Academic Freedom, Logic, and Religion [Reprint 2016 ed.] 9781512808520

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AMERICAN PHILOSOPHICAL ASSOCIATION EASTERN DIVISION

VOLUME 2

ACADEMIC FREEDOM LOGIC, and RELIGION Edited

by

MORTON WHITE for the Program Committee

1953

U N I V E R S I T Y OF P E N N S Y L V A N I A Philadelphia, Pennsylvania

PRESS

Copyright 1953 by UNIVERSITY OF PENNSYLVANIA PRESS Library of Congress Catalog Card Number: 52-4984

Papers for the symposia held at the annual meeting, at the University oj Rochester, December

28-30,1953

Officers of the Eastern Division, AMERICAN PHILOSOPHICAL ASSOCIATION President:

GLENN

Vice-President: Secretary-Treasurer:

MORROW

M A X BLACK

Lucius

Executive

R.

GARVIN

{ad interim)

Committee:

The foregoing officers and Filmer S. C. Northrop ex officio for one year, Susanne K. Langer (1953) Marvin Farber (1954) Roderick M. Chisholm (1955)

Morton White (1953) Leroy E. Loemker (1954) Milton C. Nahm (1955)

CONTENTS

Symposium:

T H E E T H I C S OF ACADEMIC FREEDOM

I.

George Boas

1

II.

Sidney Hook

19

Symposium:

ON

T H E ONTOLOGICAL

SIGNIFICANCE

OF

THE

LÖWENHEIM-SKOLEM THEOREM

I. II.

George D. W. Berry

39

John R. Myhill

57

Symposium:

A R E R E L I G I O U S DOGMAS COGNITIVE AND M E A N -

INGFUL?

I. II.

Raphael Demos

71

C. J . Ducasse

89

Symposium:

J U S T I F I C A T I O N IN S C I E N C E

I.

Frederic B. Fitch

99

II.

Arthur W. Burks

109

Symposium: I. II. THE

ETHICAL

REASONING

Abraham Edel

127

Douglas P. Dryer

143

PROGRAM

159

Symposium:

THE ETHICS OF ACADEMIC FREEDOM GEORGE B O A S A N D S I D N E Y H O O K

I . GEORGE B O A S

In discussing the question of academic freedom today, I am accepting as my own the following definition of academic freedom as given by A. O. Lovejoy in the Encyclopedia of the Social Sciences. Academic freedom, he says, is "the freedom of the teacher or research worker in higher institutions of learning to investigate and discuss the problems of his science and to express his conclusions whether through publications or in the instruction of students, without interference from political or ecclesiastical authority, or from the administrative officials of the institution in which he is employed, unless his methods are found by qualified bodies of his own profession to be clearly incompetent or contrary to professional ethics." If the term is used in this sense, then certain details should be emphasized: (1) Only the teacher or research worker in higher institutions of learning is covered. This excludes obviously the high school teacher, the elementary school teacher, and the vocational school teacher too. I cannot pretend to read the mind of the author of this statement, but it is easy to see that the restraints on the teacher in the lower schools may be founded on the immaturity of the students he is teaching. For there is still some reason to believe that a boy or girl is incapable of understanding certain subjects, that the methods of teaching the young must be adjusted to their immature minds, that they can be emotionally upset by certain methods of treatment which might be appropriate to their elders. Curricula are made up for such students by boards of education which are branches of the state and municipal govern1

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ments, and a person entering into the school system knows ahead of time that he is expected to conform to whatever restriction such boards lay down. This is not the case with higher institutions of learning even when they are supported by state governments. (2) The freedom involved extends beyond the class-room to publications and, though Mr. Lovejoy did not say so in so many words, publication might properly be defined so as to include speaking as well as printing. In other words, for our purposes when a scholar mounts a platform to deliver his views, he is publishing his views. This might be expected to be obvious, but I have found in recent discussions of academic freedom that it was supposed by some people to obtain only within the university's walls and there only in the class-room. Thus a Federal Judge of the Fourth Circuit said last February that "professors are not as free as other men. Like clergymen, they are members," he said, "of a sacred order, devoted to a sacred pursuit, responsible for a sacred institution . . . This does not mean that the professor must never say anything that could possibly injure his college, but it does mean that he is not free to speak, unless he is sure he is right." This restraint would make it practically impossible for any professor to speak even in his class-room. But the context of the speech, which I shall spare you, shows that the Judge was thinking only of speeches made outside the college walls. On the other hand, it may reasonably be expected that professors, as educated men, will be more careful of evidence and logical consistency than others. (3) The freedom involved, moreover, is supposed to be freedom from interference not merely from administrative authorities, but also from political and ecclesiastical authorities. What good would be obtained by freedom from administrative authority if churches and politicians were to restrain that freedom is difficult, if possible, to indicate. Administrations as a matter of fact have a good record of fostering academic freedom. Where they have failed, their failure seems to be attributable to pressure from without, from state legislatures, as in the famous Stokes Trial, from organized religious or patriotic groups, from organizations of veterans, from newspaper editorials. Hence freedom from administrative interference, unless it is backed up by freedom from political and ecclesiastical interference, turns the college into a cloister, isolating the professor from all intellectual contact with

