Formal validity in problem solving

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TABLE OP CONTENTS Pag© P REFACE...............................



INTRODU C T I ON..........................



OBJECT OP THE E X P E R I M E N T ..............







. * .......... .



V. CONCLUSIONS............................ VI.

C O M M E N T S ..............................

36 38

APPENDICES APPENDIX A. SURVEY OP LITERATURE Introduction..................... ..


Literature Pertaining to Rhetoric

• •


Literature Pertaining to Logic , . . •


Experimental L i t e r a t u r e ......



............. Introduction The relation of Formal Validity to .............. Problem Solving The Laws of Thought • The Nature of Formal L o g i c ....... Validity and Form . . • • . ....... Form or Structure in Argument • •• •

II.Terms, Propositions, Premises . . . . . . A. On the Nature of T e r m s ...... 6B 1. On the Representation of Terms • . 2. Assignment on Terms . . . . . . . B. On the Nature of Propositions • • • • 1. Propositions as to Quality and Quantity..................... 2. The distribution of Terms . . . . 3. Assignment on Propositions . . . . *


IB IB IB 2B 3B 4B 6B 7B 7B 8B 8B 8B 9B

C. D. III.


The Proposition as aPremise........ 1. The structure of aSyllogism.... 2. Assignment on Premises..... Assignment materials on Section II..

The Categorical Syllogism.......... 13R A. The Nature of the Syllogism.... 13B B. Rules of the Syllogism.......... 14B 1. Rule 1 ..........................2. Rule 2 .......................... 3. Rule 3 ...................... 4. Rule 4 ...................... 5 . Rule 5 . .... 6 . Rule 6 .. . ............ 7 . Rule 7 ...... ............... 8. Assignment on Rules of the Syllogism.................. 17B C. Moods and Figures of the Syllogism.. 1. The First Figure...... .... ..... 2. The Second Figure.............. 3. The Third Figure...... ... ...... 4. The Fourth Figure.............. D. Assignment materials on the Syllogism Of Conditional Arguments........... A. Of H^potheticals . ........ B. Of Disjunctives.................


The Enthvrneme.................


Glossary of Terms.............


Suggested Readings ............


Test, Form A .................. .


Test, Form B ....... .......... . APPENDIX C Part Part Part Part Part

14B 15B 15B 1CB 16B 1-7B 17B IBB 19B 19B 19B 20B 21B

24B 24B 25B


I. II. Ill * IV. V.


Page 10B 10B 10B 11B

Original Lata Validity.... Reliahilitv.. Item Analysis Results ......


Part I, Part II. Part III.

Psychology: of Thinking. . . . Argumentation and I>Lnte.« Logic and Reasoning......

ID 4D 5D

PREFACE THE PLACE OF THE SYLLOGISM IN RHETORICAL THEORY The rhetorical and logical systems developed by Aristotle have exerted a tremendous influence for more than 2000 years.

These systems as conceived by Aristotle

are closely related, as the following statement from the Rhetoric^* reveals t 01?thymeme, again, Is a kind of syllogism: now every kind of syllogism falls within the province of Dialectic, and must be examined under Dialectic as a whole, or under some branch of it. Consequently the t^e clear©st insight into the nature of syllogisms, who knows from what premises and in what ?6y may 5® COI*structed, will also be the most ent3?yra^s* once he had mastered special province th3-ngs contingent and uncertain such as human actions and their consequen­ ces:), and has learnt the differences between enthymemes and logical syllogisms. The Middle Ages, dominated by the authoritarianism the Church, witnessed the decadence and distortion of both the rhetorical and logical systems.

Rhetoric, during

this period, was concerned primarily with style and delivery.

Logic was used as a coercive device for support

of dogmatic views of the Church.

The "Logic of Consistency"

conceived by Aristotle became a "Logic of Authority" during this period.

Cooper (translator), The Rhetoric y - Aristotle. New Yorks D. Appleton-Century Company, 1932 , ieX P* 5.


Th® Renaissance and Reformation brought about a new era in history* in a new way* question*

Men began to examine the world about them "What are the facts?" became a paramount

The revolt against the authoritarianism of the

Middle Ages witnessed men like Peter Ramus defending such theses as "Everything that Aristotle said is falsa." Explanation for this revolt in its several forms can be found in at least two circumstances: (1) It must be remem­ bered that during the Middle Ages the Rhetoric of Aristotle and the better logical works of Aristotle and other Classical writers were lost; (2) It must also be kept in mind that the criticisms of this period by men like Ramus were not criticisms of the "real" Aristotle but of the "received" Aristotle.

