Doctrines of Cassius J. Keyser in relation to argumentation and discussion theories

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NAME AND ADDRESS

DATE

NORTHWESTERN UNIVERSITY

DOCTRINES O F CASSIUS J, KEYSBR IN RELATION TO ARGUMENTATION AND DISCUSSION THEORIES A DISSERTATION SUBMITTED TO THE GRADUATE SCHOOL IN PARTIAL FULFILLMENT OF THE REQUIREMENTS for the degree DOCTOR OF PHILOSOPHY Field of Speech

By ELTON STEWART CARTER Evanston, Illinois August, 1950

ProQuest Number: 10101257

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The present is the age, or the beginning of the age, of doctrinal functions. (C. J. Keyser) The subject of this work is ultimately ’speaking about speaking*. (Alfred Korzybski)

ACKNOWLEDGMENT I wish to express my gratitudes: To Mrs. Sarah Y. Keyser, whose gracious­ ness and perspicuity enabled me to feel acquainted with her husband. To Alfred Korzybski, whose penetrating Insights, broad perspective, and great diplomacy encouraged me to T,look at the old a n e w / ’ To Professor Irving J. Lee, whose guidance has ever been an inspiration.

TABLE O F CONTENTS Chapter

Page PART ONE GENERAL ORIENTATION

I.

I N T R O D U C T I O N ...................................... 2 A. B. C. D. E* F. G.

II.

The Central Focus of the Study.............. 2 Basic A s s u m p t i o n s ................... . . . 3 Questions Which Were Posed. . . . . . . . 4 The Sources and Abstractions of Data. * . 5 Procedures and Methods* .................. 3 L i m i t a t i o n s ..................... . . . * 9 Some Notes to the Reader ................... 12

CASSIUS JACKSON KEYSER, 1862-1947: AN INTRODUCTORY BIOGRAPHY....................... 16 A. B. C. D. E. F.

A Biographical S k e t c h ............. ...16 The Man ......... * ............ ♦ . 20 His Gedankenwelt * ................. 23 Some of His Listinguished Associates. • . 34 Keyser and S p e e c h ..................... . . 4 4 A List of Keyserian Memorabilia . . . . . 51 PART TWO PRESENTATION AND COMPARISON OF DOCTRINES

III.

SOME QUESTIONING OF QUESTIONS AND PSEUDO-QU E S T I O N S ............................55 A. B. C.

Speech Doctrines Concerning Questions . . 56 Keyserian Doctrine of Questions and Pseudo-Questions....................... 59 A Comparison of Question-Doctrines• . . . 63

Chapter IV.

Page PRO POSITIONAL T Y P E S ........................ A. B. C.

V.

B. C.

B. C.

88

Speech Doctrines of Relation, Analogy, Cause and S i g n ........................ 118 Keyserian Doctrines of Relation, Transformation, Function, and Invariance 133 A Comparison of Speech and Keyserian Relation-Doctrines ...................... 158 .

.............. 167

Definition in the Speech S e n s e ....... 168 Defining Terms and Describing Things . • 175 An Exposition of D i f f e r e n c e s ......... 188

THE POSTULATIONAL METHOD AND SOME OF ITS IMPLICATIONS............... A. B. C.

IX.

75 84

Speech Doctrines Related to Verbal Forms ........... 88 Keyserian Doctrines of Variables and Propositional Functions.............. 95 A Comparison of Doctrinal Emphases . . • 110

DEFINITIONS AND DESCRIPTIONS. A. B. C.

VIII.

65

RELATION, TRANSFORMATION, FUNCTION, AND INVARIANCE................................... 114 A.

VII.

Fropositlon-Doctrines In Argumentation ................. and Discussion Keyserian Doctrines of Propositions! Types. . ............................... A Comparison of the Doctrinal Families •

VARIABLES AND PROP0SITIONAL FUNCTIONS . . . . A.

VI.

65

195

Concerning Relevant Speech Theories, . . An Introduction to the Postulational Method . . . . . . ...................... Some Implications of the Postulational Method . . . . . . . . . . . ...........

A SUMMARY OF DOCTRINAL FINDINGS .

196 198 211

............ 223

PART THREE SOME FORWARD-LOOKING ASPECTS X.

CONCLUSIONS, CONJECTURES, RECOMMENDATIONS . .

230

Chapter

Page A. B. C. D.

Some Preliminary Considerations • • . • * If Keyser Were H e r e ? ............• • • • Conjectures About Keyserian Discussion and Argumentation. . . . . . . Recommendations

230 233 260 277

B I B L I O G R A P H Y ...................................... 281

PART ONE GENERAL ORIENTATION

I

i j I

CHAPTER I INTRODUCTION The Central Focus of the Study

j

Doctrines were the central focus of this study; all

else was considered subsidiary. Doctrines may be described as principles, or points jof view, or positions taken on certain issues.

They are not

jlegitimately described as dogmas, but rather as emphases; !for each is an offspring of postulates.

The ^obstetrician”--

the mathematician or logician, perhaps, or the participant In jdiscussion, or the arguer, or the man in the street--usually [attends a multiple birth; the infants are siblings; the famiily is a doctrinal family. j

i

This dissertation concerns three doctrinal families.

|i

;The first family was called Keyserian, named after the central :i-

[jfigure of this study. The appointed head of this family was l; jia man who, like Newton, "stood on the shoulders of giants.” jjHe will be introduced in the next chapter.

The second family

M

(Was called Speech, named after the profession represented by j

argumentation and discussion.

The third family was called

Auxiliary, named after the tangent roles played by its members. The last two families have no appointed heads.

2

The community

leadership was largely Keyserian.

Thus the unity of this

presentation was intended to be not only doctrinal, but also i

[Keyserian. : 'i i !i l! 1 |

B.

Basic Assumptions

One feature of this community leadership was apparent

[at once:

it seemed proper to the Keyserian manner to make

[important assumptions explicit.

Indeed, this study was

i| ]|

ilfounded upon an assumption. It was an Important one: if the I :assumption was not justified, the study itself could not be

|justified.

The assumption was that authors, teachers, and

[students of argumentation and discussion consider potentially [[useful doctrines worthy of serious examination.

Keyserian

j

ijdoctrines were therefore Investigated for the office of po!

itential usefulness.

Thus, the dominant aim of this presen­

tation is to set forth the findings--not to advocate them. For it seems proper that judgment should precede advocacy. But who are the judges? are authors, teachers, cussion.

They have been appointed.

The judges

and students of argumentation and dis­

They may be called the speech scholars.

As they

know, the speech scholars already have jurisdiction. established by precedence.

It was

The logical, psychological, rhe­

torical, and other characteristics of speech doctrines are ^testimony to that fact. And some adoptions of doctrine were II [made. Yet the judges were not compelled to make those adop­ tions, nor are they being compelled in the present case.

The

withholding of advocacy was Intended to encourage reflective

i

!deliberation*

Then, if they wish, the judges may become

'the advocates. i

Another assumption of this study was that argumenta­ tion and discussion theories are not only important, but more important, more ubiquitous, than seems to have been emi|

jlphasized openly in the speech literature examined.

It was

;j

['assumed that whenever an arguer argues or a discusser dis­ cusses, he is inevitably oriented by some theories; that these theories appreciably Influence his performance.

It

will be discovered, or rediscovered, that this assumption is not new.

And it will be discovered that it permeates every

ijchapter of this presentation. Ii C.

Questions W h i c h Were Posed

The generic, and complex, questions posed for this study were:

What, if anything, in the more non-technical^

writings of Cassius J. Keyser, would seem to be of potential 'i value for argumentation and discussion theories? Could his doctrines be meaningfully related to the speech doctrines? What are the more important differences and similitudes be­ tween these two doctrinal families?

Are there any auxiliary

doctrines? If so, what relations may be discovered among ;! lithe three families of the doctrinal community? Would this i ! II ijcomparative method yield any doctrinal residue, thereby sup­ plying the speech scholars with something worthy of serious . 1 j

T

j “Technical," as used in this connection, refers to jtechnical mathematics. That kind of mathematics made no con itribution to this study. This matter is considered In sec. |of this chapter.

(Consideration?

If so, what might be the nature of alterations

|in argumentation and discussion theories, or doctrines, if ;lspeech scholars should choose to move further in the Keyserian |direction? The attempt to an swer these questions led to the examination of relevant literature. X).

The Sources and Abstractions of Data

Except for personal interviews with Mrs. Sarah Y. keyser, Alfred Korzybski, and Professor Edward Kasner, all jof the data were derived from the printed page.

Such deri-

vation, of course, always Involves interpretations and abstractions.

As guidance in the former process, this inves­

tigator tried always to remember a jewel of wisdom written nearly a century a g o : In every instance . * * where a reader finds that his interpretation of an author contradicts the authorfs comments and conclusions, the reader should amend his interpretation, and make it conform to the authorfs comments and conclusions. • • . We read In vain if we look into a book as we look into a mirror, and receive back nothing but a reflection of our own familiar lineaments.* Concerning the abstractions of data, there were two factors.

Perhaps the more important one was the differences

In coverage of sources.

So far as could be determined, all

■jof Keyserfs doctrines were examined.

With the exception of

jKorzybski1s works, most of which were read, the auxiliary 1 ■a

T3

Tohnson, The Meaning of W o r d s , etc. (Originally Milwaukee, Wisconsin: John Windsor Chamberlin,

6 sources were employed without significant concern for cri­ teria of adequate sampling.

But the argumentation and

jdiscussion literature was sampled.

Conseauently:

there is

jj

jjno question of representativeness in (not l!oftr) Keyserian jl jisources; and, the auxiliary sources (employed as interpreItive aids) were not intended to be, and probably are not, j Irepresentative of their respective fields; but the speech S

jsources were intended to be representative of those contemi| jporary argumentation and discussion theories relevant to Keyserian doctrines.

Criteria of adequate sampling are there­

fore relevant to the speech sources, and the bibliography may j

be sufficient evidence that the sample is adequate.

For this

study, however, contingent and favorable circumstances were at work.

First, as Graves attested, the sampleTs reference

class was quite homogeneous:

fl• • • I have done m y full

:share of borrowing from the contributions of other writers l j, in this and allied fields, but the book will probably not be !condemned because it is so much like other b o o k s . A n y o n e t jwho has read at all widely within argumentation and discusjsion sources would probably agree that Graves * statement may h j; 'be safely generalized for most authors in those fields, esjjpecially since Graves wrote one of the more atypical books ij

l!In argumentation and discussion.

The second circumstance Is

jjtied up with a postulated point of view; it is that of stulr

jdent X.

Now student X was enrolled In a course in argumentation,

^H. F. Graves, Argument: Deliberation and Persuasion in Modern Practice (New York: The Cor don Co., 1938), p. v.

7 or discussion, or both, in some American college or univer­ sity, within the past decade*

X, being a typical undergrad­

uate, was expected to study some text and, perhaps, to do some collateral reading* ably encounter?

What speech theories would X prob­

The relevant answer is:

If the speech

sample is representative of its reference class for X , then X would probably encounter theories closely resembling those encountered by the present writer.

Indeed, we might have

encountered many of the same theories.

Of course, the "same”

theory might have been interpreted differently by each of us. But such interpretation must be considered as a joint product of the printed page and its interpreter; hence, If the dif­ ferences occurred, they were largely beyond control.

Further

|more, the reference to the printed page is significant. I i ■it is obvious, yet important, that the textbook and the teacher may not hold the same theories.

It Is therefore pos­

sible that X was taught Keyserian doctrines.

If so, the

teacher, and X, have been remarkably inarticulate. reasonable,

For

It seemed

consequently, to suppose that the speech sample

was fairly representative of X fs doctrinal environment so far as argumentation and discussion were concerned. that doctrinal environment,

And it is

created by speech authors and

teachers, which was assigned a prime importance:

the postu­

lation of student X had three fundamental purposes in this study, no one of which was that of creating a scapegoat for the writer. X.

Quite the contrary; the writer himself was an

The three purposes were:

(1) to provide an economical

8 means for indicating the nature of the writerTs rationale regarding the sources, abstractions, and interpretations of data, thereby describing the writer* s point of view in making those selections, abstractions, and interpretations;

(2) to

place the emphasis upon students, because no study can parade as a contribution to education unless, ultimately, the students derive some benefit from it— any other educational philosophy was and is unthinkable to this writer, involving that variety of nonsense known as a contradiction in terms; and (3) the tfX tt of student X is a variable, and if any one doctrine had been chosen as the key to Keyserian doctrines in general, that doctrine would have been of the variable.

Thus, student

X was postulated as a sheer device or technique or instrument employed as an aid in the exposition of rationale, in the placing of an emphasis, and in the introduction of the cru­ cially important doctrine of the variable on more familiar grounds than would have been possible otherwise.

Thus the

explicit references to student X were extended through an introduction to the variable in Chapter V. How the one factor concerning the abstractions of data was differences in coverage of sources.

The other factor in­

volves the sources as selected, which leads to the next topic. E.

Procedures and Methods

In this investigation, the procedures and methods were, in outline, as follows:

first, the works of Keyser were exa­

mined, and those doctrines which were judged relevant to

9 argumentation and discussion theories were abstracted.

In

doubtful instances, the selections were taken for further reference.

Second, these selections were interpreted, when

assistance was needed, with the aid of selections taken mostly from auxiliary sources. preted,

These doctrines,

as inter­

constituted the Keyserian doctrinal family.

Third,

these Keyserian doctrines were employed as criteria in judg­ ing the relevance of speech doctrines to this study, and se­ lections were made accordingly. also as Interpreted,

These speech doctrines,

constituted the second doctrinal family.

Fourth, these two doctrinal families were repeatedly compared in order to expose their similarities and differences.

Fifth,

the differences were especially scrutinized with a view to possible alterations In argumentation and discussion theories, on the assumption that speech scholars might wish to move further in the Keyserian direction.

