainment (“good entertainment”). There is nothing at all complicated about this type of inference, and we engage in it all the time, but we have to be careful that we do not become so mechanical in employing this kind of thinking that we end up making inferences which are not only erroneous but downright silly as well. Certain standard examples o f this show up in the textbooks, and I will repeat them here. Original: An elephant is an animal. Inference: A small elephant is a small animal. Original: An ant is an animal. Inference: A large ant is a large animal. What makes the inferences erroneous in both o f these cases is that the “added determinant”— “small” in the first case, “large” in the second— does not retain precisely the same meaning as applied to the subject and predicate terms, and this fact has to be made explicit in the wording of the inference if it is to make any sense. So, the correct inference in the first case would be, “A small elephant is small for an elephant,” and in the second, “A large ant is large for an ant.” From “The quarterback is a man,” it would not be correct to infer that “A bad quarterback is a bad m an,” but rather we should conclude that, “A bad quarterback is bad as a quarterback.” For all we know, he m ight be a quite decent fellow otherwise.

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Another form of immediate inference goes under the name of inference by converse relation, and once again in this instance we are dealing with a very common way of thinking. It has to do specifically with relational thinking, the kind of thinking we engage in when we relate one thing to another. It might be well to pause here and review some of the basic principles governing the idea of relation. What is the structure, the logical makeup, of a relation? Every relation is composed of three elements: its subject, its term, andits foundation. Take the proposition, “Molly is the mother of Miriam.*’ Here “Molly” is the subject of the relation; “Miriam” is its term; and the foundation of the relation— the nature of the link between subject and term—may be identified as “maternity.” In this proposition the focus of attention is on Molly, and we are explaining how she is related to Miriam, as her mother. When we engage in the process of inference by converse relation, we sim­ ply switch the subject and the term of the relation, which often involves changing the foundation of the relation as well. So, the inference I draw from, “Molly is the mother of Miriam” is, “Miriam is the daughter of Molly.” Now, Miriam is the subject of the relation, Molly is its term, and its foundation changes from maternity to what we could call “filiation.” There are certain instances of inference by converse relation where no change of foundation takes place. If I start with the proposition that “A is larger than B,” and from that infer that “B is smaller than A,” the foundation of the relation— comparative size—would remain the same for both propositions. Such would also be the case were I to move from “Bob is to the left of Ray” to “Ray is to the right of Bob,” where the foundation for the relation in both cases would be physical location. And geographical location would be the common founda­ tion for inferring from “Corpus Christi is south of Duluth” that “Duluth is north of Corpus Christi.” But the reliability of this kind of inference depends on the objective nature of the foundation which identifies any given relation. I can legitimately infer that “Aristotle was the student of Plato” from “Plato was the teacher of Aristotle,” because those particular student/teacher and teacher/student relations have been firmly established as historical facts. But when relative statements are matters of opinion or value judgments, then the inferred proposition can be given only as much credence as one is prepared to give to the original proposition. From “ War and Peace is a greater novel than Gone With the Wind,” I can infer that “Gone With the Wind is a lesser novel than War and Peace” but if the original proposition is open to dispute, so too will be the inferred proposition.

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Review Items 1. What is the nature of those propositions which are said to be opposed to one another? 2. Explain contradictory propositions. 3. Explain contrary opposition. 4. Explain subcontrary opposition. 5. Why is the relation of subalterns not an instance o f opposition, strictly speaking? 6. What, respectively, are A, E, I, and O propositions? 7. What inferences can be made between contradictory propositions? 8. What inferences can be made between contrary propositions? 9. What inferences can be made between subcontrary propositions? 10. What inferences can be made between subaltern propositions? Exercises A. Taking note of the information you are given regarding the truth or falsity of a particular proposition in each case, “solve” the two squares o f opposition below.

B. Supply the information requested in each o f the items listed below. 1. State the contrary to “No Democrats are Republicans.” 2. State the contradictory to “Some athletes don’t like to practice.” 3. State the contradictory to “All musicians are super-sensitive.” 4. State the contradictory to “Some sailors are non-smokers.” 5. State the proposition that relates as a subaltern to “Some textbooks are not expensive.” 6. State the contrary to “Every participant quit before the contest was officially scheduled to finish.” 7. State the subaltemate to “No cause is hopeless.” 8. State the subcontrary to “Some sheep are black.” 9. State the contradictory to “All sales are final.” 10. State the subcontrary to “Some historians are not accurate.”

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C. Respond to each of the questions below according to the information which is provided in each case, taking it to be the only information available to you. 1. “All Germans were Nazi sympathizers” is false. What can you infer about its contradictory? 2. “Some Estonians are not fluent in Sanskrit” is true. What can be inferred about its subcontrary? 3. “Some college students do not major in geology” is false. Is “No college students major in geology” true or false? 4. “All psychiatrists have medical degrees” is true. What can be inferred about its contrary? 5. “Some birds migrate” is true. What can be inferred regarding its subcontrary? 6. “No medical doctors like Chinese food” is false. What inference can be made regarding its contrary?

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Chapter Nine Reasoning T he T hird A ct

of the Intellect

Thus far we have explored various logical ram ifications of the first and second acts of the intellect— simple apprehension and judgment. Now we turn our attention to the third act of the intellect, reasoning, which can be rightly considered as the very heart of logic. Simple apprehension, we recall, is that mental operation by which we give birth to ideas, the critically important means by which the mind is, not simply brought into contact with the extra-m ental world, but in a certain real sense made one with that world. It is the signal mark of an idea that it encompasses the essence, the nature, the innermost identity, of the thing to which it refers, and thus when we bear any idea in mind there results a kind of commingling of essences, the essence o f the thinking subject and the essence of the object of the thinking subject’s thought. Judgment, the second act of the intellect, is the mental operation whereby we marry idea to idea. More precisely, judgm ent involves predication, the act by which, in attributing one idea to another we are com m itting ourselves to real existence, acknowledging something actually to be the case in the extra-mental world. And this is so no matter how trivial the ideas might be: The salt shaker is on the table; A bee is in her bonnet. The idea alone does not imply any commitment to real, extra-mental existence, for I can be entertaining an idea, warmly coddling its essence within my essence, but that idea, just as idea, may have no referent in the extra-mental world, the idea, let us say, to which I attach the name Uriah Heep. Now, Mr. Uriah Heep is a fictional character. Notice what I just did in writing that sentence, “Mr. Uriah Heep is a fictional character.” I expressed ajudgment; specifically, I predicated fictional status o f the subject of the sentence, Uriah Heep. I thus comm itted m yself existentially, which is to say that I made a claim as to how things stand in the real world, and there are only two responses that can be m ade to that claim , in m easuring it against the real world: it is either true or false. In this particular case, “Mr. Uriah Heep is afictional character,” can be confidently assented to, for it is a true statement.

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Mr. Heep, real though he might sometimes seem to us when we encounter him in the pages o f David Copperfield, is but a figment, albeit an altogether fascinating one, of the amazingly fertile imagination of Charles Dickens. In the second act of the intellect we conjoin ideas to make judgments; in the third act of the intellect we conjoin judgments, expressed as propositions, to make arguments. Just as words are the linguistic expressions of ideas, and statements or propositions the linguistic expression of judgments, so the type of linguistic discourse we call an argument is the linguistic expression of reasoning. A linguistic discourse may be loosely defined as a collection of sentences which, because of their logical interrelatedness to one another, form a recognizable whole. R easoning

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Aristotle defines reasoning as “an argument in which, certain things being laid down, something other than these things necessarily comes about through them.” (Topics, 100a, 2 5 )16That should sound familiar to us, for what the Sage of Stagira is describing here is the essence of what we know as the inferential move, whereby we begin with a true proposition and then conclude to another true proposition, implied by the original proposition. The “certain things being laid down” Aristotle speaks of are the truths embodied in the original judgment or judgments. And in referring to “something other than these [which] necessarily comes about through them,” he has in mind thejudgm entthatis inferred from the initial truths which are the points of departure of the reasoning process. Finally, as we shall see presently, Aristotle is referring here specifically to deductive reasoning, for what “comes about” from what was laid down comes about necessarily. Reasoning is a process, that peculiar kind of mental activity by which, beginning with a proposition which we take to be true, name it Proposition A, we proceed to another proposition, Proposition B, which we accept as true precisely on account of the truth of Proposition A, for we recognize that the propositions are so related to one another that the truth of Proposition A supports, vouches for, substantiates in a critically important manner, the truth of Proposition B. That is the nub of the preeminently human activity we call reasoning. And, as you can see, in terms of its basic structure, it is quite simple. When we reason, and when we go public with our reasoning through argument, we are attempting, not simply to state what we take to be true, but to expressway we take it to be true. Reasoning necessarily involves giving reasons, showing cause, providing information which is supportive of the assertions we make about this or that aspect of the world which we share with others. Argument is the linguistic vehicle which conveys reasoning from one mind to another. If we want to live logical lives, then we have to learn how to be good arguers. A good arguer is not to be confused with an argumentative or

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contentious or quarrelsome person. No, a good arguer is simply a good reasoner, someone who makes sound inferences, someone who doesn’t simply say things but backs up what is said. One of the greatest courtesies we can render to people, one of the best ways we can show respect for their intelligence and honor their exalted status as rational creatures, is to argue with them; that is, to present them with arguments, give them reasons for the positions we take on this or that issue, always with the understanding, o f course, that the issues in question are important ones. It would be unconscionably tedious o f me to burden people with arguments whose purpose is to explain why I never put sugar on my com flakes. Arguments can take various forms, and som etim es they can be quite complicated. But like so many other potentially complicated things in life, the essence of argument is the very soul o f simplicity. Every argument is made up of but two basic elements, one o f which is called a prem iss, the other, a conclusion. The conclusion of an argument is simply its “point,” a proposition which we want our auditors or readers to accept as true, or to be rendered more understandable to them. The function o f the premiss o f an argument is to provide supporting data for the conclusion, to give a reason why the conclusion should be accepted as true, or to make it more understandable to us. A premiss, therefore, relates to a conclusion as that which supports to that which is supported, as foundation to superstructure. Some arguments can take the simplest form possible, in that they are composed o f a single premiss and a conclusion, such as the following. Adolf Hitler was not insane, because no insane person could have acted with the kind of consistent efficiency he did for as long as he did. The argument states the conclusion first, inviting us to accept as true the contention that Hitler was not insane, and then, with the second proposition, it gives us a reason why we should take the conclusion to be true. Whether this is a good or a bad argument, whatever might be the degree of its compelling force, are questions that need not detain us here. All we want to say about this discourse at the moment is that, in terms of its basic structure, it qualifies as an argument. It is composed of two propositions, one of which clearly serves as a conclusion, one of which, just as clearly, serves as a premiss. An argument is a form of discourse which, in terms of its elementary structure— where something is said in support of something else which is said— is quite versatile in the uses to which it can be put. Certainly the most potent form of argument is one which is strictly demonstrative, an argument, that is, which employs deductive reasoning and whose conclusion therefore follows necessarily from the premisses. Such an argument can be said to prove in the strongest sense, and it yields scientific knowledge. But, as we will see in a later chapter, we also employ argument in inductive reasoning, the conclusions to which are only probable. Moreover, as I indicated above, an

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argument can serve the purpose of making something more understandable to us, something which, in the main, we already take to be true. In other words, arguments can perform an explanatory function, supplying us with information which renders more intelligible to us something which, to a certain degree, we had already known. (See Appendix A for further discussion of argument and explanation.) Given the function of the premiss in an argument, i.e., to lend support to the conclusion, if we have a problem with the conclusion of any argument, that is, if we are reluctant to accept it as true, and if we are justified in that reluctance, then invariably the seat of the problem is going to be found in the premiss. The premiss either does not support the conclusion at all, or the support it gives to it is not strong enough to make the conclusion convincing. The only responsible way to respond to an argument is argumentatively. If we are justified in considering the conclusion of an argument to be questionable—and that would be because the premisses of the argument weakly support it—then we should offer a counter-argument, which points out the weaknesses of those premisses. One of the first things we have to ascertain, in responding to an argument, is that there is a real argument to respond to. That might sound like a very odd bit of advice to give to any serious student of logic, but as a matter of fact it fairly frequently happens that one comes across discourses, oral or written, which, though they give the superficial impression of being arguments, are really not so. These are discourses which can be said to contain one element of an argument, its point or conclusion—a point which is usually repeated over and over again, often with a good deal of rhetorical razzle-dazzle—but in which there is nothing to be found which offers any support for the conclusion. I say “conclusion,” but actually a proposition which lacks supporting propositions is not a conclusion at all. It is simply a naked assertion, the expression of someone’s opinion. Everyone, as we love to say, has a right to his own opinion, and to that we might want to add that he has the right to repeat that opinion as often as he wants, with as much rhetorical razzle-dazzle as he wants, but if he is not going to take the trouble to put premisses under that opinion (which would transform it into a conclusion), all we need do is either (a) simply assent to the opinion, if we happen to agree with it, or (b) reject it out of hand, if we think it hair-brained. Non-arguments need not be responded to with arguments. C omplexity

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In more cases than not, most of the arguments we are presented with on a day to day basis come in a minimalist form; that is, they contain but two propositions, one functioning as premiss, the other as conclusion. Clay t ran out of gas out on Highway 16, so he was late for the wedding.

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Because Geraldine consistently forgot to water them, the geraniums withered up and died. There is an explanatory aspect to almost every argument; it doesn’t simply state a fact, which takes the form of the conclusion (and which we might already be aware of), but it gives us, in the form of the premisses, the “reasons why” of the fact. The principal purpose of the reasoning process is to apprise us of the causes of things. The fact that Clayt ran out o f gas explains why he was late for the wedding, and it is also the cause of his being late. Geraldine’s failure faithfully to water the geraniums explains their untimely demise, and it is what caused their demise. The distinction between cause and effect may be applied to the very structure of an argument, for the premiss can be said to relate to the conclusion as cause to effect. In a sound demonstrative argument the premisses cause me to accept the conclusion as necessarily true. In an argum ent that provides me with the cause of a fact, the premisses cause me to have a richer, more comprehensive understanding o f that fact. It makes a difference how I regard the fact that Clayt did not make it to church on time when I come to know that this happened through no fault of his own. While most of the arguments we encounter under ordinary circumstances come in the minimalist form of a single premiss plus conclusion, it is almost always the case that these discourses represent abbreviated forms of larger arguments. This means that, in order to respond properly to such arguments, especially should they prove to be problematic, we need to pause and engage in a bit of logical reconstruction, tilling in the missing pieces to the puzzle. This is a matter to which we will give due attention later in the book. The complications of complicated arguments are, as mentioned, invariably to be found in the realm of the premisses, the supporting data. An argument can be complicated simply by reason of the fact that it contains many premisses, each of which bears a more or less direct relation to the conclusion as the source of an immediate inference, and among which there is no obvious logical connection. An argument of that sort could be schematized thus:

Each of .the lettered boxes represents a premiss. Consider the following argument, of the kind represented by the schema above. Herman Melville’s Moby Dick is America’s greatest novel, because (a) of the power of its narrative, because (b) of the richness and poignancy of its imagery, because (c) of its philosophical depth, because (d) of its multi-layered allegorical quality, and (e) because of its moral force.

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Considering the argument’s five premisses, it would be difficult to arrange them in the order of their importance, and each seems to relate rather directly to the conclusion. Perhaps someone might be persuaded to accept the conclusion simply on the basis of just one of the premisses, but there is little question that, taken cumulatively, they offer a fairly impressive foundation for the argument. Premisses can be complex not simply because of their multiplicity, but also because of their logical interrelations. For example, they may be linked together in linear fashion, in such a way that one premiss is subordinate to another, and that premiss subordinate to yet another, and so on. Such an argument can be configured in this manner.

Consider this argument: Because (a) he sprained his ankle, Dave (b) did not play in the championship game, with the result that (c) the NBA scout present there did not see him play, so (d) he wasn’t offered a professional contract after all, and that’s the reason Dave is not today a twenty-two year old multi-millionaire. Arguments are ordered toward answering the question “Why?” In this instance we are given a number of reasons, four in all, which account for the fact that Dave is not a millionaire. But take note how those premisses relate to one another, how the first (a) supports the second (b), how the second in turn supports the third (c), and how the third for its part supports the fourth (d). And the result is three mini-arguments, all of which, taken together, support the conclusion. Spelled out separately, the arguments would look like this: Dave sprained his ankle, Therefore he did not play in the championship game. Dave did not play in the championship game, Therefore the NBA scout did not see him perform. The NBA scout did not see him perform, Therefore Dave was not offered a professional contract.

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An argument of this form is similar to what is called an epicheirema, which is a kind of syllogistic argument which is characterized by the fact that an explanatory reason is provided for one or both of its premisses. (See Appendix B for a discussion of epicheirema.) D eductive R easoning Lying right at the center of the reasoning process, around which so much by way of argument revolves, is what we have called the inferential move, where we proceed from one truth to another, the second truth being dependent on the first. Deduction is a particular, and a very important, form of reasoning. Because of the results it is capable of producing, perhaps we can say that it is the most important form of reasoning. Deductive reasoning is often described as reasoning that moves from the more to the less general, such as when we conclude that “The molecules of this gas are composed of one carbon atom and four hydrogen atoms” from the more general observation that “This is methane gas.” While the passage from the more to the less general does in fact constitute an important characteristic of deductive reasoning, it is not what I would regard as its essential characteristic. What then is the essential characteristic of deductive reasoning? Deductive reasoning would of course be embodied in a deductive argument, so we say that a deductive argument is one whose conclusion always follows necessarily from the premisses. If the premisses of a deductive argument are true, the conclusion must be true. In saying this we assume that the structure of the argument is sound. Deductive argument has no truck with probable conclusions; they must be necessarily true, ornothing. Consider the simple argument cited above. If it is true that this is methane gas we are dealing with, and let us say we have no doubts about that fact, then it is inescapably true that each of its molecules is composed of one carbon atom and four hydrogen atoms. That peculiar composition enters into the very definition of a methane molecule; it is that composition which identifies the essential nature of methane (CH4). It is thus true of the entire class of methane molecules that each is made up of one carbon atom and four hydrogen atoms, and, that being so, what is true of an entire class is necessarily true of any part of the class or any individual member of it, such as this or that methane molecule. This suggests the familiar inferential move from an A to an I proposition, reference to which doubtless stirs up in you fond memories of the left side of the square of opposition. To deduce something, then, in the strictest understanding of the term, is to derive with complete certainty a new truth from an original truth with which one begins. It is to recognize that the truth of a certain proposition necessarily entails the truth of a further proposition, so that the second follows from the first, and follows necessarily.

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The famous sleuth Sherlock Holmes is often cited as someone who made ample use of deductive reasoning. No doubt he sometimes reasoned deductively— we all do so on occasion—but much of what he himself would call deduction is not deduction at all. He makes many inferences, concluding to one thing on the basis of his knowledge of another, and some of those inferences are quite remarkable for their insightfulness, but in more cases than not they amount to little more than educated guesses, and do not count as genuine deductions. Let us remind ourselves of the test of deductive reasoning: the conclusion follows necessarily; if the premisses are true, the conclusion must be true. We will briefly consider the kind of case that Holmes would be brought in to solve. Bertram the butler has been murdered, stabbed in the chest with a stiletto while he slept soundly in his bed. In arriving on the scene, Holmes takes special note of a trail of muddy footprints which start at the back entry way, cross the kitchen, and lead to the door of the butler’s room, which is found on the far end of the kitchen. The footprints were made by a veiy large shoe (Holmes estimates size 13), and from the facts before him—large muddy footprints on the kitchen floor—Holmes “deduces” two things: (1) the footprints were made by a very large man; (2) he was an intruder who approached the mansion from the rear by traversing a large sparsely vegetated field that lay behind it. (Because it was a dark and stormy night, the rain had rendered the field quite muddy.) Now if Holmes’s reasoning was truly deductive, both of those conclusions would have to have been true. But they weren’t. Here’s what actually happened. Bertram the butler was murdered by Myrtle the maid, who was furious at him for having stolen her lottery ticket, which turned out to be the winner of a big pot. Myrtle is a rather petite creature, standing exacting five feet tall, and weighing 110 pounds soaking wet. Here’s how she did the dastardly deed. Exiting the mansion from a side entrance, she followed the sidewalk around to the back of the building. In one hand she was carrying a pair of men’s shoes, size 13 (Holmes was right about that), in the other, a stiletto. When she reached the back entry she slipped on the men’s shoes over her own, stomped about for about a minute in the flower garden next to the door, to get the shoes good and muddy, then entered the kitchen, crossed it to the butler’s room, entered it, and there so rearranged Bertram’s existential status that he was placed permanently beyond the possibility of reaping any benefits from his ill-gained lottery winnings. The essential characteristic of deductive reasoning, we have said, is that its conclusions follow necessarily. But why is that? Consider a simple, two proposition argument, a premiss and a conclusion. The two propositions are so related to one another, in terms of the contents of each, that the truth of one (the premiss proposition) directly entails the truth of the other (the conclusion proposition). Put in other terms, the premiss, by reason of what it actually asserts, could not be true without what is asserted by the conclusion also being

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true. You cannot assent to the truth of the one (premiss) without also assenting to the truth of the other (conclusion). An example will make this clear, the one we used above. Given the fact that “This is methane gas” is a true statement, it must also be true, and necessarily, that “This gas is com posed o f m olecules whose atomic composition is one carbon atom and four hydrogen atom s.” The second truth follows from the first because it is entailed by it. But there is a deeper reason why the conclusions o f deductive reasoning are necessarily true, and that is because deductive reasoning, as suggested above, is typically concerned with the very essences, the proper intrinsic natures, of the subjects with which it deals. To see how this is so, com pare the proposition, “This is methane gas”— a statement of fact— with the proposition, “There are muddy footprints on the kitchen floor of the M ulford M ansion,” which is also a statement of fact. From the first proposition we can make a deductive inference which, because it is that, is necessarily true; we cannot make a comparable inference from the second proposition. If we know that we are dealing with methane gas, then we know that the very nature of that gas is such that its molecules are composed of one carbon atom and four hydrogen atoms; if we are certain that it is methane, we are certain o f its composition. What are we to make of the proposition, “There are muddy footprints on the kitchen floor of the Mulford mansion”? Again, the proposition states a real fact, just as does the proposition which identifies a particular gas as methane. But here is the difference. While there is an essential connection between methane gas and molecules of a peculiar atomic com position, so that from one specific fact (methane gas) you can confidently deduce another specific fact (its molecules are composed of one carbon atom and four hydrogen atoms), there is no such essential connection between the fact o f muddy footprints on the kitchen floor of the Mulford Mansion and any other specific fact. If there were such a connection, all you would have to do is sim ply infer it from the footprints, for it would somehow be necessarily implied by those footprints. If you know the essence of methane, you know with certainty how it is composed. If you know footprints on a kitchen floor, you do not know anything with certainty beyond the footprints themselves, and that is because the footprints are related to the floor accidentally, not essentially. Holmes made a rather clever surmise when he concluded that the footprints were caused by a large man who had passed through a muddy field, but because there was no essential connection between that conclusion and the premiss (i.e., the muddy footprints), it did not, could not, follow necessarily that those footprints were made by a large man who had passed through a m uddy field, which is simply proven by the fact of his having been wrong about the matter. Of course there is always the possibility that he could have been right, but there was nothing in the circumstances themselves which dictated that he/zc/r/to be right. Holmes was engaging in inductive, not deductive reasoning.

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We are already quite familiar with immediate reasoning, that form of reasoning whereby, knowing one proposition to be true, we infer, from the truth of that proposition, the truth of a second proposition. And that is precisely what we were doing when we moved from the truth that “This is methane gas” to “Its molecules are composed of one carbon atom and four hydrogen atoms.” The immediacy of immediate reasoning consists in the fact that we move directly from one proposition to another, with no intervening propositions. Now, m e d ia te r e a s o n in g , as its very name suggests, is reasoning in which we reason mediately, which is to say, instead of moving directly from one proposition to another, we move from one proposition to another through the mediation of a third proposition, where that mediating third proposition plays an altogether critical role in the argument. So. knowing Proposition A to be true, I infer that Proposition C is true, but I arrive at the truth of Proposition C through the mediation of Proposition B. Consider these two propositions, “All men are mortal,” and “Socrates is mortal.” I think we would all quickly see that there is a clear logical connection between the two propositions, specifically in the fact that the truth of the second is essentially dependent upon, and thus follows from, the truth of the first. But 1would hope that we would also have the sense that the movement from the first proposition to the second is not a direct one. There is something missing, a missing link, a mediating proposition which, once supplied, will make crystal clear why the second proposition is not only true but necessarily true. In supplying that missing proposition we will have stated that famous syllogism which has figured prominently in countless logic textbooks since time immemorial. And here it is once again: All men are mortal. Socrates is a man. Therefore, Socrates is mortal. We wi 11have many things to say about arguments of this sort in pages to come, but here we want simply to call attention to the fact that it is an example of mediate reasoning. The conclusion of the argument, that Socrates is mortal, while founded on the truth of the initial premiss which informs us that all men are mortal, requires, in order to be completely clear and cogent, the mediating premiss which apprises us of the fact that Socrates is a man. With that mediating premiss, the full force of the logic of the argument is emphatically brought home to us. Given the fact that it is of the very essence of human beings that they are mortal creatures, given the additional fact that Socrates is a member of the class of human beings, it then follows ineluctably that Socrates is mortal. If the premisses are true, and they are, there is no escaping the truth of the conclusion. Such is the force of deductive reasoning.

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An additional word needs to be said about the example of immediate inference we used earlier, where we moved directly from the knowledge that this is methane gas to the knowledge that its molecules are composed of one carbon atom and four hydrogen atoms. Those two bits of knowledge, put in propositional form, actually compose a part—the greater part as it happens—of a syllogistic argument which, when completely fleshed out, can take a form such as the following: All methane gas is composed of molecules whose atomic composition is one carbon atom and four hydrogen atoms. This gas is methane gas. Therefore, this gas is composed of molecules whose atomic composition is one carbon atom and four hydrogen atoms. As mentioned, most of the arguments we confront on a day to day basis are composed ofjust two propositions, and some of these arguments can be treated as complete in themselves just as they stand, as instances of immediate inference. But almost all of the two-proposition arguments we encounter, if we were to stop and reflect on them a bit, reveal themselves to be abbreviated forms of syllogistic arguments. The name we give to an abbreviated syllogism is enthym em e. More aboutenthymemes in due course. Syllogistic R e a so n in g

What is a sy llo g ism ? The first thing we can say about it, and to give it the broadest kind of identification, is that it is a form of argument. But more than just that, it is a very important form of argument, playing as it does a dominant role in the whole reasoning process. To get a more precise idea of the syllogism, we go to Aristotle, who provides us with a definition and some explanations. “A syllogism,” he writes, “is a discourse in which, certain things being stated, something other than what is stated follows of necessity from their being so. I mean by the last phrase that they produce the consequence, and by this, that no further term is required from without to make the consequence necessary.” (P rior A nalytics, 24b, 20)17When Aristotle defines a syllogism as a discourse in which something follows from certain things having been stated, he can be said to be describing the inferential move, and thus citing what is common to every argument. But when he says that something follows o f n ece ssity from the things which are stated “being so” (i.e., the premisses are true), then he is telling us that the syllogism is a form of d ed u ctive argument, the key feature of which is, as we know, that its conclusion is necessarily true. When he goes on to say the “certain things” (i.e., the premisses) which are stated “produce the consequence,” he is making the important point that the premisses, or more precisely the truth of the premisses, actually cause the conclusion—that’s what he is referring to by the term “consequence”—to be true. In all argument, but most especially so in deductive argument, wherein conclusions follow

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necessarily, the relation between premiss and conclusion is one between cause and effect. By saying that “no further term is required from without to make the consequence necessary,” Aristotle means that a syllogistic argument, if it is properly constructed, and if its premisses are true, is completely self-contained, in the sense that it provides us with all the information we need, in the premisses, to substantiate the truth of the conclusion. We do not need to go outside the syllogism, seeking further information elsewhere, in order to see that the conclusion is true, and necessarily so. V

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Before we proceed in our detailed examination of the nature of the syllogism and syllogistic reasoning, we need to pause at this point and call attention to a very important distinction pertaining especially to deductive argument, and that is the distinction between va lid ity and truth. In ordinary language we sometimes use the term “valid” as if it were a synonym for “true,” as when, for example, we say, “That’s a valid statement,” by which we mean, “That’s a true statement.” However pardonable such usage might be in casual speech, it has no place in the vocabulary of logic. We have already learned that the quality of being true or false belongs only to propositions, or categorical statements. Validity, on the other hand, is a property which pertains to arguments taken as a whole. What do we mean when we say that an argument, specifically a deductive argument, is valid? We means that its stru c tu re — i.e., the a rra n g e m e n t o f its p r e m is se s — is su ch that, i f the p re m isse s a re true, then the conclusion is n ecessa rily true. Think of a valid argument as being comparable

to a well-made machine, say a brand new car just off the assembly line. No matter how well made that car is, it will not run unless there is gas in the tank. Think of the gas as being comparable to true premisses. In order for the car to function as it is intended to function, it must be (a) structurally sound (no mechanical problems), and it must be (b) properly fueled. In order for a syllogistic argument to “work” (i.e., to arrive at a necessarily true conclusion), it too must be structurally sound, and it must contain true premisses. To put it another way, a syllogism, or any deductive argument, must be sound with respect to its fo r m and with respect to its co n ten ts. To sum up, truth or falsity pertains to propositions; validity or invalidity pertains to arguments. A proposition is true if what it asserts corresponds to its referents, false if there is no such correspondence. An argument is valid if its form is sound, invalid if it is not. Strictly speaking, an argument Just as such, is neither true or false; it is either valid or invalid. What are true or false are the contents of an argument, the propositions which represent the premisses and the conclusion.

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Validity has to do with the structure or the form of an argument. The classical example o f the syllogism that I cited above, which begins with the premiss, “All men are m ortal,” and concludes with, “Socrates is m ortal,” represents a form which is regarded as the perfect syllogism, the most potent, on account o f the kind o f conclusion it is capable o f delivering— a universal affirmative proposition, o f the “All S are P” type. If we can conclude an argument with a universal affirm ative proposition the truth o f which we are certain, then we have made the strongest possible statement regarding whatever it is we are talking about. But already you might be puzzled. The conclusion of the argument we are dealing with here is, “Socrates is mortal.” Is that not, with respect to the distinctions among propositions we spelled out earlier, a singular proposition, in contrast to a general proposition? It is indeed. A singular proposition, recall, is one whose subject is a single thing, a unique entity, such as, in this case, the fellow named Socrates. W ould not such a proposition be the exact opposite of a universal affirm ative proposition? As a m atter of fact, no. Recall also that in logic, singular propositions are treated as universal propositions, so that the conclusion, “Socrates is m ortal” is identified as an A proposition, a universal affirm ative. The reasoning at work here goes something like this: W hen we have a proposition with a singular subject, such as Socrates, the Colosseum, Kansas City, M ount Everest, the Golden Gate Bridge, it is understood that we are treating the entire com prehension o f the subject, its total meaning, all the notes that are proper to it. It would be silly, as well as atrociously bad English, to speak of “all Socrates,” or “all Golden Gate Bridge,” but, from a logical point o f view, that is w hat we mean when we employ those terms (without the “all”) as the subject terms of propositions. Because every singular proposition is regarded as a universal proposition, “Socrates is mortal” qualifies as such, and therefore our syllogism is made up of three universal affirmative propositions. In order to remove all ambiguity in this matter, I will alter the famous textbook example of the perfect syllogism so that it reads as follows: All men are mortal. All Greeks are men. Therefore, all Greeks are mortal. To get a sense of the bare-bones structure of the argument, we may express it in purely symbolic terms in this manner: M —- P S — M S — P W e have already acquainted ourselves with one application of the symbols “S” and “P,” as representing respectively the subject and predicate terms of a

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proposition, as when we express a universal affirmative proposition by writing down, “All S are P.” The meanings o f“S” and “P” as figuring in the model for the syllogism bear different meanings from those assigned to them when used to symbolize the parts of individual propositions. Here “S” represents the minor term, and “P” the major term of the syllogism. The minor term may be the subject term of a proposition, and the major term may be the predicate term of a proposition, as in the syllogistic form above, but this need not necessarily be the case. The third letter, “M,” represents what is called the syllogism’s middle term. Everything to be found in the above model is meaningful, and not only the letters. The dashes separating the letters on each line represent the copula of the proposition, either “is” or “are,” depending on the proposition’s quantity. The line that separates the first two propositions (the premisses) and the third (the conclusion) is to be read as “therefore.” To recapitulate: S = minor term; P = major term; M = middle term. We see, then, that one of the key structural elements of a syllogism is that it has three terms and three terms only. The next thing we have to do is distinguish between the majorpremiss and the minor premiss, which, as it turns out, is a laughably easy task. The major premiss is simply the one that contains the major term, while die minor premiss is the one that contains the minor term, so, in the above model, “M — P” is the major premiss, and “S — M” is the minor premiss. One might rashly be led to think that the major premiss is the one that comes first, while the minor . premiss takes second place, as is actually the case in our model. But this is not necessarily so. When the premisses are arranged as above, with the major premiss first and the minor second, the argument is said to be in standardform, but, the premisses could be in reverse order and the logical integrity of the argument would be unaffected by that fact. All right, then, we can identify the major premiss because it contains the major term, and with equal confidence we can point out the minor premiss by reason of the fact that it contains the minor term. But how do we know which is which term? We know that because the minor term is always the subject term of the conclusion, and the major term is always the predicate term of the conclusion. There are no exceptions to that rule. Here then is the pattern we are dealing with: the minor term appears in one of the premisses and the conclusion; the major term appears in one of the premisses and the conclusion; the middle term appears only in the premisses, never in the conclusion. The symbolized expression of the syllogism we are interpreting has thus far provided us with a good deal of information. We know that the argument is composed of three distinct terms (which is to say, three distinct ideas), and three distinct propositions, two serving as premisses, one acting as the conclusion. And we know how precisely to identify each of those propositions, irrespective of how they might be ordered. The conclusion is not simply the proposition that comes last, but is the one whose subject is the minor term, whose predicate is the major term, and which does not contain the middle term. (The conclusion could

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very well come first, and this can have the effect of lending special rhetorical force to an argument.) The major premiss is the proposition which contains the major term along with the middle term, and the proposition with the minor term plus the middle term can be none other than the m inor premiss. But the model above tells us nothing at all about the quantity and quality of the propositions which compose the syllogism, and in that sense it is seriously incomplete, for it fails to provide information which is altogether essential to know if we are to make an accurate assessment o f the validity of the argument. Supplying that m issing information, our completed model, reflecting the perfect syllogism, takes the following form: All M are P. All S are M. Therefore, all S are P. This gives us a full account o f the structure of: All men are mortal. All Greeks are men. Therefore, all Greeks are mortal. Now, in the fully expressed symbolic model, we can clearly see that our argument is one which is made of three propositions, all o f which are universal affirmatives. And because the conclusion is a universal affirmative proposition, we refer to the syllogism as perfect, for taking its conclusion to be true, on the strength of the premisses, whatever S and P might refer to in the real world, we are making the strongest possible assertion as to how they are related to one another: each and every member o f the class S is to be found within the class P. Without fail. T he Essence

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Syllogistic R easoning

We are now properly informed as to the basic elements which make up the structure of an argument that we call the perfect syllogism. In subsequent pages of this book we will become familiar with variant forms of the syllogism, and we will test the validity of each. How well do they work as arguments? We will necessarily be giving much attention to the structure of each argument while engaged in this procedure, for it is structure which is the critical determinant of validity, and we will be giving special attention to how the various parts of an argument relate to one another. Needful as is the kind of close analysis we will be doing in order to acquire a sound understanding o f syllogistic reasoning, there is a danger that it may engender an arid, mechanical attitude toward our subject. This would be unfortunate, for we might then be inclined to divorce logic from life. W hat logic is all about, essentially, is the human mind at work, in its incessant, often frustrated but never despaired of effort to attain the truth. The

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close and detailed analysis that logic gives to every aspect of human reasoning has therefore but a single object, and that is to make us more proficient thinkers, and thus more proficient pursuers of truth. When we are first confronted with a fully and formally expressed syllogism, especially if it is put in symbolic form, it might strike us as a very odd sort of animal, having very little to do with the normal process of thinking, a process with which we are, after all, quite familiar, for it is something which we have been engaged in— and no doubt most of us would want to suppose, rather successfully—for as far back as we can remember. But strange as the syllogism may at first seem to us, it is really, in terms of the basic processes of reasoning it represents, as close to us as the most elementary operations of our minds, for in point of fact we have not been simply thinking for as far back as we can remember, we have been thinking syllogistically. The syllogism is the emblem for the way the human mind naturally functions. M. Jourdain, a character in Le Bourgeois Gentilhomme, by Moliere, is astonished to learn that, unbeknownst to himself, he had been speaking prose all his life. He probably would have been equally astonished to know that he had been thinking syllogistically all his life. Aristotle is the father of the science of logic, for, inventive genius that he was, he was the first to have given careful and thoroughgoing thought to the way we think. He was the first to bring systematic organization to the various forms of human reasoning. Aristotle may be said to have invented logic, but not logical thinking. The latter had been going on, well or badly, since the beginning; rational creatures have an irrepressible tendency to think rationally. Much less did Aristotle invent the syllogism, but he did, to our everlasting benefit, give a complete account of the various forms it takes, when we do what comes naturally to us. Before we get into the potentially distracting particulars of the close analysis of syllogistic reasoning, let us make sure at this point that we have a good understanding of the essence of that reasoning, which is revealed in the elementary principles by which it is governed. It is crucial that we do this, for it would avail us little if we were to master the mechanics of syllogistic reasoning, gain a purely superficial knowledge of how syllogisms work, without grasping the principles that explain why they work as they do. This would be like someone who has achieved the ability correctly to identify the various parts of an internal combustion engine, who can put them together flawlessly so that the assembled engine runs like a top, but who is not able to explain why it runs like a top, or runs at all. He has no knowledge of the basic principles which explain the workings of the internal combustion engine. We would say that he lacks scientific knowledge. In logic we want a scientific knowledge of our subject.