Therefore, it is only natural that,

once started, criticisms of the logical system of Aristotle have continued to the present day*

These criticisms center

on the "deductive" syllogism as treated in the Prior Analytics*

The criticisms stem from two principal sources*

First, justified criticism of the syllogism as distorted by Medieval Scholasticism, and second, criticisms arising from a lack of understanding of the nature and fuction of the syllogism. The writings of Locke,1 Campbell,2 Bacon,3 Schiller,4 SIdgwick,5 and others have perpetuated these criticisms, ^John Locke, An Essay Concerning Human Understanding, 23rd ed. London: 1817“:; ' a


and they are oft repeated in the writings of today. What are some of these cCriticisms and how valid are they?

Campbell, tacking his point of view from Locke,

condemns the syllogism as useless since f,it does not aid in the discovery of truth*11 This objection is answered clearly in the following statement by Edney: It is evident that Campbell had given Aristotlefs discovery the benefit of no more study than had John Locke* Campbell*s discussion Ignores Aristotle*s acknowledgment that the first principles of science are learned by Induction as well as the fact that Aristotle’s only purpose in proposing the syllogism waa to lay down the conditions by which science could "be sure of the validity of each step it takes*n Campbell makes a second indictment that has been made by many other writers that the syllogism Is useless because of an alleged inherent petitio princlppii * This charge Is answered by Whatel^as follows: Such an objection against Aristotle’s dictum* no one has ever attempted to establish by any kind of proof; but it has often been taken for granted; it being (as has been stated) very commonly supposed* without examination, that the syllogism is m distinct kind of argument, and that the rules of It accordingiy"cTo not apply, nor were Intended to apply, to all 2

George Campbell, The Philosophy of Rhetoric, 7th ed London: 1823. ^Francis Bacon, Novum Organum. London: W. Pickering, “ ^P*C*S* Schiller, Formal Logic: A Scientific and Social Problem. London: Macmillan and Company, Limited7~1912 1850.

5Alfred Sidgwick, The Application of Logic. London: Macmillan and Company, Limited, 1910• ^■C.W. Edney, ”George Campbell’s Theory of Logical Truth," Speech Monographs * Vol. XV, 1948, 19-32. (p. 31) ill.

reasoning whatever. Under this misapprehension, Dr. Campbell labors with some ingenuity, and not without an air of plausibility, to show that every syllogism must be futile and worthless, because the premises virtually assert the conclusion: little dreaming, of course, that his objections, however specious, lie against the process of reasoning Itself, universally; and will therefore, o? course, apply to those very arguments which he is himself adducing. Among modern writers, Nichols,^* taking his point of view from SIdgwick deals most severely with the syllo­ gism.

The following Is the essence of the criticism*

It remained for Professor Alfred Sidgwick in comparatively modern times to deal syllogistic logic a truly desperate thrust. He exposed the fact that whenever any actual, truth-discovering reasoning was necessary, the middle term was always ambiguous, it was never identical; and the syllo­ gism was merely an ex post facto structure, forakulated after the actual reasoning had been done* Thus when we follow Professor Sidgwick*s exposure to Its ultimate consequence, the syllogism is discovered to be almost useless. If the middle term is obviously the Same, as in the "mortality of Socrates" example, then the conclusion is selfevident; and even Euclid did not think it necessary to reason about axioms. On the other hand, If the middle terms in both premises are not obviously identical, then we must compare them, and again the syllogism Is futile. It cannot assure us of the Identity of the middle term, hence It cannot guar­ antee its conclusion; and the correct conclusion Is after all the entire objective of reasoning* In the first Instance the syllogism is puerile; In the second It is Incompetent* This criticism is answered effectively by Whately2 In the following statement: 2Richard Whately, Elements of Logic. William Jackson, 1832, pp. 26-27.

New York:

^*Alan Nichols, Discussion and Debate. New York: Harcourt, Brace and Company, 1$4i, pp. 3&4-337. 2Whately, op* eit.» p. 122. iv*