GEORGE BOAS

3

the outside world, except in so far as he receives communications from without but cannot answer them. Such interference from without might take several forms. It might restrict the subjectmatters which a professor could properly teach; it might restrict the method of presenting a subject-matter; it might restrict the arguments which a professor was permitted to use in lecturing; it might restrict the source material and the reading which he used in his teaching. Each of these restrictions has been enforced in the past and to some degree is being enforced today. But beyond all this is the pressure exerted on administrations not to employ or to discharge professors whose competence in their special subjects m a y be unquestioned, but whose political or religious ideas are considered by certain sections of the public to be unsound. In this case, interference with what a professor teaches becomes practically interference with his right to earn his living. (4) Finally, it should be noted that M r . Lovejoy's statement does not give the professor absolute and unrestricted privileges to teach. If he is found to be incompetent or unethical by "qualified bodies of his own profession," he may clearly be discharged. H o w to persuade professors to pass judgment on their colleagues' competence, is to be sure a difficult matter to decide. But be that as it may, the principle that the best judge of a man's competence is his colleagues, is one which most of us would be willing to accept. II If this statement is reasonable, it will be seen that academic freedom is a species of freedom of thought. Freedom of thought is guaranteed to all citizens of the United States by the Bill of Rights and usually it has been maintained that until a thought expresses itself in action, a man is free to say whatever he believes to be true. T o use old-fashioned language, such a right involves t h e correlative duty to speak the truth, for I suppose that if we were given to deliberate mendacity, as a program, then no one would defend our right to speak our thoughts, though if our interlocutors knew about our failing, they would seldom be misled by our words. T h e usual justification for closing academic doors to known and avowed communists is that they do not speak the truth b u t rather teach whatever the p a r t y leaders tell them they should teach. I t may appear strange that such subjects as mathematics

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or astronomy or physics or chemistry could be interpreted as communist or capitalist, but we know from the Lysenko incident that some subjects, apparently remote from politics, may be interpreted as having political implications. We also know that in Hitlerian Germany painting and music, medicine and natural science, in fact truth with a capital T , were supposed to vary with the blood streams of the persons interested in them. I have also heard some religious people maintain that religion must permeate all our lives, as if an atheist could not be a good mathematician. I doubt whether anyone seriously believes that the binomial theorem would be any other according to Roman Catholicism or Marxism or Fascism or Unitarianism than it is according to mathematical logic. But presumably in the case of communism, a political belief is held to pervade all knowledge and modify one's conclusions. Such modification might consist in omitting certain subjects or certain ideas from one's teaching, rather than in misinterpreting them, so that one's students would be ignorant of certain facts and theories. Thus last spring I was notified by a college president that a woman whom I had recommended for a position in philosophy was rejected on the ground that she was a Roman Catholic and hence could not be expected to teach her subject objectively. Just what "objectively" meant in this discourse was none too clear, but I gathered that it meant that the person involved would omit certain ideas from her teaching and fail to examine others critically. Now it may be said that some subjects, unlike philosophy, are well established with a funded body of knowledge which everyone accepts. Such subjects might be said to be mathematics and the natural sciences. There may be said to be other subjects in which there is no general agreement, such as history or philosophy or the social sciences. Clearly, if this is so—and I am not saying that it is—then whether a man is a communist, a Catholic, an atheist, an Eighteenth Century Tory makes little difference. He will either be competent in his subject or he will not be. In the case of the latter body of subjects, if there is no funded opinion accepted by all or by most scholars, the only legitimate conclusion to be drawn is that different points of view are possible and where feasible should be heard. I do not happen to believe in the economic interpretation of history. But it is an interpretation of history which many historians much wiser and more learned than

G E O R G E BOAS

5

I have accepted. For all I know they may be right. Furthermore I am not an adherent of the philosophic school of subjective idealism or of Thomism. Should I therefore, assuming that I had the power to do so, prevent subjective idealists or Thomists from teaching in American universities? I t is clearly impossible to have every point of view represented even in large departments, if only for financial reasons. B u t surely a teacher should not be disqualified from exercising his profession on the ground that he believes in something. This may be called indifferentism, but I think that one can find two reasons for holding to it as a program. First and foremost is the assumption that the discovery of the truth is a goodin-itself; second that all truth is not as yet discovered. Nothing, as far as I know, is simply a good-in-itself, for things with terminal value often have instrumental value as well. B u t if one orients one's mind to the utility of a subject, one is as likely as not to escape its goodness. One need not be one of the thirteen kinds of pragmatist to believe that a true idea is more useful than a false one and that the surest way to land upon a false one is to look only for the useful ones. If one wants a maximum of stability within a society, the best way to achieve it is to surround it with a wall and let no one out or in. If besides that one can keep the physical environment stable, one will never encounter any new problems and the population will know only one set of ideas. T h u s a fixed tradition will be established and it will make very little difference whether the ideas in which the population believes be true or false or down-right nonsensical. We know that certain so-called primitive societies cling to ideas which have long been rejected by more advanced societies. This has not made them less stable nor has their population been less contented. When one reflects on such things, one soon sees that if one believes in the truth because of its instrumental value, one is following the wrong track. I t may well be that the truth will set you free, but it usually sets one free from the traditions of one's group and the compulsions which those traditions entail. No one other than the scholar was ever made more contented b y discovering that the ideas in which he has believed since childhood are false. Few things are more upsetting than that experience. B u t the scholar is precisely the man who can suffer such an experience and not be downed by it. In other words his task