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T he P rinciple

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Let us put before us once again our model syllogism, stated in plain English. All men are mortal. All Greeks are men. Therefore, all Greeks are mortal. What is going on here, altogether internal to the argument itself, which ensures that its conclusion is not only true but necessarily so? The principle o f the identifying third calls attention to the critical role played by the middle term in syllogistic argument, which is, establishing an association between the major term and the minor term so as to make a true conclusion possible. The principle of the identifying third can be stated as follows: T wo things which are identical with a third thing are identical with one another. As soon as we hear the principle expressed, we realize that we are dealing with one o f the axiomatic truths o f human reasoning. The principle can be expressed symbolically thus: A=C B =C A=B If A is identical to C, and if B is also identical with C, then it must be the case that A is identical to B. When we speak o f two terms being identical to a third, the identicalness in question may be purely quantitative in nature, and in that case, so it would seem, the principle is easier to see. Consider this mathematical statement. 3+ 3=6 2+4 = 6 3+ 3 =2 + 4 However, in logic, when we refer to two terms being identical to a third— as we do when we speak o f the m ajor and m inor terms o f a syllogism being identical to its middle term— we must be careful not to suppose that we have here something like mathematical equality. The m ajor and m inor terms are “identical” with the middle term in the sense that there is a radical bond which exists among the three terms, with respect to the essences or natures whicheach of those terms represent. This is to say that the relation among the three terms is not peripheral or superficial. It does not involve a purely extrinsic and mechanical connection among them. The major premiss of our model syllogism informs us that it is of the very nature o f man (middle term) to be a mortal being (major term); humanness is identical with mortality, in that you cannot separate the one from the other. Then the minor premiss informs us of the truth that Greeks (minor term) are one and the same with human beings; they represent a particular part of the whole which is the entire class. So, here we have an exemplification of the principle of the identifying third. To be human (third term) is to be mortal (first term), and

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to be Greek (second term) is to be human (third term); thus, given the relation that necessarily exists between the first and third terms, and between the second and the third terms, a necessary relation is forged between the first and the second, or the major and the minor, terms. To sum up. We have two ideas, the idea of mortality and the idea of being Greek, which, given the very natures of each, are inextricably bound up with a third idea, the idea of being human. From this we conclude that the idea of being Greek and the idea of mortality are inextricably bound up with one another. T he P rinciple

of the

S eparating T hird

The principle of the identifying third applies only to syllogistic arguments whose conclusion is an affirmative proposition, which means that both of the argument’s premisses would also have to be affirmative propositions. To explain the underlying logic of an argument whose conclusion is negative, we need to appeal to the principle o f the separating third. In our survey treatment of propositions we saw that the difference between those that are affirmative and those that are negative is that, in the case of the former, subject and predicate are brought together in either a complete or incomplete way, and, in the case of the latter, subject and predicate are separated off from one another in either a complete or incomplete way. And thus we have the four kinds of general propositions: universal affirmative (A), particular affirmative (I), universal negative (E), and particular negative (O). As our working model for our discussion of the principle of the separating third, we will make use of the following argument: No insects are vertebrates. All bees are insects. Therefore, no bees are vertebrates. Let us first identify our terms. Because “bees” is the subject of the conclusion (clearly identifiable because that proposition begins with the logical indicator “therefore”) we know that it is the minor term, and because “vertebrates” is that proposition ’s predicate term, we unhesitantly identify it as the major term. Having thus properly identified the minor and major terms, we know that the major premiss leads off the argument, followed by the minor premiss. The syllogism is thus in the standard form: major premiss; minor premiss; conclusion. An interesting thing to take note of regarding negative conclusions, which separate minor and major terms either completely or incompletely (in the case of our model, the separation is complete), is that those separations would have no logical justification had not a positive bond been established, in the premisses, between one of those terms and the middle term. And it is for that reason, as we shall learn later, that two negative premisses render a syllogism invalid, giving it a structure that cannot guarantee a true conclusion, even if the

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premisses are true. We state the principle of the separating third as follows: When there are two things, one of which is identical, and the other of which is not identical, with a third thing, then those two things are different from one another. This principle describes what is taking place in a valid syllogism one of whose premisses is negative, and whose conclusion is also negative. That combination is a necessary one for validity. Note the phrase, “one of which is identical,” in the statement of the principle. This refers to the positive bond which is forged between one of the extreme terms (this is the collective way of referring to the minor and major terms) and the middle term. In the case of our model, the bond is forged between the minor term and the middle term: “All bees are insects.” To see more clearly what is going on in this kind of reasoning, we advert to another mathematical example. 3+3=6 3+2*6 3 + 3* 3 + 2 Once again we remind ourselves that the kind of identity and separation we are concerned with in logic are not to be thought of in terms of mathematical equality or inequality. We deal with entities that are either linked together, or separated off from one another, because of their inherent natures. Analogous to what was said regarding the principle of the identifying third, where two ideas bond with one another because o f their inherent compatibility (i.e., as with the ideas of being human and being mortal), in the case of the ideas that are involved in a negative proposition, those expressed by either the major or the minor term are separated off from the idea represented by the middle term, either completely or incompletely, and that will necessarily result in either a complete or incomplete separation between minor and major terms. Our model syllogism shows that the major premiss executes a complete separation between the major term and the middle term: “No insects are vertebrates.” Because of the very nature of the members of the class of insects, and because of the very nature of the members of the class of vertebrates, the two classes are distinct and separate from one another. There is no overlapping between them. The intrinsic intelligibility of these two ideas, the idea of insect and the idea of vertebrate, prohibits any bond ever being forged between them. But we recall that no logically justifiable separation between minor and major terms in the conclusion is possible without there having been made a positive link between one or other of them and the middle term. And this condition is met, in our model, by the minor premiss: “All bees are insects.” It is one of the foundational rules of thought that separation or disunity is dependent upon unity. More broadly stated, the negative is not possible without the positive. Expressed in moral terms: evil is parasitic upon the good. And metaphysically considered: non-being is meaningless without being. In our model syllogism, the major premiss announces that the class of insects is entirely divorced from the class of vertebrates. But now look what

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happens in the minor premiss. A new term is introduced, “bees,” and we are informed, quite truthfully, that all of the busy and buzzing individuals denominated by that term, each and every one of them, are members of the class of insects. What can we conclude, what must we conclude, from the information provided to us from the major and minor premiss? Because of the complete dissociation between insects and vertebrates, because bees are completely associated with insects, it is then necessarily the case that there is complete dissociation between bees and vertebrates. The logic of the argument is as tight as can be. It is the peculiar way the middle term functions in the syllogism, separating itself from one extreme (the major term), bonding with the other (the minor term) that makes for the inevitable truth of the conclusion. T he D ictum

de

O mni P rinciple

The basic rationale behind the principle which is called the dictum deomni (the phrase can be loosely translated as “the rule governing the whole”) is something with which we have already become conversant, as the result of our close study of the four general propositions and how they relate to one another, all of which is reflected in and summed up by the square of opposition. You will recall, regarding that square of opposition—specifically, its left side—how A and I propositions so relate to one another that if the A proposition (universal affirmative) is true, then the I proposition (particular affirmative) is true. Right there we have the demonstration of the dictum de omni principle, the principle which tells us that if something is true of a whole, an entire class, then it is necessarily true of any part of that whole. Like every other basic principle of logic, this one communicates a self-evident truth. The dictum de omni principle relates very closely to the principle of the identifying third in revealing to us the kind of logic which is operative in syllogistic reasoning. The “identifying third” we know to be the middle term, through the mediation of which the minor and major terms are conjoined. Looked at another way, from the interpretative perspective of the dictum de omni principle, the middle term is the “whole,” in the sense that something is predicated of the entire class which is represented by the middle term, and therefore can be predicated with equal confidence to any part of that class. So, for example, and with reference to our model syllogism, because mortality can be truthfully predicated of the entire class of men (“all men are mortal”) it can be truthfully predicated of any segment of that class (“all Greeks are mortal”). T he D ictum

de

N ullo Principle

Just as the principle of the identifying third and the dictum de omni go together, so too do the principle of the separating third and the dictum de nullo principle. “Dictum de nullo” can be literally translated as “the rule regarding nothing,” but that is not very helpful by way of telling us what the principle is

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all about. A better translation in this respect would be, “the rule governing negation.” This is a principle, then, which, like the principle of the separating third, applies to syllogisms whose conclusions are negative. The model syllogism we will keep in mind here is the same one we used above, where it was argued that because no insects are vertebrates, and because all bees are insects, it necessarily follows that no bees are vertebrates. The full expression of the idea behind the principle of the dictum de nullo is as follows: Whatever is universally denied of a whole, can be denied as well of any part of that whole. That should ring a bell in our memories, for what we have there is a description of what is happening on the right side of the square of opposition, when we begin with an E proposition (universal negative) which is true and then immediately infer that the corresponding O proposition (particular negative) is also true. If “no birds are reptiles” is true, it’s obviously the case that “some birds are not reptiles” is also true. If reptilian nature can be denied of the entire class of birds, we are entirely justified in denying that same nature to any portion of the class. Once again, we are presented with a self-evident truth. But how does the principle o f dictum de nullo specifically apply to syllogistic reasoning? The principle of the separating third, recall, informed us that if the class represented by the middle term is completely separated off from another class, then anything which is enclosed within the “whole” which is the middle term will also be completely separated off from that same class. We clearly see how that works with our model syllogism. The class designated by the middle term (“insects”) is completely separated off from the class of vertebrates. And because the class of bees is entirely encompassed within the larger class of insects, it then follows that the class of bees is completely .^separated off from the class of vertebrates. Vertebral nature is being universally denied of insects; this means that vertebral nature can be denied of any specific kind of insect, such as bees. D iagraming Syllogisms In Chapter Six we introduced a simple method of schematizing the four general propositions, which allows us to get a quick visual representation of how, in any proposition, the subject term relates to the predicate term. If we apply this method to the propositions which serve as the major and minor terms of any syllogism, we can immediately see how the syllogism ’s three terms relate to one another so as to produce the conclusion. The method provides us with a helpful means of indirectly testing the validity of the argument. We will now apply this method to each of our model syllogisms, beginning with: All men are mortal. All Greeks are men. Therefore, all Greeks are mortal.

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To begin, we will take the intermediate step of putting the syllogism in symbolic form, using the notation we have already introduced and explained. Doing this helps us get a clearer sense of the structure of the argument, and this makes the diagraming process easier. All M are P. A11S are M. A11S are P. Diagraming the syllogism’s major premiss, “All M are P,” gives us:

P M

The diagram shows that there is a class M, and that the class is entirely encompassed within the class P. All human beings are members of the larger class of mortal beings. Next we diagram the syllogism’s minorpremiss, “All S are M,” incorporating it within the diagram we have already constructed. Doing that yields the complete visual representation of the argument, thus:

P M S Now we can see how each of the syllogism’s terms logically relate to one another, in such a way as to make its conclusion inescapable. Because the entire class M (“men”) is encompassed within the class P (“mortal beings”), and because the entire class S (“Greeks”) is in turn encompassed within the class M (“men”), class S must also, and necessarily, be encompassed within class P. Because all M are P, and because all S are M, there is simply no avoiding the fact that all S are P. And now to our second model syllogism. No insects are vertebrates. All bees are insects. Therefore, no bees are vertebrates. We cast the argument in symbolic form, which gives us: No M are P. All S are M, No S are P.

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The first step in the diagraming process is to diagram the major premiss, which in this case is a universal negative proposition, “No M are P,” so it will be represented in the following fashion: M

P

The proposition introduces us to two classes, M (“insects”) and P (“vertebrates”), and tells us that never the twain shall meet; they are completely separated off from one another. We next diagram the syllogism ’s minor premiss, “All S are M,” superimposing it upon what we have already put down on paper, and with that we have: M s The minor premiss brings a new class into the picture, S ( ‘bees”), and tells us that the class is entirely embodied within the previously introduced class M. And, voila! We have before our eyes the unavoidable conclusion o f the argument. The two classes M and P have nothing to do with one another. But the class S is completely embraced by class M; there is nothing which is S which is not also M. That must mean, can only mean, that the class M has nothing to do with the class P. (See Appendix C fof additional commentary on the diagraming of syllogisms.)

Review Items 1. What are the basic components o f every argument, and how does argument relate to reasoning? 2. Describe a specific way in which an argument can take on complexity. 3. W hat is the essence of the reasoning process? 4. Cite the salient characteristics of deductive reasoning. 5. What is the difference between immediate reasoning and mediate reasoning? 6. Give a general description of syllogistic reasoning. 7. Explain the difference between validity and truth. 8. Give an account of the basic structure of a syllogism, naming all of its principal parts. 9. Explain the principle of the identifying third and the dictum de omni principle, and how they serve as the foundations for syllogistic reasoning. 10. Explain the principle of the separating third and the dictum de nullo principle, and how they serve as the foundations for syllogistic reasoning.

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Exercises A. In responding to each of the discourses listed below, determine (a) whether or not it is an argument, and, if it is, (b) identify its premiss (or premisses) and conclusion, and then (c) determine whether or not it is a deductive argument. 1. Sylvia would not be a trustworthy witness for the defense, because she has a tendency to be less than forthcoming about her exact age. 2. Bludgent is obviously the best candidate for the governorship. He is clearly superior to all the other candidates running for that position. Indeed, none of the other candidates can hold a candle to him. He’s better than Ward, better than Schaeffer, and it’s simply no contest between him and Peterson. All in all, Bludgent stands head and shoulders above everyone else in the race. As a matter of fact, he is arguably the best candidate we have had for the state’s highest office since the elections of ‘76. 3. Because this plane figure is a triangle, it follows that its internal angles are equal to two right angles. 4. Tom will never make it through college because the poor guy just lacks self-discipline. 5. All Chicagoans are Illinoisans. Chuck is a Chicagoan. Therefore, Chuck is an Illinoisan. 6. The walleyed pike is found in many northern Wisconsin lakes. It takes a skilled angler to catch that fish on a consistent basis. 7. Where there’s smoke there’s fire. There’s smoke pouring out of the Atkins Forest Preserve. They have a fire on their hands over there. 8. I saw Jim making the sign of the cross when the plane ran into some heavy turbulence. He must be Catholic. 9. Because this is pure oxygen, we can be sure that it’s flammable. 10. Of course she’s mad at me. Did you see that look she gave me? B . Assume that each of the statements listed below is a “point” you want to make to an audience, i.e., something you desire to be accepted as a reasonable position. Then make up at least one statement of your own which will serve to support the point. If you do not agree with any of the items as stated, then take its negation as your point. 1. The Great Depression of the 1930’s was not an unmitigated disaster. 2. Men are naturally more competitive than women. 3. Democracy is the best form of government. 4. In making important decisions we should always be guided by our feelings. 5. Smoking should be made illegal. 6. By no means should Judge Doozbanner be appointed to the U.S. Supreme Court.

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Chapter Ten The Figures and Moods of the Syllogism T he C ategorical Syllogism The two syllogisms with which we have been working so far are examples of a categorical syllogism, which is so described for the eminently logical reason that it is made up of categorical propositions. A categorical proposition is one and the same as a declarative sentence, which, being in the indicative mood, declares or indicates something in a straightforward, definitive way. A categorical proposition says something about something determinately; it tells us what is, was, or will be the case. It states facts: present facts, past facts, or would-be future facts. Of the three tenses a categorical proposition can assume, the present and the past tense would be stronger than the future tense, for facts of the past are fixed firmly forever, and the facts of the present are as undeniable as the present itself. But future facts are, at the moment, as unreal as the future itself, and in order to come to know them as facts we must simply wait and see what they turn out to be, as they flow ghost-like out of the future and take concrete, observable form in the present. Nonetheless, there are both categorical andnon-categorical ways of referring to future facts, as revealed in the difference between talking about what “will be” and what “may be,” reflecting the difference we acknowledge between a sure thing and only a possibility. Here are some examples of categorical propositions. Jane is a senior in college. Water boils at 100 degrees Celsius at sea level. Alexander the Great died in the year 323 b .c . It is easy to see why we would want our arguments to be composed of categorical propositions. The whole purpose of argument is to get somewhere, to arrive at a definite conclusion, which can only be done if we proceed from premisses which are categorical propositions, propositions which commit

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themselves to something definite. Imagine the pickle we would be in if the premisses of our classic syllogism were expressed non-categorically, thus: All men could very likely be mortal. And Greeks might be men. Where could we possibly go from there? Only to an anemic, noncommital conclusion along the lines of: “All Greeks, maybe, are mortal.” That is not very satisfying, for it leaves us in a state of uncertainty, and what we seek from arguments, from the sound reasoning that supposedly stands behind them, is certainty. We must develop the habit, in the first instance, of thinking categorically, seeking to formulate definite judgments about which we are able to be reasonably certain. Then, casting those judgments in the form of categorical propositions, we have in them the rudimentary makings of sound arguments. T he F igure

of a

Syllogism

Our two model syllogisms, besides being examples of categorical syllogisms, are also to be identified as first figure syllogisms. The figure of a syllogism is determined by the position of the middle term in its premisses. The distinguishing feature of a first figure syllogism is the fact that the middle term is the subject term of the major premiss and the predicate term of the minor premiss. Thus, assuming it to be in standard form, a first figure syllogism will be configured in this fashion: M— P S — M S — P The identifying mark of a second figure syllogism is that the middle term occupies the predicate position in both the major and the minor premiss, which gives us the following configuration: P — M S — M S — P A third possibility is that the middle term can assume the subject position in both the major and minor premiss, and it is that arrangement which precisely characterizes a third figure syllogism, configured thus: M—P M— S S— P Finally, the middle term can be the predicate term in the major premiss, as in the second figure, and the subject term in the minor premiss, as in the third figure, and with that we have a pattern which looks like this: P — M M— S S — P

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So long as other important conditions are met, we can reason successfully within the framework of all four o f these figures. Notice that the structure of the con­ clusion remains the same in every figure: the minor term is always the subject o f the conclusion, and the major term is always its predicate term. This accen­ tuates the crucial role played by the middle term in syllogistic argument. T he M ood

of a

Syllogism

In referring to the mood of a syllogism we do not have in mind whether it is in an elated or depressed emotional state, however it might at times engender those states in logicians. The m ood o f a syllogism (the word is a corruption o f the L atin m o d u s = “m ode” ) refers to the pecu liar character which the argum ent takes on by reason o f the quantity and the quality o f the proposi­ tions which com pose it. A syllogism ’s m ood identity depends principally on the character o f its prem isses, w hether they are universal or particular, w hether they are affirm ative or negative. Once more we place on the stand our classic syllogism . All men are mortal. All Greeks are men. Therefore, all Greeks are mortal. We readily identify that argument as a categorical syllogism, because its pre­ misses and conclusion are categorical propositions, and it is in the first figure, because the middle term (“m en”) is the subject term of the major premiss and the predicate term of the m inor premiss. W e note further that the syllogism’s two premisses are universal affirmative propositions, and so is its conclusion— all A propositions, in other words. This tells us the m ood o f the syllogism, expressed in shorthand fashion as AAA. Arranging those letters so that they represent an argument in standard form, we have: A A A W e read that very sparse model as telling us that we have an argument in which the m ajor premiss is a universal affirm ative proposition, as is the minor pre­ miss, and as is the conclusion. Given the fact that there are only four kinds o f propositions which can serve as the premisses of a syllogism, the four general propositions which we designate as A, E, I, and O propositions, and given the fact that there are two premisses in a syllogism, that leaves us with sixteen possible configurations for the premisses o f a syllogism, determined by the quantity and the quality o f the propositions that m ake up those premisses. Here are all those possibilities, symbolically expressed: EEEE AAAA I I I I OOOO AEIO AEIO AEIO AEIO

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If we were to take into consideration that the syllogism has four figures, and then do a little multiplication, we would come up with a grand total of sixtyfour possible configurations for the syllogism, which means that there are sixty-four possible ways of arguing syllogistically. So, for example, we would have the AA mood in all four figures, the AE mood in all four figures, and so on. But please do not let yourself be overwhelmed by that number. Yes, there are sixty-four possible ways of arguing syllogistically, but fewer than a third of that number represent valid ways of arguing. There are four valid moods in the first figure, four in the second, six in the third, and five in the fourth. We will now introduce the valid moods in each of the four figures, and show, in doing so, just why they are valid. We will examine what it is about the way they are structured, the way their terms relate to one another, that makes them work as successful deductive arguments; that is, as arguments which carry with them the assurance that, if their premisses are true, then so too must be their conclusions. T he V alid M oods

of the

F irst F igure

There are four valid moods in the first figure: AA, EA, AI, EL Those pre­ misses yield, following the same order, these conclusions: A, E, I, O. The four valid arguments of the first figure, then, are: A E A E A A I i A E I O Logicians of yore made up four words which are intended to help us remember the valid moods of the first figure. They are Barbara, Celarent, Darii, and Ferio. Take special note of the vowels in those words; they carry the pertinent mnemonic message. In each case the vowels stand for the letters that represent one or another of the general propositions. Our classic model syllogism is known as a Barbara syllogism, meaning that it is an argument all three of whose propo­ sitions are universal affirmative, or A propositions. Recall now the other syllogism we analyzed in the previous chapter. No insects are vertebrates. All bees are insects. Therefore, no bees are vertebrates.That is a Celarent syllogism, for its major premiss is a universal negative propo­ sition (E), its minor premiss is a universal affirmative (A), and its conclusion is a universal negative (E). I trust we have devoted sufficient time to the study of the Barbara and Celarent syllogisms in the previous chapter to have at this point a reliable enough understanding of why it is that, if the premisses of arguments which take those forms are true, then the conclusion must be true. But please underline in your

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mind how important it is to be aware of the two critically important conditions which must be met before we can be sure that a syllogism will produce a true conclusion: (1) the argum ent m ust be valid, that is, it must have a logically sound structure; (2) the premisses of the argument must be true. The test for a logically sound structure is this: if the premisses o f the argument are true, it is impossible for the conclusion to be false. If only one of those two conditions are met, there is no assurance that a true conclusion will be forthcoming. Now, the AAA and the EAE moods of the first figure meet the test o f validity, so if we have true premisses in these two forms of argument, we can be sure that our conclusions will ring true. But if we have false premisses, all bets are off. In that case, the form is right, but the contents are deficient. W e may, with false premisses, end up with a true conclusion, but that is something that happens quite by accident, as we will have occasion to dem onstrate in the following chapter. For now, consider the following argument. All zebras are monkeys. All referees are zebras. Therefore, all referees are monkeys. This is a perfectly valid syllogism; there is nothing wrong with its logical structure. In that sense it could be roughly compared to a machine, let’s say a car, which is in perfect m echanical condition. But there is everything wrong with the premisses o f the above argum ent, in that they are not only false but silly besides. So we might say that we have a situation here which is like a car which is in perfect mechanical condition but whose gas tank is filled with prune juice, with the consequence that the car won’t run. In the syllogism above, silly premisses lead to a silly conclusion. We now turn to another argument: No women are mothers. All Vietnamese are women. Therefore, no Vietnamese are mothers. Here again we have a valid syllogism . Its form is ju st fine, but its contents leave much to be desired; indeed, they are plainly false, with the result: no guarantee of a true conclusion. Far from it, in this case. Validity alone is not enough, nor, as we shall see later, is truth alone. The two must go hand in hand. One may have premisses which are impeccably true, but if they are incorporated within an invalid syllogism , no true conclusion necessarily follow s. The point cited above is important enough to bear repeating: for a true conclusion to follow necessarily, a syllogism m ust be valid, and its premisses must be true. Expressing a syllogism in symbolic terms tells us about the formal qualities of the argument which is being represented. It can inform us at a glance whether or not an argument is valid. Needless to say, this is very valuable information,

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but it is insufficient for a complete analysis of any argument, for we must know about its contents as well as about its form. We are presented with the following model: All M are P. All S are M. All S are P. And we are asked: Is the conclusion to this argument true? We immediately recognize the argument as a first figure Barbara syllogism, so we know that we are dealing with a valid argumentative form; there is nothing amiss with respect to its structure. But we can say nothing about the truth or falsity of the conclusion. In order to be able to make a judgment of that sort we of course have to know what S stands for, and P, and M. We need something, referring to the real world, that we can sink our teeth into. Logic, in the final analysis, is either about the objective order of things, or it is useless to us. Truth can never be merely a matter of how one purely abstract symbol relates to another. It has to do with ideas which are intended to represent extra-mental realities, and the test of truth is whether or not there is a correspondence between our ideas and objects in the real world to which they refer. What we can say about the above model is this. If a true proposition is expressed in the mode of die major premiss, and another true proposition is expressed in the mode of the minor premiss, then the conclusion of the argument would be necessarily true. T he Darii

and

F erio M oods

of the

F irst F igure

We will now take a look at the third valid mood of the first figure, called the Darii mood. That word, which, it must be confessed, does not figure prominendy in our everyday vocabulary, tells us that we are dealing with an argument whose major premiss is a universal affirmative proposition, which has a particular affirmative proposition as its minor premiss, and whose conclusion is a particular affirmative. As an example of such an argument, we offer the following: All Germans are Europeans. Some mechanical engineers are German. Therefore, some mechanical engineers are Europeans. . We next put the argument in symbolic form, to get a more immediate sense of its structure, and to see more clearly how part relates to part. All M are P. Some S are M. Some S are P. The major premiss introduces us to two classes, M and P, and informs us that the first is completely embraced by the second. The minor premiss introduces a new class, S, and tells us that there is a partial relation between it and the

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previously introduced class M. In other words, there is a definite overlapping between classes S and M. Now, if that is the case, and if the entire class M is within class P, that means that an overlapping also takes place, and necessarily, between class S and class P. Diagraming the argument will help us to see this more clearly. P M s

X

How about the premisses of the argument? Are they true? There would seem to be no problems there. Given the fact that Germany is part and parcel of Europe, it stands to reason that all Germans would qualify as Europeans. As for the minor premiss, while we could not claim that all mechanical engineers are German, it would be hard to imagine that there are not at least a couple of them in the country. W ith those two prem isses, then, and given the logical relations they establish among the three term s o f the syllogism, we can confidently assent to the truth o f the conclusion. Given the combination of valid structure and true premisses, the conclusion has to be true. The fourth valid mood of the first figure is called Ferio. The name represents a syllogism whose major premiss is a universal negative proposition (E), whose minor premiss is a particular affirmative proposition (I), and whose conclusion is a particular negative proposition (O). Here is an example of an argument which is structured according to that pattern. No atheists are theists. Some Englishmen are atheists. Therefore, some Englishmen are not theists. We put the argument in symbolic form. No M are P. Some S are M. Some S are not P. The major premiss tells us that the class M (“atheists”) and the class P (“theists”) are completely separate. This would be true by definition. The minor premiss introduces the class of Englishmen, and asserts that some o f the members of that class are to be found in the class o f atheists, an assertion which can reasonably enough be accepted as true. (I can offhand think of the names of at least two Englishmen who are atheists, although doubtless there are more.) Now, if no atheists are theists, and if there are some Englishmen who are numbered among the atheists, then just those Englishmen obviously cannot be

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theists. A diagram might help to shed greater light on the inner workings of the logic of the argument.

M

P

X S The squares labeled M and P are separated from one another, thus reflecting the information provided by the major premiss. The third square illustrates the minor premiss and how the class it introduces, S, relates to the class M. There is a partial relation between the two, illustrated by the overlapping of square S and square M. The “X” emphasizes the specific claim made by the minor premiss. In constructing the diagram I positioned the S square so that it overlaps square P as well as square M. For what reason? To show that, although the argument does not explicitly state that there is any association between class S and class P, neither does it preclude the possibility that there could be one. And I wanted the diagram to reflect that possibility. T he Potency

and

V ersatility

of

F irst F igure Syllogisms

We have already identified the first figure Barbara syllogism (AAA) as the perfect syllogism. It is perfect because of the potency of the kind of conclusion it is capable of delivering, a conclusion which predicates something truly of an entire class, thus taking the form of a universal affirmative proposition. Another reason why logicians like to dub the Barbara syllogism “perfect” is because of the ideal role played in it by the middle term. It performs its connecting function in the most efficient way, because its extension is midway between that of the other two terms, being less than that of the major term, and greater than that of the minor term. And that makes for the establishment of the strongest possible relations among the three terms of the syllogism. So, in the Barbara syllogism, the first figure can boast the most commanding form of argument. But the first figure is also noteworthy for its overall versatility. In its four moods it produces conclusions which represent all four general propositions: universal affirmative in Barbara, universal negative in Celarent, particular affirmative in Darii, and particular negative in Ferio. In logic we refer to a universal proposition as “strong,” in comparison to a particular proposition, which is denominated “weak.” And the same terminology is employed apropos of the quality of propositions, where affirmative propositions are called strong, and negative ones weak. This makes an A proposition strong through and through; an E proposition is strong for its universality, weak for its negativity; an I proposition is strong for its being

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affirmative, weak for its being particular; and the poor O proposition is weak on two counts, being both particular and negative. The conclusion o f the C elarent syllogism com bines the strength of universality with the weakness o f negativity; the conclusion o f the Darii syllogism has the strength of being affirmative but is burdened with the weakness of being particular. And the conclusion o f the Ferio syllogism is the weakest of all. Nonetheless, Ferio is a valid argum entative form, and if its premisses are true and non-trivial, its necessarily true conclusions can contribute importantly to our knowledge, such as when, for example, we arrive at the point where we are convinced that some politicians are not to be trusted. That would be the conclusion of the following Ferio argument. No one who plays fast and loose with the truth can be trusted. Some politicians play fast and loose with the truth. Therefore, there are some politicians who are not to be trusted. The fact that the conclusion o f a C elarent syllogism is universal lends it significant force, which is not in every case dim inished for the fact that it is also negative. It is not paltry knowledge to be certain that there are two classes which are completely separate from one another: e.g., “No whales are fish.” And to be able to make an affirm ative assertion, even if it applies only to a portion of a class, as does the conclusion o f a Darii syllogism , may imply knowledge which is not only useful, but som etim es even vital (e.g., “some mushrooms are poisonous”), or com m unicate knowledge which, at least in certain circles, could have pressing practical value (e.g., “some Democrats are fiscal conservatives”). A re T here O nly F our V alid M oods

in the

F irst F igure?

Consider the following argument: All mammals are warm-blooded. All cats are mammals. Therefore, some cats are warm-blooded. Putting the argument in symbolic form, we have: All M are P. A11S are M. Some S are P. We clearly have here a first figure syllogism. It is valid, and because its premisses are true, a true conclusion follows necessarily from those premisses. What is the mood of this syllogism? It is AAI. Here is another argument for your consideration: No dogs sire egg-layers. All poodles are dogs. Therefore, some poodles are not egg-layers.

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Once again in this case, we have a first figure syllogism which is valid, whose premisses are true, and thus so too is its conclusion, necessarily so. And the mood of the syllogism is EAO. What is going on here? Did I not lay it down as a solemn and indisputable matter of fact that there are but four valid moods in the first figure, which are: AAA, EAE, All, EIO? What then are we to make of these two potentially embarrassing intruders, AAI and EAO? Do they demand a retraction on my part, and should they be added to the list of valid moods for the first figure? No, and no. The AAI mood is already implied in the AAA mood, as is the EAO mood in the EAE mood. The particular affirmative conclusion in the first syllogism (“some cats are warm-blooded”) is an expression of the dictum de omni principle, which tells us, remember, that if something can be truthfully predicated of an entire class, it can certainly be predicated of a part of that class, and the premisses of the argument support our being able to predicate warm-bloodedness of the entire class of cats. As for the second argument, here we have an instance of the dictum de nullo principle at work. The premisses truthfully assert that the entire breed of dogs we call poodles, because they are dogs, are not egg-layers. Not a single one of them can perform that remarkable feat. Well, if the whole class of poodles can’t lay eggs, then surely some of them can’t. In sum, the conclusion of the AAI syllogism is simply a more limited way of expressing the AAA conclusion, just as the conclusion of the EAO syllogism represents a limited expression of the EAE conclusion. To put it differently, the AAI syllogism is contained in the AAA syllogism, and the EAO in the EAE. It would be superfluous, therefore, to list them as separate moods. One more comment, concerning the conclusions of the two syllogisms cited above, as examples of AAI and EAO arguments: they are singularly uninter­ esting and uninformative. If we know for a fact that all cats are warm-blooded, why settle for saying that only some of them are? And if there are no doubts in our mind that the entire class of poodles are incapable of laying eggs, it does not do much for the advancement of knowledge to report on only part of that class regarding that incapability. If the premisses of a syllogism justify our saying “all” or “no” in the conclusion, that is what we should say. T he V alid M oods of the S econd F igure: C esare and C amestres There are four valid moods in the second figure of the categorical syllogism, and they are: EAE, AEE, AOO, EIO. And again for the second figure we have four rather exotic words to help us remember those moods. They are: Cesare, Camestres, Baroco, and Festino. Notice that two of these moods, EAE and EIO, are also valid in the first figure. In terms of versatility, the second figure displays considerably less of it than the first. For one thing, it can produce only negative conclusions. We remind ourselves that the characteristic feature of the second figure, in terms of its structure, is the fact that the middle term takes

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the position of the predicate term in both premisses, so we have a configuration of this sort: P— M S— M S— P The first of the valid moods in the second figure which we will consider is called Cesare (EAE), where the major premiss is a universal negative, the minor a universal affirmative, and the conclusion a universal negative. Here is an example of an argument taking that form: No one ignorant of human physiology is a physician. All psychiatrists are physicians. Therefore, no psychiatrist is ignorant of human physiology. The logic which is operative in this argument is exactly the same as that we encountered in the Celarent argument o f the first figure. The major premiss completely separates two classes (in this case, people who are ignorant of human physiology, and physicians); the m inor premiss places a new class entirely within one of those already introduced (the class o f psychiatrists within the class o f physicians); and this necessarily leads to the conclusion that no psychiatrist is ignorant of human physiology. Not surprisingly, the diagram of the argument is the same as that for the first figure Celarent argument, the only difference being in the labeling of the squares. M s The full symbolic expression of the argument: No P are M. All S are M. No S are P. There would seem to be no problem with the truth of the premisses in the argument. It is a plain matter of fact that all psychiatrists are physicians, for psychiatry is simply one of the particular fields in which modem medical doctors can specialize. As for the major premiss, one would earnestly hope that it is true that there are no physicians who are ignorant of human physiology. If there are such, we would not want to be their patients. The second valid mood of the second figure is called Camestres (AEE), where the premisses are in the reverse order to that of the Cesare argument; here a universal affirmative proposition is the major premiss, and the minor premiss is a universal negative. That would give us an argument like this: All mothers are female. No NFL football players are female. Therefore, no NFL football players are mothers.

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We put the argument in symbolic form: All P are M. No S are M. No S are P. We diagram it:

M p From the diagram we see that the logic of the argument is essentially the same as that of the EAE arguments in the first and second figures. We have two classes, M and S, completely separate from one another; a third class, P, is confined entirely within class M. The conclusion is that class S is completely separate from class P. This is made clear enough by the premisses of our example syllogism. It is an indisputable fact that all mothers are women, and, the last time I checked, there were no women to be numbered among NFL football players. Thus, there are no NFL football players who could possibly be mothers. Given the fact that in the second figure we can have a major premiss which is a universal negative and a minor which is a universal affirmative, or the reverse, one might be tempted to think that the same might also be possible in the first figure. But this is not the case. Let us suppose it to be possible, and see what happens. So, we are thinking in terms of a first figure syllogism in the AEE mood, which, symbolically expressed, would look like this: All M are P No S are M. No S are P. Diagraming the argument can give us this arrangement:

P

S

M That would accurately represent what the premisses of the argument are telling us. But the problem is that the premisses are not unambiguously telling us one thing. In order to see how this is so, consider the following diagram:

P M

S

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This too accurately represents, does not do violence to, the information provided us by the premisses. But in this case the diagram shows a conclusion, “All S are P,” that contradicts the conclusion of our model syllogism, “No S are P.” The fact of the matter is, the premisses permit both conclusions. As shown in the first diagram, class S can be completely separate from class M, and be completely separate from class P as well. But nothing precludes the possibility, again, on the basis of the information given us by the premisses, that class S can be completely separate from class M and yet either be entirely within class P, as is class M, or only partially associated with it. The second diagram illustrates the first of these possibilities. When an argument’s initial move is to incorporate the middle term entirely within the major term, and then states that the middle term is completely separate from the minor term, it makes no commitment as to how the minor term relates to the major term. If I tell you, using ordinary language, that all accountants are Republican, and then go on to say that in River City there is not a single accountant to be found, I do not enlighten you one way or the other as to how the class o f Republicans might relate to the class made up of the citizens of River City. It could be that everyone in River City is a Republican, or that there are some Republicans there, or that there are none. Whenever we find ourselves confronted with a situation where an argument will allow for mutually contradictory conclusions, we can be assured that we are dealing with an invalid form. It is not that an invalid form will not permit a true conclusion—it will— but it does not guarantee a true conclusion, which is just what a valid form does, always with the provision, of course, that the premisses of the argument are true. To show more clearly the fickleness of an AEE first figure syllogism, we will consider another example of an argument in that form, this time availing ourselves of the same terms we used in our earlier example of the valid second figure AEE syllogism. All mothers are female. No NFL football players are mothers. Therefore, no NFL football players are female. The premisses are true, and so is the conclusion. Now consider this argument, in the same form: All mothers are female. No eight-year-old girls are mothers. Therefore, no eight-year-old girls are female. The premisses are true, the conclusion is false. Therefore, we have an invalid form, for it is incapable of guaranteeing a true conclusion with true premisses. It is just the situation exemplified in the second argument, where we have true premisses and a false conclusion, which is not possible in a valid syllogism, and this proves that the first figure AEE mood is invalid. As for the first example,

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though its conclusion it true, it does not follow necessarily from the premisses. This is a point which will be explained in detail in Chapter Twelve. T he V alid M oods

of the

S econd F igure: B aroco

and

F estino

The Baroco syllogism of the second figure represents an argument that begins with a universal affirmative proposition, followed by a minor premiss which is a particular negative, and which concludes with a particular negative. Here is how the argument would be symbolized. All P are M. Some S are not M. Some S are not P. And here is an example of the argument: All senators are politicians. Some Indianans are not politicians. Therefore, some Indianans are not senators. The logic of arguments like this tends not to be as immediately apparent to us as the logic of first figure syllogisms, or, for that matter, as the logic of the first two moods of the second figure, which we have just studied. The Baroco argument gives us pause; we have to stop and think about it a minute. How does that go again? We observe that the conclusion of the above argument is a particular negative proposition, weak with respect to both quantity and quality. If an “All S are P’ is the boldest kind of statement we can make, an “Some S are not P” statement is, by comparison, rather limp. For all that, however, this is a perfectly valid form of argument, the premisses we use in our example are true, so let’s see what kind of logic is taking place here. The major premiss makes a familiar move, introducing us to two classes, P and M, and informing us that one of them, P, is entirely embraced by M. The minor premiss introduces a third class, S, and tells us that it is partially dissociated from the previously introduced class M. All right, if all P are M, and if S is partially dissociated from M, then, just to that extent, S must also be partially dissociated from P. A diagram of the argument might help to clarify the logical connections that obtain

M p s

X

I diagramed the minor premiss to show what it explicitly states, and also what it permits. We know for certain—this is the unambiguous message conveyed by the minor premiss—that some Indianans are not politicians. It says nothing

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about Indianans who may be politicians, and we know from sources independent of the argument that some of them in fact are (e.g., the two U.S. senators from that state). But we are concerned only with the portion of Indianans, be it large or small, who stand outside the class of politicians. Those people, because they are not politicians, can certainly not be senators, because all senators are politicians. The Festino mood of the second figure follows the same logic of the first figure Ferio syllogism, where we have a universal negative major premiss, a particular affirmative minor premiss, and a particular negative conclusion (EIO). Consider this argument: No Carthusian monks are U.N. employees. Some Brazilians are U.N. employees. Therefore, some Brazilians are not Carthusian monks. To get a more vivid sense o f the argum ent’s structure, we give it symbolic expression: No P are M. Some S are M. Some S are not P. Does not the reasoning here seem a bit more accessible than that presented to us by the Baroco argument? The major premiss tells us that there are two classes, P and M, which are completely separate from one another, and the minor premiss tells us that another class, S, is partially associated with one of these classes, namely M. Well, then, if P and M are completely separate, if S shares something with M, then precisely to the extent that it does so, it must also be separate from P. It is just those Brazilians who are U.N. employees who are not Carthusian monks, because no Carthusian monks are employed by the U.N. Doubtless there are other Brazilians who also are not Carthusian monks, but we are not concerned with them. The Festino syllogism is diagramed in the same way as the first figure Ferio syllogism. So much for our brief tour o f the four valid moods o f the second figure which are, again, Cesare (EAE), Camestres (AEE), Baroco (AOO), and Festino (EIO). We call your attention to the fact that all of the conclusions of second figure arguments are negative— such is the limitation of the second figure. (Later we shall attempt to get an affirmative conclusion from a second figure syllogism and see what happens. Nothing good.) Just as in the first figure we saw that what appeared to be two additional moods, AAI and EAO, were really no more than limited expression of, respectively, the AAA and EAE moods, and are in fact contained in them, so we find a comparable situation in the second figure. At first blush it might seem that we also have two additional moods in this figure, in the forms of EAO and AEO. But no. EAO is implicit in the EAE mood, as AEO is in the AEE mood. The dictum de nullo principle tells us that

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if we have a true E proposition, we have a true O proposition tucked away neatly inside it. The conclusion of the example we used for a Celarent argument, above, was: “No psychiatrists are ignorant of human physiology.” If that is true, it must be true that “Some psychiatrists are not ignorant of human physiology.” The conclusion of our Camestres example was: “No NFL football players are mothers.” That includes the fact that some of those players are not mothers, and does not have to be stated explicitly. T he V alid M oods

of the

T hird F igure: Darapti, Datisi, Disamis

The third figure of the syllogism can boast of six valid moods, and, as was the case with the first two figures, we have a list of unusual words to help us remember what those moods are: Darapti, Datisi, Disamis, Bocardo, Felapton, and Ferison. Or, to put the matter more succinctly: AAI, All, IAI, OAO, EAO, and EIO. But the multiplicity of argumentative forms offered by the third figure does not necessarily make the kind of reasoning involved here more compelling than that to be found in the first two figures. Check that list of valid third figure moods, and you will see that the conclusions are all weak by reason of the fact that they are particular propositions only, and half of them are doubly weak because they are also negative. We will first consider the arguments that yield affirmative conclusions, then we will turn to those whose conclusions are negative. And we will begin with this argument: All Philadelphians are Pennsylvanians. All Philadelphians love their fellow man. Therefore, some of those who love their fellow man are Pennsylvanians. That is an example of a third figure argument, which you would have immediately recognized as such, for you know that the characteristic feature of a third figure syllogism is that the middle term is the subject term of both the major and the minor premisses, giving us a configuration of this kind: M— P M— S S — P Furthermore, the argument stated above is an example of a Darapti third figure syllogism, which tells us that its two premisses are universal affirmative propositions and that its conclusion is a particular affirmative proposition. If we were to make that important information explicit in our symbolic expression of the argument, the following model would result: All M are P. All M are S. Some S are P. The moves made by the argument’s two premisses are now quite familiar to us. The major places class M entirely within class P, and the minor places that

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same class within class S as well. How would we diagram that argument? We could do it this way: ________

P M

s If all M are P, and all M are S as well, then at least some of S must be P, that part of S that is represented by M. We might be inclined to suppose, eyeing those two universal affirmative premisses, that we could get away with a universal affirmative which would necessarily be true. But we can’t, not in the third figure. Look what would happen if we were to try it: “All those who love their fellow man are Pennsylvanians.” We can reasonably assume that there are at least some people, not residents of the Commonwealth of Pennsylvania, who live up to this noble ideal, so the statement has to be counted as false. By the way, I am aware of the fact that the truth of the minor premiss can be contested. But let’s assume— for the sake of argument, as they say— that all of the citizens o f the City o f Brotherly Love do in fact love their fellow man. In logic we sometimes must be willing to make generous concessions. The Datisi third figure syllogism differs from the Darapti in that for its minor premiss it substitutes a particular affirmative for a universal affirmative proposition, resulting in this pattern: All M are P. Some M are S. Some S are P. Which can be diagramed this way:

S And now for a real life example of this form of argument: All Russians are Slavs. Some Russians speak English. Therefore, some people who speak English tire Slavs. “Russians” is the class representing the middle term in the argument, class M. That class is entirely within the class of Slavs (P). A part of the class of Russians speak English, the minor premiss tells us. Of that particular part of the class of English-speakers, we can confidently say that they are Slavs. The Disamis syllogism reverses the order we have in Datisi: its major premiss is a particular affirmative; its minor premiss is a universal affirmative. Imagine

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that a friend (one who tends to speak very formally, and who knows a little logic) poses this argument as you stroll across campus together: Some sophomores are in a state of arrested adolescence. All sophomores are potential juniors. Ergo—Latin for “therefore,” your friend explains—some potential juniors are in a state of arrested adolescence. You are a bit puzzled by the argument, and cautiously express doubts about its validity. To reassure you on this point, your friend stops, fishes a tablet out of his backpack, and quickly sketches the following: Some M are P. All M are S. Some S are P. Then he explains. “Think about it. If there is an overlapping between two classes, M and P, and if one of those classes, M, is entirely incorporated within a third class, S, then it’s just got to be that there is some overlapping between the classes S and P. Get it? There is no M that isn’t S. But part of M is P. So, that has to mean that part of S is P, just that part of S which is the M which overlaps with P.” Then he draws you a picture.