The rules already given enable us to develop the principles on which all reasoning Is conducted, whatever be the Subject-matter of it, and to ascertain the validity or fallaciousness of any apparent argument, as far as the form of expression Is concerned; that being alone the proper province of Logic. But it Is evident that we may nevertheless remain liable to be deceived or perplexed in Argument by the assumption of false or doubtful Premises, or by the employment of indistinct or ambiguous fferms; and, accordingly, many Logical writers, wishing to make their systems appear as perfect as possible, have undertaken to give rules "for attaining clear ideas," and for "guiding the judgment"; and fancying or professing themselves successful in this, have consistently enough denom­ inated Logic, the "Art of using the Reason"; which in truth it would be, and would nearly supersede all other studies, if it could of Itself ascertain the meaning of every Term, and the truth or falsity of every Proposition^ in the same manner as it actually can the validity of every Argument. Whately1further clarifies this problem by setting forth a point of view as to the basic function of the syllogism. Logic has usually been considered by these objec­ tors as professing to furnish a peculiar method of reasoning, instead of a method of analyzing that mental process which must invariably take place in all correct reasoning; and accordingly they have contrasted the ordinary mode of reasoning with the syllogistic, and have brought forward with an air of triumph the argumentative skill of many who never learned the system; a mistake no less gross than if anyone should regard Grammar as a peculiar Language, and should contend against its utility, on the ground that many speak correctly who have never studied the principles of Grammar. For logic, which is, as it were, the Grammar of Reasoning, does not bring forward the regular Syllogism as a distinct mode of argumen­ tation, designed to be substituted for any other mode; but as the form to which all Correct reasoning may be ultimately reduced; and which, consequently, serves the purpose (when we are employing Logic as an art) of a test to try the validity of any argument; — Logic is here conceived as the "Grammar- of Reasoning."

The syllogism is the form to which all

^Whately, op. cit., pp. 8-9. v.

reasoning may be reduced for purpose of analysis and for examining the relationships expressed in the premises for "Formal Validity." Another point of confusion has resulted from attempts to apply the logical syllogism to rhetoricaX. discourse without recognizing the difference between logi­ cal syllogisms amd enthymemes or rhetorical syllogisms* The logical syllogism is designed to deal with scientific demonstration or "certainty."

The enthymeme or rhetorical

syllogism, as is pointed out in the quotation from the Rhetoric of Aristotle previously cited, is designed to deal with probabilities.

The logical syllogism requires

that the "middle term" be distributed in every case and the conclusion is "necessary" or "certain."

^he rhetori­

cal syllogism (enthymeme) admits a "middle term" that is only partially distributed and limits its conclusion to probabilities.

The distinction between the logical

syllogism and the rhetorical syllogism (enthymeme), as explained above, should be clearly understood. The limitations of the application of the logical syllogism to rhetorical discourse are explained by McBurney and Hance^* in their discussion of the principles of Continuous Variation and of Probable Inference. 1James Howard McBurney, and Kenneth G. Hance, The Principles and Methods of Discussion. New York: Harpers ana Brothers Publishers, 1939, pp. 199 -201. vi.

The principle of continuous variation does not admit the application of the "law of the excluded middle." In actual life situations it Is difficult to classify everything as A or B, "black or white, sane or insane, etc. No one will deny that there are phenomena that defy classi­ fication.

Attempts to apply the rules of the logical

syllogism to such phenomena are futile.

On the other hand,

it should be pointed out that at times it Is necessary to define, and to categorize or classify. that choices be made.

"Life" demands

On such occasions a knowledge of

the syllogism and the rules of logic can render valuable assistance to the reasoner who is Interested in the accur­ acy of conclusions in that it makes possible the "checking" of conclusions for formal validity. The second limitation which is imposed by Probable Inference, Is based on the concept that the utility of the syllogism is reduced because it can deal only with certainty. It must be admitted that In many areas "certainty" is impossible of achievement. probability.

Action must be based on

All propositions dealing with future time

fall in this category. In view of the above, it might be charged that the syllogism is useless in dealing with probable inference. However, a closer examination of the nature of both the syllogism and probable inference will reveal that this Is vii.

not the case*

As was pointed out in the discussion of the

principle of continuous variation, "Life" demands action. Choices must he made. The rhetorical syllogism, which admits of probabil­ ities, is applicable to probable Inference,

A knowledge

of the rules of logic and of the differences between logical and rhetorical syllogisms make© it possible for the reasoner to test for formal validity conclusions based on probable inference. It should be pointed out that neither the logical nor the rhetorical syllogism is a device for insuring the "material validity" or "truth" of premises.

The function

of the syllogism Is to demonstrate the validity of rela­ tions between premises.

Failure to recognize this fact

has resulted in much of the confusion of many writers, as has been pointed out in the case of Campbell.

Other Objec­

tions have been shown to be invalid In that they are based upon a misconception of the nature and function of the syllogism. The fact that the syllogism is a device for analysis of argument rather than a device for the expression of argument does not decrease its utility.