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THE ETHICS OF ACADEMIC FREEDOM

is precisely to discover the truth and to disseminate it. He will of course soon discover that all truths arise in a context of assumptions, methodological procedures, basic metaphors, within a margin of error, and all the rest. But if he is careful in his exposition, he will state all these items. On the other hand, he will probably never discover them unless he is in communication with other scholars whose views may differ from his. When one has learned a technique of research, it takes on all the compulsions of habit and seems to be the one and only way to proceed. The individual scholar who is not in communication with his fellows has built up a wall around himself and naturally concludes to the universal necessity of all his inferences. But such a technique of isolation is not the only possible technique. To take but one instance, would the modern historian be any the better off if he had been isolated from all contact with Marxist thought? Should we continue to write history from the point of view of St. Augustine or Michelet or Carlyle? But if truth has terminal value, or must be sought as if it had no other, then it is absolutely essential that some self-correcting technique of seeking it be followed. And one might conclude from the history of our own science that such a technique has been found in meetings of this sort, in arguments presented in learned journals, in dialogues and debates, in other words, in dialectical exercises. If truth is not a terminal value, and again let me repeat that I am not saying that it does not also have instrumental value, then its utility will be determined by practical ends which may be aesthetic, ethical, religious, political or even economic. The influence of such interests does of course make itself felt in any theory. It makes itself felt in the choice of premises, in the selection of problems which one believes to be important, in some of the basic metaphors in terms of which theories will be phrased. But if truth does not have terminal value, then one is free both to recognize the influence of such interests in the structure of his beliefs and to do nothing to eradicate it. If we want beautiful theories, in the sense of logically consistent theories, regardless of their relation to fact, then the choice of premises is entirely arbitrary and if we want politically or economically satisfactory theories, then the choice of premises is limited to those statements which will imply the consequences which seem desirable. But

G E O R G E BOAS

7

most of us hope that we can arrive at premises whose utility consists in their implying true propositions, that is, true propositions of fact. W e therefore wish to be enlightened about our prejudices and sometimes all our defensive mechanisms come into play when they are indicated. I do not maintain that any human being will ever reach the point at which he can be sure that his premises are chosen for purely logical reasons, or that his basic metaphors are recognized for what they are, or that he has not been a victim of what M r . Lovejoy has felicitously called metaphysical pathos. B u t at least we can make the attempt to reach that point and modify our views when we are shown that we have not reached it. B u t academic freedom is not merely predicated on the theory that truth is a good-in-itself. I t is also predicated on another assumption: that all truth is not as yet discovered. I f everything which could be known were known, then the Augustinian dictum that man is not free to err would force itself upon us as an ultimate truth. A man is free to maintain that if A is greater than B and B is greater than C, then C is greater than A. B u t he would scarcely have grounds for complaint if he were not given a chair in mathematics. B u t his weakness would be called incompetence and any body of his colleagues could sit in judgment upon him and no one could complain that freedom of speech or of opinion had been violated. I take it for granted that if there are transitive asymmetrical relations, then A is greater than C and nothing more can be done about it. B u t suppose it were discovered that for transfinite cardinals this relation did not obtain. Would anyone maintain either that a mathematician had no right to examine the properties of transfinite cardinals or that, if he did, he must keep the results of his examination secret? On the contrary, one of the unwritten laws of the academic profession is that all truth has not as yet been discovered and that it is the business of the scholar to push the frontiers of knowledge as far back as he can. In certain fields, like that of philosophy in its various branches, economics, history, sociology, biology this has proved distasteful to large groups of people within society and these groups have not been silent in expressing their distaste for such novelties. T h e y have organized not only to suppress the writings of scholars who have published their results, but have also done their utmost to suppress the scholars themselves. Books have been removed from

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THE ETHICS OF ACADEMIC FREEDOM

libraries, men's reputations have been ruined, some have even been prosecuted by law. The possibilities of discovery, it is obvious, may take at least four forms. (1) We may deduce new theorems or consequences from knowledge already in our possession. I know of no rule of either logic or scientific methodology which determines the point at which a theorem or group of theorems becomes sterile. (2) We may perceive new problems arising not only within old subjectmatters but in fields traversing old departmental lines. Thus most of the work of Clerk Maxwell or of Dalton, of Lamarck or Morgan, of Freud and his school, of Marx and his disciples, has been directed to seeing that if accepted ideas were true, then new problems would arise which would require solution and consequently new hypotheses would be required to solve them. (3) We may apply acquired knowledge to practical problems and thus institute innovations in practice. One of the best examples of this lies in the field of jurisprudence and, if I am not mistaken, in economics. So long as the law is thought of as a set of eternal maxims from which the court has simply to deduce the logical consequences, so that the terms of a statute have a meaning independent of any social context, then such bits of knowledge as we are lucky enough to have acquired from psychology and cultural anthropology cannot be used. Indeed even today, though we have copious examples of courts using such knowledge in interpreting and enforcing the law, there is still hot debate about what a court can and cannot do in determining the precise meaning of a law. Yet the very people who think of a judge as a disembodied reason will still permit him to make a distinction between a mature man in his right mind, a child, a man acting under the influence of passion, a man temporarily or permanently deranged, a man forced by circumstances beyond his control to act as he acted. But as soon as one admits that a man acting, let us say, under the influence of liquor or of a strong passion is not a man in the sense of the law, then one is applying what one knows about human action to the interpretation of the law and is not merely deducing consequences from the words used in the statute. (4) We may finally discover new knowledge by a critical analysis of traditional beliefs. This is perhaps the hardest task which the scholar has to face, for scholars are by nature no less subject to the compulsions