P M X s T he V alid M oods of the T hird F igure: B ocardo, Felapton, Ferison The Bocardo argument of the third figure is rather interesting, beginning as it does with a doubly weak proposition, a particular negative. That is followed by a universal affirmative minor, and the argument concludes with a particular negative— as it must, as we will eventually come to see. We begin with an example. Some boys are not Boy Scouts. All boys are sentient beings. Therefore, some sentient beings are not Boy Scouts. The argument in symbolic form: Some M are not P. All M areS. Some S are not P. The two terms introduced by the major, M and P, are said to be partially dissociated from one another. The minor premiss tells us that one of those

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terms, M, is to be found entirely within a class designated by S. So, what do we have? We have a situation in which two classes, M and P, are partially separated from one another. But because one of those classes, M, is entirely embraced by a third class, S, we know that there is a part of S which is necessarily separated from P— that part, M, which is partially separated from P. It is an undeniable fact that all boys are sentient beings. But if some of those boys are not Boy

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The Felapton syllogism o f the third figure (EAO) establishes a situation through its major premiss which we readily recognize: it introduces two classes, M and P, and drives an uncom prom ising wedge betw een them; they are completely separate. The argument’s minor premiss brings into the discussion a third class, S, and apprises us o f the fact that the aforem entioned class M resides entirely within it. The result? Some o f the class S has nothing to do with the class P. We diagram that situation. s M

Thus depicted, the necessary truth o f the conclusion is brought home with emphasis. In fact, what this diagram shows, without doing violence to the information provided us by the prem isses, is that “Afo S are P.” Well, why don’t we just conclude with a universal negative proposition and be done with it? Because, as we shall see presently, such a conclusion could be false. Here is another, and better, way of diagraming the argument, and which also does full justice to the information given us by the premiss. S

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In argument we must pay strict attention to precisely what the premisses are telling us, as well as to what they are not telling us, but are allowing for. In this argument we are told that M and P are completely separated, then we are told that M is completely enclosed by S. The argument says nothing about how S and P are related. Thus, nothing precludes the possibility that M can be completely separated from P and yet both M and P could be enclosed within S, as the second diagram above shows. That is just the possibility we need to keep

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open. If we assume that it necessarily must be otherwise—i.e., that M ’s being enclosed within S necessarily means that S is completely separated from P, then we are going to get into trouble. We need an example of the argument. No teetotalers get drunk. All teetotalers are human beings. Therefore, some human beings do not get drunk. The only kind of conclusion whose truth this type of argument can guarantee is one that takes the form of a particular negative proposition. It is obvious that if I were to attempt to force a universal conclusion from the above argument I would end up with a false statement, and blatantly so: “No human beings get drunk.” (See Appendix A for further discussion of the logic relating to third figure EAO and AAI arguments.) The sixth and final valid mood of the third figure, the Ferison (EIO) syllogism, is one we need not tarry over, for we have met this pattern of argument in both the first and second figures. We begin with an example. No plants are sentient. Some plants are edible. Therefore, some edible things are not sentient. “Plants” is the middle term of the argument. The class of plants is completely separate from the class of sentient beings (major term). But there is an overlapping between the class of plants and the class of edible things. Hence, edible things are partially separated from sentient beings. Just those edible things that are plants cannot be sentient, because no plants are sentient. The Ferison syllogism is diagramed in the same way as the first figure Ferio syllogism and the second figure Festino syllogism. Summing up the valid moods of the first, second, and third figures, we have the following line-up: Second Figure Third Figure First Figure EAE AAI AAA AEE AI I EAE AOO IAI AI I E IO E IO OAO EAO E IO We note that the EIO mood is valid in all three figures; the EAE mood is valid in the first and second figures; and the A ll mood is valid in the first and third figures. T he C ontroversial F ourth F igure The figure of a syllogism, we know, is determined by the position taken by the middle term in the premisses of the argument. In the first figure the middle

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term is the subject term of the major premiss and the predicate term of the minor premiss; in the second figure the middle term is the predicate term in both premisses; and in the third figure the middle term is the subject term in both premisses. There is one more possible configuration, where the middle term is the predicate term of the m ajor premiss and the subject term of the minor premiss, and that gives us the fourth figure: P — M M— S S — P The fourth figure has proved to be a controversial one over the course of the history of logic, or at least during the portion of that history which followed the incorporation o f the fourth figure into the logic curriculum. There are some textbooks which treat the fourth figure with the same care and thoroughness with which they treat the first three figures, with not so much as a suggestion that there might be some problems connected with it. Other textbooks bring it up only to dismiss as representing an illegitimate form of argument. Aristotle him self does not treat o f the fourth figure, a not insignificant fact, given the meticulous, detailed analysis he gave to syllogistic reasoning in his seminal works on logic. Most historians agree that the man responsible for introducing the fourth figure to logic was Galen ( a . d . 129-200), who, besides being a logician of no mean sort, was a biologist, a physician, and a general all-around philosopher, a man interested in many things. Five valid moods have been claimed for the fourth figure: AEE, EAO, EIO, A ll, and IAI. We can see that all of those are valid moods in one or another of the first three figures. Though I find the fourth figure highly problematic, I have to admit that its various argumentative forms are capable of producing true conclusions from true premisses, and therefore they can, it seems to me, lay claim to some degree o f legitim acy. However, whether or not that legitim acy is founded upon som ething which m ight be characterized as a kind o f logical cheating is a question whose pursual would lead us into areas too abstruse for an introductory text in logic. Suffice it to say this much then: because of their decidedly convoluted nature, the fourth figure moods do not offer us a particularly effective or illuminating way of reasoning. In contrast to the clarity and cogency of the moods o f the first figure especially, those o f the fourth figure are singularly unimpressive. Accordingly, in this book I am going to give scant attention to the fourth figure. A single example of a fourth figure argument, the AAI mood, will be sufficient, I think, to show the kind of strained reasoning promoted by this figure, and how distant it is from the way we ordinarily think. All lying is heinous. All heinous ways of behaving are deplorable. Therefore, some deplorable ways o f behaving are lying.

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Here is another example, in the same AAI mood: All squirrels are mammals. All mammals are warm-blooded. Therefore, some warm-blooded things are squirrels. One of the strikingly awkward features of fourth figure reasoning is that, given the ways the terms are arranged in this figure, it often produces conclusions which represent a distinctly backward way of thinking. Normally, when we make an affirmative statement in ordinary language, the extension of the subject term is less than that of the predicate term, so that we predicate a larger class of a smaller one, or we predicate a class of an individual thing. For example, we say, “Lying is deplorable,” not, as the conclusion of the first example above would have it, “Some deplorable ways of behaving are lying.” Or we say, “Squirrels are warm-blooded,” not, as in the conclusion of the second argument, “Some warm-blooded things are squirrels.” While there might be rare instances in our careers when a mood of the fourth figure could provide us with the most effective way of carrying a point (I must confess, however, that I cannot offhand think of a case where this might be so), the type of reasoning we find in the fourth figure, taking it all and all, is of minimal use to us as we strive to do justice to the demands for clear and cogent thinking, and communication, which we encounter in our day to day lives. Indeed, it is hard to imagine why anyone would choose to employ these tortured ways of reasoning except to confuse and confound the innocent, or perhaps simply to give a bad name to logic. (See Appendix B for further commentary on the fourth figure.) R educing Imperfect Syllogisms

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More than once we have referred to the first figure as the perfect figure. It deserves that highly laudatory designation because of the versatility of the reasoning that the four moods of the first figure is capable of displaying. We have called attention to the fact that only the first figure can produce conclusions which take the form of all four general propositions, whereas the second figure is limited to negative conclusions, and the third figure has to settle for only particular conclusions. And the jewel in the crown of the first figure is the uniquely impressive Barbara syllogism, which issues in a universal affirmative conclusion. None of the other figures can claim a mood that can do that. Aristotle describes the first figure as the most scientific figure, by which he means that it can effect demonstration of the most direct and potent kind. The first figure, he remarks, “is the only figure which enables us to pursue knowledge of the essence of a thing.” (Posterior Analytics, 79a, 20)'8In the Barbara syllogism we were using above, where we concluded that all Greeks are mortal, we were dealing with the essences of what the terms in the argument represent. “In the second figure,” Aristotle goes on to explain, “no affirmative conclusion is possible,

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and knowledge o f a thing’s essence must be affirm ative; while in the third figure the conclusion can be affirmative, but cannot be universal, and essence must have a universal character.” (ibid., 79a, 2 5 )19 Summing up his listing of the peculiar logical virtues of the first figure, Aristotle writes: “Finally, the first figure has no need of the others, while it is by means of the first that the other two figures are developed.. .the first figure is the primary condition of knowledge.” (ibid., 79a, 3 0 )20 Given the clear superiority of the first figure, as representing the most versatile and potent means o f reasoning, and which earned it the title of the perfect figure, the second and third figures, by way of contrast, came to be known as imperfect figures. (It would not be untoward to label the fourth “the very imperfect figure.”) By way of acknowledging the dependency of the second and third figures on the first, and because of the greater clarity and cogency of the first figure, logic has developed a system whereby moods of the second and third figures can be transformed into moods of the first figure, a process generally described as the reduction o f imperfect syllogisms to the firstfigure. There are two basic m ethods o f reducing second and third figure moods to first figure moods, both of which are remarkably ingenious, but to get into the details of either o f them would take us beyond the bounds o f what is proper for an introductory course in logic, so I will not attempt to do so here. However, to give you at least a taste o f what is involved in this process, I will provide a simple exam ple o f one of the m ethods, which is called direct reduction, or reduction by formula. The one mood which is common to all three figures is the EIO mood; Ferio in the first, Festino in the second, Ferison in the third. We place their symbolized expressions side by side. No M are P. No P are M. No M are P. Some S are M. Some S are M. Some M are S. Some S are not P. Some S are not P. Some S are not P. Now we want to reduce the second and third figure EIO arguments to a first figure EIO argument. This is very easily effected. All we need do is to apply the process o f conversion, which we learned in Chapter Seven. Conversion, you will doubtless readily recall, is the process whereby we switch the subject and the predicate terms of a proposition. And you will also recall that universal negative propositions and particular affirmative propositions convert simply, which is to say that the two terms are exchanged without making any alteration in the quantity of the proposition: the universal remains universal, the particular remains particular. Observe the major premiss of the second figure EIO argument above. It is a universal negative proposition, “No P are M .” As such, it can be converted simply, yielding “No M are P.” And with that we have a first figure EIO argument. Now give your undivided attention to the minor premiss of the third figure EIO argument, “Some M are S ” As a particular affirmative proposition,

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it too converts simply, giving us “Some S are M.” And suddenly, with that conversion, the third figure EIO argument is transformed into a first figure EIO argument. (See Appendix C for a more detailed treatment of reduction to the first figure.) C ategorical Syllogisms C ontaining N on -Factual P ropositions We began this chapter by identifying the nature of a categorical syllogism, which is simply an argument all of whose propositions are categorical propositions, that is, statements, declarative sentences, saying something definite about something, without waffling, subterfuge, or evasion. All of the syllogisms we discussed in this chapter were categorical, and, as such, they are to be contrasted to the non-categorical syllogisms which we will be looking at a couple of chapters hence. In the meantime, let us consider the two following arguments. A king is the sole ruler of a country. Louis XIV of France was a king. He was thus the sole ruler of his country. The more rapidly he composes, the greater is the composer. Mozart composed with amazing, incomparable rapidity. Therefore, Mozart must be regarded as the greatest of all composers. Both of the arguments are made up of categorical propositions, and yet there is a significant difference between them. The first argument, though it is admittedly not particularly interesting, is composed of propositions which simply state matters of fact, and it is hard to imagine someone who would be prepared seriously to contest any of them. Most people would accept the conclusion of the argument without demur. But the second argument represents another matter altogether. Of its three propositions, probably only the second, the minor premiss, would be accepted as a simple matter of fact, not to be disputed. The argument’s major premiss, though proposing an idea that one might be prepared to give some credence to, is certainly not on the same level as, “A king is the sole ruler of a country.” And even if we were willing to attach some weight to the idea that there is a connection between rapid composition and artistic greatness, most of us would be reluctant to deny such greatness to a composer who had the habit of composing in a slow, deliberate manner. And as for the conclusion of the argument, that clearly reflects the opinion of the arguer, an opinion which one may be willing to respect, and yet not feel that one would be responding irrationally by refusing to accept it as an incontrovertible truth. In sum, the argument does not demonstrate, in the precise sense of the term, that Mozart is the greatest of all composers. What chiefly characterizes the second argument is that the propositions which compose it, except for the minor premiss, represent what may be generally described as value judgments. They do not state matters of fact; rather, they

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present interpretations of matters of fact, but the latter can be done, please note, categorically. There is a difference between saying, “The more rapidly he composes, the greater the com poser,” and “ It could be maintained that the more rapidly he composes, the greater is the composer”; between “Mozart is the greatest o f all com posers,” and “M ozart may be the greatest o f all composers.” Is an argument to be held suspect because it deals with value judgm ents rather than matters of fact? By no means. But we should be aware of what we are dealing with, and not confuse two quite different kinds of arguments, albeit they both employ categorical statements. An argument dealing with facts can demonstrate in the strict sense. If its premisses are true, the conclusion follows necessarily. An argument dealing with value judgm ents, on the other hand, cannot, because of the very nature of its premisses, deliver conclusions which are necessarily true, and which to reject would be plainly irrational. Whatever force an argument dealing with value judgments might have would depend on the inherent reasonableness of its premisses, and their relevance to the conclusion they are intended to support. Such an argument cannot be demonstrative, but it can be more or less com pelling, depending, among other things, on the knowledge the arguer has of the subject matter he is dealing with, and his logical acumen.

Review 1. Give three examples of a categorical proposition. 2. Explain what we mean by the figure of a syllogism. 3. Explain what we mean by the mood of a syllogism. 4. What are the valid moods of the first figure? 5. What are the valid moods of the second figure? 6. What are the valid moods of the third figure? 7. Explain why we consider the first figure to be superior to the second and third figures. 8. What is the benefit of transforming second and third figure arguments into first figure arguments? 9. Must categorical propositions state only matters of fact? 10. Is the argument which deals with value judgments necessarily a bad argument just for that reason?

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Exercises A. Identify the figure and the mood of the following arguments. Your principal concern should be with the structure of the argument, not its contents. 1. No professional basketball players are poor. All professional basketball players are good athletes. Hence, some good athletes are not poor. 2. No angels are devils. Some little girls are real angels. So, some little girls are not devils. 3. All nurses are caring persons. No sadists are caring persons. It follows, then, that no sadists are nurses. 4. Some high school kids have trouble with math. All high school kids are easily distracted. Thus, some easily distracted folks have trouble with math. 5. No Muslims are Catholic. Some Indians are Muslim. Thus, some Indians are not Catholic. 6. No herbivorous animals eat flesh. Some herbivorous animals live in zoos. So, some animals living in zoos don’t eat flesh. 7. All Italians are cheerful people. No gamblers are cheerful people. Consequently, no gamblers are Italians. 8. All women are beautiful. Marilyn Heppenkammel is a woman. Therefore, she’s beautiful. 9. All airline pilots have good reflexes. Some airline pilots speak Swedish. Therefore, some Swedish-speakers have good reflexes. 10. No hard losers are good teammates. Some science majors are good teammates. So, some science majors are not hard losers.

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11. All engineers whistle when they work. And all engineers like Chinese food. We conclude that some people who like Chinese food whistle when they work. 12. All dogs are friendly. Some house pets are dogs. So, some house pets are friendly. 13. No psychologists are unsympathetic souls. All marble players are unsympathetic souls. Ergo, no marble players are psychologists. 14. Some baseball players are not Bostonians. All baseball players chew gum. So, some people who chew gum are not Bostonians. B. Make up an argument for each of the following figures and moods. 1. First figure, AAA. 2. First figure, EAE. 3. First figure, All. 4. First figure, EIO. C. Identify each of the following categorical propositions as either factual judgments or value judgments. 1. Abraham Lincoln was the 16th president of the United States. 2. Abraham Lincoln did wrong by suspending the writ of habeas corpus. 3. The Chicago Cubs will never win another World Series. 4. Quito is the capital of Ecuador. 5. The transmigration of souls is a fact. 6. The current economy is in a disastrous state. 7. I’ve got a terrible headache. 8. Grace is a very gracious person. 9. In a right triangle, the square of the hypotenuse is equal to the square of the other two sides. 10. Surely classical music is superior to jazz.

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Chapter Eleven The Rules of the Syllogism D etermining V alidity

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Having analyzed the valid moods of the first three figures, we have now gained, I trust, a stable and reliable understanding of the basic workings of syllogistic reasoning, that form of reasoning which reflects the deep-set, natural processes by means of which the human mind comes to know the truth of things. The whole purpose of reasoning is to get to the truth of the matter about which we are reasoning. If we were infallible in our reasoning, this would be a purpose easily enough achieved; in fact, it would be virtually automatic. But we are as apt to fall flat on our faces in engaging in this activity as in any other, and that’s why we need the help of logic. Validity in argument is our great guarantor; if an argument is put together correctly—i.e., if its logical structure is sound— then we can be assured that if we start with truth, we will end with truth. Familiar as we now are with the fourteen valid moods of the first three figures, if we meet with an argument that reflects one of those moods, then we know we have before us a sound argumentative structure. So, if it is a first figure AAA argument that we are to work with, we can be fully confident that, if we employ true premisses with that form, we will end up with a conclusion that not only states the truth, but does so in the strongest possible way. But if someone were to memorize those fourteen valid moods—something which is to be highly recommended, by the way—and then make those the sole criteria by which one comes to grips with validity, then one would have settled for a rather superficial understanding of one of the most important aspects of logic. It is not enough to know that a certain argumentative form is valid; the whole point behind studying logic is to know why it is valid. Again, I trust that our analysis of the valid moods had the good effect of helping us to get beyond purely surface considerations, and that we have at this juncture gained a solid sense of the “why” of valid deductive reasoning. And the hope is that the diagraming of the arguments provided us with additional illumination as to their inner workings. But the diagraming process, it should be said, has its

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limitations, for, as with the symbolic expression o f arguments, while it can offer useful insights as to how term connects (or disconnects) with term, it does not represent the most potent analytic method that we have available to us. What we need is a method which will allow us to get to the very essence of an argument. That method is provided to us by the rules of the syllogism. T he R ules

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The rules of the syllogism are both tests and guidelines. They are tests in the sense that when applied to any argument under analysis they will not only verify its validity, if it is in fact valid, but, if invalid, they will pinpoint the specific problem that causes them to be invalid. The rules are guidelines in the sense that, if we abide by them faithfully in constructing our own arguments, we can know with full confidence that our arguments will be valid. How many rules for the syllogism are there? It varies. In some logic textbooks you will find as few as three, in others, as many as ten. Still other texts differentiate between rules and corollaries, with the numbers of each varying. However suggestive this might be of reckless arbitrariness, that is not what is at play here. But how is it to be explained that one logician gives us three rules for the syllogism, and another ten? Is it that the first is withholding vital information from us, while the second is supplying it in superabundance? No, it is simply that the first believes in succinctness, while the second wants to spell things out as fully and explicitly as possible, and there is nothing in the ten rules, stated explicitly, which cannot be found implicitly in the three rules. Besides the difference in the actual number of rules, from textbook to textbook, there are, as one would expect, differences to be noted in the ways the rules are expressed, arranged, and developed, but these differences are of no great consequence with respect to the basic ideas which are to be communicated, and there are no textbooks o f which I am aware, and I know quite a few of them, where those basic ideas are not given adequate treatment. In presenting the rules of the syllogism in this book I have decided upon a set of a half dozen. All the vital information we need to know about the inner workings of a syllogistic argument is neatly encompassed within the confines of those six rules. And any information which I feel is not made explicit enough by the rules themselves will be brought fully into the open in my explanation and discussion of them. Here is how we will proceed in what follows. I will treat the rules in sequence, giving in the case of each as thorough and detailed an account as necessary of all of its significant logical ramifications. But we must approach this survey in the right spirit. Learning the rules for anything can engender in the learner a somewhat mechanical mind-set, an attitude that leads one to learn how to apply the rules without ever grasping the substance of what they are intended to control and reveal. We want to remind ourselves of the point made earlier about syllogistic reasoning, that it is reflective of the way the human mind naturally works. That being the case, engaging with the

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rules of the syllogism as they should be engaged with can provide us with some important insights into the elementary processes by which we put our ideas together, as part of that never-ending and ever-exciting process of accumulating knowledge. The order in which I deal with the rules does not necessarily reflect their relative importance. And for that matter, one could say that all of them are really of equal importance, for each, if dutifully applied, will contribute to a valid argument, and each—to consider the negative side of the ledger—if not given its proper due, will lead to unfortunate logical consequences. T he R ule G overning

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Because of the substantial knowledge of syllogistic reasoning we have already gained, we know that every syllogism has but three terms: the major, the minor, and the middle. So the first rule, which lays it down that a syllogism must have three terms and three terms only, serves but to remind us of something which heretofore was made part of our stock knowledge regarding the basic structure of the syllogism. Given what the rule tells us, we can then assert that any syllogism which has four terms would be for that very reason invalid. And, to hearken to a deeper level, a four-term syllogism would not faithfully reflect the way the mind actually functions, in putting together ideas while engaged in the process of reasoning. But one might ask, with perhaps a slight tone of impatience creeping into one’s voice, Is this not so obvious a point that it scarcely needs attention drawn to it, much less does it need to be raised to the lofty dignity of a rule? In other words, with an error as blatant as this, how could one possibly miss it? Very likely someone posing this question would have in mind a syllogistic argument expressed in symbolic form, which gives us a bare-bones view of the structure and contents of the discourse. Thus: M— P S — M S — P Looking at that configuration, we see as clear as day that a syllogism has but three terms, the middle, the minor, and the major, labeled respectively M, S, and P. Now consider this configuration: M— P S — W S — P A clear violation of the first rule! We have four letters, representing four terms. That just won’t do. So again, a pettish question might be posed: What’s the problem? Well, of course there is no problem so long as we are dealing only in symbols. In that case a fourth term stands out like the proverbial sore thumb.

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But we do not go around attempting to communicate with one another through the medium of abstract symbols. We use words, and words can be ambiguous, and it is precisely the employment of ambiguous terms, be it deliberately done or the result of simple carelessness, that can create the real-life problem of a four-term syllogism. This is a problem which, because of the very nature of ambiguity, is not always easily detected. In fact, sometimes the alteration of the meaning of a term within an argument can be so subtle that the problem of its being burdened with four terms— created by that alteration of meaning— can slip by us without our being aware of it. The first rule of the syllogism, then, is not to be considered slight in its import. T he P roblem

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A rgument

Let us imagine a syllogistic argument, expressed in ordinary language, which contains four quite distinct terms, something like this: All men are mortal. All Greeks love olives. Therefore... Therefore, what? Therefore, nothing. Actually, I mis-spoke myself a moment ago when I invited you to imagine a syllogistic argument with four terms, for such a monstrosity would not qualify as an argument at all. What we have just above is simply two statements, one following after the other. There is nothing going on between them, logically speaking. It is that trinity of terms which makes for a genuine syllogism, where one of them, the middle term, performs the crucial function of establishing an association, positive or negative, between the other two. A person would need no formal training in logic to be able immediately to see that nothing follows from those two statements. In an earlier chapter we met up with the distinction among univocal, equivocal, and analogical terms. An equivocal term is roughly the same thing as an ambiguous term, which is to say that it is a term that can have at least two distinct meanings, and those meanings can be radically different from one another. When that is the case, and when such a term is used in an argument, in one place bearing this meaning, in another place bearing that meaning—and, by the way, it is almost always the middle term that lends itself to this disservice— the ploy is so obvious that its detection seldom presents any problem. Few of us, I think, would be taken in by the following argument. Secretaries have wings. Miss Smith is a secretary. Therefore, Miss Smith has wings. Perhaps some would be taken in by it, or at least confused by it. In the event of either of those possibilities, some explanation is called for. Doubtless the first thought that would come to mind for most of us in hearing the English word “secretary” is that it refers to a clerical worker, or perhaps to an administrative

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officer of some sort, as in the Secretary General of the U.N. But the word has another perfectly legitimate meaning, referring as it does to a large bird of prey that makes its home in the southern regions of the African continent. The sly trickster who made up the above argument is using the same word, “secretary,” in two quite different senses. In the major premiss the word refers to a bird; in the minor premiss the reference is to Miss Gloria Smith, who as a matter of fact is employed as a clerical worker, at W. H. Woodhouse & Daughters, Ltd. We thus have a single word, but two terms. Remember, the term is the idea which stands behind the word, and in logic it is the term that really counts. As mentioned, few would be taken in by equivocation as blatant and heavy-handed as that employed in our example. But there are less obvious instances of fourterm syllogisms, and those are the ones we have to be alert to. The problem invariably has to do with words that have a wide range of different meanings, or with words that have a base meaning which is clear enough and commonly agreed upon, but which is surrounded by a cloud of conflicting connotations. To alter the imagery, such words might be thought of as many-faceted diamonds, and how they are viewed. Everyone who looks at the gem agrees on its essential identity as a diamond, but they have different ways of interpreting the diamond, depending on the particular facet on which they are concentrating. In referring to the gem, everyone uses the same word, “diamond,” but everyone does not mean the same thing by that word. The kinds of words I have in mind usually play a prominent role in our everyday vocabulary, and we are apt to put great store in the peculiar meanings which we attach to them. We need a concrete example to help make all this clearer. Consider the following argument. Love is essentially characterized by altruism. Don Juan was totally dedicated to love. Therefore, Don Juan was one of the greatest altruists who ever lived. It may not be immediately apparent that this is a four-term argument, but it is, thanks to the equivocal way the middle term “love” is being used. The major term identifies love with altruism, and thus in this instance we have love being understood as, say, a considerate, sympathetic, perhaps even compassionate, outgoing, solicitous, helping attitude toward other people. That would certainly count as a respectable meaning for the term, and would make it roughly synonymous with “charity.” Most people, one suspects, would favor that meaning. But then the minor premiss makes a rather devious move. The same word is being used, “love,” but now with a quite different meaning from that employed in the major premiss. We know who Don Juan was, and we have a pretty good idea what “love” meant for him: in effect, the cynical sexual exploitation of vulnerable women. We have, then, an entirely new term which has been brought into the argument, which means we have four terms, which means that the argument has thereby been rendered invalid. The arguer disingenuously is trying

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to convince us, by his clever sleight of hand, that Don Juan was a noble fellow, a “caring” person who habitually had the welfare of others primarily in mind. But we see through the fraudulence. The rampaging roue was, to be sure, a “great lover,” but that phrase properly translates as a “self-centered exploiter of others”—the farthest thing from an altruist. Consider another argument. Democracy identities the form of government practiced in China. The United States is also a democracy. Therefore, the governments of the two countries are much the same. The problem here, as can readily be seen, is with that protean word “democracy.” It is a word redolent with positive connotations, and thus much in favor throughout political circles today, both domestic and international. Rare is the country which does not want to be considered a democracy, no matter what the actual practices of the government staging its political show, and to ensure it is displaying the right public image in this regard, words like “democratic” and “republic” are conscientiously worked into the country’s official title. So we have a situation where people are using the same word, “democracy,” but not at all meaning the same thing by it. Hence they often end up talking at cross purposes when presumably talking about the same thing. There is something like a breakdown in communication being reflected in the above argument. One would be prepared to accept the conclusion of the argument only if one believed that the Chinese understanding of democracy had any similarity to what most Americans understand by the term. In fact, as demonstrated by the radical difference between the governments of each country, there is no shared understanding of the term. Another argument: The U.S. Supreme Court decides matters of justice. The Dred Scott decision was handed down by the U. S. Supreme Court. Therefore, the Dred Scott decision was a reflection of justice. This is a more subtle example. The major term, or at least the word central to it, “justice,” is being deceptively played with here. The major premiss is uncontroversial enough, and so is the minor premiss: that it is the principal business of the Supreme Court to deal with matters of justice is unarguable, and that the Supreme Court decided the Dred Scott case, in 1857, is a simple matter of historical fact. But to deal with matters of justice is not equivalent to dealing with matters of justice justly, and so it would be quite erroneous to conclude that the Dred Scott case reflected justice. It emphatically did not. How are we to be guided by the first rule of the syllogism in constructing our own arguments? By being very careful with our language, making sure, first o f all, that we have a clear idea in mind o f just what we mean by every term we use in an argument, and then taking care that we do not shift the meaning as we move from premiss to premiss. When it comes to sizing up arguments of others, testing them for validity, we should have a sharp eye out for terms that

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seem to be altering their meanings over the course of an argument The alteration may be only slight, perhaps not enough to make the argument clearly invalid (because of the presence of four terms), but enough to give it a certain wobbly character, and thus render its conclusion considerably less than convincing. T he R ule G overning

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Extreme T erms

The dictum de omni and dictum de nullo principles advise us that starting with a true proposition, there is only one direction in which we can legitimately move in making an inference, and that is from the universal to the particular, from an A proposition to an I proposition, or from and E proposition to an O proposition. When we try to reverse the process—when, for example, we assume that because “Some S are P” is true, so also is “All S are P”—we fall into one of the more flagrant mistakes in logic, as well as one of the more common. There seems to be an abiding temptation for the human mind to jump the gun in these instances. We know with certainty that something is true for part of a class, and we have this urge to fill out the picture, to pronounce the strongest kind of proposition possible, so, and without the benefit of the facts to back up our contention, we claim that something to be true of the whole class. It is misreasoning of this sort that is the foundation for most of the prejudiced thinking the world is continuously burdened by. The second rule: A term distributed in the conclusion must be distributed in the premisses. If we have a term that is not distributed (i.e., it is particular) in the premisses, and ends up distributed (i.e., it is universal) in the conclusion, then we are reasoning in the wrong direction. This mistake is often tucked into an argument so neatly that it does not call showy attention to itself, and is thus sometimes hard to detect. Every now and then we are confronted with an argument that “just doesn’t feel right”; we have more than a slight suspicion that there’s something wrong with it. Often, close investigation will reveal that the argument is indeed defective, and the source of the problem is a violation of the second rule. If the subject term of a premiss is the culprit term, the problem is easily enough detected; in fact, it would be as difficult to overlook as the famous bull in the china shop. Consider this: All Marines are members of the armed forces. Some men over forty are Marines. Therefore, all men over forty are members of the armed forces. The argument gets off to a good start (as a first figure All model—valid), but ends in disaster. We immediately see the conclusion to be false, and that is because the minor term, “men over forty,” which is undistributed in the minor premiss, is illegitimately given distributed status in the conclusion.

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I llicit M inor

When the violation of the second rule affects the minor term we have what is called the illicit minor. W hereas one need not be a super sleuth to spot an illicit m inor when it is a subject term, as in the case above, the situation is different when the m inor term occupies the predicate term position in the premisses, which happens in third figure syllogisms. In order to see how this is so we need to remind ourselves of an important principle we learned back in C hapter Six, concerning the distribution o f predicate terms. Identifying the distribution of subject terms poses no problems, for there we have the logical indicators (“all,” “no,” “some,” etc.) to make things explicit for us. But how are we to construe matters if we find ourselves faced with subject terms of propositions in an argum ent that have no logical indicators to help us out? Such as in this argument: Philosophers are fickle. Phelan is a philosopher. Therefore, Phelan is fickle. W hat are we to m ake o f that m ajor prem iss? Is the arguer talking about all philosophers or only some? He doesn’t let us know, one way or the other. Often, when we are presented with indefinite statements like that, we are on the receiving end o f a deliberate ploy on the part of the arguer. Let us say that in this case we are dealing with someone who really has it in for philosophers, can ’t stand them. In his m ajor prem iss he does not say “all philosophers,” although as a matter of fact that is what he intends his audience to understand him to be implying. But he has covered himself rather nicely here. Should he be called to task, after presenting his little argument, he can always cover himself with the protestation that he did not actually say “all philosophers,” and in fact, so he piously assures us, that is not what he meant. Well, what then? Is he then o ff the hook because everything will be made well, logically, if we read his major premiss as, “Some philosophers are fickle”? Difficult though it might be to do so, we reluctantly could concede the possibility that the statement might be true. So, let us grant that there are some fickle philosophers in the world. But if we are to take the major premiss as a particular affirmative proposition, then the argument is invalid, and the conclusion does not follow. How is that? If we adm it that part o f the class o f philosophers is made up of fickle people, and if Phelan is in fact a philosopher, the argument fails to show that Phelan is to be found in just that part of the class of philosophers. As far as anything we know fo r sure from the prem isses, Phelan, though a philosopher, need not necessarily be a fickle philosopher. But to get back to the matter of the distribution of predicate terms. Because there are no logical indicators qualifying predicate terms, we must advert to the principle that tells us: (a) the predicate terms of affirmative proposition are

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always undistributed; (b) the predicate terms of negative propositions are always distributed. Now, with that reminder in mind, consider this argument: Some printers are New Englanders. Some printers drink coffee. Therefore, everyone who drinks coffee is a New Englander. We would understandably wince at the presumptuous conclusion, however heartily it might be applauded by the Consolidated Coffee Canners Club of Central Columbia. The conclusion is manifestly false. But we have every reason to suppose the premisses to be true. And what should that tell us, right off the bat? That we have an invalid argument, for this is just the combination that a valid argument will not allow: true premisses and a false conclusion. What, however, is the specific problem that makes the argument go wrong? We have here another case of an illicit minor. The minor term, as always, is the subject term of the conclusion, which in this instance is coffee drinkers, and which is distributed: “everyone who drinks coffee.” But when we check that term as it appears in the minor premiss, we see that it is the predicate term of an affirmative proposition, and in that position it is undistributed. So, an illegitimate move is being made, from the particular to the universal. The second rule is being violated. T he P roblem

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M ajo r

When the violation of the second rule affects the major term, it becomes the problem of an illicit major. Consider this argument: All men are mortal. No antelopes are men. Therefore, no antelopes are mortal. There are two quick ways of identifying this as an invalid argument. First, it is a first figure AEE argument, and we know that to be an invalid mood; second, we have an argument with true premisses and a false conclusion, something which a valid argument does not allow. But the specific problem here, crippling the argument, is an illicit major. Of course, we know the major term always to be the predicate term of the conclusion. Here that term is “mortal” (understood as “mortal beings”), and because it is the predicate term of a negative premiss it is distributed. But as that same term appears in the major premiss, because there it is the predicate term of an affirmative proposition, it is undistributed. So, we have an illegitimate move from the particular to the universal.

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Now let’s look at an invalid third figure mood, AEE, so that we can see why it is invalid, and for a reason more interesting than the fact that it fails to make our list o f valid moods for the third figure. All bacteria are single cell organisms. No bacteria are paramecia. Therefore, no paramecia are single cell organisms. True premisses, false conclusion; therefore, an invalid argument. But can we explain, in specific terms, what is going wrong here? Once again, the illicit m ajor rears its ugly head, and the mystery is solved. In the major premiss, the term that gives the premiss its name is the predicate term o f an affirmative proposition; therefore, it is undistributed. But that same term, as the predicate term o f the negative proposition that serves as the conclusion to the argument, is distributed. The alarm bells go off. T he R ule G overning

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M iddle T erm

As we have seen, the function o f the middle term in a syllogistic argument is to forge a bond between the minor and the major terms. But the middle term can only do this if it is distributed in at least one o f its appearances in the premisses. And so we have the third rule o f the syllogism: The middle term must be distributed at least once. If it is not, no sure connection is made between the other two terms. An undistributed middle term can occur in any of the three figures, rendering an argument invalid. In the first figure: Some college students are geology majors. All UCLA undergraduates are college students. Therefore, all UCLA undergraduates are geology majors. True premisses, false conclusion, and we know what that means— an invalid argument. W hat makes it so in this case is the problem of the undistributed middle term, i.e., a middle term which is not universal at least once. The middle term is “college students,” which is clearly undistributed in the major premiss (“some college students”), but it is just as clearly undistributed in the minor premiss, for our trusty principle tells us that the predicate terms of affirmative propositions are always undistributed. Here is a third figure argument, displaying a pretty obvious case of the same problem: Some Texans are teachers. Some Texans play poker. Therefore, some people who play poker are teachers. In the third figure the middle term is the subject term in both premisses, and here logical indicators unambiguously tell us that it is undistributed in both of its appearances. You might be thinking: but that conclusion, “Some people who play poker are teachers,” could be true. Yes, it could be, and I rather suspect that it is highly likely that it is true. But the point is this: the argument does not

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prove that to be true. And why not? Because the middle term, being limited in its extension in both premisses, lacks sufficient compass to reach out and enfold within its logical embrace one or other of the extreme terms in the argument. Remember the principle of the identifying third, which tells us that if two things are identical to a third thing, they are identical to one another. Here the third thing, the middle term, does not succeed in fully identifying itself with either of the other two things, the extreme terms. Thus, nothing conclusive results. G uilt

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A ssociation

It is in second figure arguments where we most frequently encounter the problem of undistributed middle terms. This is explained by the fact that in the second figure the middle term is the predicate term in both premisses. We present for your edification and reflection two second figure arguments. Here’s one: During the 1930’s there were a lot of card-carrying Communists at Columbia University. And that was the decade when Geoffrey was at Columbia. It’s a pretty safe bet, then, that he was a Commie. And here ’s another: Heavy drinking is a major problem at Mu Mu Mu Sorority. Julia is a member of Mu Mu Mu Sorority. Well, I guess we know what that means. The problem of the undistributed middle term as it manifests itself in the second figure, and chiefly on account of arguments such as the above, has come to be known as the guilt by association fallacy. Before we take a closer look at the two arguments, we will put the problematic syllogism in symbolic form, to get a more immediate sense of its structure, and thus to help us better to see how that structure is the cause of the problem. Some P are M. All S are M. All S are P. We could pass a quick, and accurate, judgment on that argument, as invalid, simply on the basis of our knowledge that the second figure is capable of producing only negative conclusions, and the conclusion of this argument is clearly affirmative. True enough, but that is not a very analytic response to the argument. We show a bit more logical sophistication if we take note of the fact that the middle term, M, is the predicate term in both of the premisses, and that both of those premisses are affirmative propositions, meaning that the middle term is undistributed in both cases. Hence we have a violation of the third rule of the syllogism. By the way, if you are wondering why, in the symbolized version, the minor premiss and conclusion are both put down as universals, recall that, in logic, singular propositions are regarded as universal propositions.