Rather, when the

writer or speaker constructs an argumentative outline or an argumentative discourse, the pattern inevitably require® the use of enthymemes that are connected by such words as "because," "therefore," etc. In fact the very outline viii.

itself is — except for sections of an expository nature — a series of elided syllogisms with the suppressed premise Implied in each instance*

The use of premises and conclu­

sions is inherent in argumentative discourse*

In spite of

the fact that the relationships are not expressed In com­ plete syllogistic form In the actual discourse as it is written or spoken, they may he expressed in the syllogistic form for purposes of analysis.

This analysis makes pos­

sible the testing of conclusions for validity.


analysis answers the question: "Is the reasoning valid?" which is an important question for the speaker or writer who is interested in the acceptance of his point of view by others.

Since enthymemes are an inherent part of

rhetorical discourse, and since, as Aristotle points out In the quotation cited at the beginning of this discussion that: Consequently the person with the clearest Insight into the nature of syllogisms, who knows from what premises and in what modes they may be constructed, will also be the most expert In regard to enthymemes, once he has mastered their special province (of things contingent and uncertain such as humah actions and their consequences), and has learnt the differ­ ences between enthymemes and logical syllogisms,! it is the contention of the writer that a knowledge of the syllogism Is important to the student of rhetoric. The preceding discussion reveals that the syllogism does have an important place In rhetorical theory.


present study is an attempt to discover the relation of the lAristotle, op. cit. p. 5. Ix.

knowledge of the nature and fuctlon of the syllogism to the process of ^problem-solving*”






The problem of organizing and systematizing know­ ledge has been of concern to men throughout the ages* The Greeks of the fifth and fourth centuries B*C* focused their attention on this problem and the writings and teachings of Greek scholars have> occupied a central place in Western Civilization since that time*

The logical and

rhetorical "systems" of Aristotle have been an important influence In the field of education in general and of speech education in particular* Interest In this area has been the concern of the philosopher, the psychologist and the rhetorician*


various studies and contributions of each have made It a problem that has come to the present day with an ever Increasing emphasis* This emphasis has focused attention today on "critical thinking" and "problem solving" in dealing with social, economic, and political problems.

Representing an

attempt to apply "scientific methods" to problems in this area, this influence has evinced Itself in speech education in courses in discussion, which attempt to apply principles of "critical thinking" and "problem solving" to the oral deliberation of problems.

The steps in this process of

reflective thinking as described by Dewey ares


"(1) a felt difficulty; (2) Its location and definition; (3) suggestion of possible solutions; (4) development by reasoning of the bearings of the suggestions; (5) further observation and experiment leading to its acceptance or rejection; that is, the conclusion of belief or disbelief."*The present, study is an attempt to examine the place of the principles of "formal validity" in the pro­ cess of "problem solving."

In the steps in "reflective

thinking," conclusions must be drawn, and the validity of these conclusions should be checked.

A knowledge of the

principle® of "formal validity" makes it possible to check as to whether or not a conclusion is justified from the premises that have been selected.

A second important

function of the syllogism is that stating an argument In syllogistic form lays It bare for logical inspection, which may reveal important "material" weaknesses. There are many factors Involved in the conclusions we draw and/or the inferences we make*

Many of these

factors have? been investigated in previous studies in both 2 ^ the field of speech and that of psychology* ______ ________________'"H*~TI


------------------------------- — -r-t'



f I

!— ■—

^•John Dewey, How We Think. (Boston: Company, 1910), p. 2


D.C. Heath and

Among them: Alma Johnson, "An Experimental Study In the Analysis and Measurement of Reflective Thinking," Speech Monographs. Vol. X, 1943, pp. 83-96; James Henning, Presumption and the Burden of Proof in Problem-Solving. Northwestern University, UnpublTsHed"^issertation, 1946.; John Keltner, An Experimental Study of the Nature and Training of SkTTl~~In Problem-Formulation and Recognition


"Critical thinking" and "problem solving" are complex processes, and the problem of isolating a single factor for investigation is difficult*

However, the

emphasis upon "problem solving" suggests an evaluation of all those techniques which are a part of the process* What is the place of Formal Validity in problem­ solving?