GEORGE BOAS

9

of habit than other men. And yet at times in the history of philosophy men have done little more than that. The succession of Locke, Berkeley, and Hume may be interpreted, as far as their epistemologies were concerned, and usually are interpreted, as just this sort of exercise. Fichte's philosophical beginning may be seen in his critical analysis of the concept of his master's noumena. The revival of epistemological monism in the twentieth century may be seen as a more accurate analysis of the argument from what Ralph Barton Perry called the ego-centric predicament. I realize that these statements are all too superficial, but since this is not a class in the history of philosophy, but a paper to be read by critical minds, no harm will be done by them. Whatever truth is in them in any event is based upon the assumption that sometimes a thinker is inconsistent, ambiguous, fallacious in his reasoning, neglectful of certain facts, and that another thinker can point it out. This kind of exercise is sometimes condemned as sterile or destructive, but as far as I know, most of us are agreed that sometimes it produces results which are not only enlightening but fertile in reorienting the course of knowledge. Amongst the many activities of this sort is that of asking questions which traverse traditional lines of thought. I am thinking of such questions as those raised by biochemists, biophysicists, students of comparative literature, students of semiotics. Only a few years ago such questions would have been ruled out on the ground that they were neither biology nor chemistry nor physics, neither English nor French nor Italian, neither logic, nor psychology nor philology. But now that we have become accustomed to them, we begin to appreciate their significance and to see that the older classifications of the sciences rested on nothing more than tradition and that any question which makes sense deserves an answer. Nevertheless to be able to give the answer, indeed to be able to spot the problem, requires freedom from academic ritual. Ill I fail to see how restraints other than those of logic and methodology can help us in our discovery of new knowledge. For such restraints are bound to take the form either of maintaining that all possible knowledge of principles has already been discovered,

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which is the attitude of the dogmatists, or that all knowledge must be limited by its furthering of non-scientific aims. Do any such restraints now exist? First of all let me indicate some of the better known restraints which are put upon us by the general public. This ought not to take long for we are all aware of them. That there is a growing wave of authoritarianism in this country, initiated and propelled not merely by politicians, must, I should think, be obvious to all. What is this doctrine known as Americanism for instance from which the adjective Nan-American is derived? It is clearly not the simple acceptance of the Constitution with the first ten amendments, for the very sponsors of Americanism are the first to reject parts of it. They certainly reject the First Amendment and they seem to reject the Fifth. When a man writes an article or a set of articles in 1938, the meaning of which is perfectly clear to him, and then twelve or more years later is asked to state under oath whether or not the meaning of such articles is what the questioner maintains it is, and when he answers that it is not, and when he then is indicted for perjury because he says he did not mean what his questioner says he meant, then is a man free to speak? When a man can be trapped into making statements which an investigating committee knows beforehand to be false, shall he be charged with perjury? When a legislative committee investigating a man can publish its findings and at the same time not permit the man in question to defend himself, will not allow him to confront the witnesses against him, nor to cross-examine them, is the separation of powers actually in effect, even if the committee in question cannot impose penalties? When a man can be examined twice on the same charge by such a committee, pretending not to he a court, though found innocent by the first committee, is the prohibition of double jeopardy violated? When a man can lose his livelihood because he has availed himself of the constitutional right not to give evidence tending to incriminate himself, has the Fifth Amendment been violated? Now I am not a lawyer nor a philosopher of law, but to a plain man who thinks he is a loyal citizen, such practices look indistinguishable from malpractice, whatever technical name may be given them. And that they have been practised is obvious to anyone who reads the papers or the reports and hearings of congressional investigating committees. Such groups of legislators are investigating something known as

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un-American activities. If un-American activities are overt acts, there are courts which will take care of them. Moreover we have something very like a secret police which makes investigations on its own in the service of the courts. What is wanted apparently is conformity to some standard of political thinking, not action, which is so vaguely defined that it is next to impossible to know whether one is American or un-American. Is it un-American to write an economic interpretation of the Constitution? Is it unAmerican to say that the Constitution does not prescribe judicial supremacy? Is it un-American to argue that a diplomatic representative of the Vatican is in the service of a foreign power? Was it un-American for Father Cumming back in 1865 to refuse to take the oath of loyalty to the Constitution of the State of Missouri and yet to continue to say Mass? Judging from some of the letters I have received, anything which anyone does which runs counter to the opinion of one or two radio commentators is unAmerican. Whether one knows what Americanism is or not, and I confess that I do not, clearly there is supposed to be a body of doctrine, not a pattern of overt behavior, which is imperative. This seems to me to be analogous to what some religions have required of their followers, and to what the Communist Party is said to require of its members. Though I would not want to be interpreted as saying that we shift our point of view quite so rapidly as the Communists do or that the dogmas are as clear as those of the dogmatic religions, ideas are prescribed and one can be punished in effect by loss of reputation and means of livelihood if some legislative committee decides that one does not hold to these ideas. At the same time the increase in authoritarian religion is noticeable. The Partisan Review a year or so ago took official notice of this and thirty or forty so-called intellectuals were called upon for comment. An appointee to the Board of Regents of the University of Maryland was questioned by the state legislature before ratification of his nomination about whether or not he believed in God. Motion pictures and books are forced out of circulation because they offend the religious sensibilities of certain religious groups. School-room exercises are modified so as not to do likewise. The opposition to the teaching of the doctrine of evolution came from religious, not scientific groups, and it was successful in at least one state. Though we are living presumably under a