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“Geoffrey was a Commie” is taken as an A proposition, then. Also note that the major premiss is a particular affirmative, so that would give us an IAA second figure mood— clearly invalid. The basic argumentative form we are treating here can be correctly diagramed in this way:

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What the diagram tells us, reflecting the information provided by the premisses, is that it is quite possible for both class P and class S to be associated with class M, P partially and S entirely, without there necessarily being any connection betw een them. Because that is true, neither would there be any logical justification for even a “Some S are P” conclusion. Let us assume, considering the first argument above, that (1) it is quite true that there were many card-carrying Communists at Columbia during the 1930’s, and (2) Geoffrey was there at the time. If that is all the information which is available to us, we have no warrant for concluding that Geoffrey had anything at all to do with the Communist party. As to the second argument, regarding Julia, we first note that its conclusion is rather sly for the way it insinuates instead of coming right out with a categorical statement— a not uncommon rhetorical ploy in disingenuous argumentation. Let us say that it’s all too true what they say about the heavy drinking that goes on at Mu Mu Mu, and that Julia is in fact a member of that sorority. Even so, we cannot legitimately conclude from those two bits of information that it must be the case that Julia is to be numbered among the heavy drinkers. Non sequitur, as we say in Latin. It just doesn’t follow. From the knowledge we have at hand, provided by the premisses, nothing precludes the possibility that Julia, though residing with what are apparently major league imbibers, has herself never touched a drop in her life. All right, then, just because P is associated with M, and S is also associated with M, that does not mean that there is necessarily any association between S and P. But couldn’t we talk about the probability of such an association, given the circumstances? Certainly. We can always talk about probabilities in real life situations, but—a reminder—this is deductive reasoning we are involved in here, and deductive reasoning is not interested in probabilities. We might have our suspicions about Julia, given the particular situation in which she finds herself, but suspicions are not certainties. To show how egregiously wrong we can be when we construct an argument with an undistributed middle term, we put this extreme example on display: All donkeys are animals. All turtles are animals. Thus, all turtles are donkeys.

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The premisses are as indisputably true as the conclusion is indisputably false. Yes, all donkeys are in the large class of animals, and so are all turtles, but that does not mean that they are one and the same. They belong to different species, and the very definition of a species is that it is a distinct class within a larger class, called a genus. To confiise species is to undermine the earnest efforts of all our dedicated and hard-working taxonomists. (See Appendix A for further discussion of the “guilt by association” fallacy.) T he R ule G overning N egative P remisses In reviewing the elementary workings of syllogistic reasoning, we saw that the principal function of the middle term is to make a connection between the minor and major terms, so as to allow for the bringing about of a conclusion which is necessarily true, whether that conclusion takes the form of an affirmative or a negative proposition. If the conclusion is affirmative, that would mean that both of the premisses would have to be affirmative, for an affirmative conclusion tells us that the middle term was functioning in an entirely associative way, with respect to the other two terms, and not at all dissociatively. Just the opposite would be the case if the conclusion is negative. If one were to have an argument with two affirmative premisses and a negative conclusion, there would be no logical basis whatsoever for that conclusion. It would be as if it just dropped out of the sky, and it could be said to “follow” the premisses only in the purely physical sense that it comes after them on the page. Consider this: All mammals have lungs. Porcupines are mammals. Therefore, porcupines do not have lungs. The discourse simply makes no sense, and that is because the conclusion, instead of faithfully reflecting the information provided by the premisses (where the middle term forges a bond between major and minor terms), asserts something that goes directly contrary to that information. As for a negative conclusion that does logically follow from the premisses, we need to recall what the principle of the separating third has to tell us about the need for both affirmation and negation in the premisses. The successful logical separation between extreme terms can be carried .off only if an identification has been established between one or other of them. In other words, and to refer to a more elementary principle which is at work here: negation depends on affirmation. What this all comes down to, in practical terms, is stated by the fourth rule of the syllogism: No conclusion follows from two negative premisses. Consider the following argument: No males are mothers. No teenage girls are males. Therefore, no teenage girls are mothers.

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Here we have proof positive that we are dealing with an invalid argument, for we have what would be impossible were it valid: a combination of true premisses and a false conclusion. W hat is going wrong, in an argument of this form, to undermine the assurance that true premisses will necessitate a true conclusion? Because an argument can give legitimate birth to a negative conclusion only if a positive connection is made between the middle term and one or other of extreme terms, if both of the premisses are negative, the middle term is hamstrung in its ability to do this. Those two negative premisses give us nothing but disconnections, and thus the proposition in which the major term is predicated of the minor term can never be assuredly true. Put symbolically, the structure of a first figure syllogism with two negative premisses would look like this: No M are P. No S are M. No S are P. The major premiss tells us that class M and class P are completely separated, and then the minor premiss, introducing class S, tells us that that class is also completely cut off from class M. The middle term is thus rendered impotent; it cannot do what it is supposed to do. We recognize that, though class S is completely separate from class M, it could be that it nonetheless has some kind of association with class P, so that we might envision an arrangement like this:

p X

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Yes, that could be. But it does not have to be. And it is only what has to be, the necessary, that interests us. The argument can also be legitimately diagramed as follows:

M

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T he R ule G overning Particular P remisses The fifth rule of the syllogism dictates that no conclusion follows from two particular premisses. If an argument has two particular premisses, both of which are affirmative, the middle term, it is true, would be able to make a connection between the major and minor terms, but the problem in this case is that it would be doing so in insufficient fashion. A connection is made, but it is a partial one, and that cannot guarantee that there will even be a partial connection between

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the extreme terms. Here is an example of a first figure syllogism with two particular affirmative premisses. Some puppies are brown. Some cocker spaniels are puppies. Therefore, some cocker spaniels are brown. The premisses can be assented to with little strain, and it would be foolish to deny the strong possibility of the conclusion being true. But that conclusion is not proven to be true by the premisses, and if a deductive argument does not do that, it fails as a deductive argument. We must be careful not to allow ourselves to be hoodwinked by an invalid argument because it is capable of dishing up for us a conclusion that happens to be true. At first glance it might appear that there is nothing particularly wrong with the argument. After all, given the fact that there are in fact brown puppies (how could we reasonably deny it?), given the additional fact that there are cocker spaniel puppies (incontestably the case!), then does it not seem highly likely that there would be some brown cocker spaniels in the world? It does indeed. That conjecture would be a very intelligent one, and it no doubt could be shown to be sound by emperical investigation. But to do that would require moving beyond the confines of the argument, and the information provided to us by its premisses. The fact is that the argument itself does not show that there must be brown cocker spaniels now numbered among the planet’s living fauna. The specific reason for the invalidity that is brought about by two particular premisses lies in the fact that the middle term then ends up in an embarrassing undistributed state, and with that the third rule of the syllogism is violated. In the example above, the middle term is “puppies.” That term is clearly undistributed in the major premiss (“some puppies”), but it is also undistributed in the minor premiss because it is the predicate term of an affirmative proposition. It is precisely the undistributed status of the middle term that prevents it from making the strategic connection between major and minor terms. If one of the two particular premisses were negative in quality, that would solve the problem of an undistributed middle term in certain configurations, but the argument would remain invalid nonetheless. Consider this argument: Some Kentuckians are dentists. Some Americans are not Kentuckians. Therefore, some Americans are not dentists. Once again we have an argument with two true premisses and a true conclusion, but whose conclusion is not proven by the premisses. The specific problem in this case is not an undistributed middle term, for “Kentuckians” is distributed in the minor premiss, thanks to its being the predicate term of a negative proposition. Here the monkey wrench that messes up the works is an illicit major. Note that the major term, “dentists,” is undistributed in the major premiss,

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but in the conclusion it is distributed, so we are illegitimately moving from the less general to the more general. In an argument like this, with true premisses and a true conclusion, its invalidity is not readily apparent to us. It can often be more effectively analyzed, then, if we put it in symbolic form. Some M are P Some S are not M. Some S are not P. The major premiss introduces two classes, M and P, and informs us that they are partially associated with one another. Then the minor premiss brings in a new class, S, and apprises us of the fact that it is partially dissociated from the previously introduced class M. Now, stop and consider. We have two classes, M and P, which we know to be overlapping. Fine. And we know for sure that class S and M are partially dissociated. On the basis of those two items, both representing things we know are true, the argument wants to conclude that it must be the case that class S is partially dissociated from class P. But that does not follow. Why not? Because there is nothing at all to prevent the possibility— strictly abiding by the information provided to us by the premisses, and not going beyond that information— that class S, being partially dissociated from class M, could nonetheless have a quite chummy association with class P, and indeed could possibly be entirely within that class, as is shown by this diagram.

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To bring home emphatically the invalidity created by two particular premisses we will wrap up our discussion of the fifth rule by presenting two further examples of arguments in which that rule is violated, and where we have true premisses but false conclusions—the litmus test for invalidity. First this: Some athletes are males. Some females are athletes. Therefore, some females are males. And then this: Some Germans are Christian. Some Lutherans are not German. Therefore, some Lutherans are not Christian.

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We remind ourselves that particular propositions are called weak in comparison to universal propositions, and negative propositions are called weak in comparison to affirmative propositions. The sixth rule for the syllogism specifies that the conclusion must reflect the weaknesses that arefound in the premisses. In practical terms, this means that if one of the premisses is particular, then the conclusion must be particular; and if one of the premisses is negative, then the conclusion must be negative; and if both weaknesses, particularity and negativity, are present in the premisses, then the conclusion must be a particular negative proposition. Let’s see what would happen, in an argument, if we had the weakness of particularity displayed in the premisses and it went unacknowledged in the conclusion. All practicing lawyers have passed the state’s bar exam. Some women are practicing lawyers. Therefore, all women have passed the state’s bar exam. The discrepancy between the conclusion and what is given in the premisses is glaringly evident, and we have no trouble in seeing that there is no justification for the conclusion. The specific reason for this can be traced to the problem of an illicit minor. “Women,” the minor term, is clearly undistributed in the minor premiss, but that same term becomes distributed in the conclusion, so we have an illegitimate move from the particular to the universal. And now we will consider an argument in which both weaknesses appear in the premisses, and both go unacknowledged in the conclusion. The result, as you can imagine, will not be pretty. No Navy Seals are out of shape. Some Californians are Navy Seals. Therefore, all Californians are out of shape. There is a complete rupture between premisses and conclusion. The latter fails to reflect the negativity of the major premiss, and the particularity of the minor premiss. Apropos of the second problem, we have once again in this instance the presence of an illicit minor; “Californians” is particular in the premisses, but universal in the conclusion. Now if that argument had concluded with, “Some Californians are not out of shape” (those who are Navy Seals), then everything would have been just fine, and we would have an argument that was airtight. Usually the violation of the “weakness” rule is not difficult to detect in the first figure, and so an argument which is invalid on that account will seldom slip by us. But when we move into second or third figure arguments, things can get a bit more challenging. Consider this argument: Few Catholic voters really know the issues. Morever, they all vote along strict party lines. From this we may conclude that everyone who votes along strict party lines is ignorant of the issues.

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In responding to this argument, or any argument, the first thing one would naturally want to tend to is the question of the truth of the premisses. But we will put that question aside for now, for here we are chiefly concerned with validity. We have a third figure argument, with the middle term, “Catholics” in this case, serving as the subject terms in both premisses. At first glance it would appear that we have an IA pattern for the premisses, with a particular affirmative as the major, and a universal affirmative for the minor. This would suggest an IAI mood (Disamis), which we know to be a valid third figure mood. But reflect for a moment on that m ajor premiss, “Few Catholic voters really know the issues.” Though in the form of an affirmative statement, its basic import is negative, and it should be understood as saying, “Some Catholic voters do not really know the issues.” The major premiss must thus be treated as a particular negative proposition. (Moreover, given the force of the “few” in the original statement, the proposition can rightly be taken to be saying, “Most Catholics do not really know the issues.” But that does not alter the quantity or quality of the proposition.) Given that the major premiss is actually a particular negative proposition, the argument is rendered invalid on two counts. The conclusion fails to reflect the weakness of negativity, and the argument sports an illicit minor. “Those who vote along strict party lines” (i.e., some Catholics) is particular in the minor premiss but universal in the conclusion. What might we do to fix an argument as messy as this one? Assuming the premisses to be true, we could begin by rephrasing the major premiss so that it is unambiguously a particular affirmative proposition; next, we insert a new conclusion that is faithful to what is laid down in the premisses. That would leave us with an entirely different argument: Some Catholic voters are ignorant of the issues. All Catholic voters vote along strict party lines. Therefore, some of those who vote along strict party lines are ignorant of the issues. This is a third figure Disamis (IAI) argument, and therefore valid. Whether or not its premisses are true is a separate question. S ummary

of the

R ules

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Syllogism

L A syllogism must have three terms and only three terms. II. A term distributed in the conclusion must be distributed in the premisses. HI. The middle term must be distributed at least once. IV. No conclusion follows from two negative premisses. V. No conclusion follows from two particular premisses. VI. The conclusion must reflect the weaknesses found in the premisses. If we faithfully abide by these rules we have ready to hand all we need to construct valid arguments. But we must keep in mind that validity is only half

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the battle in logic; the other half is truth. It is imperative that our arguments be structurally sound, but the premisses on which our conclusions are based must be true. Of the two, it is easier to get validity right than the truth, for in the case of the former we are dealing with what essentially amounts to the mechanics of argument, and we have our fail-safe rules to ensure our getting it right on that score. But when it comes to ascertaining the truth of things there are no hard and fast rules we can follow in order to guarantee success. Achieving the truth, in whatever field we might be working, comes down to a matter of getting reality right, and that is a full-time, around-the-clock job, requiring humility, alertness of mind, inquisitiveness, pertinacity, hope, and a sense of humor. When it comes to analyzing the arguments of others, to say that the rules for the syllogism come in handy would be an understatement. These rules are, as a matter of fact, the most effective tools we have available to us for sizing up an argument with the principal purpose in mind of determining whether or not it is valid. They will never let us down. (See Appendix B for more about the rules for the syllogism.) False Premisses

and a

T rue C onclusion ?

If we know anything for sure by this stage of the game, because I have been repeating it to the point of tedium, it is that the guarantee offered by a valid argumentative structure is as follows: true premisses will produce a true conclusion. Putting the same point in different terms, it is impossible, in a valid argument, to have true premisses and a false conclusion. Now, if that is right, and it is, doesn’t it also seem right to say that, in a valid argument, false premisses will always guarantee a false conclusion? That may seem right, but it isn’t. It is quite possible to have a valid argument in which the premisses are false but the conclusion is true. This is not to say, however, that falsity in conclusions does not have its source in false premisses. Where else could it come from? Consider the following arguments, in the first of which there are two false premisses, and in the second, one false premiss, yet in both cases the conclusions are true. First argument: All monkeys are rational. All men are monkeys. Therefore, all men are rational. Second argument: All men are mortal. No pigeons are mortal. Therefore, no pigeons are men. The first argument represents a first figure Barbara (AAA) syllogism, which is of course perfectly valid; the premisses of the argument are clearly false. The second argument is a second figure Camestres (AEE) syllogism, which we

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know to be valid; its m ajor prem iss is a very fam iliar proposition, and true enough, but we cannot say much for the minor premiss. It is in fact quite false. And yet the conclusions to both arguments are as true as true can be. Here we have perfectly valid arguments, then, with false premisses, which nonetheless yield up true conclusions. A rather anomalous situation, no? Is it cause for panic? Does this call into serious question the whole project of logic? There is no need to panic, and don’t bum your logic book— at least not with the idea in mind that it was logic itself that let you down. Before analyzing our two arguments, to see what is going on in them, let us first sit back for a moment and think of this situation in general, commonsense terms. What do we have here but a state of affairs in which we have an argument which combines bad premisses with a good conclusion. Is that terribly unusual, in term s of our real life experiences? How often have you heard or read an argument which had a conclusion with which you entirely agreed—for the best o f reasons, because it was simply true— and yet you were sensitive to the fact that the conclusion was not very im pressively supported? Your friend is attem pting to make a point, you get the point, you think that it is perfectly right, but your friend does not make a convincing case for it, and you can easily imagine that for somebody else, somebody who did not already accept the point, your friend’s argument would fall on deaf ears on account of its ineffectualness. Good conclusion, bad premisses. And haven’t all of us been in circumstances where we were convinced that a point we ourselves were trying to make was as right as rain, and yet we were painfully and frustratingly aware that we were doing an awful job in showing that the point was right? Good point, poor support. In sum, it is not all that unusual to have arguments which may be lacking in one degree or another with regard to the quality and force of their premisses, and yet have conclusions which are true. In an earlier chapter, in an effort to em phasize the important difference between validity and truth, I used the analogy o f a machine, a car specifically, which was in perfect mechanical condition but which would not run because its tank was filled, not with gasoline, but with prune juice. I likened the mechanically perfect car to a valid argument, one with no flaws in its structure, and the prune juice in the gas tank to defective contents, that is, to false premisses. My point there was that for a sound argument it is necessary to have both valid form and true contents. So, if we have a mechanically defective car—let’s say its ignition system is all out of whack— but with its tank filled with the best high-test fuel that money can buy, the car will not run. That would be like an invalid argum ent with true prem isses. W e have looked at any number of argum ents o f that sort, and we have seen that, precisely because of their invalidity, they cannot guarantee a true conclusion, not even with the truest premisses in the world. But does not my analogy break down in the face of the situation we are dealing with here, where we have a valid argument with false premisses perversely delivering up a true conclusion? W ouldn’t this be

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comparable to a mechanically perfect car running like a top on prune juice? The analogy, though admittedly not perfect in every respect, does in fact hold up as applied to the situation represented by the two arguments given above. How so? Because, I contend, those two arguments do not “run” at all, seen from a strictly logical point of view. But this is a contention that needs an argument behind it, which I will now attempt to provide, as we turn to an analysis of the arguments. It is often said, in describing the situation we deal with here, that it is possible to have a true conclusion which follows from false premisses. “Follows” is to be taken in a loose sense, for strictly speaking, a true conclusion does not logically follow from false premisses. The “following” that we observe taking place in these arguments, in the form of their conclusions, is purely verbal. Understand, we are treating of deductive argument, the hallmark of which is that its conclusions follow necessarily. And whence comes that necessity? It can come from nowhere else but the premisses. Let us consider yet once again our familiar classic syllogism. All men are mortal. All Greeks are men. Therefore, all Greeks are mortal. It is necessarily true that all Greeks are mortal beings, because it is necessarily of the very essence of Greeks that they are human beings, and, antecedently, it is necessarily of the very essence of human beings that they are mortal. Again, the necessity of the conclusion derives from the necessity which is to be found in the premisses. Demonstrative argument of this kind, as the foregoing sentences make explicit, is concerned with the essences, or natures, of the things which compose its contents, as Aristotle points out. With these thoughts in mind, let us now look closely at our two arguments. The first argument ends with the statement that all men are rational. True. That quite accurately describes the nature of man. But the truth of that statement does not follow from what we are told in the premisses. That would be totally incongruous. The major premiss is not dealing with the nature of monkeys, nor is the minor premiss revealing anything about the nature of man; in fact, it is making the egregious error of equating one species with another, and confusing two radically different natures. There is nothing in the internal logic of the premisses, then, that in any way necessitates the truth of the conclusion; indeed, the third proposition in each discourse can be called a conclusion only in an analogous sense. The third proposition in each discourse turns out to be true only because of the arrangement of the words in the preceding two propositions, not because a distinct bond has been forged between the essences of the major and minor terms.

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The second argument gets off to a promising start, with a true major premiss, but then everything is spoiled by the minor premiss. It does severe violence to the nature of its subject term, pigeons, by claiming immortality for them. (This may have the effect o f temporarily raising the self-esteem of the pigeons of the world, but the fear is that, once they discover the fraud, they will be turned off logic for life.) With that, the argument enters cloud cuckoo land, and though its conclusion happens to be true, its truth has not been dem onstrated by the premisses. And this is because, also in this case, no real connection has been made between the intrinsic natures o f the major and minor terms. In sum, it is possible to have a valid argument with false premisses and a true conclusion, but the conclusion follows the premisses only sequentially, not logically.

Review 1. W hat are weak propositions? Give some examples. 2. Why must a syllogism have only three terms? 3. W hat is an illicit minor? 4. W hat is an illicit major? 5. Why is the middle term made dysfunctional if it is not distributed at least once? 6. W hat does a valid syllogism guarantee, and what is the condition for that guarantee? 7. What rule is violated to give rise to the “guilt by association” fallacy? 8. Explain why no conclusion follows from two negative premisses. 9. Explain why no conclusion follows from two particular premisses. 10. Explain why, in a valid syllogism with false premisses, a true conclusion cannot be said to follow, in a strict, logical sense. Exercises A. For each of the arguments listed below, (a) determine whether it is valid or invalid, and (b) if invalid, identify which rule or rules it violates. You should be exclusively concerned with the validity of the arguments. Assume the premisses to be true, even though they may be in fact highly questionable. 1. Some of the smartest young people in the country go to Acme College. Bridget is a student at Acme. It’s obvious, then, that she’s very smart. 2. Everyone I know who’s a Democrat lacks a sense of humor. But none of my relatives are Democrats. So, none of my relatives lack a sense of humor.

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3. Cindy is adamantly pro-choice. She is also very wealthy. Well, then, at least some very wealthy people are pro-choice. 4. N o P areM . Some S are M. Some S are P. 5. Some pro athletes earn millions of dollars per year. Some pro athletes have bad teeth. Therefore, some people with bad teeth earn millions of dollars per year. 6 . All college teachers are suave and well-educated.

Some New Yorkers are not suave and well-educated. It follows, then, that some New Yorkers are college teachers. 7. All the members of the graduating class attended the commencement exercises. Some Latinos were members of the graduating class. Thus, some Latinos attended the commencement exercises. 8 . N o M areP .

All M are S. No S are P. 9. All three-time felons will get life in prison. All three-time felons are ineligible for parole. Hence, all those ineligible for parole will get life in prison. 10. No one who cheated on the exam will receive a passing grade. Every junior enrolled in the course cheated on the exam. Consequently, every junior enrolled in the course will get a passing grade. 11. Some people allergic to peanuts hate to fly. All people allergic to peanuts read Arabic. We conclude that some people who read Arabic do not hate to fly. 12. All sailors love to spin yams. Everyone at the concert last night was a sailor. Thus, some of those at the concert last night love to spin yams.

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B. All of the arguments listed below lack conclusions. In each case complete the argument by adding a conclusion which would ensure the validity of the argument. 1. All music lovers are sensitive people. Some music lovers play string instruments. Therefore... 2. No truck drivers are ornery. Everyone in this cafe is a truck driver. Therefore... 3. No sports fans like to see their team lose. All sports fans are serious-minded people. Therefore... 4. All politicians want to be reelected. Senator Snivel is a politician. Therefore... 5. All robins fly south for the winter. No sparrows fly south for the winter. Therefore... 6 . No liberals like limited government.

All conservatives like limited government. Therefore... 7. Every serious student studies hard. Every serious student wants to succeed. Therefore... 8 . Some dentists are not bald.

All dentists repair cavities. Therefore... 9. All immigrants have to adjust to their new country. The family that lives down the block are immigrants. Therefore... 10. No vegetarians patronize butcher shops. Some Thais are vegetarians. Therefore...

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11. All good parents want what is best for their children. Some parents do not want what is best for their children. Therefore... 12 . No teachers treat their students unfairly.

Some teachers are forgetful people. Therefore... 13. No college students are lazy. Some Los Angelinos are college students. Therefore... 14. Some children are very shy. All children like to play. Therefore... C. All of the arguments listed below are invalid. In each case alter the argument in such a way to make it valid. This will involve either (a) changing one of the premisses (only one premiss needs to be changed in each argument), or (b) changing the conclusion. 1. No one who voted for Representative Reptilian has a college degree. All those who voted for him live in Cougar County. Therefore, no one in Cougar Country has a college degree. 2 . Some of those in banking are well-paid.

All of my best friends are in banking. Therefore, all of my best friends are well-paid. 3. No mountain climbers are nervous nellies. The whole Quigley family are mountain climbers. Therefore, some of the Quigley family are nervous nellies. 4. All good batters have keen eyesight. Some people in South Boston do not have keen eyesight. Therefore, no one in South Boston is a good batter. 5. All gamblers like to take chances. Some people in Kansas City are gamblers. Hence, everyone in Kansas City like to take chances. 6 . No firefighters are lacking in courage.

Some Italian-Americans are firefighters. It follows, then, that no Italian-Americans are lacking in courage.

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Chapter Twelve Variations on Syllogistic Reasoning; Making Arguments P olysyllogisms In all of the examples we have used thus far, to illustrate the various forms of syllogistic reasoning, there has been a conscious attem pt to keep the arguments as simple and succinct as possible. This was to allow us to become thoroughly familiar with the basic structure of the syllogism, and thus to become properly sensitized to the critically important m atter of validity. Validity is a critically important matter because how we frame our arguments, the structural settings we construct for our ideas, will make all the difference in the world for the success we are aiming at in our efforts to arrive at the truth. To be sure, arguments can be, and very often are, much more complex and elaborate than the examples we have been dealing with. A complex argument has its merits, and often, though not always, it is the most effective way to respond to a complex situation. But complexity in argument has its problems, the chief one of which has to do with the very nature of any complex entity; that is, any entity composed of parts. A complex argument, as an entity composed of parts, is going to be sound precisely to the extent to which all of its parts jure sound. W hat are the “parts” of a complex argument? In more cases than not they are little arguments unto themselves, and very often they take the form of one or another of the syllogistic arguments we have been examining in the preceding pages. A complex argument made up of particular arguments will be sound, then, taken as a whole, just to the degree that the particular arguments composing it are sound. The health of the entire organism is dependent upon the health of each of the organs that make it up. One of the more interesting forms of complex argument is called a polysyllogism. The prefix “poly” (from the Greek) means “many,” so what we call a polysyllogism is a unified argumentative structure which is composed of many syllogisms, or, at the very least, two of them. More precisely, a polysyllogism is a succession o f categorical syllogisms which are so arranged and

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interconnected that the conclusion of one syllogism serves as the major premiss of the succeeding syllogism. A poly syllogism consisting of three distinct first figure Barbara (AAA) syllogisms would be expressed symbolically as follows: All M are P. All S are M. All S are P. (conclusion + major premiss) All X are S. All X are P. (conclusion + major premiss) All Y are X. All Y are P. (final conclusion) Notice the pattern here. The major term, P, remains the same throughout the entire course of the argument. The minor term of the preceding argument becom es the middle term of the following argument, and in that following argument a new minor term is introduced, which then becomes, as the argument continues, the middle term of the next syllogism. Beginning with our classic syllogism, we construct a polysyllogism patterned after the model above: All men are mortal. All Greeks are men. Therefore, all Greeks are mortal. But all Athenians are Greeks. Consequently, all Athenians too are mortal. But Socrates is an Athenian. It follows, then, that Socrates is mortal as well. T he A dvantages

and

D isadvantages

of

POLYSYLLOGISTIC ARGUMENT

A polysyllogism can carry a peculiar kind of rhetorical force for the way it connects argument to argument, elaborating upon a basic idea (in the case of our example, the idea of mortality) by conjoining it with a new idea at each syllogistic step, and thus building up as it progresses to its final conclusion which, simply on account of the elaborate foundation on which it rests, can come across as more than usually compelling. The following argument is intended to serve as a better illustration of that point. Constant vigilance is the necessary condition for the preservation of democracy, and it is only an intelligent and informed electorate that is constantly vigilant, Thus, it will be an intelligent and informed electorate that will ensure the preservation of democracy. But it is only a soundly educated citizenry that can constitute an intelligent and informed electorate. It is, then, a soundly educated citizenry on which the preservation of democracy depends. And who else but those solidly grounded in the liberal arts, especially in the art of logic,

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can be said to be soundly educated citizens? In the final analysis, then, it is those who are solidly grounded in the liberal arts, especially in the art o f logic, upon whom rests the burden of preserving our democratic form of government. Logic is a practical science, and an art as well, and therefore efficiency must be one o f its principal concerns. The purpose of reasoning is to attain the truth, and the purpose of argument, which is the public expression of reasoning, is to com m unicate the truth to others, or to convince them o f a truth about which they might otherwise be doubtful. W hether or not we are successful in doing that o f course very much depends on the quality of our arguments. Now, while an argum ent which is cast in the form o f a polysyllogism can, in certain circum stances, and depending on the subject m atter with which it deals, be quite effective, it has to be employed judiciously. What most has to be avoided in using an argument o f this kind is simply overdoing it; that is, constructing an argument that contains too long a chain of component syllogisms. This can put too much strain on the attention span and memory of all but the most alert and patient o f audiences, with the result that the argument will lose much if not all o f its effectiveness. T he R ules

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Polysyllogism

Are there rules of the poly syllogism? There are, and they are precisely the same rules with which we have acquainted ourselves in the previous chapter. This stands to reason, for, after all, a polysyllogism is nothing else but a complex argum ent m ade up o f individual syllogistic arguments, so each of those individual arguments would be subject to the rules of the syllogism. Apropos o f w hat we said earlier, then, if any one o f those arguments is defective, by reason o f violating one or other of the rules, then the entire polysyllogism is spoiled. In the first example o f a polysyllogism which we gave above, each of its component parts was a first figure Barbara syllogism. Consider the following argument, also made up o f Barbara syllogisms, but one of which is invalid. All sentient organisms are capable of locomotion. All mammals are sentient organisms. Thus, all mammals are capable of locomotion. But no sea animals are mammals. Therefore, no sea animals are capable of locomotion. However, all whales are sea animals. Hence, no whales are capable of locomotion. The lead-off syllogism in this argument is a first figure AAA syllogism, which o f course is valid. Its premisses are true, and therefore its conclusion is true. So far, so good. However, things start to go wrong in the second syllogism in the series. This is also a first figure syllogism, but its mood is AEE, and we know that to be invalid in that figure. W hat is more, the syllogism’s minor premiss,

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“No sea animals are mammals,” is clearly false, and so in the middle syllogism the conclusion, which claims that no sea animals are capable of locomotion, is egregiously false. The specific problem that invalidates the middle argument is an illicit major: the major term, “organisms capable of locomotion,” is undistributed in the major premiss, but distributed in the conclusion. We might say that the argument tries to get back on track in the third syllogism, assuming as it does the form of a first figure EAE mood, which is valid, but it is too late: irreparable damage has already been done to the argument. That third syllogism begins with a major premiss which is false, having inherited it from the preceding invalid syllogism, and the whole argument ends on the very sour note of denying that whales are capable of locomotion. Tell it to Captain Ahab. T he L ogical L imitations

of

Polysyllogistic R easoning

All of the examples of the polysyllogisms we have presented thus far are of arguments which are composed entirely of first figure syllogisms. Can this type of argument be composed only of first figure syllogisms? No. As a matter of fact, any one of the fourteen valid moods of the three figures of the syllogism can be used as an effective starting point of a polysyllogism, but then, depending upon the particular form with which the argument begins, there are strict limitations as to what forms may follow. If one were to begin with a first figure Barbara syllogism, for example, there would be no formal barriers to continuing on indefinitely in that figure and mood. If you were to express a polysyllogism in symbolic form you would be unencumbered by the natural bounds set by actual ideas, and you could carry on ad infinitum, but that would prove to be a rather mindless exercise. Using ordinaiy language, one would eventually reach a terminus point because eventually, moving from larger classes to smaller ones, you would end up with an individual member of the smallest of the classes; this would be a substance/subject which, not being a class, cannot be predicated of anything. So it all stops right there. For example, in the syllogism above, where we start with the very large class of mortal beings, then move through the smaller class of men, the yet smaller class of Greeks, and the yet smaller class of Athenians, we eventually end up with Socrates. At this point we can proceed no further because Socrates, or any other individual entity, cannot serve as a middle term which can be predicated of a subject. All sorts of things can be predicated of Socrates, but Socrates cannot be predicated of anything, except, one might say, Socrates himself—e.g., we could say, “Socrates is Socrates”— but that would not really be predication. We would simply be repeating the subject, and perhaps the most we could say of such an assertion is that it serves to express the principle of identity. Here I will cite just a couple of examples to show the limitations imposed on moods other than the AAA mood, as they are used in polysyllogisms. What kind o f results could we expect if we were to begin a polysyllogism with a

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second figure AEE (Camestres) argument, which is of course a valid mood? If we do so we would then need immediately to switch to the EAE mood, and, if we subsequently stick with that m ood we will have no problems. L et’s see what happens if we start with an AEE argument, and then stubbornly try to maintain that mood. All liquids will assume the shape o f the container in which they are placed. No rigid body will assume the shape of the container in which it is placed. Therefore, no rigid body is a liquid. No metal is a liquid. So, no metal is a rigid body. The only way I could attempt to maintain an AEE pattern in the second syllogism would be to put down an E proposition, which is intended to serve as the minor premiss, but that proves to be a fruitless gesture, for my major term, whether I like it or not, is an E, not an A, proposition. W hat I therefore end up doing is constructing a syllogism with two negative premisses (violating the fourth rule o f the syllogism) and that gives me, not surprisingly, a false conclusion. Now let us consider building a polysyllogism by starting with a third figure AH argument, which we know to be valid. Here is another instance where, if I attempt to continue with that mood, I would be stymied. All birds are egg-laying. Some birds are flightless. Therefore, some flightless creatures are egg-laying. Some flightless creatures are canines. Therefore, some canines are egg-laying. What happens in the second syllogism, when I try to persevere in the All pattern of argument by positing a particular affirmative proposition for a minor premiss, is that I create an argument with two particular premisses, which gives me an undistributed middle term and a conclusion which is embarrassingly false. Is there any way I can get out of this mess? Yes, there is. If we start a polysyllogism with a third figure A ll argument— which is a perfectly legitimate thing to do— then, in the second syllogism, we switch to the IAI mood (Disamis), and we can carry on merrily in that mood for as long as our imagination holds out, allow ing us to continue to come up with viable m inor terms. Observe what happens when I do that in the argument now under examination. All birds are egg-laying. Some birds are flightless. So, some flightless creatures are egg-laying. Now, all flightless creatures are earth-bound. Thus, some earth-bound creatures are egg-laying.

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That conclusion is not particularly interesting, but I think we can all admit to its being true. (See Appendix A for a presentation of all of the formal possibilities for polysyllogistic reasoning.) S orites A sorites might be described as a trimmed-down polysyllogism. Like the polysyllogism it is a chain argument, a chain with, as it were, fewer links in i t Because of its streamlined character, it has the capacity for being, from a rhetorical point of view, more effective than the polysyllogism. Because the various “links” in the argument stand out more prominently, it is easier to follow. A sorites argument is structured in such a way that the predicate term of the first proposition becomes the subject term of the second proposition, and the predicate term of the second proposition becomes the subject term of the third proposition, and so on, following that same pattern until the final premiss. The argument concludes with a proposition whose subject term is the subject of the very first proposition, and whose predicate term is the predicate term of the penultimate proposition, the one immediately preceding the conclusion. The basic pattern of a sorites argument is most clearly seen if we put it in symbolic form. Every A is B, every B is C, every C is D, every D is E, therefore, every A is E. The logic of the conclusion of the argument is made evident with a diagram.

Here is an example of this type of argument expressed in ordinary language. Every beaver is an animal, every animal is a living organism, every living organism is a material body, every material body is a substance, therefore, every beaver is a substance. Note what this type of argument is capable of doing in terms of the classes which are predicated of the subject with which it is principally concerned: the classes get increasingly larger as the argument proceeds. The initial premiss places the class of beavers in the larger class of animals, and then the argument

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concludes by placing beavers in the largest of all classes, that of substance. Our diagram gives us a vivid visual sense of the logical relations that are established in the argument. A sorites argument may be said to have the capacity to provide a “big picture” context for any subject, for it can make a telling case for the thesis that any entity, however seemingly insignificant, can be shown to have wider and richer existential import than at first we may have realized, as we see how it fits into an ordered hierarchy of being. Consider this example: Every human being is a person, every person has intrinsic value, anything having intrinsic value is worthy of our respect, and anything of intrinsic value which is worth of our respect should logically receive our respect, every human being, therefore, should receive our respect. Here is another. Every lie told by a public official is a more than usually serious affront to truth, and every such affront to truth does damage to language, whose whole purpose is to convey the truth. W hatever damages language corrupts communication, and whatever corrupts communication loosens the bonds that hold a society together. W hatever loosens the bonds that hold a society together puts that society in jeopardy. We must conclude, then, that every lie told by a public official puts our society in jeopardy. In contrast to the way a sorites argum ent develops, moving to increasingly larger and larger classes with the predication of each succeeding proposition, the polysyllogism, in the form of its major term, concerns itself with the same class throughout the argument. T he R ules

of the

S orites A

rgument

Because a sorites argument can be “fleshed out” and expressed in the form of a polysyllogism, it is ultimately subject to all of the rules of the syllogism. But in its form just as a sorites there is only one rule that applies to it directly, and that is the sixth, which says that the weaknesses in the premisses (i.e., particularity and negativity) must be manifested in the conclusion. A sorites argument can have a conclusion which is particular, or negative, or both, but whatever its character in this respect it would simply be reflecting information contained in the premisses. There are two special rules for this form of argument that have been laid down in order to ensure its validity. The rule regarding negative conclusions: only the last premiss can be negative. The rule regarding particular conclusions: only the first premiss can be particular.