The following statements from Chapter III of

Reliable Knowledge by Larrabee,^- answer this question clearly and tersely* Group Discussion* Northwestern University, Unpublished 3Tssertation, 1 9 4 ; Karl F* Robinson, "An Experimental Study of the Effects of Group Discussion Upon the Social Attitudes of College Students," Speech Monographs. Vol* VIII, 1941, pp* 34-57; William Smiley Howe11, ^She Effects of High School Debating on Critical Thinking," Speech Monographs * Vol. X, 1943, pp. 96-103.; Winston L* Brembeck, "'Hie Effects of a Course in Argumentation on Critical Thinking Ability," Speech Monographs. Vol. XVI, 1949, pp. 177-189. 2Among them; Violet Z. Lannert, Effects of Abstract­ ness, Previous Knowledge, and Attitude on Reasoning. Northwestern University, Unpublished dissertation, 1946.; James T. Morton, The Distortion of Syllogistic Reasoning Produced by Personal Convict ion. Northwestern University, Unpublished dissertation, 1942.; M.L. Billings, "Problem Solving In Different Fields of Endeavor," American Journal Psychology. Vol. XLVI, 1934, pp. 2 5 9 - 2 P. Carroll, "Can Reasoning Be Taught?" Journal of Education. Vol. CXIV, 1931, pp. 17-21.; B.W. Dally',"lfAbTIity 'of* High School Pupils to Select Essential Data in Solving Problems," Contributions to Education, No* 190, Bureau of Publications, Teachers C/oTTege, Columbia University, 1925.; E. Heidbreder, "An Experimental Study of Thinking," Archives of Psychology, No* 73, 1924.; G.M. Peterson, "An EmpTrTcal Study of the Ability to Generalize," Journal of General Psychology, Vol* VI, 1932, pp. 90-114.; C.C. Pratt, "Experimental Studies of Thought and Reasoning," Psychological Bulletin. Vol* XXV, 1928, pp. 550-551.; M.C. W i l k i n s E f f e c t of Changed Material of Ability to do Formal Syllogistic Reasoning," Archives of Psychology, No. 102, 1928.; R.S. Woodworth and &.G. Sells, "Atmosphere


" That human minds seldom think not surprise us If we recall that consists of rules for testing the thought# and not of prescriptions kinds of thinking.n

In syllogisms should formal logic results of completed in advance for all

tfGiven the premises, does the conclusion follow inevitably? If it can be shown to follow, by all the rigid tests of class inclusion and exclusion embodied in the syllogism, then we have agreed that we are obliged, if we are to be consistent, to accept it as formally valid. 11In determining the reliability of knowledge that apparently follows from accepted premises, however, logicians are concerned with the rules for testing our inferences to see which ones are and which ones are not justified. Their concern Is with the consistency of reasoning. What they want to know Is whether or not a given inference is valid or invalid— that Is, whether or not It can be shown to follow necessarily or Inescapably from the premises upon which It pur­ ports to be based. Now an Inference, to be accepted as valid, must be rigorously demonstrated to rest upon an implication or necessary connection between the premises and the conclusion. "Men may and do quarrel endlessly about what rela­ tions shall be selected in the first place, and about the Initial reliability and exact meaning of those which they choose as premises; but, once they have come to an agreement upon those points, the validity of their subsequent deductions can be checked with entire accuracy by anyone who Is able to make a thorough analysis of the implications involved. Formal logic in its many branches deals with this analysis of Implications* "Only the outline of the combined inductive-deductive method which has emerged need be foreshadowed here. The rise of Induction forced a re-assessment of the potentialities and limitations of deduction as the Effect In Syllogistic Reasoning," Journal of Experimental Psychology. Vol. XVIII, 1935, pp. 451-460. ^Harold A. larrabee, Reliable Knowledge. (New York: Houghton-MIfflin Company, 19451. Chapter III.

6. principal key to the world in which we live. Deduction is no longer regarded as self-sufficient or all-important; and yet without it most of our preoccupation with facts would be fruitless, since we could not fit them into the increasingly deduc­ tive systems which we call sciences. The latter are man's most economical instruments. To realize how powerful a tool deduction can be for the revelation of structures hidden beneath the surface of things, it is only necessary to mention the immense part played by mathematics in all our technical thought.” The preceding quotations provide us with a clear statement of the nature and function of formal logic. Formal Validity refers to the structural accuracy of thought. The rules of Formal logic are the instruments that are used to determine this accuracy, and once we have arrived at a conclusion, we can check the accuracy of that conclusion ^or Formal Validity*

The proposed study is concerned with

the ability to do this checking in the problem-situation.



The purposes of the study may be summarized as follows 1.

To construct a syllabus that will classify the major rhetorical principles of formal logic as shown by a survey of the principal sources of materials on rhetoric and logic.