Thus it was that the

Keyserian leadership of the doctrinal community controlled the procedures and methods without dictating an a priori set of results. But procedures and methodologies are always limited by attenuating circumstances.

For that reason, limitations

had to be faced. F.

Limitations

The indicated differences in coverage of sources made the limitations of sampling obvious except, perhaps, speech sources.

for the

10 How did this writer erect the limitations of speech sources, thereby choosing some sources rather than others? Probably the clearest view of how they were erected can be obtained by an explanation given as if those limitations had been set up in accordance with suppositions about X.

Since

student X was a college undergraduate, high school materials were excluded.

Since X was enrolled within the past decade,

only the more contemporary materials were considered relevant. Since only the enrollment in argumentation or discussion courses was considered, all other courses were excluded. And since X fs reading for those courses was presumably con­ fined to argumentation and discussion literature, the only logical, psychological, rhetorical, and other "non-speech" doctrines considered were those appearing within that litera­ ture.

Sources tangent to speech were mostly of interpretive

value, being assigned auxiliary roles. Within the speech sources, however, there were further limitations. methods*

These have been indicated by the procedures and

Since the abstractions from speech sources were de­

termined by judging their relevance to Keyserian doctrines, a great deal was omitted.

As examples, this study had little

bo do with topics such as:

(1) the importance of argumentation

or discussion in a democratic society; debate;

(3) techniques of delivery;

(2) discussion versus

(4) honesty,

courtesy,

diplomacy; or (5) whether these activities are to be considered as games, or something else.

11 There was yet another sort of consideration.

Its im­

portance stems from lack of precedence for a speech student focusing upon the doctrines of a mathematician.

Such atypi­

cal behavior calls for explanation. In the first place, this study was not concerned with technical mathematics; there was no attempt to relate such things as algebraic formulas to the concerns of argumentation and discussion.

It will be observed, rather, that the empha­

sis was placed upon certain fundamental notions of mathemati­ cal philosophy.

Keyser seemed to think that these notions

were relevant to pursuits not customarily classified as mathematical*

In the Investigation of argumentation and dis­

cussion as being among those pursuits, no use was made of technical mathematics. of the first:

And a second consideration grew out

some technical aspects of otherwise non­

technical notions were left out because they were considered Irrelevant to the purposes of this study.

Perhaps, for

example, a technical definition of limits is necessary for maximum rigor; nevertheless, the less technical Illustration of a circle was used.

These did not seem to be serious as

limitations, but it did seem necessary to guard against the common misconception that mathematicians are most distinctive because of the symbols they manipulate— a misconception in Keyserfs eyes, at least, and one which he combatted with great diligence.

He excused mathematical laymen from only the tech­

nical knowledge, however, when he said that

12 Innocence of mathematical technique is doubtless venial in all but the professed mathematician. To surrender, however, or run away before every token of precise and rigorous thinking is the shame of culture. 3Instead of running away, this mathematical layman fol­ lowed t he old maxim, "When in perplexity, read on."

He was

encouraged to do so by his "teacher" of Mathematical Philoso­ phy who, in orienting the students toward the course, expressed the sort of approach taken toward mathematical doctrines in this study: It need hardly be said that no one should follow this course in the hope of thereby acquiring mathematical knowledge or skill in the usual sense of these terms. I assume that what is mainly responsible for your presence here Is a desire and a hope of a different kind: you de­ sire to gain insight into the essential nature of mathe­ matics regarded as a distinctive type of thought; you desire to acquire knowledge of what is characteristic and fundamental in mathematical method; you hope to gain ac­ quaintance with some of the great mathematical concepts, with such of the dominant concepts as are accessible to laymen; you desire to win a just sense of the spiritual significance of the science; In a word, your quest is for such an understanding of it as will help you to view mathe­ matics In a vast perspective— in relation, that is, with the other sciences and arts and the other modes and forms of human activity. Such, I take it, are the ends that define our task.^ G* 1.

Some Notes to the Header If the reader Is not familiar with the technical

terminology of mathematical philosophy (and general semantics), he will probably want to read in the order of presentation. J. Keyser, Science and Religion (New Haven: Yale University Press, 1914), pp. 53 f~ 2 C. J* Keyser, Mathematical Philosophy: A Study of Fate and Freedom (New Y o r k : E. P. Dutton and Co., 1922), pp. 6 f .

13 This order, though not sacred, was nevertheless determined by the nature of the doctrines as presented by Keyser:

kinds

of questions were associated with propositional types; doc­ trinal functions presuppose variables and propositional func­ tions, and so on.

Once the terms were introduced, accuracy

and economy demanded their repeated use without repeated clarification of meaning. 2.

A few quotations were used which require an ex­

planation of certain unconventional abbreviations employed by Korzybski in Science and Sanity:

"A" stands for "aristo-

tellan” ; "A” stands for "non-aristotelian"; "el" and "non-el” stand for "elementalistic" and "non-elementalistic" respec­ tively; "m.o" stands for "multiordinal” ; "s.r" stands for "semantic reaction or reactions"; and "etc." is variously designated by

and

These ab­

breviations were not changed because they assisted in eco­ nomizing space. 3.

Both Keyser and Korzybski firmly held that terms

are properly defined only by the undefined terms of their postulate system; and they held that this doctrine applies to every discourse.

How much of this presentation was de­

voted to an explanation of such doctrines.

And in the effort

to practice the doctrines, as well as explain them, no attempt was made to define most of the bedrock terms.

It was left to

the reader, with regret but without solution, to be guided almost entirely by contexts.

14 4.

Of course, the most important concern was to

make Keyserian doctrines clear even at the expense of greater clarity elsewhere*

The basic technique was set forth by

Keyser himself when engaged in a similar pursuit: In so far as practicable Peirce will be permitted to speak for himself* The task of interpreting and evaluating his statements will be left, not indeed wholly but mainly, to the reader. And this task of Interpretation, as the reader need hardly be told, will often require him to examine the statements in the light of the contexts whence they have been re­ spectively taken. ■*Keyser, too, was permitted to speak for himself, even at great length and without interruption.

Why?

For the

sake of accuracy, economy, and clarity; because it did not seem feasible to try to improve upon great writing.

And

Keyser guided his readers with clues, flavor, focus, orien­ tation, advice.

Many of these signposts, deemed helpful for

the traveller among Keyserian doctrines, were left standing. And it was an aim of this presentation, unlike that of K e y s e r 1s on Peirce, to set forth Keyserian doctrines in such a way that the reader would not be required to examine the "contexts whence they have been respectively taken."

Keyser

called such behavior the pursuit of Ideals. In general, this study attempted to enlist the services of Professor Keyser* tion and a biography.

Part One was devoted to this introduc­ Part Two contains the great bulk of

doctrines, with the third through the eighth

chapters sharing

■^C* J. Keyser, "A Glance at Some of the Ideas of Charles Sanders Peirce," Mathematics as a Culture Clue and Other Essays (New York: ScriptTa Mathematics, I94V), p. 156 •

15 a common organization under three sections.

The primary

purpose of each of the three sections was constant through­ out these chapters, with "A” sections devoted to a presen­ tation of speech doctrines, with wBn sections devoted to a presentation of Keyserian doctrines, and with "C" sections devoted to a comparison of the speech and Keyserian doctrines The ninth chapter was a summary of the first eight chapters. Part Three was set aside for the tenth and final chapter, which was devoted to conclusions, conjectures, and recommenda tions• Since the presentation as a whole was about a doctri­ nal community, a general orientation would not have been satisfactory unless the appointed head of that community had been introduced.

CHAPTER II CASSIUS JACKSON KEYSER, 1862-1947: AN INTRODUCTORY BIOGRAPHY The dominant aim of this chapter is to furnish an orientation for the doctrines provided by the central figure of this study.

That aim has determined the means:

(1) to

sketch the highlights of his life, pointing to some reasons why he is considered an important historical figure;

(2) to

select some outstanding features of his personality, as guides toward understanding the man;

(3) to survey some distinctive

aspects of his Gedankenwelt, as a foundation for understand­ ing the scope and the emphases which appear, and reappear; (4) to mention some of his distinguished associates, with an emphasis upon Alfred Korzybski, and to bring into focus (es­ pecially for students of general semantics) some personal and professional relations between the two men;

(5) to consider

the nature of his concern with speech, that an accurate per­ spective toward the theses of this study may be encouraged; and (6) to present a list of memorabilia, to complement the picture of the man and his works. A.

A Biographical Sketch

Cassius Jackson Keyser was born in a log cabin, Rawson, Ohio, May 15, 1862*

He attended the Ohio Normal University 16

17 from 1879 to 1 8 8 3 During 1884-85, he was a public school principal in Ridgeway, Ohio, and held a similar position in Plattsburg, Missouri, the following year.

The next two years

were devoted to the teaching of mathematics as an instructor at the University of Missouri, where he was granted the Bachelor of Science in 1892.

That same year Keyser held a

fellowship in the Thayer School of Mathematics, Harvard Uni­ versity.

Then he had two years as professor of mathematics

at the State Formal School of New Paltz, New York.

The sum­

mer of 1894 was spent in attendance at the University of Michigan, and the following academic year as an instructor in mathematics at Smith Academy of Washington University in St. Louis, Missouri.

His Master of Arts was granted by

Columbia University in 1896, whereupon he became a tutor at Barnard College from 1897 to 1900.

When he had earned his

Ph.D. from Columbia in 1901, he had already been an instruc­ tor for one year at that university.

Two years later he

spent a year as Adjunct Professor, and in 1904 he was ap­ pointed Adrian Professor of Mathematics.

Being a Fellow of

the American Association for the Advancement of Science, he sras honored with the Vice-presidency of Section A of that organization in 1908.

Six years later he was given the LL.D.

by the University of Missouri.

In 1911, and again in 1915,

^■J. Cattell (ed.), American Men of Science: A Biogra­ phical Directory (7th ed.; Lancaster, Pa.: The Science Press, 1944) • Unless otherwise specified, all other information in this section was obtained from D. Runes (ed.), W h o 1s Who in Philosophy (New York: Philosophical Library, Inc., nTdV)-.

18 Keyser served as Professor of Mathematics at the summer session, University of California, and Exchange Professor in 1916.

Pbom

1910 until 1916, he had been the Head, Department of Mathema­ tics, Columbia University.

In 1929, Columbia honored Professor

Keyser with the Sc.D.j and Yeshiva College honored him with the L.H.D. in 1942. In addition, Professor Keyser had been Mathematics Editor for the Encyclopedia Americana in 1906, a member of the American Editorial Board for the Hibbert Journal, and Associate Editor of Scripts Mathematics since 1932. In the aforementioned American Men of Science, Keyser's name is starred.

What does the star mean?

The Preface to

the first edition of that biographical directory states: These are the thousand students of the natural and exact sciences in the United States whose work is sup­ posed to be the most important. In each of the twelve principal sciences the names were arranged in the order of merit by ten leading students of the science. • * • The thousand are distributed among the sciences as fol­ lows: . . . mathematics, 80. . • . The star means that the subject of the biographical sketch is probably among the leading thousand students of science of the United States. Perhaps Keyser himself provided a further clue to the importance of his work when he said of C. S. Peirce: Peirce has been rightly called a "seminal thinker.” A seminal thinker is one whose thinking sometimes pro­ duces what we may call seed-thoughts, thoughts, that is, that germinate and grow and develop into lightgiving theories or doctrines, thus advancing human knowledge, insight, and understanding.^C. J. Keyser, "Charles Sanders Peirce as a Pioneer,” Galois Lectures (Hew York: Scripta Mathematics, Yeshiva College, 194X77 P* 96. This thesis was suggested by Mrs.

19 May Keyser be called a seminal thinker?

It would seem

legitimate to do so if one could point to seed-thoughts#

Pos­

sibilities were entertained: The first occurrence of the name, doctrinal function, which was invented by myself, is found in m y article "Concerning Multiple Interpretations of Postulate Sys­ tems" (1913), Journal of Psychology and Scientific Method. In my Mathematical Philosophy the"name is for­ mally intro duced and explained •1 Respecting my definition of Science, a distinguished mathematician, Professor Eric T* Bell, has said over his own signature: "Here for the first time there is given a definition of Science which Is worthy of serious con­ sideration by scientists and mathematicians alike, as well as by laymen#"* And Jekuthlel Ginsburg has said that "if there is such a thing as mathematical philosophy Keyser helped create it."3 And Joseph Meiers declared: • • • far beyond his immediate Influence exerted through his teaching and his efforts to Improve educational m e ­ thods in mathematics In his beloved America, beyond even his significance as a mathematical thinker and explorer of new frontiers, Keyser will become a far-radiating force through what appears to be his most original con­ tribution: the new position in which he strove to put mathematics in its philosophic aspects, in its implica­ tions for and its import on, mankind1s evolution, es­ pecially man's future# It is in this area--most notably In his outstanding work Mathematical Philosophy (1922)--that Keyser crossed the path of the ideas which have since achieved syste­ matic formulation and accelerating expansion as general Sarah Y* Keyser In a personal Interview, September 9, 1949. All theses and information in this chapter, which are not otherwise documented, were obtained In that Interview. 1C. J* Keyser, "The Nature of the Doctrinal Function and Its Role In Rational Thought," Mathematics as a Culture Clue and Other Essays (New York: Scripta Math©matIca, 1947), p# 113 n. 2 C. J# Keyser, Humanism and Science (New York: Columbia University Press, 1931), p. xil# ^(Obituary of Cassius J. Keyser), Proceedings and Addresses of the American Philosophical Association, XXII (1948-49), 465.

20 semantics. At that early time, it was Keyser who, in his above-named book, gave full recognition and praise to Korzybski's newly established principles, especially the human phenomenon of rtime-binding.'1 Was he, then, a seminal thinker? among his aims. of opinion.