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Here is an example of a sorites argument with a negative conclusion. Note that in this instance the negative premiss is the final one. A ll m edical stu d en ts have to study hum an anatom y, and human anatomy is a difficult subject. Difficult subjects demand much time and energy. The expenditure of time and energy requires strict discipline. Being strictly disciplined is not easy. Medical students, we conclude, do not have it easy. Here is an example of a sorites argument whose conclusion is a particular proposition. For the argument to be valid, its initial premiss must be a particular proposition. Some drivers are careless. Careless people are a danger to others. Those who are a danger to others are public nuisances. Public nuisances are a blot on our national character. Thus, some drivers are a blot on our national character. In the sorites argument which follows, the weakness of both negativity and particularity are expressed in the conclusion, and, accordingly, each of those weakness appears in its proper place in the premisses. Some institutions of higher learning are mediocre to bad. Mediocre to bad institutions of higher learning do an injustice to their students. Students to whom injustice is done feel bitter and resentful. Bitter and resentful people do not contribute to the common good. So, some institutions of higher learning do not contribute to the common good. Given the fact that the sorites is a chain argument, the principle that applies to chains of whatever sort applies to it as well—that a chain is only as strong as its weakest link. Perhaps there is a link or two in the examples given above that you may have your doubts about. In arguments of this kind very rarely is it the case that they are composed of propositions which are self-evidently true, and much less that there are necessary connections binding one premiss to another, so that the conclusion of the argument would follow necessarily. One could construct a sorities argument that would be demonstrative, such as the following: All men are mortal, all mortal beings are living organisms, all living organisms are material substances, all material substances have mass, therefore all men have mass. However, given the subject matter that is commonly dealt with in most instances where this type of argument is employed, the conclusions do not follow

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necessarily. The typical sorities argument, then, will derive whatever compelling force it has from the general reasonableness of its premisses, and the strength o f the relation between one premiss and another. We may not be bowled over by a particular conclusion, but if it gives us som ething which we decide is worth thinking about, the argument would not have been made in vain. (See Appendix B for additional discussion o f the sorites argument.) Enthymemes In our treatm ent o f argum ent in general, and syllogistic argument in particular, we have conscientiously endeavored, in the exam ples we have provided, to be as formal and complete as possible— for sweet clarity’s sake. But rare indeed would it be if we were to encounter in our daily conversation or in our reading a syllogistic argument which was spelled out in explicit, step by step fashion. You probably cannot rem em ber the last time you picked up a newspaper, opened it to the editorial page, and began reading there an article that began as follows: Municipalities that spend more than they take in go bankrupt. This municipality spends more than it takes in. Therefore, this municipality will go bankrupt if it doesn’t mend its ways. The fact of the matter is that we do not normally communicate with one another in so logically formal a fashion. We do not go around talking to one another in syllogisms, nor do we have a habit of exchanging syllogistic memos. Granted. But let a salient truth be repeated: though we rarely speak or write syllogistically, nonetheless syllogistic reasoning lies at the very heart of our thought processes, when we are thinking coherently at all. The kind of relations among ideas which we see explicitly displayed in a properly structured syllogism is but an explicit representation of how in fact we routinely put ideas together, and take them apart, in our minds. A valid syllogism simply shows how our minds work when they are working well. But too much should not be m ade o f the fact that we do not speak syllogistically in our ordinary everyday speech, for in a sense we do, albeit in an incomplete and stuttering sort o f manner, which takes the specific form of what is called an enthymeme. An enthymeme is simply a syllogism which is not fully stated. The word “enthymeme” comes from the Greek enthymema, which m eans “thought,” or “argum ent,” or “piece o f reasoning.” That last meaning is the best fit for what we are dealing with here, for the enthymeme, in current logical usage, refers to an abbreviated or partially expressed syllogism. More precisely, an enthymeme is a syllogism one or other of whose propositions is not explicitly articulated. A syllogism in standard form, as we know, is one that is so ordered that the m ajor prem iss comes first, followed by the minor

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premiss, followed by the conclusion. In ordinary conversation, and in most of the writing we do, even when we intend to engage in serious argument, our language tends to be elliptical, and we typically express our arguments in abbreviated form, but usually with the understanding that our auditors or readers will “fill in the blanks” and say to themselves what we leave unsaid. The logician Andrew Bachhuber is worth quoting here: “The enthymeme is the most natural way of applying a general principle to a particular case and the commonest expression of syllogistic reasoning. Outside of logic books you will find very few completely expressed syllogisms, but you will find enthymemes on almost every page you read .” 21 To this one might want to add, “and in almost every serious conversation you engage in.” T he W ays

in

W hich Syllogisms A re C ommonly A bbreviated

We have three possibilities open to us in abbreviating syllogisms: (1) omit the major premiss; (2) omit the minor premiss; (3) state both premisses and omit the conclusion. We frequently run into enthymemes in the following form, where the major premiss is left unstated. Because Socrates is human he will consequently one day surely die. Or:

There’s no way Ben is going to make it through engineering school. And the reason is, he’s just too darned lazy.

The missing major premiss in the first argument, “All human beings are subject to death,” is not something we would need to have spelled out for us. We “fill in the blank” pretty much automatically, and, by the way, the facility with which we do so can be taken as impressively solid evidence for the fact that syllogistic reasoning comes naturally to us. The second argument, now equipped with a fully stated major premiss, would be expressed this way: Lazy people do not make it through engineering school. Ben is lazy. That means Ben is not going to make it through engineering school. Here are two more enthymemes in which it is the minor premiss which is not stated: Because all men are mortal, Socrates will one day surely die. At the end of the day, all cheaters are losers. So, Cataline’s a loser. The missing minor premiss is easily supplied in both cases: “Socrates is a man,” for the first argument; “Cataline’s a cheater,” for the second. One might think that it would never be a good idea to leave the conclusion of one’s argument unstated. After all, this is the “point” we are trying to make,

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and we would want to m ake sure that people “get it.” As a general rule, it would be best to state the conclusion of one’s argument in clear, explicit terms, but there are occasions when an omitted conclusion can, paradoxically, be gotten across more forcefully by refraining from stating it explicitly. Consider these two enthymemes. Those who don’t study can’t be expected to pass their courses. Paul hasn’t cracked open a book all semester. We all know that a failure to pay attention to details will eventually lead to major problems. This department has developed the reputation, deservedly, of consistently being inattentive to details. This is the “draw your own conclusions” approach, which can be quite effective for the way it invites the audience to be an active participant in the argument. O f course, in using this approach you have to know your audience well enough that you can be confident that they will draw the conclusion you want them to draw. Having to spell out an unstated conclusion has the same anticlimactic effect as having to explain a joke. Another approach that is sometimes taken with the enthymeme, also with the end in mind o f achieving greater rhetorical effectiveness, is to state the conclusion of the argument first, followed up by either the minor or the major premiss, as in the following arguments. The fact is, Socrates is mortal, and that’s because he’s human like the rest of us. This society is doomed. Every society that succumbs to decadence is doomed. The audience to the first argum ent would have no trouble mentally filling in the major premiss, “All human beings are mortal,” and those giving ear to the second argument could quickly figure out that the missing premiss, the minor, is, ‘T his society has succumbed to decadence.” Leading off with the conclusion can be an poignant way of beginning any argument, not just an enthymeme. It is a way of imm ediately grabbing the audience’s attention. Also, it has the effect of emphasizing the two basic elements of every argument— the point, and the support for the point. “This is what I think is true,” you are effectively saying to your audience, “and now I am going to give you the reasons why I think it’s true.” R esponding

to

Enthymemes

In most cases there would be no need to pause and consciously “fill out” an enthymeme, by supplying its m issing element, in order to understand the complete argument behind it, and thus determine whether or not the argument is sound. Even so, it is important that we develop the habit o f reconstructing

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the complete arguments that lie behind enthymemes, and that is because it makes us more alert to the fact that not a few of the enthymemes that come our way on a fairly regular basis turn out to be shortened versions of arguments that are in fact quite shaky. It is only by reconstructing the complete argument from which the enthymeme is derived that we are made fully aware of this. Consider the following argument: Jack is obviously guilty of stealing the money. He was sweating profusely when the police were questioning him about it. We put the argument in the form of a first figure syllogism: Everyone who sweats profusely when he is being questioned about his possible involvement in a crime is guilty of that crime. Jack was sweating profusely when he was being questioned about the crime of stealing the money. Therefore, Jack committed the crime. The conclusion of the argument follows logically from the major premiss, and that premiss, as stated above, would seem to be just what is being implied in the enthymeme. But all we needed to do was state the premiss explicitly to see how completely feeble it is. It certainly cannot be said to represent anything remotely resembling a universal truth. We might ask: Could the fact that Jack was sweating profusely when he was being questioned about the stolen money be interpreted as a sign of his guilt? That is something that could reasonably be taken under consideration, along with many other things. But there is no necessary connection between a physiological phenomenon like profuse sweating and moral guilt, as the major premiss would have us believe. If that were to be allowed to count as sufficient evidence for determining that someone is guilty of committing a felonious act, we would all be in trouble. There could be any number of explanations for Jack’s intemperately soaking his sweatshirt, not one of which had anything to do with his being guilty of stealing the money. Maybe he forgot to take his medications that morning, distracted as he was by the news that the police wanted to talk with him, and as a result of that omission was undergoing some sort of purely somatic reaction that manifested itself in profuse sweating. Or maybe it was a very hot August day and the air conditioning system at the precinct station had broken down. Yes, Jack was sweating profusely, but so was everyone else in the room. There is no fixed method to follow in reconstructing complete syllogisms from enthymemes, but there are a couple of tips that could prove helpful. The first thing we should do is identify the conclusion of the argument. W iat’s the point? It will not always be the case that we will be aided in this effort by the presence of a logical indicator, like “therefore” or “so,” but usually the context makes clear the central point that we are expected to accept as true. Having satisfied ourselves that we have a good idea of the point of the argument, we

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should then consider the statement that accompanies it, to determine whether it fits the role o f a m ajor prem iss or a m inor prem iss. The telltale sign o f the m ajor prem iss is that it states the general truth on which the conclusion will depend; the m inor premiss cites a particular instance o f that truth. Example: All armed robberies are felonies, (major) This is a case o f arm ed robbery, (minor) W ith these two items o f vital information in hand— i.e., conclusion plus major premiss, or conclusion plus m inor premiss— it is then a simple matter o f filling in the m issing prem iss. Once the syllogism has been reconstructed, then we pose the two critical questions: Is it a valid syllogism? Are its premisses true? O f those two questions, the second is usually the more critical. In more cases than not, ascertaining the truth o f the m inor prem iss presents no great difficulty, because that premiss commonly states a simple matter of fact. In the argument we are considering here, the m inor premiss informs us that Jack was sweating profusely when he was being questioned about the stolen money. He either was or he wasn’t, and one or the other can be established either by direct observation or through reliable testimonial evidence. But it is the major premiss whose truth is the more im portant to determ ine, for this is the premiss which provides the overarching rationale for the acceptableness of the conclusion. And it is not unusual that, the more questionable the m ajor premiss, the more likely it is that it will be that prem iss which goes unstated in the enthymeme. And so it was in our example. But once the m ajor premiss of that argument was dragged into the daylight, its radical inadequacy was fully exposed. Sometimes an enthymeme can take a very skimpy form, so skimpy in fact that it does not really deserve to be called an enthymeme. W hat I have in mind are those situations in which people are effectively arguing with us, but in a totally tacit way, in the sense that all they give us is the conclusion. They definitely have a premiss behind it, but we have to draw it out of them. Once we do that, we can then decide whether or not it offers any reasonable support for the contention they are making. - Wally is never going to make a successful psychologist. - Really, you think so? W hat makes you say that? - The guy’s too mercurial. He rides an emotional roller-coaster, flying high as a kite one day, down in the dumps the next. The inquirer might be willing to accept what would serve as the major premiss for that argument—the generalization that people who are subject to what seems to be a permanent pattern of broad mood swings are unlikely to make successful psychologists— so careful attention would have to be given to the minor premiss in determining the force of the conclusion. Does the minor represent an accurate assessment of W ally’s personality? You would need to be more than casually acquainted with the man to be able to give an adequate answer to that question.

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If it should happen that neither of the propositions of an enthymeme qualify as a conclusion, then what we have on our hands, obviously, are the tw o prem isses o f the argument. In that case our task is to try to figure out w hat conclusion would logically follow from those premisses. If we cannot come up with a fitting conclusion for them, then we are justified in concluding that we have an unsound argument on our hands. Consider the following enthymeme: Only intemperate people drink wine at their meals. Professor Venard regularly drinks wine at his meals. The conclusion is left unstated, but it is evident where the arguer wants us to go with those premisses—to the conclusion that Professor Venard is an intemperate person. But by this time we should be wise to this type of argument. Our keenly honed analytic skills quickly identify a second figure argument that ends with an affirmative premiss, and we know that cannot happen legitimately in the second figure. Investigating further, we locate the heart o f the argum ent’s problem in the fact that it has an undistributed middle term. So, we rightly reject the conclusion as not having been proven by the premiss. The conclusion, we say, making a perhaps somewhat immodest show o f our Latin erudition, non sequitur— it doesn’t follow. But now consider this version of what is, in terms of its contents, the same argument, with in this case the conclusion explicitly stated. People who drink wine at their meals are intemperate. Professor Venard drinks wine at his meals. We must sadly conclude, then, that Professor Venard is intemperate. Here we have an argument that is perfectly valid, so we obviously cannot fault it on that score. The problem in this case clearly has to do with the truth of the premisses, specifically, the major premiss. It simply cannot be taken seriously as a statement which purports to be expressing a principle which a reasonable person would be prepared to accept as a universal truth. And the argument fails for that reason. The major premiss, we remind ourselves, is the foundation on which an argument is built. Foundations should be made o f stone. Here we have a major premiss which is best likened to a pile of sand. M aking

an

A rgument:

the

C onclusion

The skills we develop by analyzing the arguments that are constantly coming at us from a variety of sources are very much intended to be applied to arguments which have their origin in ourselves. When it comes to argument, we are givers as well as takers, and in making our own arguments we have to be as alert to all pertinent particulars as we are when we are analyzing the arguments of others, if not more so. The rules of the syllogism, for example, as was pointed out earlier, are not only tests by which we assess arguments that are received, but also, and very importantly, guidelines which are meant to help us make reputable

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argum entative responses to the dynam ic, thought-provoking exchanges continuously taking place in the public square, not to mention the kitchen or the local pub. M ore directly, there are a number o f specific practical steps we can take in the all-im portant effort o f making sound and effective arguments. The first step is as sim ple as it is critical: we must choose a defensible conclusion. In making a good argument, we begin at the end so to speak, that is, we first settle upon the point we intend to m ake— the fact we want to substantiate, the conundrum we want to explain, the truth we want to convince people of, the position we want to defend. W e have an idea in mind that has succeeded in commanding our attention; it captivates us; we feel a certain commitment toward it. It eventually becom es the kind o f idea we feel that we should not keep to ourselves. W e feel an urgency to go public with it. In sum, we want to argue about it. W hat we want to do at this incipient stage o f the process is to make that idea as clear as we possibly can to ourselves, and the way we do that is to put it in the form o f a clear, straightforw ard, unam biguous categorical proposition. Once we have done that, it would not hurt to say it out loud. Nothing better exposes a feeble or a frankly faulty idea than to hear its sour syllables bouncing o ff the living room wall. O nce we have determ ined upon an idea which we intend to serve as a conclusion to an argum ent, we then need to pose a crucial question: Is it defensible? Can I com e up with other ideas (taking the form o f prem isses) w hich will provide sufficient support for this particular idea? Am I able to generate a single proposition, beginning with “because,” that will serve as a reasonable “reason why” for my conclusion? There will be occasions when the idea which is serving as a conclusion of an argument refers to fact. But in that case one might wonder, Does a fact need an argument behind it? When it comes to facts, is it not sim ply a m atter o f pointing, rather than proving? To be sure, there are som e facts w hich are right out in the open so to speak, and all one needs to do is point at them. W ith others, especially historical facts, this is not the case. Im agine that you run into som eone who doubts the fact that John Adams was the second president o f the United States. You have your conclusion cut out for you, crisp and clear: “John Adam s was the second president of the United States.” In support o f that claim you could find a wealth of documentary evidence, the citing o f only a sm all portion o f w hich should be enough to convince even the m ost intransigent o f sceptics that John Adams was in fact the second president o f the United States. But m ost o f the ideas for which we feel the desire or the need to argue about are not cut-and-dried m atters o f fact. Recall that earlier we talked about arguments that turn upon value judgments. “Mozart was an eighteenth century Austrian com poser” sim ply states a m atter of fact. “M ozart was the greatest com poser who ever lived” states a value judgm ent. Value judgm ents, if they are to have any heft at all to them, can never be divorced from fact, and, as a

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rule of thumb it can be laid down that the closer a value judgment is related to fact, and hence supportable by fact, the weightier it will be. Value judgments— to stick with that very broad, generously inclusive term—have to do, we may say, with matters of fact in a complementary way, as interpreting them, or assessing them, or explaining them— especially by way of specifying their causes. Here are some examples of the kinds of non-factual ideas we typically argue about. World War Two extricated the United States from the Great Depression. Stephen Crane is a better novelist than Arthur Conan Doyle. Germany’s provocative belligerence was the principal cause of World War One. None of those statements can be said to be true in the same way that a factual statement could be said to be true. But it would seem rash to claim that, just as stated, they are incontestably false. However, if they are going to be given any credence at all, it would be just to the extent that they are bolstered up by strong supporting premisses. And if it were to be the case that each of those statements served as the conclusion to a sound, compelling argument, then their truth value could be said to rest primarily in their basic reasonableness. We would say that a good case has been made for them. There are two simple criteria for a reasonable conclusion: first, and negatively, it must not fly in the face of facts; second, and positively, it must represent a sincere, intelligent, intelligible attempt to express objective reality. A reasonable conclusion may be controversial, but it can never be self­ contradictory. Another way of describing a reasonable conclusion is to say simply that it is one that a reasonable person would find feasible. A reasonable person may not fully concur with the conclusion, but neither would he reject it out of hand, and that is because he is able to appreciate the argument behind it. He may not find the argument completely compelling, but it gives him pause. Reasonableness and defensibleness really come down to the same thing. And here we must start with ourselves. Before I can ever hope to convince anyone else of the reasonableness of an idea, I must first be able to convince myself. I must learn how to argue with myself, to test my ideas. “Is it defensible?” translates into “Is it supportable?” An affirmative answer to the question takes concrete form in the “reasons why” which, now providing a foundation for the idea, raises it to the status of a bonafide conclusion. If we are able to mount a convincing defense for an idea in the privacy of our own minds, we stand a good chance of having the same kind of success in the public forum, arguing with others. But what happens if I cannot come up with a convincing argument for a particular idea? Does that mean that the idea is, for that very fact, a bad idea,

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and should be instantly dropped? Not necessarily. To be sure, some indefensible ideas should be abandoned just for that reason; however, there are certain ideas for which convincing arguments are hard to come by, but the ideas themselves are quite sound. It is instructive to rem ind ourselves that many o f the more interesting discoveries in the empirical sciences remained for a time little more than tenaciously held intuitions, clung to by faith, for there was no convincing evidence to support them. A particular hypothesis is held to be true by a dedicated researcher, but much tim e m ust pass and m uch effort be expended before reputable arguments can be mounted on its behalf. On the one hand there are certain ideas that are incontestably true, but which are not self-evidently so, and therefore their truth has to be made evident through the m edium o f argument. And then there are those truths, o f the m ost basic kind, whose truth is self-evident, and which therefore have no need of argument. They do not have to be proved. The fact is, so elementary are they, they cannot be proved. Such are the first principles o f all human reasoning which we met in Chapter 6 : the principle o f identity, the principle o f contradiction, the principle o f excluded m iddle, the principle o f sufficient reason. W e either see these for the bedrock truths that they are, or we effectively abdicate our status as rational creatures. They cannot be proven because they are antecedent to all proof. They are the starting points, the foundational principles o f reality itself, the “givens” from which all rational processes proceed. And there are yet other ideas, those to which we typically attach a great deal o f value— ideas such as love, fairness, honesty, for example— which we certainly understand to be provable, but not in the ways logic usually has in mind. W e take such ideas to be true by reason of larger, looser forms of argument that have more to do with deeds than with words. Should thoughtful Juliet ask herself if she has sufficient proof of Romeo’s love, we can be sure she is not thinking in term s o f a particularly potent polysyllogism. Romeo proves his love by how he lives, by setting in place a whole pattern o f behavior which is maintained consistently and unwaveringly over time. His “argument” is, in a sense, his very life. M aking

an

A rgument : T he P remisses

We convince ourselves of the defensibleness of an idea by actually defending it, that is, by coming up with premisses that provide it with adequate support. In formulating solid premisses there are two matters we need to keep foremost in mind, the importance of which speaks for itself: ( 1 ) the proper stating and structuring o f the prem isses, so as to ensure the validity of the argument; (2 ) the truth o f the premisses. The second o f those can be considered first, for it does not require much commentary. It goes w ithout saying that if any prem iss in our argum ent is

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manifestly false, the argument is fatally flawed. There are only two reasons for a manifestly false premiss showing up in an argument: either the arguer knows it to be false, and deliberately puts it there; or the arguer, through carelessness, does not expend the necessary time and effort to make sure that it is true. If we have any doubts about the truth of a proposition we are thinking of using as a premiss for an argument, we should think again, and not use it. If our argument is going to take the final form of a succinct first figure syllogism, ensuring the validity of the argument should not present any special problem. But if our argument shapes up as a developed, complex discourse— say, in the form of an essay—then we will need to be especially sensitive to the matter of validity. Such an argument will have several points to it, for it will be made up of several subordinate arguments, all of which are supportive of the essays’s main conclusion. Each of those arguments will invariably manifest one form or another of syllogistic reasoning, but it is syllogistic reasoning which we would want to blend decorously into our prose, and not state it in stark major premiss + minor premiss+ conclusion fashion. But in giving due attention to style, we must not give short shrift to logic. Consider the following two passages. Homeschooled children tend to do exceptionally well in standardized tests. And they seem to have no problem in being admitted to our best colleges. Isn* t it pretty evident, then, that the best indicator of a student’s capacity to gamer maximum benefit from what higher education has to offer is the ability to do well in standardized tests? Everyone who has anything directly to do with socialized medicine reports it as being monumentally inefficient. In this country, thank goodness, we do not have socialized medicine, which means that here the field of medicine is completely free of inefficiency. The first passage, if looked at closely, will be discovered to be an argument that takes the form of a third figure syllogism with two universal affirmative propositions as premisses. That in itself is no cause for concern. But the conclusion of the argument—cutely put in the form of a question to which the reader is expected cooperatively to give the nod of assent—goes way beyond the evidence of the premisses in the claim that it is making. The second passage has neatly packaged within its prose a first figure syllogism. We would balk at its major premiss. How reliable is the information it is so confidently communicating to us? As for validity, it fails to make the grade. Given careful scrutiny, the argument reveals itself as a first figure AEE syllogism, which we know to be invalid. But let us say that in making an argument we want to keep things simple and succinct, so we decide we want to formulate, in the cause of bringing about

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what we hope to be a telling rhetorical effect, a first figure Barbara syllogism— the perfect syllogism. Here are two “conclusions” for which we would want to find proper premisses. The Nazi government in Germany severely restricted individual freedom, especially in religious matters. The quality of U.S. public education has fallen off drastically. Almost all of the syllogistic arguments to which we have given our close study thus far were presented as examples o f deductive reasoning, taken in the strict sense, where we have an argument which, (a) if valid, (b) if equipped with true premisses, will yield a conclusion that is necessarily true. And a necessarily true conclusion can result only from prem isses within which is to be found a necessary relation between subject and predicate. To put it more simply and directly: a necessarily true conclusion follows from necessarily true premisses. But as a matter of fact, given the world in which we live, of which contingency is perhaps its single most prominent feature, most of the arguments we formulate do not terminate in conclusions that follow necessarily. Rarely, then, are our arguments demonstrations in the strict sense. Does that mean that they lack any compelling force, or worse, that they are simply bad arguments? Not at all. If in most instances having to do with our ordinary everyday lives we cannot argue dem onstratively, that does not m ean that we cannot argue well, and convincingly. We put down premisses which, though not necessarily true, can pass the test of reasonableness: they do not contradict any known facts, and they can be seen as a genuinely possible way o f representing the objective order of things. They are propositions which, though perhaps disputable, cannot be rejected out of hand as false. With those considerations in mind we return to our two “conclusions.” In deciding upon a m ajor premiss for each, we should form ulate a proposition which makes a universal or general claim, and this will provide something like a conceptual um brella for the whole argum ent. Here are two completed arguments. Totalitarian governments invariably restrict the individual freedoms of citizens, especially with regard to religious matters. The Nazi government in Germany was a totalitarian regime. So, the Nazi government in Germany severely restricted the individual freedom of its citizens, especially with regard to religious matters. Whenever memorization is depreciated, the quality of education falls off drastically. In U.S. public education, little emphasis is given to memorization. Thus, the quality of U. S. public education has fallen off drastically. The degree to which anyone is prepared to accept the conclusions of those arguments will be precisely to the degree that they find the premisses acceptable.

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The minor premiss of the first argument would seem to be uncontroversial enough, but the major premiss may be open to challenge, or at least to some pointed questioning. “What do you mean by totalitarianism?” “What is your understanding of a totalitarian government?” Usually when we lay down a major premiss for an argument, the expectation is that our auditors or readers will be prepared to accept it as more or less self-evidently true. But if they don’t, and if they are being sincere in not seeing it as such, then there should be only one response to that reaction on our part, and that is to go to work in trying to make it evident, or at least more convincing. The best and most effective way of doing this is simply to supply another argument whose conclusion will be the major premiss of our original argument. And maybe it will take more than one additional argument to do the job. These need not be tight syllogistic arguments in every case. What is called die argument by example could be quite effective. Thus, in answering the question, “What is your understanding of a totalitarian government?” one could provide a list of what one regards as totalitarian governments (name names, in other words), and then, more pointedly, cite the specific characteristics which those governments have in common, and which justifies their being labeled totalitarian. As for the second argument, again here the minor premiss is not likely to be problematic, but the major premiss presents a different story. The arguer, if he wants serious consideration given to his argument, would very likely need to back up and offer additional arguments that would support the contention of the major premiss, that there is a determinable connection between a disemphasis on memorization and a depreciation in the quality of education. After doing that, or perhaps in lieu of doing that, the arguer may elicit some counter­ arguments from his challengers, inviting them to provide some evidence for why they consider certain of his premisses to be questionable. This kind of give and take is healthy, for argument is an ongoing process if ever there was one. Short of our presenting a strict demonstration, in which case to reject its conclusion would be irrational, most of our arguments do not settle any issue definitively, as much as we would wish it to be otherwise. Argument spawns more argument, which in almost every case is needful. Further argument should clarify, explain, provide more extensive and/or solid supporting data from what was found in our original attempt. Two additional comments regarding the premisses of our arguments: first, they must be relevant; second, they must be strong. Relevancy and strength— those are the two touchstones for good premisses. They are closely intertwined. A wildly irrelevant premiss would necessarily be a weak premiss; a strong premiss, on the other hand, could not be anything but relevant to the conclusion. In a three proposition syllogistic argument, the relevancy criterion can be met with relative ease. However, in constructing lengthy arguments which contain many premisses intended to offer direct support to a single conclusion, we have to take special care to ensure that all of the premisses are germane. Not

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only does an irrelevant premiss not contribute to the force o f the conclusion, it actually detracts from it, for it serves as a distraction. It may be that all the prem isses in a lengthy argum ent pass the test o f relevancy, but they do not support it with an equal degree of force and directness. In other words, and to state the obvious, some things are more relevant than others. In such a situation it is a good idea to so arrange the premisses that the weaker are stated first, with the strongest immediately preceding the conclusion. Here is an example of an argument in which the arguer attempted to follow that bit o f advice. Ellsworth Beane is a personable, outgoing, friendly man. Among his other accom plishm ents, he has served as a Boy Scout troop leader for a dozen years, and as a volunteer fireman for ten. He started his own business and developed it into a thriving enterprise, so he obviously knows som ething about administration and finance. He earned his bachelor’s degree in history from a small liberal arts college, which shows that he is not a narrow-minded specialist. He is a family man, with a lovely wife, Jeannine, and five remarkable children. Finally, Ellsworth Beane is an honest man. I have never known him in all these years to speak or act in devious or deceptive ways, much less ever tell an outright lie. For all these reasons I consider Mr. Beane to be the very best candidate for mayor of our fair city. A P sychological N ote The first purpose of logic is to enable us to reason well, to reason in such a way that we can be consistently successful in ferreting out the truth of things. The purpose of argument is to enable us to reason well with others. In an ideal world all o f us rational creatures should be engaged in a grand, communal effort in which we consistently and cooperatively employ our reasoning and argumentative powers in the service of truth. All indications have it, however, that we do not live in an ideal world. Thus it is that there are any number of people who have an altogether wrong idea about argument. They think that the principal purpose behind it is to win, to expose your opponent as a pathetic dolt, and in the process give yourself another opportunity to waggle your finger triumphantly at the cameras and declare yourself to be number one. Now, in argument sometimes your opponent is in fact clearly in the wrong, and part of your task, your obligation, is to show that to be the case, but not in order to put the other fellow down, but in order to put the truth up. That is the ideal we should be striving for as we argue in a less than ideal world. Admittedly, it is a high one. Another observation, not a particularly heartening one, but which has to be made nonetheless. A second result of our living in a less than ideal world is

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that there is a goodly number of people in that world (I have no hard and fast numbers ready to hand) with whom we simply cannot argue, notwithstanding all the best efforts on our part to do so. Now, mind you, I am talking about argument, not quarreling. There are always plenty of people who are willing, even eager, to quarrel, than which there is no more monumental waste of time. These people with whom you cannot argue are not necessarily stupid people; some of them are very smart indeed, and they often have sterling silver tongues to match their fourteen-carat gold intellects. Nor is it that they are somehow constitutionally incapable of arguing. No, it is not that they can’t argue; it is that they won’t argue. And this is because.... But I am unable to complete the sentence. It is way beyond my competence to try to explain why people who can argue will not argue. That is a problem for psychology, not logic. Here we are concerned with simply presenting a fact of life that has immediately to do with logic. And we accompany it with a modest suggestion. How to deal with people with whom you cannot argue? D on’t deal with them, at least not argumentatively. You will thus save yourself much needless wear and tear on your nervous system.

Review Items 1. What is a poly syllogism? 2. Describe an advantage in employing an argument that takes the form of apolysyllogism. 3. What is a sorites argument? 4. What is the condition that has to be met in order to have a valid sorites argument whose conclusion is negative? 5. What is the condition that has to be met in order to have a valid sorites argument whose conclusion is a particular proposition? 6 . Explain what an enthymeme is, and give an example of one. 7. If you are presented with an enthymeme that has a conclusion and one premiss, how can you immediately determine whether the missing premiss is the major or the minor? 8 . What are the questions you should ask to determine whether a particular idea will serve as a viable conclusion to an argument? 9. In the arguments we make to respond to the ordinary affairs of life, is it frequent or rare that we can come up with an argument which is a strict demonstration? Explain. 10. If you are constructing an argument whose conclusion will not follow necessarily, what should be the general criterion by which you judge the fittingness of the premisses for the argument?

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Exercises A. All of the arguments listed below are valid syllogistic arguments. Transform each of them into a polysyllogisms by adding a second argument to the original. 1. All those who work hard will be successful. Dedicated people work hard. Therefore, dedicated people will be successful. 2. No Alabaman is an Austrian. All the citizens of Mobile are Alabamans. Therefore, no citizen of Mobile is an Austrian. 3. Some diabetics are New Mexicans. All diabetics have to watch their diet. Thus, some people who have to watch their diet are New Mexicans. 4. All melancholic types are given to much brooding. No member of the Happy Go Lucky Club is given to much brooding. Hence, no member of the Happy Go Lucky Club is a melancholic type. 5. All successful sales agents are friendly and outgoing. The whole appliance department is staffed by successful sales agents. Therefore, everybody in the appliance department is friendly and outgoing. 6 . Some politicians are not power hungry.

All politicians have an obligation to be honest. Therefore, some o f those who have an obligation to be honest are not pow er hungry. B. Complete the following sorites arguments. 1. Some theologians know Hebrew, all those who know Hebrew know a Semitic language, all those who know a Semitic language are very clever, all very clever people have a good effect on the world. Therefore... 2. All Alaskans are rational creatures, all rational creatures are capable of laughter, everyone capable of laughter has a healthy perspective on life, but no one with a healthy perspective on life watches television. Therefore...

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3. All St. Paulites are citizens of Ramsey County, all citizens of Ramsey County are Minnesotans, all Minnesotans are Midwesterners, all Midwesterners are Americans. It follows that... 4. Some second basemen play chess, everyone who plays chess is a thoughtful person, thoughtful people make good company. However, no people who make good company are punsters. Therefore... 5. Every modem tyrant has been an egomaniac, egomaniacs are often powerful orators, and powerful orators can deceive many otherwise intelligent people. Therefore... 6 . Some people are very indecisive,

all indecisive people waste a lot of time, people who waste a lot of time are easily discouraged, and people who are easily discouraged contribute little to their community. Therefore... C. Supply the missing proposition for each of the enthymemes listed below. 1. There’s no way he should be elected. The man’s dishonest. 2. Anyone who would enjoy that movie has got serious problems. Sylvester thought it was great. 3. All gases will expand when heated. Helium will expand when heated. 4. All deer hunters are scrupulous conservationists. No deer hunters are bad citizens. 5. Some kids are overweight. Some people who like sweets are overweight. 6 . Everyone who enjoys opera is sophisticated.

Some of my classmates enjoy opera.

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7. Some Portuguese are not highly emotional. Some Portuguese are not artists. 8. No bakers are allergic to wheat flour. Some Sherlock Holmes fans are not allergic to wheat flour. 9. All professors are absent-minded. All professors are sensitive to criticism. 10. He’s sure to win the scholarship. He has several relatives on the selective committee.

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Chapter Thirteen

Conditional Reasoning T

he

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We speak categorically, and we think categorically, and we do so because we are certain about the subject matter with which we are dealing. I confidently assert, “It’s snowing,” because I know beyond the shadow of a doubt that that is precisely what is happening outside my window right now. Under the assumption that I am not just seeing things when I look out my window, and that I am speaking truthfully in making the assertion that it is snowing, there is a correspondence between my words and my thoughts, and if my thoughts are sound there is a correspondence between them and what is actually taking place in the extra-mental world. Because that extra-mental world is a shared world, you are able to judge the veracity and the soundness of my assertion by measuring it against that to which it refers. If you are not at the moment positioned to be able to look out a window when I say that it is snowing, and if you consider me to be a trustworthy person, you will take my assertion to be a true statement of fact. But if you have some doubts about my veracity and come to my window to see for yourself, only to discover, looking out, that it is not snowing at all—the sky is cloudless and the sun shines brightly and warmly—you will rightly judge me to be a liar, and my assertion to be an emphatically false one. Categorical propositions allow for, indeed invite, that kind of definitive response. But if I were to say things like, “It may be snowing in Sioux Falls now,” or, “The letter could have gotten lost in the mail,” or, “I might go to see Macbeth tomorrow night,” nothing definite is being laid down, and therefore no definite response is called for. It can be said, by way of generalization, that the principal cause of our thinking and speaking in non-categorical terms is uncertainty, an uncertainty that may take any number of different forms. The uncertainty expressed in the first two statements above stems from ignorance. I simply don’t know whether or not it is snowing in Sioux Falls, and I am equally ignorant about the true fate of the letter. As to the third statement, the uncertainty there

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probably has its source in irresolution on my part; I simply have not made up my mind what I am going to do tomorrow night. Non-categorical propositions express conjectures, estimates, guesses (educated or otherwise), projections, assumptions, presumptions, and any attitude which has its roots in one degree or another of uncertainty. One o f the more fascinating forms the non-categorical proposition takes is the conditional, or hypothetical, proposition, the proposition which begins with that very small but very potent word, “if.” A conditional proposition is a compound proposition, meaning that it contains two distinct propositions, the first preceded by “if,” the second introduced by “then.” “If .. .then” language figures prominently in our speech, reflecting as it does the conditional thinking that lies behind it, a kind of thinking we freely indulge in. “If I manage to finish mowing the lawn in time, then I will go to see Macbeth tomorrow night.” The first part o f the proposition sets a condition, states what needs to happen in order that what is stated in the second part can happen. Our lives are shot through and through with such contingencies. Som etim es the condition that is to be met is under our control, to a more or less degree. I have something to say in the matter of whether or not the lawn gets mowed in timely fashion tomorrow. Sometimes the condition is quite out of our hands, and we simply have to wait to see what happens, hoping for the best. “If it doesn’t rain tomorrow, w e’ll have a picnic in the park.” That the conditional mode of thinking is as common, and necessary, as it is simply reflects our totally rational response to the pronouncedly contingent world in which we live. By a contingent world I mean an unpredictable world. Not completely unpredictable, o f course, for if it were the very term “unpredictable” would make no sense, for we can only identify the unpredictable by comparing it with the predictable. But there is enough unpredictability, enough uncertainty, in life to keep us loose and agile in our thinking. We recognize the conditional quality of the world in which we live, its pronounced iffiness, and we think and act accordingly. A lot of things can happen only if other things happen first; a lot of things can be true only if other things are true. Hypothetical A rgument Because we think and speak categorically, we make categorical arguments; and because we think and speak conditionally, we make conditional, or hypothetical, arguments. We have spent a good deal of time examining the ins and outs of categorical argument; now we turn our attention to the intriguing world of hypothetical argument. Our familiarity with the categorical argument could at this stage be rightly described as intimate. It would not surprise you to be advised that, as does categorical reasoning, conditional reasoning too expresses itself syllogistically. The result is what is appropriately called the conditional syllogism, or the hypothetical syllogism. The two terms are

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interchangeable, and logicians tend to favor one or the other, with m ost o f them going with the latter. My own pick is “hypothetical syllogism,” and that is the term I will be using henceforth. The hypothetical syllogism has a structure comparable to that of the categorical syllogism in the elementary sense that it is made up of two premisses and a conclusion. The major premiss is the compound “if...then” proposition; it sets the condition, tells us what has to happen in order for something else to happen, what has to be true in order for something else to be true. A relation of dependency is thus established between the two parts of the major premiss, with the second part being dependent upon the fulfillment of the condition which is specified in the first part. The function of the minor premiss is to resolve the issue, in one way or another, and it can do that only because the minor premiss is, interestingly, a categorical statement. At least that is the case in the most common form of the hypothetical syllogism, called the mixed hypothetical syllogism, which will receive the brunt of our attention in this chapter. All right, then, once the minor premiss settles the issue raised by the condition specified in the major premiss, by definitively stating what is actually the case, the conclusion follows necessarily. Because of that necessary conclusion, hypothetical argument is properly identifiable as a form of deductive reasoning. But for a true conclusion to follow necessarily in a hypothetical syllogism, the same two critical conditions that apply to the categorical syllogism apply here as well: the argument must be valid, and its premisses must be true. Those general descriptions and observations out of the way, we now turn to a more minute examination of the hypothetical syllogism, so that we might become fully acquainted with its structure, and come to understand the logic behind its operations. T he A natomy

of the

Hypothetical Syllogism

As we do in our analysis of the categorical syllogism, so too when we focus our analytic eye upon the hypothetical syllogism, we express the argument in symbolic terms so that, among other things, we can get a clear idea of its basic structure. Here is the most common form of the hypothetical syllogism, which we may regard, because of its prominence and prestige, as being on the same plane as the first figure Barbara categorical syllogism. PdQ P___ Q Everything in that model has a meaning. The letters P and Q are comparable to the S, P, and M that we use in symbolizing a categorical syllogism. Though P and Q have come to be the most commonly used letters for designating the parts of a hypothetical syllogism, any two letters would do the job just as well. (Whether there is any connection between the popularity the letters have gained

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in logical usage and the homey admonition, “W atch your P ’s and Q ’s!” is something about which I am not prepared to make a categorical statement.) The first line of the argument is of course representative of the major premiss, which, remember, is a compound or two-part proposition. So, P stands for a specific, complete proposition, as does Q. The first part of the major premiss is known as the antecedent, and the second part is called the consequent. With a little linguistic fleshing out, the major premiss is more explicitly expressed as, “If P, then Q.” Its complete logical meaning is as follows: If P is true, or is actually the case, then Q is true, or is actually the case, and necessarily so. To repeat a principle cited earlier: the necessity of a conclusion has its source in a necessity to be found in the premisses. The symbol connecting P and Q, “ 3 ” means that there is a necessary connection which obtains between the antecedent and the consequent. So, then, we should take that major premiss as telling us that the truth of P necessarily implies the truth of Q; P could not be true without Q also being true. We have the strongest kind of bond between antecedent and consequent. From that very informative major premiss we move to the minor premiss, simply P. And it is simply P in the significant sense that it is now P without being qualified by an “if.” P as it appears in the major premiss specifies a condition. Here the conditional status of P is removed and the minor premiss states categorically that P is actually the case. With that, the logical tightness of the argument becomes manifest. If it is so that the relation between P and Q is such that it is impossible for P to be true without Q also being true (the truth of P necessarily implies the truth of Q), and this is precisely what the major premiss is telling us, and if it is so, as the minor premiss next tells us, that P is in fact actually the case, then it must be true, as the conclusion then tells us, that Q is also in fact actually the case. Given the premisses, it could not be otherwise. Reflect a moment more on that m ajor premiss. It is, quite obviously, a conditional or hypothetical proposition, and as such it stands in marked contrast to a categorical proposition. But for all that there is a certain categorical dimension to the proposition, specifically with respect to the relation that it bears between antecedent and consequent. The proposition is informing us, in what are effectively, and rather emphatic, categorical terms, that the relation between antecedent and consequent is a necessary one. There is nothing conditional about it. The proposition is not telling us that if P is true, then Q might be true; it is telling us— categorically, if you will—that if P is true, then Q must be true. The foregoing was intended to provide an introduction to all of the salient formal aspects of the hypothetical syllogism. But argument is never pure form, it is not skeletal structure only; it is as well, and more importantly, matter—the ideas which constitute the flesh and blood of argument. We need now an example of the hypothetical syllogism expressed in ordinary language. The one I provide

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is very simple, and useful; in this and the other forms it will take in later pages, my thanks to the cooperation of a very accommodating fellow by the name of George. If George is running, then George is moving. But George is in fact running. Therefore, George is moving. The necessary connection between the antecedent (“if George is running”) and the consequent (“then George is moving”) is clear enough. There is an unbreakable link between them. It is impossible that George, or anyone else, could be running without at the same time be moving. And that is because running is a kind, or species, of moving. To say running is to say moving, just as to say rabbit is to say animal. The one necessarily entails the other. The major premiss makes evident to us the necessary connection between a running George and a moving George, but it is all very, well, hypothetical. We do not know, at that stage, what George is actually doing, if indeed he is doing anything at all. But along comes the minor premiss to report that George, no doubt about it, is now doing laps in the field house. What remains is a foregone conclusion; George is moving. T he P ure Hypothetical Syllogism The hypothetical syllogism we have been examining, to repeat, is called the mixed hypothetical syllogism. It represents the most im portant form of conditional reasoning, but it has a companion in what is called the pure hypothetical syllogism. The pure hypothetical syllogism is interesting in its own right, and it has its uses, but they are rather limited in comparison to those to which the mixed hypothetical syllogism can be put. We introduce it here to provide a fuller picture o f the range and variety to be found in conditional reasoning, before returning to our investigation o f the mixed hypothetical syllogism. The pure hypothetical syllogism might be described, not entirely facetiously, as an unconditionally conditional argument. It does not allow us to escape from the iffiness which is the key characteristic of conditional reasoning. What this means, in specific terms, is that both the premisses and the conclusion of this form of argument are hypothetical propositions, and that is why it is called a “pure” hypothetical syllogism. It is uncontaminated, as it were, by any categorical propositions. The pure hypothetical proposition has the same structure as a categorical syllogism, the significant difference between the two being that whereas a categorical syllogism is characterized by the fact that it is composed of three distinct terms, a pure hypothetical syllogism is composed of three distinct propositions, one of which serves the same function as does the middle term in a categorical proposition, forging a bond between the other

1

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two propositions. To get a better sense of the structure of this type of argument, we first express it symbolically. If B, then C; if A, thenB ; therefore, if A, then C. In term s o f its basic structure, we have before us a very fam iliar type of argument, for, as you would notice, we have the same pattern as found in a first figure Barbara syllogism. But note well that here the three letters, A, B, and C, signify complete propositions. The major premiss tells us that if proposition B is true, so is proposition C. Then the minor premiss introduces a new proposition, A, and tells us that if it is true, then proposition B is true. Proposition B is thus set up as a “m iddle proposition,” apropos o f the function it performs in the argument, as uniting the other two propositions. But all this takes place within the realm o f the conditional; the argument does not arrive at any categorical determination. Here is how a pure hypothetical syllogism is more fully expressed in symbolic terms, in such a way to make clear that each of the propositions in the argument is a compound proposition, made up of two distinct propositions. If S is M, then S is P. If S is R, then S is M. If S is R, then S is P. And now the argument put in ordinary language: If anyone is committed to justice, then he is a good citizen. If anyone has a proper respect for the person, then he is committed tojustice. Therefore, if anyone has a proper respect for the person, then he is a good citizen. Though such an argument remains entirely within the confines of the conditional, it is not, for that reason, without its peculiar kind of force, for if you accept the conditions as laid down, then the conclusion can be quite compelling. The above argument is in the Barbara mood. It is possible to construct a pure hypothetical syllogism according to the patterns o f all o f the fourteen valid moods, but because conclusions which take the form of particular propositions are not very inform ative, the im portant moods are those which conclude with universal propositions, affirmative or negative, which means the following: Figure I, AAA and EAE; Figure II, EAE and AEE. Here is an example o f a Figure II, EAE pure hypothetical syllogism. First we put it in symbolic form: If S is P, then S is not M. If S is R, then S is M. If S is R, then S is not P.