2. To construct tests that will measure the ability of the student to (a) recognize valid and invalid conclusions, (b) select valid arguments, and (c) construct valid arguments.



To determine the logical validity of the syllabus and tests as shown by the Judgments of a "Board of Expert a" that the material is a representative samp­ ling of the kinds and proportions of the major factors in formal logic*


To determine the empirical validity of the tests as shown by a comparison of scores on related measures which are presumed to have a close relationship to logical abilities of (a) students of superior ability with students of inferior ability as shown by scores on the American Council of Education Psychological Test, (b) students skilled in debate and discussion with students who had had no work in these areas, and (c) scores of college students in a Calculus II class with an equated group who had had no college mathe­ matics*


To determine the reliability of the tests as shown by (a) the inter-correlation of forms A and B when they are administered approximately two weeks apart, and (b) the coefficient of reliability of each of the forms calculated by the method of "Rational Equiva­ lence *11


To determine the effectiveness of a given course of training In the handling of representative test situ­ ations as measured by the significance of difference


In the gains on the tests for the experimental and reliability or control groups given only the test and retest.



Construction of the Manual.

It was discovered that

no single source of Information could be found in the logi­ cal or rhetorical literature that treated adequately all the elements to be studied In this experiment; therefore, it was necessary that a manual of Instruction be con­ structed*

In this connection# it should be pointed out that

a survey of rhetorical literature^* reveals that in practi­ cally all cases the authors treat some aspects of this problem# yet careful examination reveals that none of the treatments Is adequate for the purpose of this study*


survey of the literature2 on logic reveals that in spite of the fact that most of the books treat these elements, the treatment Is not clear as to rhetorical implications; therefore, none of these could be used. The procedure used In the construction of the manual consisted of three principal steps*

First, a survey

of logical and rhetorical literature to determine the ^See Appendix A, Part I, Section A* 2See Appendix A, Part I, Section B.


nature and treatment commonly afforded the syllogism* Second, the construction of a trial manual and its sub­ mission to a MBoard of Experts*”

(On the basis of sugges­

tions and classroom tryout, the manual was revised*) Third, final revision of the manual in its present form*^ The work was started in the summer of 1948*


preliminary outline of topics was drawn up and used in an argumentation and debate class during the first semester of the school year 1948-49*

This experience provided much

helpful information, and it was evident that further clarification and simplification was necessary. During the second semester and the summer of 1949 further work in development was continued.

A trial manual

was developed and used in the instruction of a class in argumentation and debate during the first semester of the 1949-50 school term.

Following this experiment, the manual

was revised into the present form* The length of the manual presented the greatest problem in construction*

Ordinarily, such a unit of

instruction in a conventional course in argumentation should not occupy more than a period of two weeks*


treatment of the material was developed with this idea in mind. Early experiments showed that the necessary topics for treatment were terms, propositions, the categorical ^See Appendix B.


syllogism, (its rules, moods, and figures), condltlonal argument (hypothetical and disjunctive forms) and the enthymeme*

The emphasis in the development of the manual

was to present a complete and clear analysis of the fac­ tors involved in determining the formal validity of argument * Constant efforts were made in class to apply principles to actual situations in the analysis of argu­ ment*

Current newspapers, magazines and speeches were

analyzed for the purpose of making application.


exercises were especially helpful In that they gave the student an understanding of the logical principles being studied*

Due to the fact that this material was to be

presented in a period of not to exceed two weeks and that the persons taking this training would be those who had had no previous training in this area, it was necessary that the material be simplified and illustrated in such a manner that it could be grasped easily and quickly*


objective was kept constantly in mind. The scope and nature of treatment of the materials were conditioned primarily by two factors: First, it waa necessary that all the essential items in determining the formal validity of argument be covered.

Second, it was

necessary that the material be presented in a clear and simple manner so that it could be grasped easily and quickly.


Cons true11on of the Testa*

A survey of existing

tests failed to discover any test that would satisfactorily measure the elements to "be tested in this experiment* Watson-Grlaser1 tests of ”Critical Thinking”


contain some

items of the type used in Part I of the test developed for this experiment; however, they are inadequate in that they fail to cover all aspects of logical reasoning in terms of the moods, figures, and rules of the syllogism, valid and invalid forms*

It was impossible to find a test that

checked the ability of the student to construct or to select an argument based upon an enthymeme* The Johnson test ”Do You Think Straight?”2 has a section on syllogistic reasoning, but it is not complete enough for the purpose of this experiment*

Then too,

Johnson’s test is designed primarily as a test of reflec­ tive thinking, and logical reasoning Is a secondary feature of the test*. Other tests surveyed5 were found to be inadequate. Therefore, it was necessary that tests be constructed which would measure the ability of the student to ^Qoodwin Watson and Edward M. Glaser, Critical Thinking, (New York, 1939).