That was surely

Was the aim accomplished?

That is a matter

Keyser did "advance human knowledge,

insight,

and understanding"; it was helpful to think of him as a semi­ nal thinker.

His name may be spoken by generations yet un ­

born; he might be called the father of the doctrinal function. B.

The Man

Although Professor Keyser was a distinguished man who may be well judged by the company he kept, his dignity should not be mistaken for aloofness.

Quite the contrary.

a great love for all living things:

He had

"Wherever there is a

nerve that hurts, there is my sympathy"; and he was full of fun and nonsense:

"nonsense keeps me sane."

As a young man

he had "played the fiddle," but he gave it up because it would rob his time from mathematics.

And though he remained

a music lover, his hobbies were perhaps too few.

For the

most part, his work was his play. The supreme interest of Keyser's life was mathematics, which he equated with logic.

In his conception of it,

^(Obituary of Cassius J. Keyser), Etc.: General Semantics, V (1947), 56.

A Review of

^This paragraph was paraphrased from: (1) C. J. Keyser, "A Glance at Some of the Ideas of Charles Sanders Peirce," Mathematics as a Culture Clue and Other Essays (New York: ScrIpta Mathematica, 1947), p p . 155-188 passim; and (2) C. J. Keyser, "William Benjamin Smith," Ibid., pp. 189197 passim.

21 mathematics is quite unsurpassed by any other subject in extent or in dignity or in human significance.

Mathematics

was, for him, discourse of reason, a w a y of thinking, and, quite as genuinely as poetry or music, a finely characteris­ tic manifestation and product of the higher spirit of Man. Is it any wonder, then, that he was disturbed by a lack of logic? Now Keyser was full of righteous indignation, espe­ cially at lack of logic; but also at false pretense; and, as he called it, academic stupidity.

As examples:

Did not Babbage or somebody invent an adding machine? And does it not follow, say Holmes and Schopenhauer, that mathematical thought Is a merely mechanical pro­ cess? Strange how such trash is occasionally found in the critical offering of thoughtful men and thus ac­ quires circulation as golden coin of wisdom. But far more pernicious, because more deeply Im­ bedded and persistent, Is the fallacy that the mathe­ matician's mind Is but a syllogistic mill and that his life resolves itself into a weary repetition of A is B, B is 0, therefore A is C; and Q . E.D. That fallacy Is ¥he Carthago delencTa of regnant methodology. Reasoning, indeed, m the sense of compounding propositions into formal arguments, is of great importance at every stage and turn, as In the deduction of consequences, in the testing of hypotheses, in the detection of error, In purging out the dross from crude material, in chasten­ ing the deliverances of intuition, and especially in the final stages of a growing doctrine, In wielding to­ gether and concatenating the various parts into a compact and coherent whole* But, indispensable in all such ways as syllogistic undoubtedly is, it is of minor importance and minor difficulty compared with the supreme matters of Invention and Construction.^ C. J. Keyser, nMatheraatics,w The Human Worth of Rigo­ rous Thinking (3d. ed.; New York: Scripta Mathematics, 1940), p. 292. Ibid., pp. 292 f.

22 Righteous indignation?

Yes; at times a biting, sting­

ing pen left no question where its master stood. was not his dominant trait.

But this

There were others:

The pursuit of excellence, whether in writing or in other work, is the proper vocation of man. You have a sure talent for the discerning of excellence? And, when you see it, it causes you to cry out with the ac­ cent of admiration and joy? Then I salute you as a public benefactor, a good neighbor, and a most amiable companion.l Keyser began with the morning--he was an early riser; his day was planned (he disliked "having things sprung on him")— and engaged in the pursuit even before breakfast (his interest in household tasks included "excellence in the fry­ ing of bacon").

There were no indications that his "crying

out" was confined to any particular time of day or occasion. Excellence, it appears, was the compass of his devotion. Above all else, it was a human devotion: It is warm enswathing human interest that distin­ guishes the Columbian from such illustrious English masters as Whitehead and Russell. . . . It is highly significant and appropriate that these discussions have taken the form of lectures to students, or rather of the most familiar talks, in which the author figures almost as an elder brother. Most of all . . . it is the fine humanity of the work, that touches the heart and awakens the sympathy of the reader. It is not Logic merely as Logic, nor Mathematics as Mathematics, nor even Philosophy as Philosophy, that is the most immediate and pressing interest of this vol­ ume; its most intimate concern is with Man as Man, with human life, with the human soul, with the "Emancipation" (as the Professor loves to call It) of the Human Spirit. . • . It is Democracy that Keyser wants made safe in the world; not a mere political or economic, a capitalistic C. J. Keyser, "Mathematics and the Dance of Life," Mathematics as a Culture Clue and Other Essays (Hew York: Scripta Mathematics, 1947), p. 199.

socialistic organization, but a spiritual Democracy, a Republic of minds, of emancipated souls. The goal seems indeed far off, but the author*s foresight is clear and steady, his Will is set and unwavering.^

op

The Professor "would deserve the title of the Grand Old Man of Mathematics— were it not for the fact," wrote Kasner, "that it would never occur to anyone that Keyser at 78 is anything but youthful."^ G•

His Gedankenwelt

Thinking is not indeed essential to human life. beings are inhabitants of so to speak, of the world the world of thought.3

essential to life, but it is All men and women as human the Gedankenwelt*-citizens, of ideas, native citizens of

Citizen Keyser lived a life of thought. said:

As Mrs. Keyser

"When I greeted him upon returning from work, I did not

ask him, What have you been doing? been thinking?"

I asked him, What have you

It seemed unlikely, therefore, that an ade­

quate understanding of the man and his works could be conveyed without a preliminary introduction to his "world of ideas." The thesis is that Keyser perceived the world as a mathemati­ cian and mathematical philosopher.

^*W. B. Smith, "Nuptials in High Life" \a review of Keyserrs Mathematical Philosophy! , The Monist, XXXIII (1923), ----------620 f. J 2 B. Kasner and J. Newman, Mathematics and the Imagi­ nation (New York: Simon and Schuster , 1940), p. 366. 3

C. J. Keyser, Mathematical Philosophy: A Study of Fate and Freedom (New Y o r k : ~E. P.' button and Co., 1922), p. 1 6 .

24 Although his "Principia Mathematical were in the tra*1

dition of Whitehead, Bussell, Frege, Couturat, and Peano, it might be misleading to identify his profession as the philosophy of mathematics*

For mathematical philosophy and

the philosophy of mathematics * • . are very different things, the former being iden­ tified mainly by its method, the latter by its matter. An example of mathematical philosophy is the famous at­ tempt of Spinoza to geometrize the philosophy of Descartes or his yet more famous attempt to construct the Ethics after the manner of Euclid. On the other hand, the philosophy of mathematics . . . is primarily concerned with sueh unanswered questions as arise in reflecting upon the nature of mathematics and the character of its foundations Perhaps the most important concern with the philosophy of mathematics was that Keyser subscribed to "the thesis of modern logistic” :

"Logic is not a tool of mathematics--

logic is^ mathematics.”

The thesis was explained by one who

helped establish it: . . . starting with premisses which would be universally admitted to belong to logic, and arriving by deduction at results which as obviously belong to mathematics, we find that there is no point at which a sharp line can be drawn, with logic to the left and mathematics to the right *4 According to that thesis, mathematics has .lust as much to do with speech as logic does.

But not all of logic

•^Smith, op. clt., p. 626. P C . J. Keyser, A Review of Introduction to Mathematical Philosophy by Bertrand Russell, in The American Mathematical Monthly, XXVII (1920), 213. 3 C. J. Keyser, ”Mathematics as a Career," The Scientific Monthly, XVII (1923), 429. ^B.Russell* Introduction to Mathematical Philosophy (2d ed.; London: George Allen and Unwin, Ltd., 1920),' p'. 194.

25 could be lumped together* Professor Keyser was among the first to teach the Principia Mathematics of Whitehead and Russell.

And portions

of Keyser1s writing tend to enhance the distinctiveness and point up the contributions of modern logistic: The emancipation of logic from the yoke of Aristotle very much resembles the emancipation of geometry from the bondage of Euclid; and, by its subsequent growth and diversification, logic, less abundantly perhaps but not less certainly than geometry, has illustrated the blessings of freedom.**The demonstration by symbolical means of the fact that the three laws of Identity, Excluded Middle and Non-contradiction are absolutely independent, none of them being derivable from the other two; the discovery that the syllogism is not deducible from those laws but has to be postulated as an independent principle; the discovery of the astounding and significant fact that false propositions imply all propositions and that true ones, though not implying, are implied by, all; the discovery that most reasoning is not syllogistic, but Is asyllogistic, in form, aid that, therefore, con­ trary to the teaching of tradition, the class-logic of Aristotle Is not adequate to all the concerns of rigo­ rous thought; the discovery that Relations, no less than Classes, demand a logic of their own, and that a similar claim Is valid in the case of Propositions: no intelligence of these events nor of the immense mul­ titude of others which they but meagrely serve to hint and to exemplify, has been cabled round the world and spread broadcast by the flying bulletins of news.2 This dissertation, of course, was concerned with some of those discoveries.

Part Two bears testimony that Keyser, as

a logician, was up to date; that he perceived the world in terms of relations, postulates, etc.

If he saw with the eyes

of a mathematician, it would be essential to grasp his view C. J. Keyser, "Principia Mathematica," The Human Worth of Rigorous Thinking (3d ed.; New York: Scripta Mathematica7 1940), p. 2 1 8 . 2Keyser, "Mathematics," op. cit., pp. 279 f.

26 of mathematics in order to understand his perceptions.

A

few indications were adequate for present requirements: As an enterprise mathematics is characterized by its aim, and its aim is to think rigorously whatever is rigorously thinkable or whatever may become rigo­ rously thinkable in course of the upward striving and refining evolution of ideas. As a body of achieve­ ments mathematics consists of all the results that have come, in the course of the centuries, from the prosecution of that enterprise: the truth discovered by it; the doctrines created by it; the influence of these, through their applications and their beauty, upon the advancement of civilization and the weal of man.-*He saw mathematics as fTthe ideal to which all thinking . . . Q

constantly aspires.”

It is not n . . . a n insulated science,

dwelling apart in isolation from other forms aid modes of conceptual activity” ;

the ”Mathematicisation of thought”

is not ”the importation of a tool into a foreign workshop.”^ One might say that such was Keyser* s philosophy of mathema­ tics.

But what of his mathematical philosophy?

That ques­

tion leads to a most important reply: Why is it that the standard of logical rectitude is so clearly revealed in Mathematics? And why is it that Mathematics is famous for approximate conformation to the standard? The secret lies in the method of Mathematics--the method of carefully selected and clearly enunciated postulates, of sharply and complete­ ly defined concepts, find of painstaking deductions or C. J. Keyser, ”The Human Worth of Rigorous Thinking,” The Human Worth of Rigorous Thinking (3d ed.; Hew York: S cr ipt a Mathemat i ca, 1940), p. 3. 2 Ibld., p. 14. *2

C. J. Keyser, ”The Human Significance of Mathematics,” The Human Worth of Rigorous Thinking (3d ed.; New York: Scripta Mathematica, 1940), P* 47.

4 Keyser, "Mathematics,” op. cit., p. 298.

27 demonstrations. Because there is no field in which a worker can escape the necessity of making conscious or unconscious use of postulates, nor the necessity of formulating definitions and of attempting deductions and demonstrations, it is as clear as noonday that mathematical procedure furnishes a model for the gui­ dance of criticism of all discourse of reason, no matter what the subject or field to which the discourse pertains If Keyser saw with the eyes of a mathematical philo­ sopher, he saw in terms of method, the method of mathematics, the postulational method--and mathematical formulations were deemed useful, if not indispensable, as prototypes.

Again

and again throughout Part Two, Keyserian doctrines were in­ troduced as prototypes; and, In Chapter VIEI, the postula­ tional method was finally allowed to emerge.

The emphasis

was on mathematical philosophy to such an extent that it was assigned the leading role in his Qedankenwelt.

Citizen

Keyser had things to say about ideas, the world of ideas; the world of the Possible— that is what the master called his beautiful house of many mansions: Ideas, you know, are givers of light;if the inner eye be fit, and, like stars, they differ in glory. It sometimes happens that folk are color-blind. I trust that none of us are idea-blind. Our being here . . . is some evidence that we are not.^ This world of the Possible was placed in sharp contrast with the world of the Actual--and the distinction seemed to be so basic to Keyserian doctrines that one would not hesitate to give warning:

fail to understand the distinction, fail to

^Keyser, Humanism and Science, op. cit., p. 221. ^Keyser, "Charles Sanders Peirce as a Pioneer," o p . cit., p. 91.

28 grasp his characterization of the Possible, and the incom­ prehensibility of crucial Keyserian doctrines is virtually guaranteed.

So, the Professor was permitted to speak for

himself, at length, without interruption: We are going to deal with ideas— with their charac­ ters, with their meanings, with their relations. Now, an idea is in itself an eternal thing and the relations of an idea with other ideas are eternal. An idea is just what it is and it is unalterable; a relation among ideas is just what it is and it is unalterable. We do, indeed, often speak as if such were not the case; we ha ­ bitually speak as if ideas and their relations were tem­ poral affairs, impermanent, mutable, malleable, capable of growth, of modification, of decay, of destruction, as when we say, for example, that we have ”changed” our ideas or that such-and-such an idea has ”grown” in im­ portance or has ”become” sterile or is ”dead.” It is, I fancy, hardly necessary to say that all such ways of speaking are figurative,— convenient no doubt, often pleasing, sometimes very effective, yet thoroughly fi­ gurative,— and that, if taken literally, they quickly and inevitably lead to scientific and philosophic disaster. You or I may abandon an idea that we have held and we may adopt an idea that is new to us; the ”old” one and the ”new” one may closely resemble each other; they may indeed be identical in some respect and may even be called by the same name; but neither of them has been transmuted into the other; each of them remains and will remain just what it was.*** There were occasions for reference to the static Pos­ sible and the dynamic Actual, as, for Instance, in discussing the nature of variables and relations.