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Now in English: If a man is courageous, then he is not vicious. If a man is cowardly, then he is vicious. Therefore, if a man is cowardly, then he is not courageous. The basic logic of the argument is clear: courage is completely separate from vice; but cowardice is a vice; therefore, cowardice is completely separate from courage. Because the pure hypothetical syllogism follows the same patterns as the categorical syllogism, it is subject to all the rules governing that syllogism. (See Appendix A for additional commentary on the pure hypothetical syllogism.) T he M ixed Hypothetical Syllogism : M odus P onens It is the mixed hypothetical syllogism with which we are principally concerned in this chapter, for it represents the most common form of conditional reasoning. It is called the “mixed” hypothetical syllogism because it is not entirely made up of hypothetical propositions. As we have already seen in our preliminary discussion of this form of argument, it has but one hypothetical proposition, the major premiss, while the minor premiss and the conclusion are both categorical propositions. The example that we have already looked at, which was concerned with George and his running, represented a case of what is called modus ponens, which is one of the two valid ways one can argue within the framework of this argumentative form. The Latin term modus ponens can be literally, but not very informatively, translated as “the positing mode.” It refers to what takes place in the minor premiss of the argument, where the antecedent (i.e., the first proposition in the compound major premiss) is affirmed, that is, declared actually to be the case. The conditional element is thus removed. Once that is done, given the nature of the relation between antecedent and consequent established in the major premiss, the conclusion follows necessarily. Here once again is the pattern of modus ponens. PdQ

P___ Q P necessarily implies Q; but P is the case; therefore, Q is the case. Here is another ordinary language example of this valid form of conditional reasoning. If any entity is a material body, then it has mass. But this is a material body. It must therefore have mass. And another: If the geranium plant is deprived of water, then it will die. The geranium plant will be permanently deprived of water. Thus, the geranium plant will die.

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As we can see, whether or not the conclusion of the argument follows necessarily all depends upon the nature o f the relation between antecedent and consequent in the major premiss. In both of the examples above we seem to have a genuinely necessary relation in place. It its hard to imagine something which we normally identify as a m aterial body which is not possessed of what we call mass. And our ordinary experience assures us that there is a rigid link between the watering o f plants and their continuing vitality. T he M

ixed

H ypothetical S yllogism : M odus T ollens

T he second valid way o f arguing according to the pattern o f a mixed hypothetical syllogism is given the name m odus tollens, “the taking away or rem oving m ode.” It refers to the action o f the m inor prem iss whereby the consequent o f the m ajor premiss is denied, declared not to be the case. PdQ ~ Q___ ~ P Reading the m ajor premiss, which is exactly the same as in m odusponens, we are informed that the truth o f P necessarily implies the truth of Q. But then the m inor premiss presents us with a bit of a surprise, telling us that in point of fact Q is not true. From this it necessarily follows that P is not true. This conclusion is not as intuitively obvious as the conclusion of modus ponens, so we need to pause over it a moment. W e might be tempted to wonder: Couldn’t Q be false, or not happen, and yet P be true, or happen? No, not given the nature o f the relation that exists betw een them . As was suggested earlier, it is helpful to think o f the antecedent as a species o f the consequent, taking the latter to be its genus, or, less technically, to think o f the antecedent as an instance of a class of activity represented by the consequent. Given this way o f looking at the two, if we take away the genus, we necessarily take away all species within that genus; or, if we take away a certain class o f activity, we necessarily take away any particular instance o f that activity. To put it in the m ost general terms, if we take away the whole, we take away any and every part o f the whole. If there are no animals, there are no rabbits; if there are no games, there is no baseball. Let us call in George at this point, to ask his help in giving us a more vivid idea of the logic o f the argument. If George is running, then he is moving. But George is not moving. Therefore, he is not running. Running is one of the many ways a person could be said to be moving, but if a person is not m oving at all, then he obviously could not be said to be engaged in any particular form of movement. Here is another example o f modus tollens: If the water is heated to 100 degrees Celsius, then it will boil. The w ater is not boiling. W ell, then, it has not been heated to that degree.

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Another kind of relation that is common between the antecedent and the consequent of the major premiss, besides that which exists between species and genus, is the relation of cause and effect. The very intelligibility of the cause/effect relation is such that, if the effect is absent, then so too is the associated cause. In the argument above, the major premiss’s antecedent (heating the water to 100 degrees Celsius) is the cause of its boiling; it is what brings about that particular effect. Given that relation, we can conclude that if we do not have the effect, neither then do we have the cause. Here is yet another example of modus tollens, one that poses an interesting problem. If Clarke is appointed president of Classy College, the institution will go into a veritable tailspin of rapid deterioration. Now, three years later, Classy College has not deteriorated in the least. From this we can conclude that Clarke was not appointed president after all. There is no warrant for the supposition which is made in the conclusion. Recall the principle that advises us that if there is going to be anything like necessity in the conclusion of an argument, it has to have its source in the premisses. The problem with this argument is to be found in its major premiss. W hoever Clarke might be, and whatever the particulars of his career and qualifications, there is nothing in the very nature of things that says that if he becomes president of Classy College, then it is inevitable that the institution will topple from the ranks of the Top Ten of the nation’s institutions of advanced research cosmetology and sink ignominiously into the lower depths of academic mediocrity, never, perhaps, to rise again. This does not necessarily have to be the outcome of his appointment. There are too many contingencies involved in situations like this. Let us say that Clarke is an incompetent administrator, but knowing his limitations in this respect he is canny enough to surround himself with six deans and six assistant deans, all of whom are administrative geniuses, and these people not only prevent Classy College from deteriorating, but lead it to new heights of academic excellence, making it the envy of the Ivy League itself. (See Appendix B for further treatment of modus ponens and modus tollens.) A ffirming

the

C onsequent

Modus ponens and modus tollens are the two valid ways we can argue within the framework of a hypothetical syllogism; in the first case we affirm the antecedent, in the second we deny— or sublate, to use the technical term—the consequent. There are two other moves that it is possible to make in this form of argument: we can affirm the consequent, and we can deny the antecedent. Unfortunately, both of those result in an invalid argument, and thus they cannot ensure a conclusion that follows necessarily. Let us first consider the illegitimate

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move of affirming the consequent. Here is how such an argument would look in sym bolized form: P

d

Q

Q___ P A t first blush that mode o f reasoning may not appear to be all that terribly wrong. Is there not a possibility that, if Q is true, then P could also be true? Yes, indeed, that is a real possibility, but we work here within the realm of deductive argum ent, and by this tim e there is no need, I hope, for the rem inder that the signal feature o f that m ode o f argum ent is that the conclusion follows necessarily. As to the argum ent above, it would be helpful if we were to pay special attention to the direction o f the inference which takes place in the major premiss: it is from the antecedent to the consequent, exclusively. This is not a tw o-w ay street. (By the way, this is the key feature o f the m ajor premiss of every mixed hypothetical syllogism, for the major premiss is invariable in all o f the forms.) The truth o f P necessarily implies the truth o f Q, but the truth of Q does not necessarily imply the truth o f P. Therefore, in an argument like the one above, if P turns out to be true, we have no basis for supposing that it is so because Q is true. George, please come in and help us out with this one. If George is running, then he is moving. But George is moving. Therefore, George is running. W ith that real life example, we can clearly see that the conclusion does not follow. One can acknowledge the presence of a certain class o f activity— in this case, movement— but that does not provide us with sufficient information to allow us to say that a particular kind of that activity is taking place. George could be m oving in all sorts o f ways besides running. But do we not have a quite different situation when we consider the relation between antecedent and consequent in terms o f the cause/effect relation? Not necessarily. W hile it has to be admitted that there are some cause/effect relations that seem so tight, so limited and exclusive with respect to the cause, it is hard to imagine the presence of the effect without its being explained by one particular cause and no other. One o f the exam ples used above could serve as a case in point. If the w ater before us is boiling, w hatever explanation for that could there be but the fact that the water, from whatever source, has been heated to 100 degrees Celsius? But not all cause/effect relations are that tight and exclusive with respect to the cause. There are certain effects that could be brought about by a num ber o f causes. Let us say that we have a particular effect, X, which we know to have at least four possible causes, A, B, C, and D. Now, here is X right before us, an incontestable matter of fact. We cannot, simply on the force of the presence o f the effect, X, conclude that it was necessarily caused by, say, B. It may have been caused by B, but we have no way of knowing that for sure, if all

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the information we have to work with is the presence of the effect. Consider this argument. If an earthquake occurs, this building will surely collapse. The building has collapsed. Therefore, an earthquake has occurred. Given the precarious state of the building in question, an earthquake would serve as a sufficient cause in bringing about its collapse. But if all the knowledge we have available to us is simply the fact of the collapsed building, we cannot, on the basis of that knowledge alone, conclude that it had to be an earthquake which was the cause of the collapse. It could have been a tornado that did the job, or a bulldozer. Or perhaps the building was in so dilapidated a condition that one fine day it just collapsed in upon itself, falling of its own weight as it were, as certain governments have been known to do. A R eciprocal R elation B etween A ntecedent

and

C onsequent

Looked at from a purely formal point of view, that is, in terms of its logical structure, a hypothetical syllogism is always rendered invalid when we attempt to affirm the consequent. But regarded materially, that is, in terms of the actual conceptual contents of the argument, it is possible to have a situation where there is a reciprocal relation between antecedent and consequent, a relation, in other words, which allows us to affirm the consequent and end up with a conclusion (the antecedent) which is undeniably true. This should not particularly surprise us, if we recall the kinds of situations which we have run into in previous investigations, where an invalid argumentative form will permit a true conclusion; however, this results, not from the form itself, but from the peculiar nature of the ideas contained in the argument, and how they relate to one another, independently, as it were, of the structural imperatives o f the argument. The situation we are considering here is of that sort. As noted above, the invalidity of affirming the consequent is made clear by recognizing the direction of the inference that is taking place in the major premiss. It moves exclusively from antecedent to consequent. There is not, then, a reciprocal relation between the two. But there are certain arguments in which, given their actual contents, there is indeed a reciprocal relation between antecedent and consequent, such as the following. If Pierre is a human being, then he is a rational animal. But Pierre is a rational animal. Therefore, he is a human being. Now, there is a clear case of affirming the consequent, and it would be difficult to take exception to the conclusion of the argument. But what allows for this anomalous circumstance, which on the face of it seems to contradict our contention that affirming the consequent is an invalid move, is not the formal

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qualities o f the argument— its structure and the logic intrinsic to it— but, once again, the peculiar contents o f the argument, the specific ideas with which it is concerned. In this case, what allows for the reciprocality that exists between antecedent and consequent is the fact that the m ajor prem iss effectively constitutes a definition, with the antecedent serving as the definitum, and the consequent, the definition itself. “Rational anim al” is a definition o f “human being,” and because all logical definitions are convertible, one can make a true statement by either applying the definition to the definitum, or, reciprocally, by applying the definitum to the definition. In other words, one can say either, “A human being is a rational animal,” or, “A rational animal is a human being.” But now let’s take a closer, a sterner, look at the argument. One can say, as I did, that what we have here is a case of affirming the consequent, but strictly speaking that is not really the case. Given the peculiar contents o f the argu­ ment, it would not be accurate to refer to the fact o f being a rational animal as a consequence of being a human being. The two ideas do not in fact relate to one another as true antecedent to true consequent, for they are referring to one and the same thing, though expressed in different words. So we can say that what the argument is actually doing is not so much affirming the consequent as simply repeating the antecedent. D enying

the

A ntecedent

The second invalid move that can be made while arguing within the confines of a hypothetical syllogism is denying the antecedent. Expressed symbolically, an argument which displays that mistake would take the following form: P=3Q ~ P___ - Q

The major premiss is conveying the same message as before: the truth of the antecedent necessarily implies the truth of the consequent. The minor premiss then claims that the antecedent is not true, and on the basis of that claim seeks to bring about a conclusion which claims that the consequent is not true. But this will not work. To better see why this is so we turn our attention once again to the relation between antecedent and consequent, considering it in terms of the relation between species and genus, or between the instance of a class and the class itself. Just because a particular instance of a class is not present, that provides no basis for ignoring the class as a whole, with all the other particular instances it contains. Or, to think in terms of species and genus once again, the fact that a given species is absent does not mean that the genus itself is no longer represented, in the form of other species. There may be no more rabbits left in the world, but we would be making a grave logical mistake if we were to conclude from this that there are no animals left in the world.

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If we were to consider the relation between antecedent and consequent in terms of the relation between cause and effect, we would have another productive angle from which we could see the illogic of denying the antecedent. Let us say that there is a bona fide cause/effect relation between A and B. Time and time again A has shown itself to be a sufficient cause of B. But it may not at all be a necessary cause, by which I mean simply the one and only cause. There may be other causes of B, such as X, Y, and Z. This being the case, if all I know is that A, a sure cause of B, is absent, I cannot conclude, on the basis of that knowledge alone, that B will not occur. It may very well occur, as caused by X, Y, or Z. So, there is no necessity in the conclusion of a hypothetical syllogism which makes bold to deny the antecedent. The conclusion may be true, yes, but it need not be. It is time to invite George back to our pages. If George is running, then he is moving. But George is not running. Therefore, he is not moving. Running is but one instance of moving, of which there are of course many others. The fact that George is not moving in a particular way does not mean that he is not moving in any way at all. Here is another example of an invalid argument of this kind, one in which George plays no part. If the patient has malaria, he will have a high fever. But he doesn’t have malaria. Therefore, he doesn’t have a high fever. Granting that there is a necessary connection between having malaria and having a high fever, if a person is beset with malaria we would naturally expect him to have a high fever. But a high fever is one of those effects for which there are multiple causes, and if the only datum we have before us is the sure knowledge that the patient does not have malaria, we cannot confidently claim, on the basis of that information alone (and this is all the information the argument provides us with) that he does not have a high fever, brought about by a disease other than malaria. Denying the antecedent, like affirming the consequent, is an easy enough logical mistake to fall into when we are engaged in conditional reasoning, especially when we are working with a major premiss in which there is a questionable connection between antecedent and consequent. Consider this argument: If there is extreme poverty in a society, there is much moral degradation. Our society is one of the wealthiest in the world. Therefore, we are not plagued by moral degradation. It would seem that a case could be made for the contention that extreme poverty is a cause of moral degradation. But it would be precarious to claim that it is the only one, and we would be remiss, while reflecting on the matter, to overlook

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the possibility o f extreme wealth as being another cause o f moral degradation. In any event, granting that there are multiple causes for something like moral degradation, if we remove one o f those causes, which is what the minor premiss does in this argument, we cannot, as the conclusion o f the argument attempts to do, claim that we are not suffering from the cited effect. We may very well be, but as brought about by a different cause, or causes. T he R elation B etween C ategorical Syllogisms H ypothetical Syllogisms

and

Both categorical syllogisms and hypothetical syllogisms are forms of de­ ductive argument which reflect two modes of reasoning which, though differ­ ent from one another, are nonetheless closely interrelated. As a practical dem­ onstration o f the foundational comm onalities that exist between categorical thinking and conditional thinking, we have the possibility of transforming a categorical syllogism into a hypothetical syllogism, and vice versa. We will start with the classic textbook example o f a categorical syllogism. All men are mortal. Socrates is a man. Therefore, Socrates is mortal. This can be expressed hypothetically thus: If Socrates is human, then he is mortal. But Socrates is definitely human. So, then, Socrates is mortal. Why would we want to do something like the above, other than simply to engage in a logical exercise? Sometimes speaking in straightforward categorical terms can be a bit too direct for the particular circumstances in which we find ourselves, and we would be better advised to cast our language in softer hypothetical terms. Here is one way in which a particular point can be made through categorical argument. Anyone who is a dolt and a nincompoop should be thrown out of office. Smith is clearly that, and more. Therefore, he should be thrown out of office. Here is another argument which aims at making the same point. Besides using less inflammatory language, it comes in the form of a hypothetical syllogism. If it appears that Smith lacks the wherewithal to continue in office, it then seems advisable that we should seriously consider the possibility o f his being removed. I do think that a case can be made for the thesis that he is really not fit for the position which he now holds.

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I would like to suggest, then, that we give serious attention to the option that his tenure in office be immediately discontinued. Now we begin with a hypothetical argument, in a form with which we are now quite familiar, the modus ponens syllogism, and in which George plays the starring role. If George is running, then he is moving. But George is running. Therefore, George is moving. That argument can be easily stated in categorical terms: Anyone who is running is necessarily moving. This fellow George is now running. Therefore, he is moving. One reason someone might want to transform a hypothetical argument into a categorical argument is to be able to make a point less tentatively, more directly and forcefully. Consider first this argument. If we are prepared to put sufficient effort into this enterprise, I think we then stand a fair chance of succeeding at it. I recommend that we do so. And with that we would stand a fair chance of succeeding. Now here is essentially the same argument, put in the form of a categorical argument— specifically, a Figure II, EAE syllogism— and expressed in more vigorous language. The people who fail are people who don’t go all-out in whatever they put their hands to. We are the kind of people who do go all-out in whatever we put our hands to. Conclusion? We won’t fail. T he D ilemma A rgument: M odus P onens One of the more interesting ways an argument can take on complexity is by assuming the form of a dilemma, which is a variation on the hypothetical syllogism. The word “dilemma,” which, like so many of our English words, comes from the Greek, can be loosely translated as “two propositions.” When in ordinary speech we talk about being in a dilemma, what we have in mind is the kind of a situation in which we are confronted with two possibilities, A and B, and we are hard pressed to choose between them. It might be the case that the cause of our consternation is that the two possibilities are equally delectable, and our difficulties arise from the fact that if we choose the pleasant A that would mean that we would have to forego the equally pleasant B, or the other way around. More often than not, however, being in a dilemma means to be

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confronted with choices—usually two, but it could be more—that are equally ugly, so we will end up in a rather sorry situation no matter how we choose. The latter is typically the kind of situation with which the dilemma argument concerns itself, or perhaps we could say, exploits. The two basic forms that the dilemma argument takes are called respectively the constructive and the destructive ; the first follows the logic of m o d u s p o n e n s , the second that of m o d u s to lle n s . We will begin by setting down the simple constructive dilemma in symbolic form. If A is B, then E is F; and if C is D, then E is F. But either A is B. or C is D. Therefore, E is F. Note that the first line of the argument, the major premiss, is composed of two hypothetical propositions. The antecedent of the first is “A is B,” and of the second, “C is D”; the consequent for both propositions is the same, “E is F.” The minor premiss of the argument is a disjunctive proposition, and it tells us that one or other of the antecedents stated in the major premiss is true. Remember that, in a disjunctive proposition, one of the disjuncts must be true. The conclusion of the argument can thus state categorically that the consequent. “E isF,” is true. The logical essence of the argument can be captured in the following scenario. Imagine that you are saying to someone: Look, you have two courses of action open to you, A and B. If you go the route of A, you'll end up with C, and if you opt for B, you’ll also end up with C. So, whether you choose A or choose B, the result will be the same—C. And now for an ordinary language example of the argument, a rather upbeat example, as it happens. If you propose to Ruthie at Rollie’s Restaurant, she’ll accept; and if your propose to her on her parents’ front porch, she’11accept. You will propose to her either at Rollie’s Restaurant or on her parents’ front porch. She’ll accept, either way. That may be described as a no-lose situation. Either course of action is going to lead to a happy outcome, so one cannot go wrong whatever choice is made. But as I mentioned earlier, the dilemma argument is most frequently used to put people in a bind, that is, to present them with a situation in which, whatever course of action they choose to follow, they are going to end up in sorry circumstances. Here we would have a no-win situation. Traditionally, this is known as being on the horns of a dilemma: A rather vivid image, suggesting that we are going to get gored whichever way we turn. Consider this considerably less than upbeat argument.

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If you tell the truth, they will find you guilty; and if you lie, they will find you guilty. You will do one or the other. And they will find you guilty either way. How to escape the horns of a dilemma? The most promising tactic in attempting to do so is simply to challenge the truth of the major premiss, for the force of the whole argument rests on what is posited there. Is it actually the case that whatever course we take. A or B, it will inevitably result in C? More pointedly, is there a necessary connection between the antecedents and the consequents of the two hypothetical propositions which make up the major premiss? If we have good reason to answer those two questions in the negative, we have good reason not to be intimidated by the argument. Next we will consider a more complicated version of the constructive dilemma, fittingly called the c o m p l e x c o n s t r u c t i v e d i l e m m a . This argument differs from the one we have just considered in that the conclusion takes the form of a disjunctive proposition. First we will state the argument symbolically. If A is B. then E is F: and if C is D. then G is H. But either A is B, or C is D. Therefore, either E is F, or G is H. Note the added complication the major premiss brings to the argument. Here there are not only two antecedents, but two consequents as well. That added complication eventually manifests itself in the conclusion, which, like the minor premiss, is a disjunctive proposition. The logical nub of the argument may be expressed more succinctly in the following terms: We have two courses of action open to us, A and B; if we opt for A. the result will be C. and if we opt for B, the result will be D. We will take either course A or course B, and that means we will be left with the result of either C or D. Consider this argument. If you sell the business, you will not get nearly what it's worth; and if you don’t sell it, you will continue to lose money from it. You will either sell the business or hold onto it. With the result that you’ll either take a big loss or go deeper into the red. Here again, we have what has all the earmarks of a no-win situation, if the major premiss is giving us a reliable account of the circumstances. It might be an altogether too pessimistic assessment of the actual state of affairs. If that is in fact the case, the danger of being impaled on one or the other of the horns of a dilemma is removed. T

he

D

il e m m a

A

rgument:

M

odus

T

ollens

As a variant form of the hypothetical syllogism, the dilemma argument can follow the logic of m o d u s t o l l e n s , as well as m o d u s p o n e n s . Here is how a

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simple destructive dilemma, following the modus tollens pattern of argument, would look, expressed symbolically. If A is B, then C is D; and if A is B, then E is F. But either C is not D, or E is not F. Therefore, A is not B. The interesting thing about the major premiss of this argument is that it is just the opposite o f that which begins a sim ple constructive dilemma: in that argument we have different antecedents but the same consequent, but here we have the same antecedent but different consequents. The major premiss in this argument informs us that there is a single course o f action, A, which will have two results, B and C. But then the m inor prem iss, follow ing the method of modus tollens, tells us that either it is not going to be B, or it is not going to be C. And that leads to the denial o f the antecedent, A. If Eddie is to be enrolled in law school, he will have to pass the entrance exam; and he will have to get the money for tuition. Eddie will either not pass the entrance exam, or he will fail to get the money for tuition. So, Eddie will not be going to law school. R ather som ber news for Eddie. But he need not allow him self to be bowled over by this argument. As in all dilemma arguments, this one can carry the day only to the extent that the major premiss is presenting what is truly an inescapable bind. There would seem to be a pretty strong connection between passing the entrance exam and getting into law school; but as to the second proposition, who is so prescient to be able to say definitively that Eddie— having passed the entrance exam with flying colors— is not dedicated and industrious enough to be able to come up with the money needed for tuition? The fourth basic form the dilem m a argum ent takes is called the complex destructive dilemma. This is also a modus tollens argument. Without further preliminaries we present the argument dressed in symbolic garb. If A is B, then E is F; and if C is D, then G is H. But either E is not F, or G is not H. Therefore, either A is not B, or C is not D. The sim ple form s o f the dilem m a argument, be they either constructive or destructive, culminate in a conclusion which is a categorical proposition, while the complex forms of the argument, be they either constructive or destructive, end with a conclusion which is a disjunctive proposition, as is the case with this argument. The major premiss of the argument is complex by reason of the fact that in the two hypothetical propositions that compose it, we have different antecedents and different consequents. The essence of the argument’s logic may be stated briefly as follows: If A is done, B will follow; if C is done, D will follow. The m inor premiss asserts that either B is not the case, or D is not the

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case. And this leads to the disjunctive conclusion that either A is not the case or C is not the case. Here is an argument of this type expressed in ordinary language. If you want to be happy, you will join our club; and if you want your family to be happy, you will persuade them to join our club. But either you won’t join our club, or you won’t persuade your family to join. So, either you don’t want to be happy, or you don’t want your family to be happy. As can be seen by most of the examples we have used, the dilemma argument typically tries to put people on the spot—to fix them on the horns of a dilemma. Once again, the best course to follow in order to escape that fate is to give close scrutiny to the major premiss, and subject it to the credibility test. One does not have to dwell very long on the major premiss of the argument above to see how tenuous it is. Does my happiness hinge on joining the club, and is the happiness of my family dependent on their doing so as well? It seems highly dubious. I am considerably less than convinced that my failure to join the club, and my refusal to try to persuade my family to do so, warrants the argument’s conclusion that I am thereby forsaking any chance of happiness for myself and my family. P robable Hypothetical A rguments Categorical arguments that are strictly demonstrative have conclusions, we know, which follow necessarily, and this is because of the necessary relations which are to be found in the premisses. But we also know that it is rarely the case, given the material contents of the arguments we most commonly engage in, that we are able to come up with arguments that are in fact strictly demonstrative. So it is with categorical arguments, and so it is with hypothetical arguments as well. But if we cannot produce conclusions which in every instance are necessarily and inescapably true, we should always be striving to deliver conclusions which are as sound and reasonable as we can possibly make them. Our study of the hypothetical argument has shown us that whether or not the conclusion of such an argument follows necessarily depends specifically on the nature of the relation which exists between the antecedent and the consequent of the major premiss. If that is a truly necessary relation, then the conclusion follows necessarily; if it is not, it does not. But most of the conditional thinking we do pertains to rather messy, real-life situations in which the antecedents of our arguments do not in fact necessarily imply the consequents. We have the task of making our way the best we can in a contingent universe, the immediate practical result of which is, as far as logic goes, that we must be satisfied with arguments which end with probable, not necessary, conclusions. Knowing its limitations in this respect, should we be hesitant about employing hypothetical argument in our everyday affairs? Not any more than we should be hesitant about employing categorical argument in our everyday

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affairs. And we could not refrain from engaging in either, even if we tried. After all, what lies behind categorical argument but categorical thinking, and what lies behind hypothetical argument but conditional thinking, and we could no more stop thinking along those peculiar lines than we could simply stop thinking. This is especially so when it com es to conditional thinking, for this is the natural, the logical, way of responding to the contingent world in which we live. To be sure, there is a very im portant distinction to be made between demonstrative arguments and non-demonstrative arguments, between those whose conclusions follow necessarily and those whose conclusion do not, but we would be rash, while giving due recognition to that important distinction, to suppose that probable arguments are in every respect intrinsically inferior to demonstrative arguments, and, worse, that they are all more or less the same in terms of their logical prowess. There is a broad range of probable arguments, some clearly better than others, as judged by their intrinsic soundness and strength. Probability, in other words, comes in degrees. Consider the following hypothetical propositions. If I win the lottery, then I will give all the money to the poor. If the weather is fair next Wednesday, we will take a twenty-mile hike. If you work hard, you will surely succeed. The first thing to be noticed about these propositions is that there is clearly not a necessary connection between the antecedent and consequent of each. Absent that, we would want to consider the strength of that connection, just as it stands. W hat is the likelihood, given the fulfillment of the condition, that the consequent would then follow? Another important consideration, focusing on the antecedent, would concern the possibility of the stated condition ever being realized. Some conditions are so far-fetched that they would not be worth taking seriously, as would be the case were I to say, “If I become a lead tenor in the M etropolitan Opera Com pany, I would be very gracious to my fans.” The chances that the condition set down in the first proposition in the list above— the possibility of my winning the lottery— will ever be realized are, to put it mildly, very remote. But let us say, per impossibile, that I do win the lottery. Our next step would be to reflect on the nature o f the connection between antecedent and consequent. Does the fulfillment o f the condition mean that I will now promptly give the fifteen million dollars swelling my bank account to the poor? One may be permitted to doubt it. Meditating on my millions, I begin to think of all the possible uses to which they can be put, most of them, oddly enough, having a distinctly self-advantageous slant to them. The poor become for me a vague, fast-fading memory. The second proposition represents the kind of thinking which is very common to all of us. We are constantly making plans for the future, but because it is of the very nature of the future to be unknown to us (How can we know what does not exist? St. Augustine would ask), conditions are set for those

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plans. “I’ll call you in the morning if I’m not too busy.” “If the tickets come in time, we’ll go to the first performance.” “If he chews me out like that in public one more time, I’ll quit.” In each case we simply have to wait and see if the condition will be met: my not being too busy in the morning; the tickets coming in time; the boss chewing me out in public again. But in each case the condition could be met without the stated consequence ever taking place. That happens all the time, and shows that there is anything but a necessary connection between antecedent and consequent. And now to the second proposition in our list. So next Wednesday arrives, as Wednesdays have a tendency to do. From a meteorological point of view, it is a peerless day.. .but we don’t take the twenty-mile hike. Things come up, “unforeseen circumstances,” and we have to drop our plans for a vigorous trek in the country. Maybe the following Wednesday we’ll take a hike, if the weather is fair, and all other things being equal. In the third proposition we have what most people would accept as a fairly strong relation between antecedent and consequent. It is by no means a necessary one, for a lot of people work hard, very hard, but never achieve success, as success is usually understood at any rate. Even so, it would not strike us as extravagant to claim that if one works hard, in more cases than not beneficial results will ensue. Reviewing these three rather commonplace hypothetical propositions, then, we can see that there are differences in how antecedent relates to consequent. None of the consequents must follow if the conditions set by the antecedents are in fact met; the probability of that happening varies. You would not want to hold your breath waiting for me to turn over fifteen million dollars to the poor, not simply on account of my fickleness, but principally because of the very slim chance that the condition which was set for the possibility of my doing so will ever be met. But the probability of our going on a hike on Wednesday seems fairly high, as does the probability that one who works hard will reap positive benefits from doing so. Now for a couple of practical suggestions for formulating respectable hypothetical arguments. The most important thing we would want to do is to lay down a major premiss which is as strong as we can possibly make it. The strength of the major premiss would be reflected in two criteria: (1) the condition which is set should have a high likelihood of actually being met; (2) there should be an equally high likelihood that, once the condition is met, the consequent will actually follow. How do we determine if a condition which we lay down has a high probability of being realized? Consider what we are doing, in the majority of cases, when we express a hypothetical proposition. We are speculating about the future, and making a supposition as to what could happen in that broad and nebulous no-man’s-land. The surest guide we have in making reliable speculations about the future is the past, specifically, the sum total of lived experiences, our own and those of others, which come to us out of the past. In sum, the actualities of the past provide us with pertinent information

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for making sound judgments about possibilities for the future. To give a concrete instance o f what I am driving at here: if I want the chances to be good that we will go on a hike on Wednesday, then I would want the chances to be good that the principal condition I set for that possibility will be realized. In other words, I would want it to be highly probable that the weather will in fact be fine on W ednesday. And I would know if it is highly probable or not in terms of past meteorological patterns pertaining to my geographical locale and the season of the year. If I am in northern Minnesota and it is January, the probability of next W ednesday being a good hiking day would not be as high as it would be if I were in southern California and it is May. However, when it comes to setting conditions that are dependent on human behavior, things become much less certain. Information provided by the past can be helpful here— this is always the case— but it needs to be treated more cautiously. The weather, for all its vagaries, is more predictable than human behavior. “If Bernie brings home the bacon, then w e’ll eat high on the hog tonight” can be a strong hypothetical proposition— in the sense that there is a high probability that the condition set by the antecedent will be realized— if you know Bernie to be a very reliable fellow. If sometimes he is and sometimes he isn’t, the fare tonight m ight turn out to be crackers and cheese. Next W ednesday arrives; it is a lovely day; no unforeseen circumstances intervene; and yet, we don’t take a hike. Why not? For no particular reason. We just don’t feel like it. Human behavior is predictable, up to a point, but the point seems always to be shifting.

Review 1. Provide a general description of conditional reasoning. 2. What are the two basic components of a hypothetical proposition, and, in order to effect a true demonstration, how must they relate to one another? 3. W hat is the function of the minor premiss in a modus ponens argument? 4. W hat is the function of the minor premiss in a modus tollens argument? 5. Explain why affirming the consequent is an invalid form of reasoning in hypothetical argument. 6. Explain why denying the antecedent is an invalid form of reasoning in hypothetical argument. 7. In what practical way can categorical reasoning be shown to be related to hypothetical reasoning, in terms of the arguments which are expressive of each? 8. Describe the basic logic at work in the simple constructive dilemma. 9. Describe the basic logic at work in the simple destructive dilemma. 10. To what should one pay special attention in constructing a strong probable hypothetical argument?

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Exercises A. Complete each of the pure hypothetical arguments listed below by supplying the conclusion. 1. If Bob plays football this year, he will surely earn a letter. If he recovers from last year’s injuries, he’ll be able to play football. Therefore... 2. If Jill marries Jack, she will move to Los Angeles. If she turns down Jim, she will marry Jack. Therefore... 3. If we win the war, then we won’t be occupied. If the Utopian Peoples Republic comes to our aid, then we will win the war. Therefore... 4. If the recession is foreshortened, then prosperous days will return. If Weakman is elected, then the recession will be foreshortened. Therefore... B. Below is a list of mixed hypothetical syllogisms. For each of them determine (a) whether or not it is valid, and then, (b) if it is valid and yet is nonetheless problematic, explain why it is so. 1. If a match is touched to these oil-soaked rags, they will burst into flames. But no match will be touched to them. Therefore, they will not burst into flames. 2. If I let go of this bowling ball, then gravity will cause it to drop to the floor. I let go of the bowling ball. Therefore, it drops to the floor. 3. If Wannebe gets fired, he will go on a drunken spree. He didn’t get fired. Therefore, he didn’t go on a drunken spree. 4. If Uncle Ruby comes to town, he will pay us a visit. Uncle Ruby is now in town. So, he will pay us a visit.

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5. If he lies on the witness stand, the jury will not believe him. But the jury did not believe him. Therefore, he lied on the witness stand. 6. If the gas isn’t heated, then it w on’t expand. And it w asn’t heated. Therefore, it didn’t expand. 7. If we give this rock a push, it will roll down to the bottom of the hill. It rolled down to the bottom o f the hill. That means that we gave it a push. 8. If Tessie Lou gets that plush job, she will break her engagement with W arren. But she didn’t get the job. So, she will break the engagement. 9. If it rains this afternoon, the game will be postponed. But the game wasn’t postponed. That means it didn’t rain. 10. If I’m in Miami on Monday, I’ll give you a call. I was in Miami on Monday. So, you got your call. C. Transform the categorical arguments below into hypothetical arguments, and the hypothetical arguments into categorical arguments. 1. All men are mortal. All Greeks are men. Therefore, all Greeks are mortal. 2. No Bungadoolians are reliable. The entire Tripod Tribe is Bungadoolian. Therefore, the Tripod Tribe is unreliable. 3. If the peaches are ripe, then they can be sold at the farm ers’ market. They are ripe. Therefore, they can be sold at the farm ers’ market. 4. Every work by Dickens is a pleasure to read. The Pickwick Papers is a work by Dickens. Therefore, The Pickwick Papers is a pleasure to read.