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regime of the separation of church and state, we are also told that we are living in a Christian country and the word "Christian" is left so vague that "non-Christian" can be used to criticise and libel anyone whose views of Christianity are not in harmony with those of any powerful enough Christian sect. One has only to think of the attack on President Conant, Paul Blanshard, and The Nation, to realize how effective this type of authoritarianism has become. But one finds the same tendencies in such apparently remote fields as that of literary criticism. If there is anything clear and obvious to a student of the history of criticism, it is that taste has changed and that the standards of literary excellence are seldom the same for over a hundred years. Who would maintain that the style of Vergil was that of Chaucer or Dryden or Pope or Wordsworth or Tennyson or Robert Bridges or Mr. Eliot? Yet the propaganda of such men as Charles Maurras in France, Messrs. Babbitt and More in the United States and now Mr. Eliot in England, have tended to produce a state of mind in critics which leads them to maintain that there is only one standard of excellence and, what is more, that there never has been more than this one. Thus we are back in the days of Boileau and Pope who knew for certain what a poem should be in order to be a great poem and who, if their standards were actually applied to the entire corpus of even English poetry, would rule out four fifths of it as bad. If I may judge from the reaction of my students, there has arisen a sort of feeling of guilt on the part of men who do not conform to the standards of whoever the most eminent critic may be, so that such critics have become a kind of Academy whose word is supposed to be law. T h a t they have not been laughed out of court is evidence of the submissiveness of the American public to the demands of authoritarians. It is as if they assumed a priori that of course there must be some one standard of aesthetic excellence which can be applied regardless of time and place. It is precisely that assumption which is a restriction on freedom of thought, for it takes it for granted that any view which might be labeled relativistic or pluralistic is by that fact alone wrong. But the threats to academic freedom do not come exclusively from outside the universities. The inertia and timidity of the academics themselves in defending their rights is an even greater

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threat. Anyone who has ever served on the administrative and investigative committees of the A A U P will recognize this. W e professors have lain down under attacks from irresponsible radio commentators, newspaper columnists, ecclesiastics, politicians, and have never thought of counter-attacking. If one makes the most obvious gesture of good-will towards a colleague accused of un-American or quasi-subversive activities, if one says aloud that he at least should be accused for overt acts rather than for his opinions, one is either shunned by one's colleagues or hailed as a hero. B u t such counter-attacks are the most natural thing in the world when men have a feeling of security and confidence in their own integrity. I f the professors had taken the same stand that some college presidents took when Congress threatened to censure reading lists, or if they had reacted as vigorously as the Press has reacted to threats of censorship, or as the clergy reacted when Congressman Velde hinted that he might have to investigate the churches, this wave of intolerance and what amounts to persecution would have broken before it had become more than a ripple. If the Faculty of the University of California had maintained their solidarity, as they solemnly voted they would, seven hundred professors would have refused to take the Regents' oath instead of seventeen. And the irony in that case was that the Courts upheld the non-signers. How powerful are these threats to academic freedom I have no way of knowing. But I do have a way of knowing how effective they are. Their efficacy is natural enough when one considers that opinion is now regimented in so many ways that few people have even the opportunity of making up their minds on anything except the most narrow of specialties. One can now buy editorial opinion from agencies which sell opinions on almost any issue. Pretty nearly every newspaper carries a syndicated column not of news but of opinion. Even cartoons are syndicated. Daily purveyors of opinions broadcast their ideas on this, that, and the other, never stopping at libel or slander, and apparently, even philosophers listen and repeat their lessons. Various book-clubs determine what the public will read by financial inducements, and though we have not yet got to the point where there is a philosophical book-of-the-month, the paucity of philosophical journals and the very limited space for reviews in them, acts almost as if there were one. This crystallization of philosophical opinion

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has not yet reached alarming proportions and I would not like to give the impression that it had. But one has only to survey the changes in philosophical interests which have come about in the last fifty years to see that logical conviction has not brought about this homogeneity. But the very organization of instruction, at least in philosophy, acts as a restraint on freedom. The old division of philosophy into natural, logical, and ethical still forms the body of courses offered in most colleges. Historical courses still follow for the most part the outlines drawn up by Hegel. New problems, with the exception of those stemming from logic, are seldom discussed except in periodicals. Philosophy is what the textbooks say it is. How many students are ever given the opportunity to perceive a philosophic problem for themselves? The professor thinks he must cover a certain amount of ground and that acreage is laid out in a book. If we exist to make money for publishers, then we must expect to be limited in what we can talk about. But if we exist to perceive and attempt to solve genuine problems, then we should toss most of the textbooks into the trash-bin. Why is it that the student entering a course almost always asks what text will be used? Is it not because he takes it for granted that the professor's intelligence is not the text? We have set up or allowed to be set up a ritual of instruction and we have for the most part constituted ourselves as practitioners of the ritual. One might as well be teaching the minuet. IV I cannot escape the conclusion that the professor has certain responsibilities to his subject and to the state in which he lives which make it imperative that he foster academic freedom, not as a voluptuous delight which he should be granted in distinction to other men, but as a duty resident in the nature of his calling. My point is simply that he cannot be a good professor or researchworker unless he enjoys freedom. By this I do not mean that he should teach falsehoods, or present his ideas in obscene or otherwise indecorous language, or that he should disregard the religious scruples of his students. But if he did any of these things, he would not be condemned on the basis of his violating the rights of a citizen but on the basis of his being an incompetent teacher. The distinction may seem purely academic and could to be sure