And it seemed that

Keyser must have seen a dynamic world In terms of static ideas two worlds, split asunder yet somehow related.

If Keyser

saw stability of and for the Actual, he saw at least some of It in terms of Invariants: In our environment there exist certain great invariant massive facts that now are and always will be necessary

^■Keyser, Mathematical Philosophy, op. cit., pp. 2 f.

29 and sufficient to constitute the basis of a curriculum or a theory of liberal education* These facts are ob­ vious and on that account they require to be pointed out, just because, In the matter of escaping attention, what is very obvious is a rival of what Is obscure.^ The past is ever with us, so the need for history and "the literature of antiquity"; we are "literally immersed" In a physical universe,

so the need for natural science; our wel­

fare depends upon "the human Gedankenwelt," so the need for logic and mathematics; "every man and every woman is a born member of a thousand teams," so the need for political science and "the greatest of all the arts--the art of rhe­ toric"; we are ever growing into the future, so the need for instruction in prophecy, and "every department of study is a department of prophecy. to foretell,"

It is the function of science

And finally ” , • . i t must be remembered

that not the least service . . .

is that of disclosing to

men and women and to their fellows their respective powers and limitations."

This was a mathematical philospher look­

ing at education--and how?

As one might expect; he looked

at education in terms of a mathematical formulation, one which there was occasion to discuss with reference to speech. But Invariance was not the only mathematical formulation which seemed to shape Keyserian views.^ Ho sane person could be dogmatic about the "habits of ^C, J. Keyser, "The Permanent Basis of a Liberal Edu­ cation," The Human Worth of Bigorous Thinking (3d ed.; New Y o r k : Scripta MathematTca, 1940), p. 164. ^Ibid., pp. 164-172 passim.

30 mind1* of a man like Keyser; one can, at best, characterize by speculation.

And that is what was' done.

But there is

ample evidence to support the unqualified assertion that Keyser perceived the world in terms of limits: In this connection I cannot refrain from saying, what I have repeatedly said elsewhere and shall never miss an opportunity to say, that genuine ideals are not goals to be reached but are perfections to be endless­ ly pursued. Genuine ideals are like those mathematical limits whose variables approach them ever more and more nearly but never attain them.^Keyser repeated this principle, that Ideals are not goals, at least forty times, in not less than three books, ten essays, and two reviews.

If one were confined to a

single feature by which to characterize the man, his life of thought, of teaching, of writing, this would seem to be It; If there was king in his Gedankenwelt, this principle wore the crown.

He gave it his best attention, if one may

judge by repetition, by clear examples, by beauty of dis­ course.

An adequate understanding of mathematical limits—

adequate for the purposes at hand--may be gained from a most vivid example: How beautiful a thing is a circle. In a circle let there be inscribed an equilateral triangle, then a regu­ lar hexagon, then a polygon of a dozen sides, and so on forever, going from step to step of the summitless scale by the simple device of ever doubling the number of sides. Infinitely many are the polygons so obtained. Each of them has a certain size, a certain area; the first is the smallest, the second is next, and so on forever. Let us suppose all these areas arranged in a series, In the order of size, beginning with the smallest. Indeed, they are already so arranged. There now lies before us for

■^Keyser, Humanism and Science, op. cit., p. 207.

31 our contemplation a literally endless sequence of everincreasing terms, of ever-increasing polygonal areas* In respect of size, these approach nearer and nearer, as close as we please, to the size of the c i r c l e d area, yet they remain inferior to it forever* And so we say, in technical language, that the circle’s area is the sequence’s limit * It is important to note that the se­ quence’s limit is not a term in the sequence, for all these terms are polygonal areas--shapes bounded by polygons— but that of the circle is not, for the circle is not a polygon. The totality of all areas whatever that are bounded and shaped by polygons I shall call the Domain of Polygonal Areas* Within that domain are con­ tained, among many other polygonal areas, all the terms of our sequence but not the sequence’s limit: the cir­ cle’s area does not belong to the domain of polygonal areas but is a thing upon its border* The terms of the sequence may be viewed as the steps of a path beginning with the first term and thence proceeding on and on, within the domain of polygonal areas, step after step endlessly, on and on out towards the border, getting closer and closer to it, just as near as we please, and, though never attaining It, yet Indicating by the law of approach an unmistakable something that lies thereupon, namely the circle’s area* Here, then we have a clear presentation, within a given domain, of something that is not within: we have a clear presentation, by the law of an inner sequence, of a limit on the rim— of an Ideal, if you please, which, so long as we operate within the domain, may be aspired unto, approached and pursued for­ ever, but can never be attained.^ • * * It is thus evident that ideals are not things to gush over or to sigh and sentimentalize about; they are not what would be left if that which is hard in reality were taken away; Ideals are themselves the very flint of reality, beautiful, no doubt, and precious, without which there would be neither dignity nor hope nor light; but their aspect is not sentimental and soft; it is hard, cold, intellectual, logical, austere. Ideali­ zation consists in the conception or the intuition of ideals and in the pursuit of them.2 Why mention this great emphasis which Keyser placed upon Ideals and limits?

Because, on many occasions, mathema­

tical prototypes were presented--and they were viewed as XC. J. Keyser, Science and Religion (New Haven: University Press, 1914), pp. 54-56.

Yale

^Keyser, Mathematical Philosophy, op* cit*, p* 294*

32 ideals; because mathematics itself, as defined by Keyser, viewed in all its precision, may be said to be a vast ideal for the treatment of precisely those problems to which the applicability of mathematics

(as "defined” by some laymen)

has been denied; because "every sort of human activity * . • admits of a peculiar type of excellence""**; and because a phenomenon sometimes discussed in speech circles was des­ cribed in terms of limits: A limit-begotten generalization always originates in the work of some limit concept operating in some established domain • * • wherein the concept leads us into the pre­ sence of baffling phenomena, waking our wonder, giving us a painful sense of failing to see something we ought to see, a sense of logical suffocation, of being hampered, hemmed in; we seek emancipation and at length achieve it, not solely by purely logical means, but partly by obser­ vation . . ♦ , partly by reasoning and partly by an act of will— in short, by generalization; this deed gives us a new domain of thought— a new field of ideas . ♦ *;the new domain, once thus established, is as actual for us as the old one; with reference, however, to any viewpoint within the old one, the new domain is and forever remains a 'sheer ideal, not to be attained by any process or operation--however oft repeated, swift or prolonged--within the old domain; and finally, a new domain • . . may in its turn become, in the manner indicated, an old one in rela­ tion to another domain • . « which, though itself actual, is, with respect to the former, an eternal ideal*2 But perhaps most important of all in this connection is the need for understanding the Keyserian orientation— "most im portant" because to miss it would be to miss the way in which prototypes, in their aspect as Keyserian ideals, were employed Ln this study.

That orientation was eloquently expressed:

^"Keyser, Mathematical Philosophy, op* cit*, p. 295. 2Ibld., pp. 292 f.

33 Ideals are not things to be grasped, they are things to be reached for; they are not subjects for conquest, they are objects for aspiration; they are not properties to be possessed, they are perfections to be pursued; logic can not harness them, it can not reduce them, as it reduces ideas, to the ranks of obedient servants in the fields of reason; they hover aloft; they can not be pounced upon; to realize an ideal Is not to possess it; it Is to own its authority, to respond to its appeal, to follow its leading, to be drawn to higher elevations by the charm and persuasiveness of its majesty and beaut y .*■ Now in order to appreciate the Keyserian Gedankenweltand one would have to be idea-blind to miss its significance for a study such as this--an obvious, old, deeply profound, and (in the opinion of this writer) far too often forgotten jewel of wisdom had to be Included*

It says much to illu­

minate the Keyserian orientation and scope: Nature does not greatly respect our little academic custom of carving her up and calling the pieces depart­ ments of study* Chemistry, physics, mechanics, geometry, metaphysics, psychology, logic, ethics, esthetics, and the rest all penetrate and overflow the walls we surround them with, and mingle their waters in one vast sea* In the great world of Nature,--the subject of all thought,— there are emphases indeed but no fixed divisions corres­ ponding to our pretty ologies, ograph!es, and ics, and even the emphases perpetually shift their Incidence. And yet there is a sense in which such divisions and walls are not artificial but are natural for they are made by man, and man is a part of nature--the part that studies the whole* In that sense, man-made divisions of nature are natural divisions, made by Nature herself to facili­ tate the process of self-understanding; but they are not aboriginal and they are not permanent,--they are experi­ mental devices, mere conveniences for the service of a people or an age, and destined to c h a n g e . ^ nEvery major concern among the intellectual concerns of man Is a concern of Mathematics." No doubt that ^C* J* Keyser, The New Infinite and the Old Theology [New Haven: Yale University Press, 1915), p. 21*

2

Keyser, Mathematical Philosophy, op. cit., pp. 402 f.

34 statement will seem to some to be extravagant. Yet the statement is true and the truth of it ought to be made known to all*1 D.

Some of His Distinguished Associates

The Friends of Cassius Jackson Keyser was born fol­ lowing his death in 1947.

All the members of the publica­

tion committee for that organization knew Professor Keyser personally. Among other reasons, they are distinguished for not foreign to Keyser*s pursuits. mathematician.

k

>rk

Lillian R . Lieber is a

Her husband, Hugh Gray Lieber, is an artist.

They have collaborated in the authorship of popularizations in the best Keyserian tradition.

Edward Kasner has been

Adrian Professor of Mathematics at Columbia University since 1937— a Chair held by Professor Keyser from 1904 until his retirement and Emeritus Adrian Professorship in 1927.

Philo­

sophy is represented on the committee by William P. Montague* Jekuthiel Ginsburg is probably best known as the Editor of Scripta Mathematica.

And probably best known of all was

Nicholas Murray Butler, honorary chairman of the committee, and Keyser*s close friend and ardent backer.^ The man whose influence upon Keyser*s professional life seems to be clearest was his teacher and friend, William Benjamin Smith, with whom he remained in close communication ^Keyser, Humanism and Science, op. cit., p. 222. ^Statement by Professor Edward Kasner, personal inter­ view, September 9, 1949.

35 until Professor Smith’s death in 1934: Will you allow me a word of personal experience? I count it a great good personal fortune that as a young man I received mathematical instruction from one in whose teaching the logic, the philosophy, the psychology, and the poetry of the subject mingled together and fortified each other like the parts of an orchestra. I refer to Professor William Benjamin Smith, now of world-wide fame as a Biblical scholar and critic.1 Other associates were David Eugene Smith, sometime President of the American Mathematical Association; and, Eric T. Bell, a student of Keyser1s, and the author of The Queen of the Sciences together with other mathematical and popular works.

The final associate to be mentioned was, at

one time at least, his professional protege^ During Alfred Korzybski*s earlier days in America he had not yet mastered English.

It was during those days,

Korzybski said,^ that his first brief manuscript of Manhood of Humanity was written and taken to Professor E. H. Moore, an outstanding mathematician at the University of Chicago. Professor Moore judged himself incompetent to evaluate that particular wcrk, so he introduced Korzybski to Professor Keyser.

Now at that time, of course, Korzybski was not

familiar with the literature in English pertaining to mathe­ matical philosophy, etc.

Consequently, Keyser, being an

inveterate reader, was able to advise Korzybski in what to ^"Keyser, Mathematical Philosophy, op. cit., pp. 410 f. o The personal and professional relationships of the two men was explained by Korzybski In a personal interview during the 1949 Summer Seminar-Workshop at the Institute of General Semantics.

36 read.

And, Keyser being an accomplished writer, was able

to assist Korzybski with a rewriting of the manuscript. Korzybski told this writer that Keyser "spent incredible time editing, and in some places rewriting" The Manhood of Humanity.

So the hand of Keyser was directive in the pre­

paration and heavy in the writing of that book. Through these and later years, the two men remained personal friends, although the older m a n Ts assistance di­ minished.

Does it need to be said that friends sometimes

disagree, and still remain friends?

Korzybski was careful

in explaining to this writer that such was the case.

As

an example, Korzybski*s semantic definition of number did not replace Keyser*s preference for "class of classes." So it might be an invitation to confusion to classify Keyser as a general semanticist, and let that be an end to the matter.

Such classification might cover up differences,

and becloud important issues.

But it invites no confusion

whatever to recognize Keyser as one of the five men whose doctrines probably influenced Korzybski most.1

In fact,

general semantics might be considered as evidence that Keyser was a seminal thinker.

If so?

Korzybski indicated

in interview that the seed-thought would be that of doctrinal ^The five were named by Korzybski in his "Pate and Freedom," an article which acknowledges "heavy obligations." See I. J. Lee (ed.), The Language of Wisdom and Polly (New York: Harper and Brothers, 1949), p. 342. Keyser* s wo rk s are also among those to which Korzybski dedicated Science and Sanity. ------

37 function.'*'

Perhaps this notion of doctrinal function, more

than any other, accounts for Keyser1s name appearing as one of the mentioned five.