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5. If an organism is sentient, it will display the characteristic of irritability. The tsetse fly is sentient. It will therefore display the characteristic of irritability. 6. If the fan is plugged in, it will not run. It will not run. Therefore, it is not plugged in. D. Complete the dilemma arguments listed below by supplying a conclusion foreach. 1. If Dave wins the match, he will be satisfied; and if he loses the match he will be satisfied. He will either win the match or lose the match. Therefore... 2. If the dog barks, the cat will hiss; and if the dog barks, the parrot will squawk. But either the cat won’t hiss, or the parrot won’t squawk. Therefore... 3. If Capon is elected, the Republicans will complain; and if Feeder is elected, the Democrats will complain. But either the Republicans won’t complain or the Democrats won’t complain. Therefore... 4. If we move to Florida, Casey will be disappointed, and if we move to California, Carrie will be disappointed. But we are going to move either to Florida or to California. Therefore...

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Induction

Ever since we arrived at that stage o f our course which had to do with the third act o f the intellect, reasoning, we have been giving exclusive attention to that form o f reasoning called deduction, where, com m encing with universal truths, we then apply them to particular cases. So, we begin with the universal truth that all human beings are mortal creatures, and from that we conclude that Greeks are mortal, and that is because they are numbered among the class called hum an beings. A nd if in deductive argum ent our starting point, the m ajor prem iss, is expressing a universal truth which is necessarily true— which the proposition, “All human beings are mortal creatures,” seems very much to be doing— then our conclusion is necessarily true. The great strength, and beauty, o f deductive argument lies in the certitude which it is capable o f providing. If we begin with truth, we can be certain that we will end with truth, and if our beginning truths are necessary ones, so too will be the truths expressed in the conclusions o f our arguments. Deductive argum ent characteristically moves from the more general to the less general, from universal truths to particular truths; that was the pervasive pattern in the arguments dealt with in the previous pages. Inductive argument moves in just the oppositive direction. W hen we reason inductively, we begin with the less general and move to the more general; or, to be more precise, we begin with particular instances, with individuals, and we ascend from these, working our way up to general propositions, which reflect what was learned from the investigation o f particular instances and individuals. The second key difference between deductive argument and inductive argument is the fact that, whereas deductive argument, if strictly demonstrative, yields conclusions which are necessarily true, the conclusions of inductive arguments are always probable. This is o f course no small difference between the two types o f argument. But should that lead us to conclude that deductive argument is therefore superior to inductive argum ent? No. As we shall presently see, there are any number of

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real-life situations which can only be intelligently dealt with by inductive reasoning. Furthermore, as we saw in the previous chapter, there are varying degrees of probability, and the conclusions of some inductive arguments are so highly probable that, for all practical purposes, they can be considered to be virtually necessary. Deduction begins with universal truths, generalizations about which we can be certain, and which have the widest possible application. Inductive reasoning, for its part, begins with truths pertaining to particular instances, the truth of individuals. However, there is a set of more basic truths— the most basic, in fact—upon which both inductive and deductive reasoning is founded, and from which both proceed, and those are the first principles of all human reasoning, which, because of their importance, we call attention to yet once again: the principle o f identity, the principle o f contradiction, the principle o f excluded middle, and the principle o f sufficient reason. In sum, the principal features of inductive reasoning are as follows: (1) it begins with singulars, particular instances or individuals; (2) it aims at establishing general propositions which will serve as universal truths or laws; (3) the arguments which it constructs yield probable conclusions. W here Inductive R easoning B egins Though deductive reasoning could be said to have an advantage over inductive reasoning, in that it is capable of producing conclusions about which we can be completely certain, nonetheless it would be rash to declare it to be unqualifiedly superior to inductive reasoning. In any event, we need one just as much as the other. They work together, and are closely interdependent. During the course of any day, even the slow ones, we liberally make use of both forms of reasoning in our thought; we are constantly ascending from particulars to generalities about those particulars, and descending from generalities to the particulars to which they pertain. Josh, having just consumed a large bunch of red seedless grapes, contentedly proclaims, “Those were good grapes!”— a general proposition about grapes based on his personal gustatory experience with x-number of individual grapes. “Poetry is boring and a waste of time,” Fanny boldly asserts, intending that her audience understand that this judgment is to apply to each and every instance of poetry, past, present, and future. Though it is idle to ask if one form of reasoning, deductive or inductive, is superior to the other, it would not be altogether untoward to think of inductive reasoning as enjoying a kind of priority with respect to deductive reasoning, looking at the matter from the perspective of the history of the individual, and then of the race as a whole. In the early stages of a child’s development, all appearances indicate that inductive reasoning is the dominant mode of thought. The child’s intellectual energies are principally given over to becoming acclimated to the world, a world which is all quite new, gathering and storing

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data from experiences o f particular instances and individuals, data which, at a later stage, will become the material for forming generalizations about the world. And then, in due course, those generalizations will serve as the points of departure for the first attempts at deductive reasoning. Thinking in larger terms, it does not seem too far-fetched to suggest that a pattern something like that may be ascribed to the historical developm ent o f the entire human race. According to this scenario, we were, in the beginning, in the main inductive reasoners, chiefly preoccupied with getting the lay of the land, becoming familiar with A, with B, with C, until it eventually came about that we were confidently m aking generalizations about ABC’s, and from there we launched into deduction. Here I am myself engaging in inductive reasoning, so my conclusions are probable. Inductive reasoning is more rudimentary, more earthy, than deductive reasoning, in the sense that it is the mode of reasoning we commonly employ in our direct encounters with the physical world, the world we first come to know through sense experience. We can reason deductively, and quite effectively, without making any reference to, or depending upon, the physical world, as we do when we think mathematically, but if it is the physical world itself which is the focus of our concern, if we want to come to know that world, to understand how it works, inductive reasoning will be the principal means of doing so. We exercise inductive reasoning most productively when we engage in the close, analytic study of the particulars of the physical world for the purpose of discovering the causes of things, for if we know the causes of things, then, as Aristotle taught, we have true scientific knowledge of them. And, as we discern the patterns evinced by the whole panoply of causal activity, we are led to the discovery o f those laws which govern the overall workings of the physical world. (See Appendix A for a discussion of inductive reasoning and inference.) T he U niformity

of

N ature

There would be no logic to the contention that we go to the physical world to understand it— as we do when we follow the ordered, systematic ways laid out by the empirical sciences— if we did not believe at the outset that the physical world is in fact understandable. Three of the most basic assumptions underlying and informing our investigations into the physical world are: (1) that world is intelligible; (2) the human intellect has access to that world; and (3) the human intellect is capable of achieving real knowledge of that world as it is in itself. The world is intelligible because it is an ordered world— it is a cosmos, not chaos— and this is evidenced by the uniformity of nature, the patterned, regular way in which it operates. The natural causes are discoverable because they operate according to set laws, hence the principle: “the same physical causes, acting under similar conditions, produce similar results.” There is constancy and consistency in natural causes, and that is what makes scientific prediction possible. If we know it to be the case that A is the cause of X, given the conditions

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B, then we will confidently say that if it should happen tomorrow that A occur, under conditions B, then X will occur. If nature lacked this kind of uniformity, such predictions would be entirely impossible. Actually, however, that would be the least of our worries, for if there were no uniformity in nature, there would be no nature, only chaos. The very term, “nature,” refers to a coherent, ordered whole, which, precisely because of its coherence and orderliness, is intelligible. If we could imagine ourselves living in a truly chaotic (i.e., incoherent and disordered) environment, we would not even know it, for our minds would be as disordered as the environment. The mind can respond intelligently only to what is intelligible. There have been certain philosophers, generally described as idealists, who have claimed that we can have no direct, reliable knowledge of the world outside our own minds, that in the final analysis the proper object of the human mind is the human mind, or, more particularly, the products of the human mind—ideas. The subjective world thus takes precedence over the objective world. Our ideas are not so much points of contact with the extra-mental world, as they are the means by which we effectively establish the ordered reality of that world. Ideas, according to this way of thinking, are not necessarily the result of our interactions with the external world, but can be part of the intellectual equipment with which we are bom. We cannot know, the idealist philosopher avers, the essence or nature of things in the external world. The extreme form of idealism reduces everything to ideas, and is prepared to regard as dubious the very existence of the physical world. If idealist philosophy had managed to gain the ascendency in Western culture, the remarkable advances made by the empirical sciences— those sciences founded upon the knowledge we gain from sense experience—which we have witnessed over the passed 350 years or so would have been quite impossible. One does not devote one’s entire life to the investigation of a physical world whose existence is deemed doubtful. Idealism became as influential it did because there were too many people who put too much emphasis on deductive reasoning, and not enough on inductive reasoning. If inductive reasoning is going to enjoy any success at all in discovering the laws that govern the workings of the physical universe, it must necessarily be fortified by full confidence in the fact that the human mind is capable of gaining real knowledge of that world, as it is in itself. Besides accepting as axiomatic that the physical world is intelligible and that our intellect has direct access to it, we must also take it for granted, if our induction is to accomplish what it is intended to accomplish, that we can come to have real knowledge of that world, specifically with respect to the causes that underlie and explain all its complex operations. We mentioned earlier that one of the most basic kinds of knowledge on which we depend when we engage productively in inductive reasoning is the knowledge we have of the first principles of all human reasoning. This is especially the case with respect to the principle of sufficient reason, a direct corollary of which is the principle of

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causality. Because this is a first principle, it embodies a self-evident truth, so that as soon as it is expressed we immediately see that it cannot be anything but true. The fact that everything that exists must have a reason for its existence is not something that needs to be proved. Every effect must have a cause. Indeed, the two terms, “cause” and “effect,” are correlative; each is meaningful only in terms of the other. To identify anything as a cause is necessarily to imply that it has an effect, something of which it is the cause. By the same token, it would make no sense to identify something as an effect if we were to preclude from thought any consideration of a cause. The principle of causality tells that everything that is, everything that happens, has an explanation for its existence, for its happening. Things do not simply exist; there must be a reason for their existence. And, as we like to say, “things don’t just happen.” Their happening demands an explanation. There is a causative agent behind their happening. It is the assiduous pursuit of those causative agents which is the principal task of inductive reasoning. There have been philosophers who have called into question the ability of the human mind to know real causal relations in nature. They maintained that all we can know are the external phenomena, not whatever internal relations which may lie beneath the phenomena. But a position such as this ignores the real possibility, not to say the obvious fact, that the external phenomena reflect the “internal relations.” Or, to put it differently, the external phenomena declare precisely the reality the sceptic chooses to be doubtful about—a causal relation. Otherwise the external phenomena, just as such, are meaningless, and our sense knowledge devoid of significant content. Philosophical sceptics of this sort would seem to be prepared to say— to use a simple example o f efficient causality— that when we see the cue ball strike the eight ball, and then see the eight ball moving toward the comer pocket of the pool table, we cannot know that there was any causal connection between the cue ball and the eight ball. But if we cannot know that, then the burden is on the sceptical philosopher to explain the motion of the eight ball, for presumably he is not prepared to deny that from its previous stationary position it is now in motion. Things like moving eight balls don’t just happen; they are effects, and as such they must have causes. Or do they? There are some philosophers who suggest that we may have to abandon the very notion of causality, or at least revise it radically, for there seem to be things going on in this wide universe of ours, specifically on the subatomic level, for which we cannot assign definite causes, and therefore we should be prepared to admit that they are behaving without benefit of any causal influence at all. But this is to make a rather serious logical mistake, that is, to conclude that because we do not know the causes of XYZ, there are no causes for XYZ. It is to promote an epistemological problem (our ignorance) to the status o f an ontological problem (what is actually the case in the extra-mental world).

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C auses

The principle purpose of inductive reasoning, that in which most of its energy is invested, is discovering the causes which are operative in nature. The task is far from an easy one, for there are myriads of causes at work in nature, and they often interrelate with one another in highly complex ways. If we are studying a particular phenomenon, X, and attempting to discover its cause, we should not expect that we will eventually hit upon a single thing, A, which will provide us with a full explanation of X. It may happen that we find out that there are multiple causes of X, namely A, B, and C, and all of them must be operatively in place before X, the effect, makes its appearance. Or we may discover that, though A is the proximate or immediate cause of X, A itself is the last in an entire chain of causes, and therefore, to have a complete and satisfactory explanation for X, we need to know, not just A, but the entire chain of which it is the final link. But this should be the ideal for which we strive: to find for any phenomenon, say X, its single and indispensable cause, its one and only cause, so to speak. There are any number of phenomena which can have multiple causes, A, B, C, not as acting conjointly and cooperatively, but as acting separately. In other words, in any given circumstance, either A or B or C could be the cause of X. So, if we have X before us as an incontestable matter of fact, we know that A, B, and C are sufficient causes of X; each alone could do the job of bringing about X. But what we want to find out, if it is at all possible, is not only the sufficient cause of X, but, given certain circumstances, its necessary cause; in other words, the one and only explanation for its presence. If we can do that, we then have the wherewithal for some very helpful deductive reasoning we can then advert to: having established, say, that A, given circumstances B, is the necessary cause of X, we can predict what will happen should A, in circumstances B, occur in the future. Recall that in our discussion of conditional reasoning we considered one of the invalid ways one can argue within the mode of the mixed hypothetical syllogism, an error called affirming the consequent. Let’s remind ourselves of the pattern of that particular way of arguing. Pz>Q Q___ P That is an invalid conclusion because the mixed hypothetical syllogism is a deductive form of argument, in which the conclusion follows necessarily. But in this case the conclusion does not follow necessarily. Think of the relation between antecedent and consequent as reflecting the relation between cause and effect. Now it could very well be, and we may even presume it to be so, that P is the sufficient cause of Q. But it may not be the necessary, the one and only, cause of Q. There may be other causes of Q, so the mere fact of the presence

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of the effect, Q, does not allow us to say with certainty that it was this cause, and only this cause, i.e., P, which is the explanation for Q. But now recall something else we encountered earlier, the situation where we can have a reciprocal relation between antecedent and consequent, a situation in w hich one can affirm the consequent and yet end up with an acceptable conclusion. W e had focused our attention on an argum ent where its major premiss was a definition; therefore, the antecedent (definitum) and consequent (definition) were convertible. A much more interesting situation than that, and one which has a direct bearing on our discussion here, is one in which we have a cause/effect relation being expressed in the m ajor premiss, and where the cause (antecedent) is both the sufficient and necessary explanation for the effect (consequent), in which case— adm ittedly a rare one— it would not be an illegitimate move to affirm the consequent. By doing so we would be effectively saying the following: Here is an effect, X, and I know that there is one and only one cause o f X, namely A. Therefore, if X happens, A happens. As an example of the reciprocal cause/effect relation I would refer to the one used in the previous chapter, where boiling water is the effect, and heating it to 100 degrees Celsius is the cause. W hen we think of causality, it is almost always efficient causality we have in mind. The efficient cause is that agent which is the explanation for the very existence o f something, or for its existing in a certain manner, the difference here being between substantial existence and accidental existence. Parent rabbits, male and female, would be the efficient causes of bunnies, in that they account for their very existence. The cue ball striking the eight belli is the efficient cause o f the eight ball existing in a certain manner, that is, as moving. The efficient cause o f the very existence o f both cue ball and eight ball would be whoever manufactured them. It is not surprising that whenever we think about causality we should think principally o f efficient causality, for it plays a very public role in the operations o f nature. But the efficient cause is not the only cause at work in nature, and therefore, for an adequate understanding of the natural world, we m ust take into account other causes as well. To acknowledge the operative presence of efficient causality alone is to adopt the view called mechanism. Aristotle identified three other causes besides the efficient cause; they are the m aterial cause, the form al cause, and the fin a l cause. All four of these causes must be taken into account in inductive reasoning. The material cause is simply the matter, the physical stuff, of which a material thing is made. The material cause of copper wire is copper. Obviously, to know the material cause o f something is to be possessed of important information about it. But why do we call such knowledge a cause? Because a cause is an explanation, and the knowledge of the material makeup of a thing has significant explanatory value. To know that the wire is copper is to know, among other things, that it is a very good conductor o f electricity. The formal cause of a thing is what explains its being precisely the thing it is and not something other than what it is. The formal cause is the identifying cause; it determines matter to be of a particular

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kind, such as copper. On a less fundamental level, the formal cause determines the peculiar shape of a material thing. If we have three pieces of furniture before us, a bookcase, a dining room table, and a rocking chair, all of which are made of oak wood, it cannot be the material cause that will distinguish one from another, for they all have that cause in common. What distinguishes them are the different forms taken by the oak wood in each instance. In the natural world it is the formal cause, that which determines a thing to be precisely what it is and no other, that serves to distinguish copper from lead among the chemical elements; it is what distinguishes a rosebush from a giant sequoia among the flora; it is what distinguishes a turtle from a tiger among the fauna. The material and formal causes are especially important because they give us special insight into the essence or nature of whatever phenomena we are dealing with in the physical world. Unfortunately, given the mechanistic view of nature which continues to limit the vision of some scientists and philosophers, the very notion of essence or nature is often considered to be irrelevant, if not simply empty of any assignable content. Thus we have a state of affairs where what is literally essential is spumed, and exclusive importance is attached to what effectively becomes unintelligible—i.e., efficient causality— when it is not considered along with the other three causes. To attempt to understand efficient causality in isolation is, ironically, not to understand it all, for if an efficient cause is a material entity, it must have a material and a formal cause, and the efficient cause cannot operate as such if there is no final cause. The cause most often roundly rejected by the modem empirical sciences is the final cause. However, as it turns out, that rejection is, indeed has to be, entirely theoretical in character, for in practice it is impossible to avoid the reality of final causality, and that is because it is an integral and inextricable part of the way the world works. Certain empirical scientists may deny that there is final causality in nature— this is tantamount to denying that there is any purpose in nature—but then the scientific findings for which they themselves are responsible show purpose popping up all over the place. This is especially the case in the biological sciences. And then there are all those philosophers who also deny purpose, presumably on purpose. The final cause of any physical entity is simply the end, the culminating resolution, toward which its activity is directed. A fundamental metaphysical principle advises us that “every agent acts for the sake of an end.” This principle is illustrated in an especially overt and obvious way in the realm of the artificial. Any man-made thing, a tool for example, is tellingly explained when we know what it is for, the uses to which it is to be put. But the final causality in the artificial realm is but a reflection of the final causality which is to be found everywhere in the natural realm. This is as true for inanimate things as it is for animate things. And the ubiquitous finality or purposefulness in nature is the principal explanation for its orderliness, for the fact that it is cosmos rather than chaos. It is because all things in the physical world act always or for the

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most part so as to achieve determinate ends that scientific prediction is possible. If there were no final causality in nature— if, as some want to maintain, it is but a fiction— there sim ply would be no science, no knowledge o f any kind. Everything would be up for grabs. Your guess would be as good as the local b o o k ie’s as to w hat m ight happen if you let go o f the rock that you are now holding in your hand. You release your grip on the rock, and it hovers before you in mid-air, or it flies off into outer space and goes into orbit around Neptune. Y ou plant an acorn and you would have no reliable ideas as to what might com e o f it in due season— a peach tree, a poison ivy plant, or a guided missile cruiser. (See Appendix B for a discussion of ultra-physical causes.) S cientific M ethod If we are to investigate productively the physical world, using inductive reasoning for the purpose o f discovering the causes operative in that world, then we m ust go about it in an organized, systematic way. In other words, we need a m ethod. A m ethod is simply an ordered way o f proceeding, a plan of action which will allow us, as efficiently as possible, to achieve the purposes that we set for ourselves. W hat procedures should we follow in order to discover the causes in nature? A comprehensive, logical understanding of method defines it as the organization of thought in such a way as to facilitate, if not ensure, the discovery o f truth. One often runs across references to the scientific method, suggesting that there is a single, neatly unified set of rules which, if faithfully followed, would virtually guarantee success in uncovering the secrets of nature. But to intimate that there is but one way o f engaging in scientific research is simply not consonant with the facts as we know them from the long and checkered history o f science. There are many methods, but if any given method is to qualify as being truly scientific, it m ust give primacy of place to two basic activities: observation and experiment. The em inent philosopher and logician, P. Coffey, provides us with some general guidelines which can help properly to dispose the mind for productive scientific research. His first bit of advice is that we should not take on too much too fast. We should begin with things which are relatively simple and with which we are well acquainted. Second, we should proceed gradually in our investigations, carefully setting up and then closely monitoring every move we make. The old saw that haste makes waste applies here, and what we are most apt to waste is time, for if we rush things we will invariably botch them; then we have to go back and clean up the mess we made before we can go ahead again. Third, we should not expect to attain a greater certitude than the nature o f our subject matter will allow. We can gain a very high degree of certitude in mathematics, less in physics, less in biology, less in economics, and less still in ethics. Fourth,

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we should be ever mindful o f the critical importance o f final causality, keeping steadily focused on the end we are attempting to achieve.22 O bservation

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Again, the two activities that must be included in any method deserving of the name “scientific” are observation and experiment. Some scientific fields, such as astronomy, lend themselves only to observation. There is not much we can do to control the behavior of distant galaxies, especially since, presumably, we are peering at celestial antics which are very ancient history. In this field we are strictly observers. We can alter, adjust, improve our instruments of observation, or invent entirely new ones, but in the final analysis, no matter how sophisticated and cutting-edge be our instruments, whatever they are capable of delivering must eventually terminate with the human eye, the human ear. And then it is up to the human mind to interpret the data which is collected through observation. There are scientific fields in which we are able to add experimentation to observation, but we deliberately choose not to do so, lest it alter the nature of what we are observing. We limit ourselves to non-obtrusive observation. Take, for example, the case of a zoologist who wants to establish certain facts about the natural habits of zebras. In setting up his research project he would be illadvised to confine his investigations to various zebra-holding zoos. True, there he could observe zebras close hand, and at little inconvenience to himself, but the animals are in a totally artificial environment, which would of course frustrate the ostensible purpose of his research. Zebras in a zoo are not going to behave as they do in the wide open spaces of, say, Zimbabwe. Our zoologist, then, if he is serious about gathering the facts he purports to be interested in, must travel to Africa and observe how zebras conduct themselves while at home, and while there he must take pains to make his observations as covertly as possible, so that his observing activity will have little or no altering effect on the behavior of the animals. Observation might seem to be so natural and simple a process that anyone could do it with scientifically beneficial results. This is not the case. Let us remind ourselves of the elementary difference between looking and seeing. Two people can be looking at the same thing and yet, in any number of ways, not really be seeing the same thing. A good observer is one with a knowing eye, which is to say a trained eye. We have to know what to look for and when to look for it in order to see what is really there to be seen. There are no pat rules to be followed in order to ensure productive observation, but some general comments on the subject may be ventured. To be a good observer requires, in the first instance, a certain mind-set, a favorable psychological disposition, which makes one alert, wide-awake, expectant, prepared to pick up subtle hints as well as what is overt and explicit. The good observer is patient and

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persevering, keeps on looking in the expectation that he will eventually see something. The good observer takes notes, both mental and literal, the latter especially, for our memories can play puckish tricks on us. Good observation is selective. The good observer limits his field of vision, focuses his attention, does not allow him self to be distracted by the irrelevant. Finally, and to give special stress to what was already said above, the good observer must be knowledgeable. He must have as thorough a knowledge as possible of the field he is investigating. Only the knowledgeable observer is able to see what others do not see, and that is because he knows the terrain and what it is most likely to reveal, and where. Experim entation is not an activity which is substantially different from observation. Dr. Coffey regards experim entation as simply observation conducted under controlled conditions. That is a fruitful way of looking at the matter. Surely observation is the more basic, the more natural, activity. Let us say that a researcher is engaged in inductive reasoning to achieve its principal purpose o f discovering causes, specifically the cause, or causes, of X. But because of the great complexity resulting from the tangled interplay of causes, it is very doubtful that he would be able to discover the cause of X simply by observation alone. So, by setting up an experim ent he endeavors to create a situation where he can control various causal influences, and thus be able to determine what are and what are not genuinely causal factors in the explanation of X. By way o f providing a simple example of the method, we will consider a recent experiment conducted by Dr. Sharon Shebo, M.D., Ph.D. In her capacity as a chemist, she recently developed a new medication, Formula Supra, which, she fondly hopes, will act as the long-awaited cure for the common cold. But now its efficacy must be tested. Will it act as a sufficient cause to bring about so happy an effect? An experiment will be conducted. She calls for volunteers to participate in it, all o f whom must be suffering from serious colds. Dr. Shebo practices in a large East Coast metropolis, and it is the month of March, so she gets scores o f qualified people who volunteer to participate in the experiment. Sixty volunteers are selected, and divided into two groups of thirty each. The selections are made very carefully, so that each group represents the greatest possible diversity with respect to differences in sex, race, ethnic background, economic condition, etc. In this respect each group is pretty much the mirror image o f the other. Next, Dr. Shebo makes arrangements to allow for all the participants to live in the same facilities for a period of six days; they will sleep there, have their meals there, and all follow essentially the same daily routine. The purpose here was to have all the participants living in an environment where they were subjected to the same general causal influences. The stage was now set for the experiment itself. One of the groups, Group Alpha, was given a daily dosage of Formula Supra; the second group, Group Beta, was given what looked like medicine but which in fact had no medicinal

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value whatever. To obviate the possibility that certain psychological factors could skew the results of the experience, both of the groups were kept in the dark as to which one was receiving Formula Supra and which one the nonmedicinal substitute. The plan was to examine the members of each group after the termination of a four day testing period, in order to determine, in accordance with carefully developed quantitative criteria, what changes took place within each group. Of course what Dr. Shebo wanted principally to determine was whether the members of Group Alpha saw significant improvement in their health because of their being treated for four days with Formula Supra. The results of the experiment were as follows: in Group Alpha, 50% of its members, fifteen in all, showed “significant improvement” in the state of their health; in Group Beta, 50% of its members, fifteen in all, also showed “significant improvement” in the state of their health. These results led Dr. Shebo to conclude, sadly, that Formula Supra seemingly had no beneficial effect on those suffering from the common cold. Disappointed but not discouraged, she decided that the only thing to do was to go back to her laboratory and try again. As there is no one scientific method, neither is there only one way to conduct an experiment, but, as a general rule of thumb, one should try to create an environment in which one can identify, keep track of, and control the influence of as many potentially causal influences as possible, thus heightening the chances of discovering the cause one is looking for, or, as in the example above, so as better to test the efficacy of what one is proposing as a causal agent. F orming Hypotheses When we are involved in a serious investigative engagement with the physical world, with the intention of discovering causes, it is necessary, as we saw above, to enter into the process with a workable program in mind. Experiment might be thought of as a way of wrenching answers from nature which could never have been gotten from observation alone. Scientific inquiry, if it is to be successful, must be inquiry which is dynamically active, pesteringly persistent, even a bit pushy at times. Perhaps the single most important action we take in order to give productive shape and direction to our investigations is the forming of hypotheses. Isaac Newton is reported to have once said that he made no hypotheses. If that was intended to apply to all of his scientific work, then the claim must be taken along with the proverbial grain of salt. In fact, Newton was constantly making hypotheses. His achievements would not have been what they were otherwise. An hypothesis has been described as an educated guess, an informed conjecture, a shrewd estimate as to how things might in fact be. It is the first really critical move we make in inductive reasoning, for it sets the stage for everything that is to follow. It is to serve as an activating proposal, for the whole idea behind forming a hypothesis should be to stimulate research, to

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give im petus and direction to serious and system atic experim entation, the purpose o f which is to find out if the hypothesis is in fact true. In order to form a hypothesis that stands a good chance o f turning out to be true, we have to be capable o f creative and constructive wonder. Before Pasteur discovered that fermentation was caused by organic intervention, he first wondered if that could possibly be the case. Then he formed the hypothesis: fermentation is caused by organic intervention. T hen he set up his ingenious experim ents to test the hypothesis. It tested positive. A cause is an explanation; a hypothesis is a tentative explanation. As a general rule, a hypothesis is better the sim pler it is. A hypothesis must be verifiable, that is, once put to the test, it must be capable o f being proven to be either true or false. It stands to reason that if a hypothesis is im m une to either proof or disproof, it is quite useless as a viable explanation o f how nature works in this or that respect. If I form the hypothesis that the cause o f a particular type of allergy endem ic to the residents o f Lancaster, Iowa, is the malign telepathic influence upon the residents o f a cube-shaped planet situated in the NGC 4414 galaxy, no one, I rather suspect, w ould be prepared to take my hypothesis seriously, for there is no way in which it could be tested. As w ith other aspects o f inductive reasoning, there is no neat set o f rules w hich w ill guarantee success in the form ation o f good hypotheses, but once again in this case Dr. Coffey offers us some general guidelines which are quite helpful. In presenting them here, besides putting them in my own words, I take the liberty o f expanding som ewhat upon the basic idea which is the subject of each. (1) Hypotheses should be based upon observation. Indeed, they should be the natural outcome o f the kind o f active, intrusive observation alluded to above. A good hypothesis is sometimes said to “come out of the blue.” If that is intended to mean that it comes out o f nowhere, it is nonsense. The “blue” is always the fertile field o f the researcher’s knowledge and experience. (2) H ypotheses should be self-consistent, and they should not contradict any firm ly established truths about the physical world. A hypothesis lacking in self-consistency would be one which is proposing a cause for X containing elements that are incompatible with one another, as, fo r exam ple, the attem pt to explain rising prices by an increase in supply and a decrease in demand. (3) A hypothesis should be based on an analogy between itself and already known causes. Dr. Coffey gives much emphasis to this criterion. If my hypothesis that A is the cause o f X is to show promise, it must bear some comparison, and as closely as possible, to other firmly established cause/effect relations. Thus, A is a good bet to turn out to be the cause of X if A is very m uch like B, and X is very much like Y, where B is the proven cause o f Y.

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(4) The fourth criterion should stand as the highest ideal in the formation of hypotheses. In Dr. Coffey’s own words, and as emphasized by him, a hypothesis should be verifiable as “the only possible explanation o f the facts it purports to accountfor.” 23 T esting Hypotheses In most cases, hypotheses are tested by experimentation. There may be some cases where observation alone must be relied on, as in the instance cited above regarding the zoologist studying zebras. Take a like instance, regarding an ornithologist who formed a hypothesis having to do with a feature of the migratory habits of a certain species of bird, a matter concerning which there were sharply differing opinions within the profession. In order to test his hypothesis, and in the hope of settling the question once and for all, our intrepid researcher took to the great outdoors, binoculars slung about his neck, prepared to follow the birds wherever they might fly, as they winged their migratory ways over the face of the earth. In testing a hypothesis, we can begin with the question: If the hypothesis is true, what associated things could I expect also to be true? For example, if I am hypothesizing that A is the cause of X, and if I have established an analogy between the putati ve causal relation A — X and the proved causal relation B — Y, then if I note that B, in causing Y, has the accompanying features of E, F, G, I can anticipate that, if A is indeed the cause of X, it will also be accompanied by E, F, G. Is it? An historian hypothesizes that the Iraq war caused much social unrest in the United States. He compares it to the Vietnam War in that respect, and he calls attention to the facts that the Vietnam War (1) was not declared by Congress, (2) was broadly unpopular, and (3) was actively opposed by most of the country’s intellectual elite. Can these same features be associated with the Iraq war and, if so, does that lend significant weight to the hypothesis? Various forms of deductive reasoning can be used in the testing of hypotheses, such as, for example, the disjunctive syllogism. This is a very simple form of argument where the major premiss is a compound disjunctive proposition made up of two or more disjuncts. Recall that in a disjunctive proposition at least one of the disjuncts must be true, so in a disjunctive proposition containing two disjuncts, if it can be shown that one of them is definitely false, then the remaining one is necessarily true. The function of the minor premiss in the syllogism is to negate one or more of the disjuncts so that only one remains. What we have displayed in this kind of argument is essentially a process of elimination. Below is an example, in symbolic form, of a simple disjunctive argument, with a major premiss containing two disjuncts— an “either.. .or” proposition. AvB ~B A

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Let us say that A and B represent two possible causes for X. Observation and experiment show that B cannot qualify as the cause; therefore, we can conclude that A is the cause o f X. O f course, for this argum ent to have any force at all, we have to be sure that our m ajor premiss faithfully represents the actual state o f affairs, that, in other w ords, our investigations have shown that all other possibilities, besides A and B, have been ruled out as potential causes of X. This process o f limiting possibilities must be counted among the most difficult tasks in inductive reasoning. In m eeting it successfully, the ingenuity and inventiveness o f the researcher count for a great deal. But this is true of so m any aspects o f inductive reasoning. O ver a particular fall weekend there is a serious outbreak o f the stomach flu at Acm e Academy, a boarding school in Maine. The officials at the school, aided by the county Commissioner of Health, decide that the cause of the disease was m ost likely associated with the meals that were served over the weekend in question. Having gotten that far, they then ask themselves: Was there anything about those m eals, or anything associated with them , which was markedly different on that particular weekend? In answer to that question they came up with three items: (a) the regular cook was off that weekend, and his place was taken by a recent graduate from c h e f s school; (b) because o f a severe storm there was a power outage on Saturday, and the kitchen freezers and refrigerators w ere w ithout electricity for over six hours; (c) a local resident had donated a generous supply of venison, which served as the main meat dish for the evening meal on Saturday. With that information available to them they had the makings o f a disjunctive proposition composed of three disjuncts which would serve as the m ajor premiss for a disjunctive syllogism: A v B v C. The hypothesis they form ed was as follows: The flu was caused (a) by some questionable culinary practices on the part of the substitute cook, or (b) by foods served at the evening meal that had been previously frozen or refrigerated and were spoiled because o f the pow er outage, o r (c) by the donated venison. Further investigation intended to test that hypothesis elim inated the first two possibilities, leaving only the third; and the venison did in fact turn out to be the cause. A specimen o f the m eat was exam ined by a local lab and it was found to be tainted. H ypothetical deductive reasoning, particularly in the form o f the mixed hypothetical syllogism, m odusponens, can be employed in testing hypotheses. Consider this argument: If A, then not-C; but A; therefore, not-C. And now this one: If not-A, then C; but not-A; therefore, C.

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These arguments reflect the type of reasoning Pasteur used in testing the hypothesis that organisms are the cause of fermentation. It went something like this: One begins with the hypothesis that organisms are the cause of ferm entation. An accompanying assumption (or it can be regarded as an additional hypothesis) is that those organisms are transported on the air and settle on the liquid, which subsequently undergoes fermentation. Now, if that assumption/hypothesis is true, a potentially fermentable liquid which is protected from exposure to the air will not ferment, whereas a liquid not so protected will undergo fermentation. Pasteur then set up his experiment to test the basic hypothesis, and it was duly verified by the results. In the vessels that were protected from exposure to the air, fermentation did not take place (“not-C* in the first argument above). But it did occur (“C” in the second argument above) in the liquid in the unprotected vessels. Here are the two arguments expressed in English. If a potentially fermentable liquid is protected from the air, fermentation will not take place. This potentially fermentable liquid was protected from the air. Therefore, fermentation did not take place. If a potentially fermentable liquid is unprotected from the air, fermentation will take place. This potentially fermentable liquid was unprotected from the air. Therefore, fermentation took place. As for the disproving of a hypothesis, usually it takes but a single contradictory instance to do the job. For example, in my hypothesis that A is the cause of X, if A occurs without X occurring, I should be prepared to look around for other possibilities as the cause of X. But one must be careful not to be overly hasty, especially when dealing with a complicated situation. Perhaps the fact that X did not occur when A occurred was the result of sloppy experimentation on my part. F rom Hypotheses

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Laws

The purpose of inductive reasoning is to find the causes of things, so that from them one can then determine the laws of nature, laws which might be described as the generalizations that tell us how nature operates. Induction begins with particular instances, with individuals, and works its way up to generalizations which, once firmly established, then become the starting points for deductive reasoning. Once we have the law of gravity to rely on, then if we know the masses of two physical bodies, and their distance from one another, we can make exact calculations as to how they attract one another. Newton could not explain what gravity is, any more than we can today; the only thing his law sought to do—and this is all any law of nature seeks to do—is to explain how gravity works. The puzzling part about the law of gravity, or any other law

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o f nature which simply tells us the “how” of things, is that if we do not know what gravity is, then our knowledge of causality in this weighty matter is rather tenuous. One might simply say: the causes o f what we call gravity sire just the physical bodies themselves, their respective masses, and their relative distance from one another in space. That could do, but are not those better described as the necessary conditions which have to be present in order to allow that m ysterious and elusive “thing” we call gravity to operate as we know it to operate? Be all that as it may, the law o f gravity, and all the other laws o f nature which we have managed to discover to date— generally understood as “any uniform series o f connected phenom ena” 24 — are what account for, are the explicit manifestations of, the coherence and orderliness of nature, which in turn, as we observed earlier, creates the scene for and makes possible inductive reasoning. The causes of nature may be regarded as the specific contents of the laws, in the sense that we have a uniform series of connected phenomena only because o f the consistent, regular (thus predictable) operation of interrelated causes. This is especially seen to be the case if we are mindful of the fact that causality is not confined to efficient cause, but includes as well material, formal, and— very importantly— final cause. It is the combination of material and formal cause which constitutes any physical entity, that by which we identify the essence or nature of a thing. In that respect the material and formal cause may be regarded as the foundational explanations for efficient causality, because a physical entity, be it inorganic or organic, acts according to what it is; its essence or nature is revealed by its observable behavior. And the fact that the physical universe is made up of entities with stable and identifiable essences accounts for the patterned consistency in their functioning as efficient causes, and that in turn accounts for what we call the laws of nature. And then there is final causality, the fact that everything that acts, acts for the sake of an end. Final causality is inseparable from efficient causality, for we are only able to recognize an efficient cause as such because we-see it as action directed toward a determinate end. It is simply unintelligible otherwise. To say that final causality is everywhere operative in the physical universe is simply to say, in the plainest of terms, that we live in an ordered and purposeful universe, and ordered because purposeful. T he C anons

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Induction

The nineteenth century English philosopher John Stuart Mill laid down a set of five rules or canons (a “canon” is a law or rule) for inductive reasoning. They have w eathered rather well over the years, and they have made their appearance in many a logic textbook since Mill first published them in 1843.1 have decided to include them in this textbook, at least four of them, for I take one to be repetitious. I offer them here, as put in my own words— M ill’s

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Victorian prose can be somewhat convoluted at times—because they can prove useful if properly understood, as general guidelines for inductive reasoning, particularly with respect to the principal task of discovering the causes of things. They should not be thought of as comparable to the rules of the syllogism, for example, which give us very precise and reliable criteria to ensure success in deductive reasoning. Mill’s canons have been subjected to a considerable amount of thoughtful criticism by several logicians. The eminent Dr. Coffey, among others, rightly faults Mill for failing to recognize the key importance of the hypothesis in inductive reasoning. Also, Mill does not seem to have sufficiently appreciated the kind of hard, slogging, and sometimes hit-and-miss kind of work which, as I have suggested in previous pages, and though it must have a method behind it, cannot be reduced to a tidy program which can be carried out according to a precise set of rules. If someone without any actual experience in the field were to take Mill’s canons as definitive directives, he could easily be led to believe that this whole business of inductive research is rather simple and straightforward. All that having been said, however, the canons, if taken with other pertinent criteria for inductive reasoning, can prove to be quite helpful. As mentioned, I express the canons in my own words, not M ill’s, and I have modified them here and there to take into account various justifiable criticisms made by other logicians. 1. The m ethod of agreem ent. I f two events, A and B, regularly and consistently accompany one another, there may be a causal connection between them. An association of this sort may offer a significant clue indicating a real cause/effect relation, but it certainly does not offer sufficient evidence on that score. It is a clue that must be pursued. It is quite possible, and not especially unusual, that two events or happenings may consistently accompany one another without there being any causal relation between them. Certain organisms always come accompanied by certain parasites, but from that we do not conclude that the organisms caused the parasites, or vice versa. There are some who jump to the conclusion that there is a causal connection between two things, A and B, because A always precedes B, but this is a mistake on two counts. In the first place, mere repeated sequence, i.e., B always following A, like mere accompaniment, does not prove a causal connection. Secondly, and more germanely, the cause/effect relation is never a matter.of chronological sequence— first the cause, then the effect— for the two, with respect to the causative action itself, are simultaneous. The moment the causal agent acts as a cause, there is at that very moment an effect. The cause can be said to precede the effect only in the elementary and obvious way that it must exist, as an entity with the potential to produce an effect, before it actually does so. 2. The m ethod of difference. One thing, A, can be considered to be the possible cause o f another thing, B, when, if A is present, B is present, and when, if A is absent, B is absent. This is a much sturdier principle, or “method”— that is M ill’s term—than the first one. To use a simple example: if there is

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smoke (the effect) we can be sure that there is a fire (the cause), and if there is no smoke we can be at least reasonably sure that there is no fire. (There are some fires that are low on smoke but big on damaging heat.) This method can be put to good use in testing a hypothesis. I want to test the hypothesis that A is the cause of B. I discover that whenever I put A in place, there is B, and whenever I remove A, B is nowhere to be observed. That is a pretty good reason for entertaining the suspicion that there is a real causal connection between the two. And it would not look at all good for my hypothesis— that A is the cause of B— were I to put A in place and B failed to show up, or if B were to show up unaccompanied by A. If fact, that would be sufficient evidence to disprove my hypothesis. It should be noted that neither of these two criteria preclude the possibility that there could be multiple causes for B. We are certainly entitled to recognize A as the sufficient cause o f B, but there may be others as well. So, even if further investigation firmly nails down A as a real cause of B, it may not be its necessary cause, which is to say, its one and only cause. 3. T he m ethod of concom itant variation. I f two phenomena always vary together, other circumstances remaining the same, they may be connected as cause and effect. This is a pretty strong indication that some real causal activity is afoot. Once again using A and B to designate respectively putative cause and putative effect, if I observe that A varies in a quantifiable way at the same time that B is varying in precisely the same way, that is significant information. So, for example, if I observe that the leaves of the oxalis plant begin to close up with diminishing light, and that they unfold as the light increases, I have good grounds for concluding that it is the varying light which is causing the variations in the leaves of the plant. It was the discovery of the concomitant variations in the relative positions of earth, sun, and moon, on the one hand, and the variations in the tides, on the other, that led to the conclusion that the form er were the causes of the latter. 4. The m ethod o f residue. I f certain phenom ena remain unexplained by causes already discovered, fu rth er causes m ust be sought to explain those phenomena. The basic idea behind this principle is best explained by an example. Say that you know the exact weight of a certain semitrailer truck. That truck now drives onto the scale fully loaded. You want to know the weight of the load. In other words, you want an exact quantitative description of the cause of the weight that is actually being registered over and above the weight of the truck. Because you already know the weight of the truck, you simply subtract that weight from the total weight that is registered on the scale indicator. The cause o f the weight of the truck is already known, the truck itself, so you need to seek a cause to explain the residual, the weight that is over and above that of the truck, and that is the load the truck is carrying. This method might be described as a bid for the importance of thoroughness in inductive reasoning, the need to account for all the phenomena we are seeking to explain.