Tests of

^Alma Johnson, ”Do You Think Straight?” Unpublished dissertation, Northwestern University, 1942. ®Among them* Victor H. Noll, ”What Do You (New Yorks 1934; J. Wayne Wrightstone, ”A Test of Thinking In the Social Studies” (New York, 1939); Thouless, tests appended to How to Think Straight rev* ed*, 1941).

Think?” Critical Robert H. (New York


recognize valid and invalid conclusions in all the moods and figures of the syllogism* check the ability of the student to select valid arguments based upon an enthymeme, and construct valid arguments based upon enthymemes. Construction of the tests paralleled construction of the manual.

Preliminary drafts of the testa, including

all three of the types of exercises used in the final forms, were first used with a class in argumentation and debate during the fall semester of 1948-49.

Further work and

checking on the development of these tests were carried out during the summer of 1949 and again during the first semes­ ter of 1949-50. Originally, approximately 200 items of the type used in Part I were tested.

Fifteen items of the type used

in Part II were constructed, and twenty-five items of the type used in Part III were used.

These tests were admin­

istered to sixty-two students during the first semester of the 1949-50 school year.

These data were analyzed and on

the basis of the information gained the final forms of the tests were constructed. The following procedure was adopted for the con­ struction of the final forms of the test.

For Part I, two

items representing each of the nineteen valid moods of the syllogism of approximately equal difficulty were selected. Second, two items representing the ten most common fallacies as represented by the rule violations were selected.



additional item was constructed for each form of the test to make the total number of thirty items on each form* One-half of these items constitute Form A, the other half Form B of Part I of the test*. Part II of the test was originally composed of two forms of twenty—five items each*

It was discovered that

five carefully selected items were approximately as accur­ ate a measure of a student’s ability on this section of the test as the twenty-five Items.

Therefore, five items were

selected for each form of the test with the following considerations determining the selection: one item was selected for each form In each of the four valid moods of the syllogism in the first figure*

Since the first figure

is the "perfect figure" and the only figure through which all. four types of conclusion may be drawn, these items sur­ vey the ability of the student to draw all four types of conclusion through the syllogism.

The fifth item selected

was an EIO syllogism in the first figure* Part III of the test requires that the student state an enthymeme in the form of a complete syllogism. The enthymemes in this section of the test are so stated that again, as in Part II, the student must construct syllogisms In each of the four valid moods of the first figure, and an additional item, an EIO syllogism in the first figure*


The length of the test was designed so that it could be completed in a single fifty or fifty-fiveminute class period.

Form A and Form B of the test are

equated in that the items are of similar difficulty and the parts of the test are identical on both forms. Tests-.

The assignment of values to

the items in the test presented a major problem. the difficulty of the items varies widely.


For example,

the items in Part X of the test range from very easy to very difficult.

Xn Part XX* the items are more nearly of

equal difficulty; and in Part III* item number 2 calling for the construction of an AXI syllogism in the first figure is much easier than any of the other four items* which are apparently of approximately equal difficulty. However, on the basis of results from the pilot study, the reliability groups and the experimental groups* the following values seemed best to fit the test: each Item in Part I answered correctly* two points; each Item in Part II answered correctly three points; each item in Part III answered correctly, five points. The test as a whole* on this basis* has a value of 100 points.

Part I has a value of 60 points; Part II,

15 points; Part III* 25 points.


TABLE I SCORINGr OF THE TESTS Analysis of the scores of 150 students in terms of the percentages of correct responses on the three parts of of the Logical Reasoning Test F,1


Possible scores (Raw Score) Scores, Form A: (Raw Scored Scores, Form B: (Raw Score)

4500 2000 2016

750 297 307

Possible score: (Weighted Score) Scores, Form A: (Weighted Score) Scores, Form B: (Weighted Score)

9000 4000 4032

Percentage correct, Form A: Percentage correct, Form B:



750 163 190

6000 2460 2513

2250 3750 891 815 921 950

15000 5706 5903

44.4 39.6 21.7 44*8 40.9 25.3

Relation of responses to parts of tests in terms of percent age. Raw Scores

Values Weighted scores

P . l ...... 75# P.2 ...... 12i$ P.3 ...... 12i$ Form A Raw Scores- Weighted scores p.l 81.3$ 70.1$ P. 2 12$ 15.6 B.3 6.7$ 14.3$


....... 15$ ........ 25$ Form B Haw scores Weighted scores 80.2$ 68.3$ 11.8$ 15.6$ 8$ 16.1$


The raw score assigns each item of the test a value of one point; giving Part I, a value of 30 points; Part II, a value of 5 points; and Part III, a value of 5 points; a total of 40 points on the test. Coefficients of reliability and wtw are higher on the weighted scores than on raw scores In all cases; however> both systems of scoring were used. Table 1 presents an analysis of the scores of 150 students, showing the number of correct responses on each part and the percentage of correct responses on each part, raw scores and weighted scores.