And logical fate, which Korzybski

considered important, may be included as an inseparable part of doctrinal function theory: The ’Brotherhood of Man*, of which we all dream, can be accomplished only and exclusively by the ’Bro­ therhood of Doctrines’. . . • ’Mathematical Philosophy’ by Keyser is one of those mile stones of everlasting significance. In this monu­ mental work there are discoveries of the gravest impor­ tance . Keyser is one of the three in the world, as far as I know, who is blazing a new trail in this field. • • . This discovery of logical fate and freedom, Is of such importance that, were it the only one in the work, the work would live for ever. After some reflection, its practical bearing becomes evident in all that our talking about ’Brotherhood of M a n ’ or ’Democracy’, etc., are beautiful words but meaningless so long as we do not inquire into the basic premises which underly those doctrines and investigate If the premises are true; be­ cause, if the premises should prove to be false, this ’logical fate’ would drive us to disasters. • • • Because of logical fate, the analysis of doctrine, which underlies all human activities, becomes the most important--nay the all-important--fact for all the future of man. Keyser, to the best of my knowledge, is the dis­ coverer of a new mathematical method . . . ; in a won­ derfully precise aid clear way, he elaborates the theory of postulates and doctrinal functions. Most of what he has to say is either entirely new, or given in a new form. . . . 2 Although not all Keyserian doctrines may be identi­ fied with general semantics, there were yet other striking •^Those to whom ”doctrinal function” is a strange term may wish to read beyond this chapter. It is not until Chapter V H T that the notion emerges with any significant completeness. o Alfred Korzybski, ’’The Brotherhood of Doctrines,” The Builder, August, 1924, pp. 51-56 passim.

38 similarities to general semantics doctrines found in Keyser's wor k s : 1*

Concerning what Korzybski called semantic con­

science : Dictional sensibility Is a hopeful sign, being con­ clusive evidence of life, and, while there is life, there remains the possibility and therewith the hope of readjustment.^2.

Concerning symbols as representatives of objects

and relations: Let it be said at once that, Inasmuch as words have no inherent meanings, the meanings they have are assigned meanings; words denote what they are employed to denote, symbolize what they are employed to symbolize, signify what they are employed to signify; they are to be con­ strued as having the sense, or senses, In which they are used, and as having no other.2 Any one versed in symbology knows that whatever is a symbol symbolizes; symbolizes something, which it need not resemble; and symbolizes for a recipient or recipi­ ents.3 Again, it is of the utmost critical importance to see clearly, and to keep steadily in mind, the fact that the symbolic character of a symbol is never intrinsic or in­ herent In it. Although it is true that anything what­ ever may be employed as a symbol, yet no thing ever is or can be a symbol except, when and so long as it is em­ ployed as such. In other words, all the symbols that occur in human discourse are man-made— that is, manchosen or man-invented for the purpose--and the meaning of any symbol Is man-given, or man-assigned. If I be one of the legion who either in their theory deny the ■l

C. J. Keyser, "Mathematical Emancipations: Dimen­ sionality and Hyperspace,” The Human Yiforth of Rigorous Think­ ing (3d ed.; New York: Scrlp¥a~ Mat hematic a, 1940 )T'p’*" 10?. 2 C. J. Keyser, The Pastures of Wonder: The Realm of Mathematics and the Realm of Science (New York: Columbia University Press, 1929), p. 118. C. J* Keyser, "Mathematics and the Question of Cosmic Mind,” Mathematics and the Question of Cosmic Mind with Other Essays.(New York: Scripta Mathematics,"19357/ P. 61.

39 fact stated or in their practice ignore it and violate it, then I belong to the immense logolatrous class of mankind, I belong to the superstitious multitude of symbol-worshippers, I have not yet achieved emanclpation. from the ages-old world-wide tyranny of verbal magic. 3.

Concerning functions of language:

• . • Its operation is so ubiquitous, so constant and so familiar that the symbolic or logical function of language seldom becomes a subject of conscious and deliberate attention; yet it is hardly possible to over­ estimate the importance of its role in the life of our human kind. For without It, without the power to sym­ bolize ideas by words, and judgments by propositions composed of words, without the power to organize thought by the concatenating agency of logically interlocked propositional forms, without the power to communicate thought by speech, what we call Civilization could not have been produced; and were humans suddenly deprived of that power, they would suddenly sink to the intellec­ tual level of dumb animals; they would cease to be human and human civilization would quickly perish.2 4.

Concerning similarity of structure:

I desire to emphasize the prime importance of concepts that correspond to facts. . . .3 . . . Because the doctrine, whether true or false, matches the doctrinal function, statement for statement, and because the statements (propositions) composing the doctrine and the corresponding statements (propositional functions) composing the doctrinal function are identical In respect of form, we say that the doctrine and the function are themselves like in form, or structure.^ 5.

Concerning abstraction, and levels thereof:

•^Keyser, "The Nature of the Doctrinal Function . • op. cit., p. 93. 2Keyser, The Pastures of Wonder, op. cit., pp. 108 f. 3C. J* Keyser, "The Nature of Man," Science, LIV (1921), 206. 4Keyser, Mathematical Philosophy, op. cit., p. 109.

40 On m y table lies a slender rod* As seen there, it appears to be straight. I place it at a slant in a vessel of water. As seen there, it appears to be bent* Is the rod straight or bent? That is not the question* If it were, we should have to invoke the testimony of at least aiother sense, which, however, for the purpose of the illustration, I exclude. I am admitting vision only* To vision, then, the rod presents two contradic­ tory aspects— now straight, now bent. Are they, as aspects, false? Is either, as an aspect, false? Nei­ ther, as an aspect, is false: as aspects, both are true, both are genuine, both actual. How surmount them? The answer is by recognizing that the rod is such a thing in our world that it does, In truth, present to vision both aspects— and that recognition is a valuable event because it tells a truth about the rod, about our world, and about our vis Ion* All impressions, all views, all theories, all doc­ trines, all sciences are false in the sense of being partial, imperfect, incomplete. . . . Every one must see that, but for the helpfulness of views which be­ cause Incomplete are also in a measure false, even the practical conduct of life, not to say the advancement of science, would be Impossible. There is no other choice: either we must subsist upon fragments or perish. 6.

Concerning semantic environment:

. . . For what is our environment? Is it wholly or mainly a matter of sensible circumstance— sea and land and sky, heat and cold, day and night, seasons, food, raiment, and the like? Far from it. It is rather a matter of spiritual circumstances— ideas, sentiments, doctrines, sciences, institutions, and arts*^ 7.

Concerning indexing:

Discrimination, as the proverb rightly teaches, is the beginning of mind. The first psychic product of that initial psychic act is numerical: to discriminate is to produce two, the simplest'possible example of multiplicity. The discovery, or better the invention, •^Keyser, The New Infinite and the Old Theology, op. cit., p. 111. 2C. J. Keyser, "Graduate Mathematical Instruction for Graduate Students Not Intending to Become Mathematicians," The Human Worth of Rigorous Thinking (3d ed.; New York: Scripta Mathematics, 1940), pp. 184 f . 5 Ibid., pp. 181 f.

41 better still the production, best of all the creation, of multiplicity with its correlate of number, is, there­ fore, the most primitive achievement or manifestation of mind* Such creation is the immediate issue of intellec­ tion, nay, it is intellection, identical with its deed, and, without the possibility of the latter, the former itself were quite impossible 8.

Concerning objectification:

If people would stop objectifying abstractions, which they probably never will, or if they would stop objectifying abstractions unconsciously, which they might learn to do, at least half the pseudo-questions, befuddling the world today as they have befuddled it from time immemorial, would vanish, and that would be a very, very great gain.2 9.

Concerning the static and dynamic--special con­

sideration might profitably be given here; for this view, which is reinforcement of a most distinctive feature of Keyserfs Possible as contrasted with his Actual, seems decisive.

It

may be remembered that Keyser equated logic and mathematics. According to this view, ”dynamic logic” is not dynamic.

As

general semanticists know, Korzybski not only subscribed to this view; he generalized it; extended it, that is to say, as a general principle applying to all language.

In the

generalized view at least, "continuous variation” occurs in the non-verbal realm (Keyser1s Actual), yet it may be talked about with a static language: Functions, propositional functions, doctrinal func­ tions, propositions, classes, points and point configu­ rations, numbers and systems thereof--mathematical ■^Keyser, Mathematical Emancipations . . . cit., p. 101.

op.

2C. J. Keyser, ”Hard to Ask Questions,” Mole Philosophy and Other Essays (New York: E. P. Dutton and Co., 1927), p.“ 44".

42 entities in general, simple or complex, elemental or composite,--are, all of them, stable things; immobile and immutable; they neither come nor go; they are not born and they do not perish; they have neither origin nor destiny, neither past nor future; they are timeless-inhabitants of eternity; they a r e : the world of mathe­ matical entities is a static world; it owes its unity and integrity to the presence within it of an infinite system of interlocking relations; and those mathematical relations, too, like the entities constituting them and related by them, are static. ♦ . ♦ We have seen that in the world of logic things and their relations are timeless, they are--all are present at once; but the things of the other world and their transformations are temporal, they are not all present at once, but occur in temporal order--each thing becomes its own successor and, in so becoming, ceases to be, so that there is a Past (which is empty) and a Future (never filled)— only a mobile Now, sole field and ve­ hicle of change and transformation. How can either of these sharply contrasted worlds represent the other— the things that a r e , standing for the things that happen, the permanent for the changeful, rest for motion, relations for transformations, the beginningless and ever­ lasting for the momentary children of birth and decay— "k*1© timeless for the temporal? . . . We can not rid ourselves of the feeling that points do not move, that numbers do not change, that relations are not transmu­ tations, and that, in general, logical and mathematical entities are immutable. And so . . . the troublesome factor of Time is to be suppressed; instead of dynamicising the static world of conception and logic, we are to staticise the dynamic world of sensation and physics. • . Perhaps, by now, it has been made fairly evident that some Keyserian doctrines did Korzybski and his formulations no harm.

Perhaps the two men shared a common aspiration:

to

establish mathematics as one of the humanities; to humanize and democratize it; to make its methods available to nonmathematicians; to reveal its importance, especially as a prototype or model, to the workaday world.

Korzybski, in

“Sceyser, Mathematical Philosophy, op. cit., pp. 173176.

43 interview,

indicated that such was the case.

He indicated

that even if the approaches of the two men differed, their aims were similar. thesis in question.

Their writings seemed to confirm the In those writings, it has been indica­

ted, Korzybski acknowledged his Keyserian obligations.

Ap­

preciation was mutual; but Keyser adopted the role of bene­ factor:

backing, boosting, and giving credit.

Chronologi­

cally first, and first in the emphasis he placed upon it, are Keyser*s remarks on time-binding: Theology has sought to understand man by viewing him as a depraved creature, a lost soul, requiring miraculous redemption. Biology has sought to under­ stand man by viewing him as an animal. But in study­ ing the genesis of human knowledge, in studying the fact and the process of knowledge-accumulation, and in studying the phenomena of acceleration which the process presents, we are studying man, not as a lost soul and not as an animal, but as man.-*When Science and Sanity was published in 1933, Keyser wrote a review.

It was found to be the best single source

to indicate Keyser1s “queries, doubts, reservations** about general semantics. study his comments.

Students of the subject may wish to Here, limitations permit only a fragment

of that review: Despite all the reservations that I have felt con­ strained to make and of others that might be made, I feel bound to say that this work, taken as a whole, is beyond all comparison the most momentous single contri­ bution that has ever been made to our knowledge and understanding of what is essential and distinctive in the nature of Man. There can be no doubt of its being a work that every serious student, no matter what the field of his special interest, ought to have as an indispensable ^Keyser, Humanism and Science, op. cit., p. 108.

44 part of his equipment. With its findings, all capable men and to men desiring to he in touch with the best thought of their time will be obliged to reckon. Ho library that has not at least one copy of Science and Sanity can rightly claim to be quite up-to-date.i As the Professor himself once terminated a long list of quotations from C. S. Peirce, "Can you beat that l" E*

Keyser and Speech

This section was not intended to evaluate Keyser as a rhetorician or speaker, nor to criticize his comments. Even here, the central focus was doctrinal. Keyser the philosopher; mathematician; inveterate reader; great admirer of Daniel Webster, Tom Paine, Robert Ingersoll; writer; teacher; and speaker, was an interested— albeit a competent--layman in his thinking about public ad­ dress.

It was not discovered that he was an enemy of speech

in any of its cardinal forms. sham speech in any form:

He was, rather, an enemy of

trivial speech, passed off as If

it were not; speech devoid of his logical rectitude, pre­ tending rigor when rigor there is not.

His views on speech

appear as those of a mathematical practitioner in speech who disliked mere practitionism.

His hostilities, which

left little room for augmentation, were more like rifle bullets than buckshot.

He was often discriminating.

criteria were notably mathematical: clarity, limitations, etc.

His

rigorous thinking,

And, of course, any speculations

^C. J. Keyser, "Mathematics and the Science of Seman tics," Mathematics as a Culture Clue and Other Essays (New York: Scripta Mathematics, 1947), p . 153.

45 about what Keyser might say concerning argumentation and discussion theories would quite obviously depend upon these statements as clues. "The greatest of all the arts,

. . . the art of

human expression in living speech,”'*' would seem to involve at least two major steps, with the Keyserian emphasis de­ pending upon distinction and sequence: States of mind are for the most part induced in us by the sentiments and faiths of the household, the neighborhood, and the family newspaper. We derive our states of mind from the social atmosphere by a kind of cerebral suction. But a conviction is a result of hard, patient, and honest thinking--the rarest activity of man. Honest thinking is attended by serious doubt. ”In ex­ perimental science,’1 wrote Louis Pasteur, ”it is always a mistake not to doubt when facts do not compel you to affirm.” It is not less so in mathematics, in philosophy, in economics, in ethics, in politics. One cannot right­ fully say ”1 am convinced that such and such a proposition is true,” unless one has successfully endeavored to doubt its truth, and has, by honest consideration of all the objections that one has been able to think of, finally come to the conclusion that the proposition is Indeed true. It is necessary to distinguish: to test for truth is one thing; to utter is another. Of these two things, the former is the duty to which men must be driven by criticism if they be not drawn to it by love of truth. Once the test is made and the doctrine found not wanting, then, and not before, It may be legitimately urged home with full ardor by all the arts of utterance even though the truth be thus made to burst upon us like the thunder of Wagnerian music, making the mountains tremble, the seas vibrate, and seeming to shake the very rafters of the sky.3 C. J. Keyser, "Educational Ideals that Are Most Worthy of Loyalty,” The Human Worth of Rigorous Thinking (3d ed.; New York: Script a Mathematics, 1940), p~. 3'I"9. ©

C. J. Keyser, "Convictions and States of Mind,” Mole Riilosophy and Other Essays (New York: E. P. Dutton and Co., 1§4V), pp. 28 f. Keyser, Mathematical Philosophy, op. cit., p. 152.