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be abused. But in actual practice it has not been abused in recent years to any alarming extent. But whatever the subject a man is studying, it demands, as we all know, a scrupulous fidelity to a certain method of work, to the facts in the case, to the laws of logic, to critical analysis, to correct documentation. This fidelity would seem at least to me to have priority over the duty some say we have to the feelings of parents and civic authority. One realizes that parents and politicians may be scandalized by the philosophic views of thinkers like Spinoza or Hobbes, or indeed of almost anyone in the history of philosophy. I should not introduce this objection to academic freedom had I not heard it voiced recently by a scholar of some repute. The question boils down to whether we are to pursue our studies in sincerity or hypocritically. When a person is not sure of his facts, there is no reason why he should not say so, and it would be an excellent example of professional ethics if more teachers would say so. But to avoid stating certain conclusions because they may turn out to be painful to parents, clergymen, or politicians would be cowardly and faithless to one's calling. To be free to follow the lead of one's investigations wherever common-sense corrected by reason may take one is a necessity if one's science is to advance. But here again one has to assume that one's science is not completed: for if it were, it obviously could not be expected to advance. Just as the scholar has a responsibility to his subject, he must also admit that he has a responsibility to the state and to society. I shall avoid the thorny question of civil disobedience and assume for the sake of argument that no man should disobey the law. I say that this is a thorny question for there are many occasions on which one actually does not understand the law and hence does not know whether he is obeying it or not. It will be simpler then in this context to omit the whole matter and act as if we always did understand it. But strict obedience to the law does not interfere in any way with academic freedom, unless the law should limit it. Let us then agree that we should all obey the law. This does not, however, exhaust the scholar's duty to society, for he is more intimately related to the welfare of society than the industrialist, the merchant, or even the statesman. He provides the substance on which laws are made, which nourishes both industry and the arts. His duty therefore to society is im-

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possible of fulfillment unless he also does his duty to his subject. If, for instance, the genetic theories of Lysenko are false, as I presume they are, in the long run it is Russian society as a whole which will suffer. Our duty to the state cannot be fulfilled unless we forget the state and its pronounced interests, the clamor of the people who are elected to speak for it, and give ourselves over whole-heartedly to our subjects. T h e problem is complicated by the question of who is society or the state, if one prefer? Is Congress society, is the majority party society, is the dominant religious group society, are the larger industrialists society, are the wage-earners society? This would be a stupid question if there were not often serious conflicts of opinion between members of these various groups. These conflicts extend beyond matters of fact to matters of policy. One can iron them out by devices which are well known, running from annihilation to persuasion. There is very little virtue in diversity for its own sake, but there is some question whether all diversity should be eliminated. Here is a question which philosophers might be expected to debate for if there was ever a term which required clarification, it is "unity." Philosophers should not be expected to talk with the tongues of angels, but it is not too much to expect that they talk with the tongues of rational animals. Such individuals can approximate an attitude of objectivity, though they may never reach it, and as they approximate it will see where the conflicts lie and what hope there is of diverse opinions living together without civil war. This does not entail the assertion that the philosopher should have no views of his own but merely that he of all men ought to be able to disentangle his assumptions from his conclusions and state them clearly. I take it, for instance, as an assumption that the diversity of economic, social, religious, and philosophic interests in a country like our own should not be reduced to unity. Is that going to prevent my seeing the desirability of internal ideological peace and tolerance? Only if I refuse to admit that my premises are assumptions. We have no way of knowing whether what might be called the Protestant tradition of individual conscience is to prevail in this country or not. But for the time being it does prevail and so long as it prevails there can be no reasonable idea of a society which is completely unified and whose interests demand satisfaction. But even if conflict of ideas were eliminated, academic free-

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dom would be a patriotic duty as well as a scientific duty. For one can be as utilitarian as one wishes; a society which wishes to apply knowledge to the manipulation of the world will have to possess the truth. Otherwise it obviously cannot apply it. Even Hitler possessed the truth about mob-psychology, though he was pretty shrewd about concealing certain truths from the mob. And though he howled and stormed about Deutsche Wissenschajt, it is certain that in the manufacture of munitions he used the same kind of Wissenschajt as the Pluto-democrats. My argument then reduces to a simple enough form. First, all knowledge is not as yet discovered. Second, it is desirable to know more than we now know. Third, discovery, if limited by restraints other than those of logic and sound methodology, cannot effectively proceed to further discovery. Fourth, it is in the interests both of a science and of society to encourage unhampered research and instruction. Fifth, the most effective form of encouragement is academic freedom.