Part II of Table I shows

the relation of correct responses to parts of the test in terms of percentages.

The analysis of this Table Indicates

that the weighted scores are a more accurate index than the raw scores. The Validity of the Tests.

Logical validity may

be claimed for the tests on the following bases: First, Part I of the test covers all of the valid moods of the syllogism in all four figures and the ten most common rule violations or invalid moods.

This involves a

knowledge of terms, propositions, and the rules, moods, and figures of the categorical syllogism. Part II involves the selection of valid arguments from a given enthymeme and three major premises, only one of which follows; three minor premises, only one of which follows; and three conclusions, only one of which follows.

17 This section of the test requires that the student relate the over-all syllogistic structure to the enthymeme. These items are so constructed as to require that the student have a knowledge of terms and propositions, and of the rules, moods and figures of the categorical syllo­ gism and the ability to state an enthymeme in complete syllogistic form. Part III of the test requires that the student be able to construct a valid syllogism from a stated enthymeme in each of the four valid moods of the first figure.


again, demands a knowledge of terms, propositions, rules, moods, and figures of the categorical syllogism, and the ability to state an enthymeme in complete syllogistic form. Second, the Items which comprise the test were selected only after they had been checked by a "Board of Experts*w

On the basis of this checking, questionable

items were eliminated, and all Items that were not clear and that resulted in confusion were thrown out or revised before the final forms of the test were constructed. Third, only Items that "measured” were used in the final forms of the test; that is, all Items that were missed by all, or nearly all of the students in preliminary trials and all items that were answered correctly by all or nearly all in preliminary trials were discarded.


as the results reveal, there Is a wide range of difficulty among the items.


Fourth^ the test® were so constructed from the standpoint of selection of items as to present a test for persons who had been trained, as well as those who had not been trained.

This factor presented one of the major

difficulties in the construction of the tests*

While this

arrangement makes the means low for untrained groups, it will be observed that the means for the trained groups are considerably higher and that had the test been made easier, the measuring of the results of training would have been less accurate. Statistical Validity, Statistical validity of the test may be observed from the data in Table II.


number one compares the A.C.E. Psychological Test scores with the Logical Reasoning Test scores of twenty freshman from the upper quartile on the A.C.E. Psychological Test scores with twenty freshman from the lower quartile on the A.C.E. Psychological Test scores. Item two, compares the scores of ten debaters from Amarillo High School with a speech class of non-debaters from the same high school on Form A or the Logical Reasoning Test. Item three, compares the scores of eight debater® from Seminole High School with the scores of a Senior English class from the same high school on Forms A and B of the Logical Reasoning Test.

It should be mentioned that

in this case, six of these debaters were sophomores, one a


junior, and on© a senior, while all the members of the English class were seniors* Item four, compares the Logical Reasoning Test scores of a Calculus II class at Panhandle A. & M. College with scores of students of similar age, sex, and college standing, who had had no college mathematics. It will be noted from Table I, that in all cases the difference of the means is so great as to indicate that there Is little question that those who are high on the A.C.E. Psychological Test will also be high on the Logical Reasoning Test; that students who have had mathe­ matics through Calculus II are definitely superior to students who have had no college mathematics, on the Logical Reasoning test scores; and that debaters are super­ ior to non-debaters on the tests* (See Table II, p. 20). Reliability of the Testa.

Two methods were used

for Investigating the reliability of the tests.

First, the

duplicate test technique was used for establishing the intercorrelation of Forms A and B of the test.

Second, the

method of 11Rational Equivalence”1 was used for computing the reliability of each form of the test* 1 *Henry E. Garrett, Statistics in Psychology and Education. (New York: Longmans, Green and Company, 1947"J• pp. &65-S6. ”The assumption is made In formula (79) that all test items have the same degree of difficulty, i.e., that the same proportion of subjects (but not necessarily the same persons) pass"*each Item. In a power test items are


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