46 The Keyserian emphasis was placed on the former process of gaining conviction; on conception over ratio­ cination*^; on the premises: Most errors of thought are due, not to bad logic, but to false ideas,2 After carefully reading • . . Sumner and Keller’s Science of Society • • • I think it safe to say that the astounding falsity of the conclusions drawn by * ♦ • primitives is, like the falsity of those often drawn by civilized folk, due not so much to lack of logical faculty as to lack of knowledge, not so much to bad reasoning as to ill-defined ideas, not so much to il­ logical inference as to false premises.3 And there were indications that Keyser would not be one to cover up differences of opinion: Indeed, given a competent jury, hardly any other undertaking could be more stimulating than to defend mathematics, even in dog days, from a charge of being unworthy to occupy, In the hierarchy of arts and sci­ ences, the high place to whieh, from the earliest times, the judgement of mankind has assigned it* But, unfor­ tunately, no such assertion has been brought, brought, that is, by persons of such scientific qualifications as to give their opinion in the premises weight enough to call for serious consideration.^ But differences of opinion must be genuine In order to gain Keyser’s approval.

Considerable weight was assigned to this

point of view, Interpreted as the necessity for agreement 1Ibld., p. 311. o C. J. Keyser, "Exercises in Thinking About Number and Space: Transition to Algebra and Geometry (I),” Educational Review, XXVI (1903), 249. 3C. J# Keyser, "Elements of a World Culture: 1* Science and Mathematics," World Unity, VII (1930), 14. ^C. J. Keyser, "The Study of Mathematics," Columbia University Quarterly, XVI (1914), 237.

47 of meanings before differences of opinion could be known to be genuine.

And the functions of language were brought into

view: Contradictory opinions are always interesting; in matters so far above the illiberal cares of concrete life, they are even agreeable. To be highly enjoyable, however, contradiction must not be seasoned with mis­ apprehension of meaning. It must be a pure antithesis, maintained and beheld in the light. For, whatever may be true of the language of diplomacy, that of science and philosophy craves, above all things else, to be perfectly understood.^ What of Keyser1s preference among the forms of speech?

He stated no preference as such.

of mathematics, he favored dialectic.

But, as a teacher

Again, he placed an

emphasis: . . . I need not say that such a handling of ideas im­ plies much more than a verbal knowledge of their defi­ nitions. It implies familiarity with the doctrines that unfold the meanings of the Ideas defined. It is evident that, in respect of this matter, the scripture must read: Knowing the doctrine is essential to living the life. The evidence was evaluated as one-sided, consistent, and overwhelming that Keyser placed the emphasis on the pre­ mises, on "knowing the doctrine," on conviction before per­ suasion, on logical structure after the manner of the doc­ trinal function; and furthermore, those who had no respect for this emphasis had none of Keyser1s respect.

The evidence

•^C. J. Keyser, Reply to Bertrand Russellfs Criticism of "The Axiom of Infinity,” The Hibbert Journal, III (1905), 380. ^C. J. Keyser, "The Humanization of the Teaching of Mathematics,” The Human Worth of Rigorous Thinking (3d ed.; Hew York: ScrIpta Mathematics, 1940), pp. 78 f .

48 was found clearly understood in terms of the Keyserian doc­ trines of criticism, and the need for that criticism.

That

emphasis, as interpreted, was of major importance in this study; hence, an attempted summarization and a documentation of principle sources was presented here, and presupposed hereafter: Concerning the need for criticism, there are generali­ zations.

Judgements are severe.

”The Few Wisdomtf is not

to be intrusted to conventional methods merely because they are conventional: "lectures, reading, writing, and discus­ sion,” all of them linguistic, sometimes produce ”only gas, gas, infinite gas.”

Some advocates invent, and advocate, p a ”smeary amorphous mess,” which may be characterized as having no concern for ”great, vague, undefined, often indefinable”

terras.

The ”evil” of such ’doctrines*

"persists

and grows despite much hearing of lectures, much reading, 4 much writing, and much discussion.” ”. . .

We are, in general, much less concerned to

have our doctrines ultimately true than to have them instantly effective. . . . ”

And, ”We are n o t ,--however much we pretend

to be,--endeavoring to enlighten our fellow men--we are ^tfA Word About the Few Wisdom and Its Obligations,” Columbia University Quarterly, XXI (April, 1919), 118-124 pass i m '. gI b l d . 3 Ibid.

4Ibid

49 endeavoring to influence them.

. . ,"1

it is "the practician,

the partisan, the propagandist" who most desires to avoid ’k*16 "light" and retain the "h e a t . Well, you may say, what is to be done about it? What is the remedy? The remedy is— Criticism--the Gad­ fly: patient, unsparing logical criticism of one's own work In doctrine building; and, In all subjects, keen, merciless, stinging, gadfly criticism of any and all half-baked, logically amorphous, flabby doctrines pre­ tending to be important embodiments of truth or vessels of wisdom. Men must be driven by art,--the art of criticism,--to levels of excellence higher than those to which they are drawn by unenlightened nature.^ The nature of that criticism was summarized in such a way that the pattern of the doctrinal function is unmis­ takable: The type of criticism I am here advocating and urg­ ing as supremely important shapes Itself, as you see, very simply. Confronted by a doctrine in any department of thought, Criticism demands answers to these questions: What is assumed--what are the postulates? What are the undefined, or variable, terms? What are the theorems or proved propositions and what the defined, or cons-bant, terms? How have the theorems been deduced, and the de­ fined terms defined? What meanings have been assigned to the variable terms, and how? Upon these questions, criticism, if it is to be criticism of Thought, is bound to Insist--there is no alternative. Such criti­ cism is a civilizing agency— the guardian of the prin­ ciples of freedom. Without it, the world becomes-a wilderness of error and lust--the garden of the Devil. Easy to ask, the questions are, in general, not easy to answer, and the difficulty of answering rightly is usually greatest just where it is most important to compel an answer--in the case, that is, of amorphous, emotion-charged "dynamic” doctrines that pretend to aim at enlightenment but really aim at victory and win it by appealing, not to love of truth, but to lust for 1 146.

Keyser, Mathematical Philosophy, op. cit., pp. 144--- ------------------ -------------

2Ibid. 3 Ibid.

50 power or gain. If the author be unable to answer, criticism must drive him back tothe silence of the cloister for further study.*** Thus it appeared

that the Keyserian emphasis was

unmistakably placed; that "emphases perpetually shift their incidence” ; that mathematics and speech "penetrate and overflow the walls we surround them with, and mingle their waters in one vast sea": Are mathematicians rhetoricians? Rhetorician? "That is, of all things"--the mathematician will say--"exactly what I most certainly am not." And he should not be harshly blamed for disowning the character; for, by empty-headed advocates of good causes and by full-headed advocates of bad ones, the art of rhetoric has been so much abused in the world that "rhetorician" has come to be, oftener than not, a term of reproach. Nevertheless Rhetoric is a perfectly good name for the greatest of all the arts--the art of expression by speech. "Thought," said Henri Poincare', "is only a flash of light between two eternities of darkness, but thought is all there is." How much poorer we should be, had the great thinker not expressed this thought, so beautiful and so poignant, all will know who have worthily meditated upon life and the world. Thought unexpressed is thought concealed, and concealed thought--light hid under a bushel--fades and perishes with the thinker. Expressed, however, it lives and grows, engendering its kind, adding its flame to the flame of other thought, and so that radiance which is "all there is" increases and tends to abide: it is expression, and especially expression in speech,--expres­ sion by the art of rhetoric,--that gives Increase and perpetuity of light to the narrow vale between the dark eternities• And, now, rightly using the term "rhetoric" to denote the art of expression by speech, my thesis is that mathe­ maticians are all of them devoted rhetoricians and the best of them masters of the art. The thesis is not diffcult to maintain. For what does the art demand? What are the first qualities of Style? Clarity? Energy? Order? Unity? Convincingness? Restraint? Beauty? In respect to these things no literature surpasses the litera­ ture of mathematics. It may not Indeed be easy to under­ stand, for the understanding of it requires a fair measure

^Ibid., pp. 151 f

51 of mind,--imagination, especially, and logical sense,— but the difficulty inheres in the subject and not in the manner of handling it, for the latter is clear-clear in its definitions, clear in its enunciations, clear in its demonstrations; its energy may not be easy to feel, for the feeling of it requires a certain order of sensibility, but energy is always present in a high degree--indeed the whole vast symbolism of mathematics, invented with a view to the effective use of intellec­ tual energy, is charged therewith beyond the measure of common words; its order may not be easy to appreciate, for it is the order of logic, beginning with principles and pursuing their destined consequences under the subtle rule of fate; itsunity may not be easy to grasp, for it is the unity of a whole owing its integrity to the inner bond of implication; its convincingness may not be easy to sense for it is disinterested, dispas­ sionate, purely intellectual, ideal; its restraint is the restraint of direct achievement by the simplest means; and its— Beauty? Its beauty is two-fold; the exquisite austere beauty of sheer form; and a unique kind of dictional beauty, due to the union, in mathema­ tical nomenclature, of two qualities not elsewhere united. I mean a certain literary quality, not essential to mathe matics as such, and a certain perfection of logical quality which neither "the literature of power" nor (out­ side of mathematics) "the literature of knowledge" attains .■** P.

A List of Keyserian Memorabilia

Among the books Keyser praised was Memorabilia Mathematica, in which Robert E. Moritz listed, from his tenyear collection, thousands of quotations. term, however, was incidental.

Borrowing his

What Keyser said in closing

two chapters on limits in his Mathematical Philosophy might b© paraphrased, to read:

"I have now spoken of Keyser and

Keyser conceptions at far greater length than I had originally Intended to do.

If I have thus exhausted your interest and

■^Keyser, Mathematical Philosophy, op. cit., pp. 170172.

52 patience, I assure you that I have by no means exhausted the subject.**

These memorabilia were intended to complement,

reinforce, round off this introductory biography: Absolute certainty is a privilege of uneducated minds--and fanatics. It is, for scientific folk, an unattainable ideal.3Freedom of thought,--intellectual freedom,--is con­ ditioned, restricted, limited; but it is fundamentally limited by only one Law--the law which says to Intel­ lect, "Thou shalt not Incur a contradiction in terms.*1 This law is the eternal guardian of intellectual interity; reverence for it,--the disposition to keep it,— s the absolute invariant of intellectual life; dis­ regard of the law,--I do not mean inadvertent violation of It,--means intellectual extinction: for intellect, disloyalty is death. Incidentally, we thus glimpse ano­ ther phase of the truth . . . that mathematics is the study of Fate and Freedom.2

f

When, in the course of an address, Charles Sanders Peirce, a great logician, had named Imagination, Concep­ tion, and Generalization as being the characteristic elements in the constitution of geometric genius, and paused, some one in the audience called out the challenge: “What of Reasoning?** Instantly came the response: “Ratiocination? That is but the smooth pavement on which the chariot rolls.'*3 The critical mathematician has abandoned the search for truth. He no longer flatters himself that his propo­ sitions are or can* be known to him or to any other human being to be true; and he contents himself with aiming at the correct, or the consistent. The distinction is not annulled nor even blurred by the reflection that consis­ tency contains Immanently a kind of truth. ...

We must not forget that, In respect of knowledge,

^Mathematical Philosophy, op. cit., p. 120. 2 Ibld., pp. 241 f. 3

.

“Mathematics and the Dance of Life,** op. cit., p.

202

4

“Principle Mathematics,” op. cit., p. 216.

"the present is no more exempt from the sneer of the future than the past has been."-*The next to the most difficult thing in the world is to get perspective; the most difficult is to keep it. The fate that has fashioned the languages of man is no doubt a very great poet but, as a logician, it appears to have been fairly idiotic,3 Adequate statement economizes argumentation.^

n G. J • Keyser, "The Walls of the World; or Concerning the Figure and the Dimensions of the Universe of Space," The Human Worth of Rigorous Thinking (3d ed.; New York: Scrip^a Mathematics, 1940), pp. 93 f . 2C. J. Keyser, "Speech at Butler Dinner," Columbia University Quarterly, XIII (1911), 9. ^The Pastures of Wonder^ op. cit., p. 115.

^Science and Religion, op. cit., p. 59.

PART TWO PRESENTATION AND COMPARISON OF DOCTRINES

CHAPTER III SOKE QUESTIONING- OF QUESTIONS AND PSEUDO-QUESTIONS But why pause to investigate questions as such? Why concern oneself with questions about questions when it so vitally important and so difficult to meet the inces­ sant demands of questions about the world of non-questions— the world of things? A sufficient answer, though brief and incomplete, is found, I believe, in the following considerations: (1) A serious study of questions as such might be ex­ pected (a) to disclose a criterion (or criteria) for discriminating questions from pseudo-questions, and (b) to yield sorely needed skill in applying such a test (or tests) to concrete cases, which continually arise# That consideration has the advantage or disadvantage— according to temperament or taste--of being semi-utili­ tarian. (2) A more disinterested or idealistic motive is fur­ nished by the fact that questions, at once innumerable and endlessly diversified, are a unique kind of rela­ tions. . . ♦ The j»elation-aspect of questions is P©rfectly obviously [si(Tl and highly significant. A mind M asks a question Q about an object Q (here supposed to Be neither a question nor a mind). § is a go-between; it connects M and 0; it is a relation having M for a re­ ferent and 0 fora relatum. One's primary interest may be in the I's or in the Q's or in the O's. In any case the interest Is legitimate, needs no defense, is, like beauty or joy, its own excuse for being. . . . (3) The relations called questions are facts, or phe­ nomena, of Nature, being quite as natural as bodies or minds or sounds or sunshine or colors. A given question, or question relation, has a form or physiognomy and it has a structure or anatomy. I have said "physiognomy because, as Wittgenstein has pointed out, sentence forms, though they cannot be said, can be shown and perceived. In respect alike to their physiognomy and to their ana­ tomy, questions, or question relations, differ enormously, quite as much as do the minerals of the earth or Its plants or its animals.