Symposium:

T H E ETHICS OF ACADEMIC FREEDOM GEORGE BOAS AND S I D N E Y H O O K

I I . SIDNEY HOOK

Even though few teachers are philosophers and not all philosophers are teachers, it is entirely appropriate for philosophers as philosophers to concern themselves with the nature of academic freedom. But what may we legitimately expect from a "philosophical" analysis of academic freedom? Something more, I believe, than a partisan discussion of moot questions of politics, and something different from a journalistic pointing with alarm at the state of the nation. Whatever else such a discussion turns out to be, it should result in a clarification of the precise points at issue in the problems that have arisen involving academic freedom, and in the introduction of a set of distinctions which may prove fruitful in resolving them. Tn accordance with instructions from the Program Committee to second symposiasts, I shall devote a considerable part of my paper to a critical discussion of Mr. Boas' contribution. I shall then briefly discuss some important problems related to "The Ethics of Academic Freedom"—briefly because I have treated them at length in my recent book, Heresy, Yes—Conspiracy, No. My criticisms of Mr. Boas' paper are offered under three heads. I. He has cast his net so wide that it has brought up a number of problems not essentially related to each other or to the question of academic freedom. The consequence is that those who have perfectly legitimate philosophical differences with him are taxed either with not believing in academic freedom or holding views incompatible with such belief. II. His statements of fact are grossly exaggerated even when they are relevant to the question of academic freedom which is not always the case. On the other 19

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hand, there is an entire class of facts decidedly relevant to the issues of academic freedom which Mr. Boas ignores or slights. I I I . He does not carry his analysis far enough in considering the ethical aspects of academic freedom. I As a point of departure, I, too, accept Mr. Lovejoy's definition of academic freedom although it seems to narrow unduly its institutional scope. But I cannot see how Mr. Boas derives from this definition many of his conclusions. The essential point of the definition, it will be recalled, is that teachers should be free from administrative, political and ecclesiastical control provided they are competent and do not violate the canons of professional ethics —which provisions are to be enforced by their own peers. 1. According to Mr. Boas, academic freedom is a species of freedom of thought which is guaranteed by the Bill of Rights of the Constitution. This would make academic freedom, like freedom of speech, press and assembly, a constitutional or civil right. Our Courts have never recognized this; nor has the AAUP ever made such a claim. The history of education in the U.S. shows that despite the flourishing existence of the Bill of Rights from the very beginning, academic freedom, in the sense of Mr. Lovejoy's definition, hardly obtained until the turn of the present century. A similar situation prevailed in Great Britain whereas in pre-Imperial and Imperial Germany, academic freedom enjoyed a relatively luxuriant growth despite the primitive state of civil liberties. The valid exercise of academic freedom is dependent upon the fulfillment of certain professional and moral qualifications. It is forfeited when these qualifications are compromised or lost. This seems to me to be true of any reasonable conception of professional freedoms which like teaching affect the public interest, e.g., freedom to practice medicine, law, and engineering. All of these require freedom of thought and research to develop properly. Parity of reasoning, if we were to follow Mr. Boas' argument, would lead us to conclude that they are all civil rights guaranteed by the Constitution. But this is absurd. What is wrong here? The assumption, it seems to me, implicit in Mr. Boas' position, that because academic freedom is impossible without freedom of thought, freedom of thought is impossi-

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ble without academic freedom. T h a t this is an error is a p p a r e n t from the fact that a man whom M r . Boas would discharge from a University for saying that " a is greater than b, and b is greater than c but a is not greater than c " has a constitutional right to proclaim it from the very housetops without suffering any legal pains or penalties. Mr. Boas properly insists that the vocation of a scholar requires fidelity to fact and logic and an almost religious dedication to the t r u t h . But if these conditions were imposed on the constitutional rights of speech, we would be living in the era of the Great Silence. T h e confusion between moral and legal questions has bedevilled the discussion of academic freedom to a point where it has been i n f e r r e d — a n d by philosophers, t o o ! — t h a t because certain actions are not illegal, they cannot be immoral or constitute violations of professional ethics. I shall return to this theme below. Another reason for keeping legal and ethical issues distinct, which I am sorry to observe Mr. Boas consistently fails to do, is t h a t usually constitutional rights are asserted without a n y limitation. When academic freedom is considered as a constitutional or civil right, its self-limiting character is unlikely to receive adequate attention. When in addition, the refinements a n d ambiguities of constitutional law are overlooked, the situation becomes even more obscure. For example, when M r . Boas says t h a t "academic freedom is a species of freedom of thought," he really means t h a t it is a species of freedom of speech or expression. H e then distinguishes speech from other forms of action a n d tells us t h a t "usually it has been maintained that until thought expresses itself in action, a man is free to say whatever he believes to be true." N o t only is this irrelevant to the question: when is academic freedom being fulfilled or betrayed?, but it is a dubious and revolutionary interpretation of constitutional law. For according to Anglo-American law a man is not free to libel another even when he believes what he says is true. Indeed, sometimes he is not free even to tell what is actually the truth, for under certain conditions the courts have held that malicious tale-bearing about a reformed criminal's past is actionable. At a n y rate, court cases involving academic freedom have been usually considered under the law of contracts or of statutes regulating employment of state or municipal employees and not as breaches of civil rights. 2. E v e n more questionable than