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to the

The point has been iterated and reiterated that the principal task or occupation of inductive reasoning is to ferret out the causes of things. But inductive reasoning occupies itself in another important way as well, and that is by endeavoring to gain more knowledge about classes or groups of things, so as to be able to provide reliable generalizations regarding the membership of those classes. Actually, though this type of research may not be explicitly and consciously aimed at the discovery of causes, it is nonetheless, and inevitably, caught up in causal realities. And there is nothing to be surprised about in this, for causality is at work everywhere around us, and of course we ourselves are causal agents. More fundamentally, our very composition, as both material and spiritual creatures who act as efficient causes, is explained by material and formal causality. And whenever we act as efficient causes in one way or another—as I just did when I got up and shut the back door—we are necessarily involved in final causality, for I got up from my desk with an express purpose in mind, to close the back door. And so I did. All of these causes operate together as providing the fullest explanation for whatever the researcher, as he studies classes of things, is specifically interested in. Consider this situation: a researcher, perhaps at first through casual observation, notes that several members of a certain class of organisms display a particular feature— say, with respect to their physiology, or with respect to their behavior—and this sets him to wondering. Is this feature something which is exclusive to this portion of the class only, the portion he has observed, or is it to be found in the class as a whole? Is the feature common to a species? If the feature is not trivial, if ascertaining whether or not it belongs to the class as a whole would constitute a genuine contribution to knowledge, then he has the makings for a potentially productive research project. Now, if one sets out to determine whether or not a certain feature, call it W, belongs to each and every member of a given class, call it N, the procedure to be followed is rather simple. One begins at the level of individuals, checking one after another for the presence of the feature in question, W, until, finding no individual in the class without that feature, the point is reached where one feels justified in making the generalization, “All N are W.” But where exactly is that point? In other words, how many members of a class have to be observed, until there is sufficient evidence to formulate a potentially true generalization about the entire class? One answer to the question is: the point is reached when one has exhausted the class, having surveyed each and every one of its members. To do that is to have executed what is called complete enumeration, or complete induction, and there is no gainsaying, at least from a purely quantitative point of view, that it would provide some rather impressive evidence in support of a

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generalization about a class. However, such an accomplishment could turn out to be less informative than it might at first appear, for there is a way of conducting a complete enum eration o f a class which amounts to being little more than superficial head-counting, for it fails to come to grips with the essential natures o f the members of the class, which is rather important information, for it is, after all, what warrants their being put in that class in the first place. But the fact o f the m atter is that most of the classes which inductive re­ search deals with are so huge that complete enumeration of their membership is entirely impossible. What then is the alternative? Must we simply abandon our research project as a hopeless cause, and go back to working crossword puzzles? Not at all. There is an alternative to complete enumeration and it is called, quaintly enough, incomplete enumeration, or incomplete induction. This is the normal, indeed the necessary, procedure which is followed in the kind of inductive reasoning we are now concerned with. So, we have a class, N, and we want to ascertain whether a certain feature, W, is common to that class as a whole. Knowing that it is out of the question that we could ever do an exhaus­ tive survey of the class, we concentrate our attention on a portion of the class, a subclass which we will designate as T. We carefully examine the members to be found in subclass T, and then, on the basis o f what we discover by our examination, we venture a generalization pertaining to the class as a whole. Let us say that as a result of our careful investigation of the subclass T, we find that as a matter of fact each and every member of that subclass possesses the feature W. On the strength of that finding, we call a news conference to proclaim to the world that, “Every N is W .” The value o f our research project, and more particularly the value of the generalization with which it culminates, entirely depends on the quality of that portion of the entire class which is the focus of our investigative attention. That portion o f the whole is called the sam ple, and the critical criterion which it must meet if it is to bear the weight of the burden placed upon it, is that it must be representative. A representative sample is one which in every salient re­ spect is reflective of the whole of which it is a part. If class N is the macrocosm, then subclass T should relate to it as a microcosm, as a smaller version of the class as a whole. How does one ensure that a sample is truly representative? It is not necessarily the case, as one might think, that the larger the sample, the more members of class N that have been studied, the more representative the sample. A sample that constitutes a significant portion of a class, for all its impressive size, may be leaving out factors that really belong to that class. For example, let us say that our researcher is a zoologist, again, who in this case is studying the behavior of rats. He has noticed, from the limited number of the laboratory specimens he has observed, that they display certain behavioral patterns in their feeding habits, and this leads him to wonder if those behavior patterns, W, are peculiar to domesticated rats, or whether they are to be found among rats in general. He is

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determined to find out. He plans a research project, manages to land a generous grant, selects a squad of trusty assistants, and goes to work. At project’s end, he and his assistants have carefully studied the behavior of 28,915 rats, surely a sizable sample. However, the sample was not truly representative because, as it happened, all the animals examined were urban rats, none came from suburban or rural areas; furthermore, all the rats examined hailed from the temperate zone, none from the tropics; finally, for practical reasons, all of the rats, after being captured, had to be brought to the laboratory for study, but this placed them in a decidedly artificial environment, and it is reasonable to suspect that their feeding habits were altered on that account. The rats living in the sewers of New York could very well be engaging in behavior which is quite different from that of their captured confreres in the laboratory. With all these considerations in mind, the published findings of the research project, which appeared in The International Journal o f Rodent Research under the title, “All Rats Have Feature W,” cannot be accepted without many serious reservations. Randomness is often cited as an important, if not essential, feature of a sample. The idea behind a random sample is this: that every member of a class, N, has a chance equal to any other member to be selected as a member of the sample, the subclass T. Random selection does not mean arbitrary or uncon­ trolled selection. As a matter of fact, considerable control is exercised over the process of selection to ensure randomness, given the importance attached to it. Even so, there would seem to be no common agreement as how best it is to be achieved. From a strictly logical point of view, it would seem that the only basis on which one could state with perfect confidence that each member of the class stands an equal chance of being selected for the sample is no more than the bare fact that they are all in the class from which the selections are going to be made. Be that as it may, there is no avoiding the fact that a significant amount of conscious control must go into the assemblage of a sample. It cannot be left to pure chance. The idea is to assemble a sample that represents a cross-section of the class as a whole, with every significant aspect of the whole making its appearance in the sample. But this can only be done by those who have at least a reasonably comprehensive acquaintance with the class, allowing them to rec­ ognize the kind of relevant diversity which is to be found in it. If one is dealing with classes whose general complexion changes over time, such as human popu­ lations, it is imperative that periodic adjustments be made to the sample to ensure that it continues faithfully to reflect such a class. A non-static class requires a non-static sample. At this point you might be recalling, perhaps with troubled mind, something to which we gave much emphasis when, working with the square of opposition, we were familiarizing ourselves with the basic principles of logical inference. Given our knowledge of the square of opposition, we know that it is illegitimate

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to infer the truth of an A proposition on the basis of the truth of an I proposition. I cannot, while knowing that it is quite true that “Some S are P,” blandly conclude that “All S are P” is also true. Clear enough. But is not that exactly what we are doing in inductive reasoning? At the end of our inductive investigations we have at hand a set of data which, put in propositional form, would be correctly expressed as “Some N are W ,” and then do we not, on the force of that claim, make bold to pronounce a broader claim, indeed the broadest o f claims, that “All N are W ” ? Are we not com m itting an egregious logical error in doing this? No, we are not. We need only remind ourselves that because we are working within the realm of inductive reasoning here, the conclusions to the arguments we construct are probable conclusions. In the strictest sense, then, “All N are W ” is a probable conclusion because, although we are confident that it is true as it stands, it does not have to be true by the very nature o f things. Further investigations down the line could turn up a member or two of class N which did not have feature W, and with that our generalization would come crashing to earth. It takes only a single exception of an empirical generalization, as “All N are W ” would be, to render it false. But we should keep something else in mind, that there are degrees of probability, and that there are certain conclusions from inductive reasoning that are so firmly established, because of the quality of the evidence supporting them, that it would be hard to imagine they could ever be overturned. B ut e v ery th in g depends on the stren g th , on the com prehensive representativeness, of the sample. One might suppose that, were it ever possible to conduct a com plete enum eration o f any class, that this would be unquestionably superior to any sample, no matter how carefully constructed, but this is not necessarily so because, as noted earlier, a complete enumeration could be superficial for not taking into account the peculiar nature of the members of a given class. A judiciously assembled sample, though representing only a relatively small portion of an entire class, could thus be far superior to a complete enumeration, or to a sample which is very large but carelessly put together. Besides the general suggestions given above to ensure a representative sample, the most important factor is a knowledge, on the part of the researcher, of the essence or nature of the members of the class being investigated, insofar as this, or something analogous to it, is possible to ascertain. Members of a class, such as a natural species, are such precisely because of the fact that they share a com m on nature. Thus, if you have knowledge of the nature of the m em bers o f a particular class, you have at hand an eminently useful bit of information. Theoretically, acquaintance with but a single member of a class, with regard to what you judge to be an essential feature of that member, would then be sufficient to enable you to say what is true of the class as a whole, for that single member is essentially the same as all the other members of the class.

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There is no need to launch an elaborate investigation in order to discover whether human beings are mortal, for it is of the very essence of each and every member of the class of human beings to be mortal. The strongest and most reliable sample, then, would be one which is founded upon a knowledge of what pertains to the essence or nature of the members of the class. Such knowledge is not always easily come by, but its value is inestimable. O pinion Polls The opinion poll, for better or worse, figures large in contemporary society. Politicians certainly put much stock in it, presumably guided by the conviction that the savvy sailor always needs to know which way the wind is blowing, and commercial enterprises rely heavily upon it as well, enabling them the better to know, presumably, the prevailing preferences of the potential customer. The kind of work that goes into the making o f opinion polls is heavily dependent on inductive reasoning. The pollster endeavors to put forward what he hopes will be reliable generalizations about large classes of people. Because it would be impossible ever to conduct a complete enumeration of the classes of the size he typically deals with, he must focus on a carefully selected portion of a class— the sample. Once the population and character of the sample is determined, the actual polling is usually done as expeditiously as possible, for the value of a poll very often depends on its timeliness. The major polling agencies have brought an appreciable amount of so p h istic a tio n to the p ro cess o f p u ttin g to g e th e r sam ples w hose representativeness is attested to by the degree of accuracy that many polls have managed to achieve; for example, in predicting the outcome of elections. The classes with which these polls deal are often enormous in size, containing millions of members— e.g., the American electorate— but the number of members in the sample is often well under two thousand. Again, given the accuracy of many of these polls, this vouches for the kind of care that goes into the assemblage of the samples. It also reinforces a point made above, that a large sample, just as such, need not necessarily be truly representative. But, however impressive might be the quality of the inductive reasoning that can go into the making of polls, there are a couple of balancing considerations regarding the whole process which are worth bearing in mind. The first is that opinion polls can be used for a wide variety of less than edifying purposes. The very nature of the process is such that it is open to dishonest manipulation on the part of people who are not at all concerned, in creating and conducting their polls, with coming up with an unbiased reading of public opinion. Blatant dishonesty in poll taking is principally evidenced (a) in the assemblage of the sample, and (b) in the composition of the questions that make up the poll itself. A sample can be so assembled that it is not at all representative of the population of a given class, but reflects only a carefully

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selected segment o f the class, whose members— and this is the point of skewing things in this way— are very likely to respond to the poll in ju st the way the pollster wants them to respond. Then there is the makeup of the poll itself, i.e., the questions it contains. G reat care, not to say positive deviousness in some cases, is taken by the pollster in phrasing the questions, so as to elicit from those surveyed the responses he is looking for. Polls o f this sort, which are the products of an abuse of inductive reasoning, fraudulently claim to be accurately reflecting public opinion— when in fact their actual purpose is to shape public opinion. A second consideration regarding opinion polls relates to the obvious but perhaps insufficiently reflected on fact that what they are exclusively concerned w ith, after all, is opinion, one o f the most unsubstantial and ephemeral commodities on the face of the earth. Let us say that we have a polling agency w hich is im peccably honest and conscientious, consistently follow ing procedures which are a credit to inductive reasoning. The samples they assemble are models o f scientific expertise, and the questions contained in their polls are conscientiously formulated so as to exclude any bias, and are happily free of the “leading” question. But with all that, the end product remains the same— opinion. Opinion is not knowledge, is in fact but a poor substitute for knowledge. The results o f a poll may solemnly inform us, and with a respectable degree of accuracy, that 57.8% of Americans are of the opinion that X is not Y. That may count as an interesting bit of information from a purely sociological or historical point o f view, but looked at from the point of view of logic, a point of view w hose concern is not with how people think X and Y are related, but rather with how, as a matter o f fact, they are related. And what if, speaking of matters o f fact, it so happens that X is Y? Inductive R easoning

and the

S ocial S ciences

Almost all o f our discussion of inductive reasoning has had to d© with the ways it is applied to physical nature, for the purpose of discovering the causes operative therein. But inductive reasoning is by no means limited to that field of inquiry, as is exemplified in the case of opinion polls. And of course we are using inductive reason continuously in our daily lives, albeit more often than not in rather loose ad hoc fashion. Another important field o f inquiry for inductive reasoning, besides physical nature, is the vast, diversely complex, and endlessly interesting field of human behavior, the field to which the social sciences give their full investigative attention. Disciplines such as history, political science, sociology, economics and psychology are each in its own specialized way dedicated to the discovery of causes, in this case the causes of human behavior, be it individual or collective. And at least some of the social sciences— one thinks especially of economics in this respect— attempt to establish laws which presumably are to be understood as roughly analogous to

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the laws that govern physical nature. So, then, inductive reasoning is put to work in investigating the realm of the human as well as that of the non-human. However, important differences are to be noted regarding how it operates in those two realms. The biggest difference pertains to the peculiar quality of the cause/effect relation as found in each realm. The physical realm is one in which necessity reigns supreme; this is the foundational explanation for the uniformity of nature, the stable regularities which constitute the physical world, and which make scientific prediction possible. It is not always easy to discover physical causes, but once identified they can be relied on to come through for us with unfailing consistency. In the physical universe everything acts for the sake of preestablished ends, determinate resolution points that are fixed and invariable. This state of affairs is, to say the least, quite helpful for the empirical scientists, for, given the right conditions, a known physical cause will necessarily produce the effect proper to it. The social sciences, with their focus on human behavior, are working within a realm that is radically different from that of physical nature, and what spells the difference is that rather remarkable phenomenon called free will. In the large and often tumultuous arena that constitutes human behavior, there are any number of physical causes that exercise significant shaping and limiting effects on our activities. A human being, as a physical body, is, for example, as subject to the law of gravity as is Mother Earth’s moon, or any other physical body. But of the many causes that shape, limit, and direct human activity, there is free will, and this is by far and away the most important one. The human will is a very special kind of cause because it is free, not necessitated, as are all the causes we find in physical nature. Because the human will is a free cause, the specific way in which it will exercise its power in any given instance is, to put it mildly, very difficult to say. It is not that human behavior is entirely unpredictable, but it is subject to more or less accurate prediction only within rather broad parameters, and as relating to large groups of people rather than to individuals. One can take a statistical stab at how most people are likely to act in a situation of a given kind, but it is virtually impossible to predict how Joe or Jane will act in that same situation. When it comes to the actions of individuals, it is mostly a matter of guesswork. Terms like “cause” and “law” cannot be applied in the social sciences in precisely the same way as they are in the physical sciences. Economists, for example, may, after the fact, spell out the putative causes for specific instances of phenomena like recessions, depressions, an inflated currency, and rises and falls in the stock market, but these phenomena are not to be compared to the purely physical phenomena of the natural world, which are subject to fixed and invariable laws that cannot be thwarted. The ultimate originating source of the actions and antics o f “economic man” is human free will, and that is what renders making reliable predictions about them so notoriously difficult.

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Some thinkers have had the boldness to suggest that human history is to be conceived as analyzable in ways not fundam entally unlike how we analyze physical nature. Thus, according to them, human history is governed by laws as rigid and unyielding as those which make the m oon go around our globe. This being so, all the perspicacious scientific historian has to do is to discover those laws, and, with them he can then not only give us a full explanation of the meaning o f the past, but also inform us exactly as to the unfolding of the future. In doing the latter, he is not trafficking in idle hypotheses, but simply stating what m ust inevitably happen, given the laws o f hum an history which he has discovered. Is this responsible inductive reasoning? Is this science? We needed only to wait and see to find out. Tim e passed. But the supposedly inevitable failed to transpire, according to the particulars and timetable which had been confidently predicated by the historian. The purportedly implacable laws of history rose like acrid smoke from Joe Stalin’s pipe, and disappeared into the sometimes thin but always bracing air o f reality. Inductive reasoning can be employed productively within the social sciences so long as we keep in mind the tentativeness of the findings they make available to us. Recall the general guidelines that, follow ing Coffey, were laid down earlier, particularly the item that cautioned us against looking for a degree of certitude greater than a particular subject m atter is capable of providing. We should not expect to find, in the social sciences, the kind o f sure and stable knowledge which, through the assiduous application of inductive reasoning, is available to us through the physical sciences. A

rgument by

A nalogy

Analogical reasoning is based on the making of comparisons. We are always thinking analogously, because we are forever making comparisons. Whenever we learn anything new, for example, we compare what we are coming to know with what we already know, then we integrate the new with the old. Earlier in this chapter we saw how analogical reasoning figures in the forming of hypotheses: our hypothesis that A is the cause o f X gains considerable weight by the fact that A bears a close resem blance to B, as does X to Y, when we already know that B is the cause of Y. The basic idea behind an argument from analogy is quite simple, and runs according to the following line of reasoning: two things, or events, A and B, are compared, and it is shown that they have several salient features in common; it is further pointed out that because an additional feature of signal importance, Z, is possessed by A, we may infer that the same feature is also to be found in B. O f the two item s being compared, A and B, there must be no ambiguity about the fact that one of them, A, possesses the feature Z. But it is an open question whether that feature is also possessed by B. The whole purpose of the argument, then, is to show that, because A and B have so many other features

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in common, it is reasonable to suppose that they would have this feature in common as well. The basic pattern of the argument can be mapped out thus: (1) (2) (3) (4) (5)

Object A has features V, W, X, Y. Object B also has features V, W, X, Y. Object A, besides features V, W, X, Y, possesses feature Z as well. It is debatable, on the face of it, whether Object B possesses feature Z. However, on the strength of the fact that Object A and Object B have V, W, X, Y in common, we infer that they also have Z in common.

We immediately recognize this as an inductive argument in that (a) it is based on an enumeration of singulars (in this case, the specific features shared by Object A and Object B), and (b) its conclusion is clearly probable. There is obviously no necessity in the fact that, because objects have several features in common, they must, just for that reason, have an additional feature in common. It does not follow, as being necessarily true. And it would certainly be reckless to argue that because two objects are similar in several important respects, they are similar in all important respects. Nonetheless, the argument from analogy, if carefully constructed and used temperately, can have real force to it. There is nothing untoward or irresponsible in arguing that, on the basis of two things having several important things in common (this would have to be established as a firm matter of fact), it is reasonable to suppose that they may have other important things in common as well. At least the matter would be worthy of further investigation. The strength of an argument by analogy depends entirely on the value of the specific points of comparisons that are made regarding any two objects. Are they really important features o f the objects? A large number of points of comparison, just in themselves, does not provide a sound basis for a compelling argument by analogy, for they may be of peripheral importance, not bearing any direct relation to what is essential about either object. An often cited example of a poor analogy is the case where someone wants to argue that the mouse and the elephant are very much alike because they both have a mouth, two eyes, two ears, four feet, and a tail, but the rather significant feature of their comparative size is left out of the picture. The argument by analogy is often used by historians and political theorists, and often intended by them to serve predictive purposes. For example, one occasionally runs across comparisons being made between the decadent social conditions that preceded the fall of the Roman Empire, and the present state of European culture. Various features of the declining Roman civilization are cited, and then comparable features are said to be found in contemporary Europe. The somber conclusion of the argument, put in the starkest terms, is that Western Europe will eventually collapse into political and social disarray, just as did ancient Rome, because it is now suffering from ills much like those suffered by Rome before it collapsed. As with all arguments by analogy, the strength of this one depends on the pertinence of the points of comparison between the

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two situations. And then there is this question to be asked: Granting, for the sake o f argum ent, the existence o f some real sim ilarities between the two situations, might it not be the case that there are also differences, which are just as real, and which in fact outweigh the similarities? Every com parison m ust o f course involve a m inim um o f two objects. Theoretically, there is no limit to the number of objects which can be compared in an argument by analogy, but practical considerations should set limits to just how many are actually used. To attem pt to handle more than two objects can prove cumbersome, and tends to diminish, I believe, the potential effectiveness of the argument.

Review Items 1. What, in general, distinguishes deductive and inductive reasoning? 2. Explain how these two ways of reasoning are necessarily related to one another. 3. W here does inductive reasoning begin, that is, with what kind of knowledge? 4. Describe in general terms what we mean by the uniformity of nature. W hat is its importance for inductive reasoning? 5. W hat two activities are essential to the scientific method? 6. W hat are some of the general principles one should keep in mind in forming viable hypotheses? 7. W hat are the canons of induction, as systematized by John Stuart Mill? 8. Explain the function o f the sample in inductive reasoning. 9. W hat qualifications should be made regarding inductive reasoning as it is applied to the social sciences? 10. Explain argument by analogy.

Exercises A. Each of the propositions listed below are to be taken as generalizations that were the culmination of a process of inductive reasoning. For each of them provide at least two items that would support the generalization. You may, if you wish, argue the point of view opposite to the one stated in the proposition. 1. 2. 3. 4.

U. S. involvement in World W ar Two was unavoidable. W estern civilization is now in a state of steady decline. It is not fit that women should be on the battlefield as combatants. Children should be carefully monitored with regard to the quantity and the quality of the television they are permitted to watch.

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5. Computers are in every respect a positive aid to a more effective education. 6. In education, it is a bad idea to put too much emphasis on memorization. 7. Regular exercise is imperative for good physical and mental health. 8. The study of logic should be part of every high school curriculum. 9. The so-called right to abortion is a specious right. 10. Any law that has its source in a duly established legislative body must be obeyed by the citizens of the country which that legislative body governs. B. A hypothesis is a tentative explanation for a certain situation or state of affairs. For each of the situations described below, provide what you would regard as a reasonable explanatory hypothesis. 1. In recent months cockroaches have shown up in great numbers in the house at 678 Lousy Lane. 2. Johnny Jumbo, age 11, has gained 30 pounds over the last six months, but at the family meals he just picks at his food, hardly eating anything at all. 3. Though all the doors and windows were locked, and there was no visible damage to the house resulting from a forced break-in, we found our very expensive sound system was missing when we returned from a two-week summer vacation. 4. The Peoria Powerhouses have (a) one of the best rosters in professional football, (b) an excellent coaching staff, and (c) fiercely loyal fans. But they have lost their last six games in a row. 5. There has been a sharp rise in unemployment, prices have gone up across the board, and the stock market is falling precipitously. 6. I am told that Professor Fidget showed a great deal of anger when he passed back the quizzes in his biology class this morning. 7. An old beat-up edition of Peter Piper’s The Metaphysics o f Marbles, published in 1874, costs $ 142, and yet you can buy a modem reprint of the book for only $17.95. 8. The extremely rich Baron Bertram Budinsky, in perfect health, died * suddenly right after having tea with his impoverished niece Natasha, and just two days after he had made out his will. 9. All of the students in Mr. Pockle’s advanced placement geometry class are doing very poorly. 10. A large percentage of American college graduates could not correctly identify the name James Madison, nor give even approximately accurate dates for the Civil War and the Korean War, nor say how many times Franklin Roosevelt was elected president.

A

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C. Listed below are a number of possible cause/effect relations. In each case decide whether you think the relation is reasonably strong, or weak. 1. Hypothetical cause: Mrs. Steamboat viewing the movie Rambo. Hypothetical effect: Mrs. Steamboat naming her next child “Rambo.” 2. Hypothetical cause: I had lunch today at a “greasy spoon” cafe. Hypothetical effect: Later in the afternoon I had an upset stomach. 3. Hypothetical cause: Miriam, age 5, hops and skips around the living room, saying, “Look at me, I’m a ballet dancer!” Hypothetical effect: Her sister Betty, age 3, hops and skips around the living room, saying, “Look at me, I ’m a belly dancer!” 4. Hypothetical cause: A genuinely friendly, willing-to-assist frame of mind Hypothetical effect: A smile. 5. Hypothetical cause: Irresponsible carelessness on the part of one or both drivers. Hypothetical effect: Collision o f two cars. 6. Hypothetical cause: Sheer stupidity on the part o f the student. Hypothetical effect: Failing grade in Introduction to Economics course. D. In the examples listed below, “A” represents a cause, and “B” an effect. In each case determine whether the analysis that accompanies the description of the situation is justifiable. If it is not, explain why it is not. 1. Situation: B is present, but A is absent. Analysis: B cannot be caused by A. 2. Situation: Both A and B are present. Analysis: A must be the one and only cause o f B. 3. Situation: A is present, but B is absent. Analysis: A may be the cause of B. 4. Situation: A varies in the manner x, y, z. Analysis: B also varies in the m anner x, y, z, and therefore may be caused by A. 5. Situation: B alone is present. Analysis: It is possible that it may not have a cause. 6. Situation: First A occurs, then, a few minutes later, B occurs. Analysis: A is necessarily the cause of B.

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Chapter Fifteen Fallacious Reasoning W hat I s Fallacious R easoning ? Fallacious reasoning, described in the broadest terms, is simply mistaken reasoning, reasoning which, because of one faulty mental move or another, and whether done intentionally or unintentionally, has gotten off track, and is no longer heading toward that end which our intellectual energies should always be directed—the truth. We all make mistakes in reasoning, but the hope is that, when we do, it is never with malice of forethought. Of course we are also on the receiving end of mistaken reasoning, which comes at us from a variety of sources, and, given the world in which we live, on pretty much a nonstop basis. This fallacious reasoning, like our own, may be unintentional but in a good many cases, more than it is pleasant to admit, it is quite deliberate. Its purpose is to deceive. And so it has been, all too often, since time immemorial. The linguistic origin of “fallacy” is instructive in this regard. Our English word comes from the Latin noun fallacia, which translates as “deceit,” “trick,” “fraud.” What this suggests, then, is that fallacious reasoning, insofar as it is intentional, has a moral dimension to it. To want deliberately to deceive people through reasoning does not necessarily indicate a lack of intelligence on the part of the deceiver, but always a lack of character. Fallacious reasoning has to be battled against on two fronts. First of all, it has to be battled against on the home front, that is, in ourselves. It goes without saying that we should never deliberately engage in fallacious reasoning, for this is to abuse the mind and sabotage the very purpose of language. What we need most to guard against is mental laziness, inattention to the task at hand, which allows us to lapse into sloppy thinking. There are what we can call honest mistakes in reasoning, mistakes which slip in here and there in spite of ourselves, a sober reminder, if we needed one, of the fallibility of the human intellect. But sometimes those so-called honest mistakes are not so “honest’ after all, and that is because they result from carelessness on our part. They could have been avoided, had we been more attentive to what we were doing. Secondly, fallacious

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reasoning has to be battled against in the public forum. This is principally a matter of defensive warfare, in which we endeavor to protect ourselves against the damaging effects of the fallacious reasoning everywhere round about us. The first line o f defense here is the kind of knowledge which allows us to be able to spot fallacious reasoning when we see it. When it manifests itself in a fully developed argument, much fallacious reasoning is generally interpretable as a form of the non sequitur mistake. That is to say, we have a situation, in an argument, where there is a breakdown between premisses and conclusion of the sort that the premisses simply do not support the conclusion, and therefore we say that the conclusion “does not follow ” from them, that is, in a logically meaningful way. O f course the conclusion could follow the premisses in a purely physical fashion, in that it comes after them on the printed page, but that is trivial. The important point is that the conclusion cannot be accepted as true on the basis of the information provided to us by the premisses. There is no standard, universally agreed upon list of fallacies. Indeed, it is highly improbable that any such list could ever be compiled, for the various ways we can go wrong in reasoning are countless. However, there are certain and oft repeated patterns to be discerned, certain types of mistakes that the human mind makes again and again, for even in the matter of mis-reasoning the limitations of our originality are much in evidence. The fallacies which I have assem bled for this chapter represent, I believe, those which are most commonly committed, and which therefore deserve to have attention called to them in a logic textbook. Each of them is distinct enough, but you will notice that, looked at from the point of view of certain basic kinds of mistakes— such as the non sequitur already mentioned, or hasty conclusion, or missing the point, or using emotion as a diversionary tactic— that there is a fair amount of overlapping to be found among them, and a particular fallacy can sometimes be correctly identified in more than one way. Many of the fallacies have fixed names, others do not. Names are of course important, but, in studying the fallacies, it is more important to understand the nature of the problem which a particular fallacy represents, than to be able to affix the right label to it without that understanding. Whenever a fallacy has a fixed, traditional name, I employ it. Several of these names are in Latin, in which case I supply what I regard as a helpful translation of each. When I give my own names to fallacies (i.e., to those without fixed names), I try to make the names clearly descriptive of the essential nature of the fallacy in question. (See Appendix A for a discussion of the element of deception in fallacious reasoning.)

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W hy Study Fallacious R easoning? The brunt of this book has been given over to all matters pertaining to the right way of reasoning, and that is just as it should be. But is it appropriate that we should be spending any time at all, here in this final chapter, considering the various ways in which reasoning can go wrong? Might it not be regarded as little more than a waste of time, a prolonged distraction, or, worse, as a positive danger, in that, by learning about bad reasoning, we might pick up some bad habits and thus turn out to be fallacious reasoners ourselves, and rather proficient ones at that? Whatever worries you might be entertaining along those lines can be safely put to rest. “We shall have a better grasp of the ways in which we ought to think,” Dr. Coffey writes, “when we have contrasted these with the ways in which we ought not to think.” 25 In mastering logic, as in mastering any other skill, the first order of business is of course to know how things go right, but it is also important—and I am almost tempted to say equally important—to know how things go wrong. Often doing things right is chiefly a matter of conscientiously avoiding doing them wrong, but in order successfully to engage in this kind of avoidance strategy, one must be aware of just how, specifically, things can go wrong. A good athletic coach teaches his players not only how to make the right moves, but also takes great pains to point out the moves that must be eschewed. A knowledge of the basic patterns of fallacious reasoning, then, is unquestionably beneficial, in the first instance, for the sake of our own right reasoning. But it is also beneficial, and perhaps more importantly so, as a defense against the bad reasoning that we have to contend with on a fairly regular basis. If we are aware of the specific ways that reasoning can be abused, we will be made protectively alert to them, and will be much less likely to be victimized by those who traffic in fallacious modes of argument. F ormal

and

Informal Fallacies

In the early pages of this book attention was called to the distinction between formal and informal logic, the first having to do principally with the form, the structure, of our thought as expressed in language, and the second dealing with the material content of our thought, which is to say, ideas. There is a comparable distinction which we apply to fallacies, marking the difference between the formal fallacies and the informal, or material, fallacies. A formal fallacy, as its name indicates, is one which relates to the formal makeup of our arguments. We have in previous chapters, where deductive reasoning was discussed, already given a considerable amount of attention to the formal fallacies, particularly in pointing out the various kinds of mistakes that can be made in syllogistic arguments. We saw that a structurally defective argument, that is, an invalid argument, will not guarantee a true conclusion, even though the premisses are

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true. An invalid argument is one which is beset by a formal fallacy. All of the invalid moods of the syllogism are formally fallacious; they represent, by dint of their structure, mistaken ways of reasoning. Informal, or material, fallacies have to do with the ideas which make up the contents of our arguments. Because they are principally concerned with ideas, the basic stuff of our thought, the informal fallacies give full exposure to the various ways the mind can go wrong. After a brief general review of the formal fallacies, we will devote the greater part of our attention in this chapter to the informal fallacies. G eneral R eview

of the

F ormal Fallacies

The six rules of the syllogism, or more precisely the violation of those rules, provide us with prominent examples of formal fallacies, for what effectively happens when a rule is violated is that the form of the argument is so altered that it can no longer function properly as a vehicle of deductive reasoning. We will now review each of the rules to show how that is so. When the first rule is violated, so that there are more than three terms in the argument, its structure is altered in such a way that no bond can be made between the m inor and the m ajor terms, hence no conclusion follows. We recall the principle of the identifying third, which tells us that if two things (e.g., minor term and major term) are identical to a third (e.g., the middle term), then they are identical to one another, and this is the underlying logic of a syllogistic argum ent which ends with an affirmative conclusion. But in a four-term syllogism there is no single “third thing” to which the other two things can establish identity. The second rule is violated when either the minor or the major term, as they appear in the conclusion, are distributed, but in the premisses they are undistributed. With this, the scene is set for the illicit logical move from the less general to the more general. Rule three lays it down that the middle term must be distributed at least once; like the first rule, the purpose of this one is to ensure that a connection can be made between minor and m ajor terms. W hen the middle term is undistributed in both of its appearances, the argument suffers a structural defect and the critical connection between minor term and major term is prevented. The fourth rule of the syllogism prohibits two negative premisses, for if both premisses were to be negative the argument would be so structured that any positive connection between terms would be blocked. No necessary conclusion could be drawn as to how the minor term might relate to the major term. And the same holds true if both of the premisses were to be particular propositions, which is disallowed by the fifth rule. Two particular premisses, if both are affirm ative, give rise to an undistributed middle term, and if one is

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affirmative and the other is negative, the result is the illicit move from the less general to the more general. The sixth rule specifies that the weaknesses which are to be found in the premisses, in the form of particularity and negativity, must be displayed in the conclusion. If this is not done, the structure of the argument allows for the illicit move from the less general to the more general, or the argument ends up by making a claim in the conclusion that goes beyond the information which is provided in the premisses. The two invalid ways of arguing in using the mixed hypothetical syllogism— affirming the consequent, and denying the antecedent—brings about a structure that prevents the production of necessary conclusions, which of course undercuts the very purpose of deductive reasoning. As we know, in a mixed hypothetical syllogism a true antecedent guarantees the truth of the consequent, given the logical relation that exists between the two, but it doesn’t work the other way around: a true consequent can tell us nothing for certain about the truth of the antecedent. And while a false consequent falsifies the antecedent, a false antecedent can only leave us in doubt as to the truth value of the consequent. F allacies R elated

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Language

Because language is the means by which ideas are conveyed from one mind to another, it is imperative that the conveyance be entirely reliable. What this means, specifically, is that the language we use in logical discourse must be— first, last, and always— clear and ambiguous. There is a place, even a purpose, for fanciful language in poetry, but not in logic. There are certain ponderous ideas that are difficult enough to grasp when they are expressed in the clearest terms possible, but the task is made considerably more difficult, perhaps rendered impossible, if such ideas are cast in murky and obfuscating language. The importance of clarity in logical language cannot be exaggerated, and the two greatest enemies of clarity are vagueness and ambiguity. Language is vague when it fails to communicate a definite, discernible meaning. Vague language is fog-bound language. Whatever meanings it contains are like ghostly specters that flit about elusively among the words, defying any attempt to give them precise definition. Ambiguous language creates a problem of a different sort. It embodies multiple meanings: they are clear enough in themselves, but often they are in conflict with one another, and we are puzzled as to just which ones we are to accept and which to reject. Three specific problems that inhibit clarity in language are equivocation, amphibole, and the complex question. Equivocation. We are equivocating in our language when we use words or phrases that can have at least two distinct meanings, and the context within which we use them does not make it clear which meaning we are intending to convey. Every language has its store, large or small, of equivocal or ambiguous words, words like, in English, “table” (a piece of furniture, a list or orderly

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display of data, a plateau), “trunk" (the main axis of a tree, the center section of the human body, a large container, the proboscis of an elephant), and “horn" (a hard boney structure growing out of the head of certain animals, a musical instrument, the warning device of a motor vehicle). Usually the context in which such words are found will tell us which of their several meanings is intended. The following statements, isolated from their context, could give us pause. Lorenzo stood upon the table, lost in a brown study. Cissy’s trunk was full of water. He had only one word for the horn—“ugly." Is Lorenzo standing on a piece of furniture, or on a geological formation? Is Cissy an elephant, or Cal's sister-in-law, and if the latter, what is the trunk being referred to? Is the horn in the third statement a musical instrument, or the distinguishing characteristic of a unicorn? We can end up employing equivocal usage either through carelessness, which is bad enough, or because we have the conscious intention of deceiving people, which is appreciably worse. The formal fallacy of a four-term syllogism is usually brought about by a calculated shift in meaning in one of the terms, usually the middle term. This can be done in so heavy-handed a way that it is quite easy to detect, but subtlety is the order of the day if the perpetrator wants to get away with committing his crime against logic. Consider the following argument. Democracy is government by the people. Many of the world’s governments identify themselves as democracies. Therefore, many of the world’s governments are governments of the people. Words like “democracy,” “justice,” “freedom," “art,” “reasonable,” “love,” and scores more like them bear multiple meanings. Two people can be using any one of those words, such as “freedom,” and yet have in mind entirely different ideas. The tried and true method of avoiding equivocation in argument is always to abide by the admonition: define your terms. If you are going to argue about democracy, begin by telling your audience exactly what you mean by the term. (If you can’t do that, then you shouldn’t be arguing about democracy.) By the way, do you think that the prop