55

56 Such considerations make fairly evident, I think, the possibility of a theory or doctrine or Science, if yon please, of Questions— of questions regarded as relations between Mind or minds and the universe of things that en­ gender Curiosity, or beget Wonder. Of that science there would be two distinct, though closely related, branches, which might be respectively called the Comparative Physi­ ognomy, and the Comparative Anatomy, of Interrogations. The development of these branches would be both suffi­ ciently difficult and sufficiently significant to engage o n e Ts best powers of analysis.3A.

Speech Doctrines Concerning Questions

In the first chapter, that most important personage, student X, was introduced.

What would X probably encounter

as question-doctrines? In the speech literature examined (all of it confined to argumentation and discussion), varieties of questions were found.

They may be considered as belonging to two types.

The speech authors said what seemed to amount to this:

First,

there are questions for discussion, which may be considered a s , or analogues of, propositions for argument.

These are

notably complex in the sense that they are designed to elicit discussion.

If they called for answers that were too simple,

such as Tfyestf or "no," they would not be suited to their primary purpose.

They are advisedly geared to the group or p audience interests, capacities, knowledge, and purposes :

^C. J. Keyser, "Panthetics,n Mathematics as a Culture Clue and Other Essays (New York: Scripta Mathematics, 1947), pp. 265-267. ^See, for example, J. H. McBurney and K. G. Hance, The Principles and Methods of Discussion (New York: Harper and Brothers, 1939 ), p p . 51-56. Proposit ions for argument, though sometimes called questions, are being deliberately slighted here because they are considered elsewhere, especially ch. IV.

57 they must be suited to speakers and listeners.

When properly

formulated, they tend to stimulate, delimit, and direct the discussion.

Second, there are "ordinary” questions.

These

may, often do, undoubtedly should occur during many--if not all— phases of either argumentation or discussion. speaker questions his sources of data, in reading,

The in inter­

views, etc.; he questions authorities, and pretenders to that office; he questions his own assembled evidence and reasoning, and that of his fellow participants. receive questions, as well as ask them. fellow participants and audiences.

And speakers

They come from

Although the authors have

been neither universally concerned with questions, nor (when explicitly concerned) disposed to mention every foregoing aspect, all of them must have realized that speakers are literally immersed in a sea of questions.

"To escape ques­

tions," the authors might say, "would be to escape argumen­ tation or discussion." It appeared to be no news to any speech author that questions of the first type should be carefully formulated. But concerning questions of the second type, student X ’s discovery of question-doctrine would depend upon where X looked;

so would the nature of the doctrine depend upon it.

A few examples should suffice: A debater often encounters an opponent whose power lies less in his ability to prove an issue than in his ability to evade it. Such an opponent is facile in shifting ground and can readily becloud the point in dispute. He is like a cuttlefish that squirts the water full of a black excretion and escapes in the darkness.

58 In exposing and cornering such a man, there is hardly a better way to "pin him down” than to compress the point in issue into a single, clear, direct question and demand an answer* The question, of course, needs to be framed in such a way that it cannot be readily evaded or distorted from its intended meaning; also, in asking the question, it should be presented In such a forcible and imperative manner that a failure to answer will be unsafe** There are some questions which defy an answer* Jesus frequently used the question to confound his opposition. When in the temple teaching, his authority was questioned by the priests and elders. He asked them this, "The baptism of John; whence was it? from heaven, or of men?” They had no answer. To say from heaven condemned them for not accepting it; to say from men would bring upon them the disfavor of the people* With this master stroke Jesus confused and silenced his opposers. This, of course, creates a dilemma.® The wording of * . * questions should receive the same careful consideration which is bestowed upon the wording of a proposition* The questions must be clear and unambiguous and must call for definite and direct answers* Ho opportunity for evasion should b© allowed. Furthermore, these question® must be worded forcibly and emphasised in such a way that an opponent will not dare to leave them unanswered. On the other hand, if an opponent propounds certain questions to which answers are demanded, the debater must either answer these questions satisfactorily or show good reason why they should remain unanswered*^ Or, student X might have read what is perhaps the ful­ lest available treatment of "ordinary” questions in Judson and Judson*^

They list ten "wrong kinds,” seven "right kinds,”

^J* M* 0* If©ill, 0. Laycock, and R. L* Scales, Argumen­ tation and Debate (Hew York: The Macmillan Co., 1927]",’ pp. 410 f ^Crocker, Argumentation and Debate (Hew York: Book Co., 1944), pp.fiSST?

American

A* Ketcham, The Theory and Fractice of Argumentation and Debate (Hew York: ffiSe1Ha'cSllIan 'ho., l9^ & ), pp. 133 f* Judson and E.Judsaa* Modern Group Discussion (Hew York: The H* Vtr* Wilson GO., 1938), pp * 125-124' pa aa Ira.

59 and five kinds which vary in form and complexity.

But X,

this writer, or anyone could not have found, anywhere in the speech literature examined, a treatment of 'pseudo-questions equivalent to the Keyserian doctrine. B.

Keyserian Doctrine of Questions and Pseudo-Questions

!lNot everything having the form of a question is a question.

It is easy to write something that looks like a

question or to make a noise that sounds like a question but is not one.’1***

It was apparent at once that Keyser seemed

to explore where some others had assumed.

Except for the

formulation of questions for discussion, the speech authors, for the most part, neglected to state or Imply such doctrines as these: It is commonly but erroneously believed that it is easy to ask questions. A fool, It is frequently said, can ask questions that a wise man cannot answer. The fact is that a wise man is able to answer many question that a fool cannot ask. A question is something that calls for, and admits of, an answer.^ Some innocent people sometimes try to show their pro­ fundity by trying to ask unanswerable questions. They always succeed in showing it--to those who know that there can be no such thing as an unanswerable question. Questions do not fall Into two classes, the answerable C. J. Keyser, wHard to Ask Questions,” Mole Philosophy and Other Essays (New York: E. P. Dutton and G o ., 1L927), p. 39. ^Keyser, "Panthetics," op. cit., p. 262. C. J. Keyser, Humanism and Science (New York: bia University Press, 1931), p . 54•

Colum­

60 and the unanswerable* All questions are answerable* To speak of an unanswerable question is like speaking of a footless tripod or a round square--a contradiction in terms* Every possible question belongs either to the class of those that have been answered or to the class of those that have not been answered yet but can be — ignoramus we admit, of course, but no ignorabimus^ What are sometimes

called unanswerable questions were

given a different name, their importance was signalized, their nature was described, and examples were given— all in order to show the more relevant aspects of Keyserian doctrines Had it been easy in all cases to discern whether a word combination having the form of a question was really a question or only a pseudo-question, the world of man­ kind would have been spared an immeasurable amount of pathetic mythologizing, theologizing and philosophizing as well as countless quarrels, persecutions, and wars.2 I wonder when, if ever, there will be produced a thorough-going Critical History of Human Curosity. Ob­ liged to cover every manner of human thought and human speculation--mythologies, cosmologies, religions, ethi­ cal systems, theologies, philosophies, and science in all its stages and forms-~such a work would have to be truly encyclopedic in scope. At least one volume of it would be required to portray what we may call the Role of Pseudo-Questions in Human Thinking--to tell, that is, the long pathetic story of the deep ponderings, the eager researches and meditations, the countless books, the end­ less debates, the bitter strifes and persecutions and murders and wars that have resulted in the course of the centuries because men, mistaking pseudo-questions for questions, have been so bent on finding answers to them, though there were none to find, that, unwilling or unable to admit defeat, they invented pseudo-answers, and then, mistaking these for genuine, endeavored by persuasion and by force to impose them as truth upon the world.® A pseudo-question is a word combination which has the form of a question but has no meaning and so admits of 1 Keyser, "Hard to Ask Questions," op. cit*, pp. 38 f. p

^Keyser,

Humanism and Science, op* cit., p. 57.

^Keyser, "Panthetics," op. cit., p. 263.

61 no answer. It is meaningless in the sense that, either explicitly or implicitly, either plainly or subtly and obscurely, it involves a contradiction in terms. Pseudo­ questions abound. A fool can propound them; so can a wise man; and they do it often, both of them, without intending to do it. A few examples will serve to clarify. Who made the maker of all things? Which is more Identical, the true or the beautiful? When did time begin? ¥tfhat will be the velocity of light after time has ceased to be? What are the outer walls of space? How did being originate? What is the essence of electricity? Why Is a circle round? Why does the sun attract the earth? Why do the opposite sexes attract one another? Why do oxygen and hydrogen combine to form water? Why are things as they are? Why do events happen as they do? Why is there anything at all? Such are a few random specimens of pseudo-questions. Many w h a t - 'questions,* most w h y - 1questions,r a majority of ’questions' respecting absolute essences and origins, and many others, are pseudo-questions--meaningless, un­ answerable .I Presented with a question-form, how did Keyser handle it?

There were two examples which seemed to be (1) represen­

tative, and (2) indicative of about how far Keyser went toward a “science of questions” : The other day a distinguished Hindu philosopher said to me: “Permit me to ask you a question.” And then he said: "What is the relation of the personal pronoun I to Consciousness?” Is that a question? Presumably the philosopher re­ garded the pronoun I as denoting something and the term Consciousness as denoting something and would have said that his “question” is equivalent to this: “What is the relation of that which the personal pronoun I denotes to that which the term Consciousness denotes?” But does the pronoun I denote something or somethings--many dif­ ferent things? The latter, it seems, for the philosopher, being a Hindu, may say: ”1 think it wrong to eat meat.” And John Bull will reply: ”1 don't.” Certainly the two I's do not denote the same thing. So the "question” now stands: “What is the relation of the many things which the pronoun I denotes to that which Consciousness denotes?” Of course one may wonder whether the pronoun I really de­ notes. But let that query pass. We must ask, however, whether there is something which the word Consciousness

Keyser, Humanism and Science, op. cit., pp. 55 f.

62 denotes, for, if there is not, that fact would itself show that the "question” is a pseudo-question* I am certain that I arn sometimes conscious and I believe that you are so, too* But from the fact that there are conscious beings in the world it does not follow that the world contains an object called Consciousness, just as from the fact that there are sweet things in the world it can not be inferred that there is such a thing as "cosmic saccharinity." Again, our philosopher speaks of "the relation" as if there were but one* There may be none but, if there be one, it is very probable that there are many. I will not pursue the matter further. Verily it is not easy to ask questions.1 Yonder, not far away, is an orchard. Let us call it yonder orchard. And let us suppose that Brown, the owner, and no one else, knows it contains exactly eight (8) trees. He may confront us with the following questions: (1) How many trees are there in yonder orchard? (2) How many count-words are needed to count the trees in yonder orchard, and in counting them what countword will be thus used last? (3) What is the numerical designation (the proper name) of the class (of equivalent classes) of which the class whose members are the trees of yonder orchard is a member? (4) What is the number of trees in yonder orchard if the orchard be such that "if 2 were 3, the trees of the orchard 12 would be"? Examination of these questions shows: (a) that there are 5 of them since (2) is double; (b) that their dif­ ferences of form or physiognomy and their differences of structure or anatomy are some of them obvious and some of them exceedingly subtle; (c) that to each of the questions the right answer is eight T 8 )J (d) that in the answer to either of the questions (2) the answer to (1) is contained implicitly but not explicitly; (£) that the answer to (1) or that to (2) is implicit but not explicit in the answer to (3); (f) that the answer to (4) contains the other answers neither implicitly nor explicitly; (g) that, though all of the questions seem to involve the orchard essentially, (4) does not; and (h) that each of the ques­ tions, (1), (2), and (3), sends us to the orchard for an answer but (4) does not, the answer to (4) being found solely by inspection of its terms, without any reference to the external w o r l d .2 •^Keyser, "Hard to Ask Questions," op. cit., pp. 42-44. 2Keyser, "Panthetics," op. cit., p. 267.

63 Such were the question-doetrines as set forth by Keyser. C.

A Comparison of Question-Doctrines

When the speech views were compared with the Keyserian views, these seemed to be genuine differences: 1.

The Keyserian literature contained no distinction

comparable to that made for speech between questions for discussion and "ordinary" questions; but the Keyserian dis­ tinction between questions and pseudo-questions, though not found in the speech literature, would seem to be applicable to all question-forms•

The speech authors seemed to view

a question as any question-form which has the function of eliciting, delimiting, directing, and,

in general, stimulating

talk; they should be unambiguous, unmistakable, and answerable. But a speech "answer" could be a Keyserian pseudo-answer to a pseudo-question unless "demand an answer," "defy an answer," and similar phrases are equated with "answerable" and "unan­ swerable ." 2.

In general,

the speech literature was not found

to contain doctrines equivalent to these Keyserian doctrines: (1)

that question-forms may be misleading;

be "hard to ask questions";

(2) that it may

(3) that a question, to be a

question, must be answerable; (4) that it may sometimes be difficult to distinguish between questions and unanswerable question-forms, and that failure to make the distinction may account for some supposedly undesirable disagreements;

(5)

64 that questions may differ as to how answers may be obtained according as they pertain to Keyserian realms of the Actual or Possible; and (6) that perhaps not all "answers" are genuine answers# With perhaps more concern for contrast than precision one might make the difference one of self-reflexivenesst Keyser questioned questions, whereas the speech authors ques tioned things#

CHAPTER IV PROPOSITIONAL TYPES As forms for answering questions proposltional forms are so superior to all others that they may properly be regarded as the forms for that purpose. It became evident in the earliest stages of the study that "proposition" had been assigned multiple meanings by the various authors.

For the sake of economy and clarity

therefore, types of meanings were distinguished by prefixes. Propositions for argument (and questions for discussion) are said to be of three types: propositions);

propositions

(1) of fact (F-

(2) of value (V-propositions); and (3) of

policy (P-propositions).

Outside the quotations from Keyser

where confusion might arise, "K-" was used for "Keyserian"; thus, "K-hypothetical" or "K-categorical" distinguishes the Keyserian and speech usages.

Where "K-" does not appear,

except In quotations from Keyser, the conventional 'speech usages were intended. A.

Proposition-Doctrines in Argumentation and Discussion

The various usages of "proposition" were similar enough to warrant unusual precautions in the attempt to T

C. J. Keyser, Humanism and Science (New York: Co­ lumbia University Press’, 1931), pp~. 61 ~f.

65

avoid confusion.

Ordinarily, some usages could be ignored.

Since numerous factors were involved, however, a highly condensed summary seemed preferable.

Then those usages

which might have been ignored could be retained, thereby providing a more adequate foundation for comparisons,

sum­

marization, and inferences. 1.

The distinction between propositions for argu­

ment and questions for discussion is no doubt important for many purposes.**-

For the sake of greater simplicity, however,

p r o p o s i t i o n for argument" was used jas including "question for discussion."

This deliberately emphasizes their simi­

larities, which were considered much more important than their differences for this study. 2.

By "proposition for argument" the speech authors

said they meant such things as:

(1)

• • the expression of

a judgment in language • • . stated in a declarative sen2 tence . • (2) "the statement to be supported or attacked 3 in an argument (3 ) " . . . a statement of the posi­ tion which the writer or speaker must establish or overthrow. .. ***J. H. McBurney and K* G. H'ance, The Principles and Methods of Discussion (New York: Harper and Brothers, 1939), pp. 55, 183 f. ^J. M. O ’Neill and J. H. McBurney, The Working Prin­ ciples of Argument (New York: The Macmillan Co., 1932), p. 12. The authors1 meaning of "judgment" was explained on p. 72. 3 J. A. Winans and W. E. Utterback, Argumentat ion (New York: The Century Co., 1930), p. 28. 4 J. M. O ’Neill, C. Laycock, and H . L. Scales, Argu­ mentation and Debate (New York: The Macmillan Co., 1927), p T T s : ---------------

67 and (4)

. . that which is stated or affirmed for the pur­

pose of discussion.

It is a provisional statement, usually

stated affirmatively,

the truth or falsity of which must be

demonstrated in the argument. 3.

. . .

Different aspects of the distinctions and inter­

relations among F-,

and P-propositlons, as sampled from

the speech literature, were useful when the comparison of doctrinal families was made. F-propositions:

(1) 11. . . are those which are con­

cerned only with the truth or falsity of assertions.

They

involve the existence of things, the occurrence or classifi­ cation or causation of acts or events.

They depend wholly

upon the establishing of fact for proof”

(2) ” . . . are

really not good propositions for debate, but are rather propositions for investigation” ;

(3) ” . ♦ . do not suggest

any change from the status quo” ;^ (4) raise . . . the simple question: Is this true? It is probably safe to say that most questions of this type do not lend themselves to profitable discussion. It Is futile and senseless to spend much time discussing a question which can be settled simply and accurately by observation, measurement, classification, or experi­ mentation.° For instance, do not debate the question 1 A. M. Pellegrini and B. Stirling, Argumentation and Public Discussion (Boston: D. G. Heath and Co., 1936), p. 7. %£. H* fsFagner, Handbook of Argumentation (New York: Thomas Nelson and Sons ,~I936~), pZ 15 . ^J. M. O ’Neill and R. L. Cortrfght, Debate and Oral D i s ­ cussion (revised ed.; New York: The Century Co., 1931), p. 41. ^ O ’Neill and McBurney, op. cit., p. 18. 5

McBurney and Hance, op. cit., pp. 46 f.

68 of a horse's weight; weigh the horse,1 This does not mean, of course, that a complex problem of many facts, such as the causes of war, Is open to the same objec­ tion; 2 and (5) affirm • . . the existence of some particular relation between two ideas. Any relation may be employed in such a pro­ position, but among those most commonly affirmed is that of classification* • • • cause and effect, • , * and • , • analogy.^ V-propositions: * . . are those which assess the worth of the subjects in dispute* They assert that something is or is not beneficial; they call for approval or disapproval of a belief or an idea. They differ from questions of fact in that, whereas in the factual question the tests of facts are generally agreed upon, and may be secured by a consultation of qualified experts, as a rule, in those of value no such agreement exists, and It is necessary to prove them by other means than the use of testimony. In other words, propositions of value attempt to declare that to be true which can never be accepted as a fact, but which may be accepted as probable, If made to conform to certain approved and applicable standards of judgment, of taste, or of weight,4 P-propositions:

(1) are "the most usual and probably

the most valuable problems for discussion,

. . ,

Here the

typical question raised Is:

What should be done? or, Should

this action be t a k e n ? " a n d

(2) "* • • are characterized by

the fact that they always suggest a change in policy or a ^O'Neill, Laycock, and Scales, op. cit,, p. 30. Nichols, Discussion and Debate (New York: Brace and Co., 1941")', pp. 23 f . ^Winans and Utterback, op* cit., p. 50. 4 Wagner, op, cit., p. 16. 5

McBurney and Hance, op. cit., p. 49.

Harcourt,

69 new policy, that is, some departure from the status quo."^ And related to, but distinguished from P-propositions is another kind: Propositions advocated as theoretically sound differ from propositions of policy in that they do not suggest any change from the status quo; they do not call for personal action, nor do they call for the endorsement of a policy change. The only question that is raised is the desirability of a given policy, entirely apart from the question of adopting or abolishing the policy.^ Also closely related to P-propositions is a kind of problem with which they may be concerned: The problem of belief is concerned with belief in, or approval of, a speci'fic proposal. It does not neces­ sarily depend upon an ascertainment of facts for Its answer, nor does it always demand support for enacting a specific proposal. Sometimes, indeed, it is impossible to provide a conclusive factual basis for an answer. !,Would a federal union of leading democracies bring world peace?’* Is a problem of belief* We may believe that a union would bring peace and yet not be able to prove it, and we may not be willing to approve steps to create such a union Now the word "should" is commonly taken as a distinc­ tive mark of P-propositions.

What does it mean?

It has been

said that ,!In representative questions of policy the term should is equivalent to i£ it_ a practicable proposal?"^ Though distinguishable,

these F-, V-, and P-propositions

Neill and McBurney, op. cit., p. 17. 2 Ibid., p. 20. *H. L. Ewbank and J. J. Auer, Discussion and Debate (New York: F. S. Crofts and Co., 1947), p. 80. 4

A. C. Baird, Discussion: Principles and Types (New York: McGraw-Hill Book Co., 1943), p. 32. Also see F. W. Lambertson, "The Meaning of the Word 1Shouldf in a Question of Policy," The Quarterly Journal of Speech, XXVIII (1942), 424.

70 were said to be closely interrelated.1 mined in terms of facts and values.

Policies are deter­

Since policies concern

the future, they are predictive and uncertain to some de­ gree.

But facts are the foundation for predictions.

Fur­

thermore, no P-proposition, nor presumably any other propo­ sition for argument, is proved all at once; there are stages In establishing the main proposition which may be described as establishing sub-propositions. supposedly, may be of any type.

These sub-propositions, Indeed, F-, V-, and P-

propositions are so closely interrelated that (1) the classi­ fication may be too sharp, and It may be a matter of the speaker*s Intention rather than statement form, but (2) Fpropositions should be phrased as (converted into) P-propositions. Now at least two authors were aware of a relevant ilimitation of argumentation and discussion: To argue over a fact implies a misunderstanding of what facts are, a disagreement over the reasonableness or source of the facts, or a disagreement over the meanings of the facts in question. If there is misunderstanding as to what facts are, argument over them is beside the This paragraph was based upon McBurney and Hance, op. cit., p. 49; G. Boas, Our New Ways of Thinking (New York: Harper and Brothers, 1930)V~pp. 4 f.; IlT P\ Graves, Argument: Deliberation and Persuasion in Modern Practice (New York: The "Gordon Co., 1938), pp. 20 f., 91; H. G. Kahskopf, "Questions of Fact vs. Questions of Policy," The Quarterly Journal o f Speech, XVIII (1932), 64 f.; O ’Neill, Laycock and Scales, op. cit., p. 19; Winans and Utterback, op. cit., p. 32; Pelle­ grini and Stirling, op. cit., pp. 11 f . R. M. Alden, The Art of Debate (New York: Henry Holt and Co., 1900), pp. 98 f .; and O ’Neill and McBurney, op. cit., p. 90.

71 point, because facts are found not through argument but through Investigation.! Discussion . . . has definite limitations in dealing with questions of fact. Facts may be worked over, clarified, and interpreted in conversation, but they can seldom be discovered by conversation. This does not mean that good discussion can get along with­ out facts. Nothing is further from the truth. It means rather that discussion must rely on facts which are brought in by members of the group, facts which have been got by direct observation, by practical ex­ perience, and by experimentation. These are the methods by which we tackle nature directly and wrest therefrom the facts and materials which must continually be forth­ coming If discussion and deliberation by and large are to escape stagnation and sterility.2 Turning now from propositions for argument to propo­ sitions of argument (or discussion):

categorical, hypotheti­

cal, and disjunctive propositions were commonly found to be associated with— indeed, they determine--syllogistic types. As examples:^ The categorical syllogism Isthe form in which cate­ gorical deductions are stated. It is characterized by the fact that its major premise is always a categorical or unqualified statement of either a relationship of causation or resemblance which admits of no conditions or exceptions.^ The disjunctive syllogism is the form in which ■^McBurney and Hance, op. cit., p. 141. ^Ibid., p. 34.

Also see pp. 13, 28, 177, 178 f.,

195. ^Similar doctrines may be found; e. g.; ibid., pp. 196 f; Pellegrini and Stirling, op. cit., pp. 33-35; Ewbank and Auer, op. cit., p. 156; Graves, P* 103; Nichols, op. cit., p. 332; Winans and Utterback, op. cit., pp. 73, 75; 0 *Neill, Laycock, and Scales, op. cit., p p . 179, 131; L. Crocker, Argumentation and Debate (New York: American Book Co., 1944), p. 119; and A. C. Baird, Public Discussion and Debate (2d ed. rev.; Boston: G-inn and Co., 1937), p p . 130, 136.

^CMNeill and McBurney, op. cit., p. 140.

72 disjunctive deductions are stated* It is characterized by the fact that its major premise is always a disjunc­ tive statement setting forth certain alternative possi­ bilities* Whereas a categorical statement expresses an unconditional relationship of causation or resemblance, a disjunctive proposition states alternative relation­ ships of causation or resemblance as follows: "Either a cyclone or earthquake caused the destruction of the city"; or "The books on this shelf are either biography or fiction."! The hypothetical syllogism Is the form in which hy­ pothetical deductions are stated* It Is characterized by the fact that its major premise always expresses a hypothetical or conditional relationship of causation or resemblance* We shall refer to the conditional or "if” clause In the major premise as the antecedent, and the clause to which the condition is applied as the con­ sequent.- Thus In the following syllogism, if the drouth continues, is the antecedent and, the crop will be lost, is the consequent: I* If the drouth continues, the crop will be lost* II* The drouth continued. III. Therefore: The crop was lost.** Not only should attention be called to the fact that the major premise may state either a relationship of causation or classification, but also to the fact that either of these relationships may be expressed categori­ cally, hypothetically, or disjunctively. It is on this basis that we classify syllogisms. If the major premise is a categorical statement of causation or classification, any deduction from it is stated in a categorical syllo­ gism; if the major premise is a disjunctive statement, a disjunctive syllogism results; and if it is a hypothe­ tical statement, the hypothetical syllogism results.3 One author seemed to express a more extreme orienta­ tion by statement forms:

"The categorical syllogism begins

with ’a l l 1 or ’every,’" Crocker^ wrote, begins with ’some* or ’if.’" ^Ibld ., p. 143. g Ibid., pp. 144 f. 3 Ibid.. p. 139. 4

Op. cit*, p* 115.

and it

* . never

73 Others had a different emphasis:

Among the speech

authors who gave propositional and syllogistic types con­ siderable attention, some were apparently concerned to show that any one form can be translated into any other form, "so'that we should have but one set of principles to which all formal reasoning can be reduced. Again, the speech authors wrote enough about induc­ tion and deduction to warrant a sampling.

As expressed by

the speech authors, these doctrines were quite important in comparisons and inferences; hence, it seemed wise to preserve the exact wording: Deduction attempts proof, while induction seeks probabilities. That is, deduction attempts proof in the sense that if premises are accepted as valid and if their relationship is sound they prove the conclusion. Xn the case of induction, however, the assembled evi­ dence impels the formulation of an hypothesis which asserts only a probability.* The great value of deductive reasoning is that when the premises of the syllogism are once accepted, the de­ duction from them is clear, concise, and cogent. For instance, twenty pages of Joseph H. Choatefs argument before the Supreme Court in the Income Tax Case are de­ voted to the proof of the premises in the following syllogism, which, once the premises are granted, estab­ lishes in a few lines the point Mr. Choate was conten­ ding for. An unapportioned direct tax is forbidden by the Constitution; the income tax is, in part at least, an unapportioned direct tax; therefore the income tax ***J. H. Hyslop, Logic and Argument (New York: Charles Scribner !s Sons, 1899), ~p. 15