the notion that

academic

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freedom is a civil right guaranteed by the Constitution is M r . Boas' view that certain philosophical positions in aesthetics and other disciplines constitute restrictions on academic freedom because they are restrictions on freedom of thought. T h u s of the belief that "there must be some one standard of aesthetic excellence which can be applied regardless of time and place," he writes that, " i t is precisely that assumption which is a restriction on freedom of thought, for it takes it for granted that any view which might be labelled relativistic or pluralistic is by that fact alone wrong." Now I happen to share Mr. Boas' objective, relativistic pluralism but I confess myself baffled to understand in what way a disbelief in that doctrine, and more specifically a belief in invariant standards of aesthetic excellence, constitutes a restriction on freedom of thought or on academic freedom. No one prevents me or Mr. Boas from holding, teaching and defending our views. No outside authority prescribes to those who disagree with us that they must profess absolutism. Absolutists I have known usually reach their conclusions through a long process of thinking—of what seems to me sophistical and mistaken thinking. But they repay the compliment and the argument goes back and forth. Ironically enough, the last absolutist I argued with taxed naturalists and relativists with holding assumptions that would restrict his freedom of thought but he couldn't make the charge stick. I invite Mr. Boas to show how he reaches his conclusion about the "authoritarian" nature of the aesthetic doctrine of invariant standards from the definition of academic freedom he took as his point of departure. I t seems to me that to tar those who disagree with one's philosophical position as opponents of academic freedom, unless they advocate practices incompatible with Mr. Lovejoy's definition or unless advocacy of such practices is entailed by their assertions, is to substitute abuse for argument and to illustrate a type of discussion which Mr. Boas himself so rightly deplores. I t is unjust and unwise to regard as enemies of academic freedom those who on the basis of their own thinking regard our position as false or meaningless. It is only when such critics are under an extraneous outside discipline, change their mind in accordance with a party line, or try to prevent us from criticizing their doctrines that they threaten academic freedom. But Mr. Boas has been

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giving absolutists in aesthetics a much sorrier time than they have been giving him. Suppose it were believed that there is only one absolutely valid principle in morals independent of time and place. Would such an assumption also constitute "a restriction on freedom of t h o u g h t " save in the innocent sense that its truth would be incompatible with its denial? A philosopher might very well hold that this assumption was absolutely true and yet defend the right of others to contest it. K a n t ' s ethical views may have been mistaken but he was not an opponent of academic freedom. Plato was an opponent of academic freedom but his opposition is no part of his theory of Ideas. Or suppose it is assumed, as almost all philosophers do, that there is and always has been, only one valid system of logic. This entails the view that if there are many-valued logics they are either special cases of this basic logic or that they are self-contradictory (a question-begging conclusion). It does not entail, however, any restriction upon freedom of thought, or if one cavils at the word " t h o u g h t , " then say, freedom of talk. Were M r . Boas right in his strictures, then anyone who believed t h a t any statement was certain would therewith be convicted of an illiberal attitude in respect to alternative views concerning what he claimed certainty for. This would make an uncommonly large number of philosophers unwitting opponents of academic freedom. It would include even those empirical philosophers who believe that nothing could be probable unless something were certain. 3. If the character of philosophic beliefs has little relevance to academic freedom, the present organization of instruction in philosophy has even less. I t m a y be that outlines of historical courses in philosophy follow Hegel rather than Russell or even Boas' excellent short book. But unless it can be shown that administrative or political or ecclesiastical authority has been employed to coerce a teacher to a d o p t one approach rather than another, it is possible that he still follows Hegel because he finds some wisdom in doing so. And if teachers of philosophy (not to speak of other subjects) use textbooks, there may be good and sufficient pedagogical reasons for such practice. In my own limited experience I can cite a dozen textbooks from Dewey and T u f t s ' Ethics down to some recent introductory logical texts which have proved very valuable. I agree with M r . Boas that it is an impertinence

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to dictate to a teacher what textbooks to use. It is no less impertinent to denigrate him for his uncoerced use of them. As I read M r . Lovejoy's definition of academic freedom, it includes the right to lecture or not to lecture, to use textbooks or not to use them. It excludes only the attempt of nonqualified persons to bully or command teachers on their materials of instruction. Mr. Boas to the contrary, it is the most natural thing in the world for a student to inquire about the text of a course. He shows commendable common sense, if not philosophical acumen, in assuming that the intelligence of his teacher reflects itself in the choice of a text—if there is a text. We should all be grateful to Mr. Boas for his teaching helps. But they have nothing to do with the subject of academic freedom. 4. I have argued on many occasions that one of the justifications of academic freedom is that it helps us to win new knowledge. But I am not satisfied that the case for academic freedom rests on the assumption or presupposition that all truth is not yet discovered in the sense that it is a necessary condition for belief in academic freedom. Mr. Boas writes that "if everything which could be known were known, then the Augustinian dictum that man is not free to err would force itself upon us as an ultimate truth." I do not see why. Augustine, of course, did not believe that everything knowable was already known, yet he held that no man is free to err about anything known to be true. And there are others who, differing with Augustine about what it is we know to be true, agree with him that men are not free to err concerning it. In such cases we could defend the right to err, even about what is known to be true, among other reasons, on the ground that freedom to err is part of freedom of inquiry, and that the habits of free inquiry will lead to new truths. But suppose everything were known. I still would disagree with Augustine and Mr. Boas. I would hold that to find out things for oneself is often morally more important than being right, and that a certain violence is done to the mature human personality if it is compelled to yield to the compulsions of any authority except the luminous coercions of logic and scientific method. Morally, a society in which mature human beings are free to err about truths seems to me superior to one in which they are compelled to accept as truths what they do not understand

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as truths. T h i s is not the same thing as Lessing's preference for the striving for truth to the possession of it. I go further than Mr. Boas here in denying the statement that "all t r u t h has not yet been discovered" is a necessary presupposition of a belief in academic freedom. I believe that we should permit a scholar whose competence has been established to challenge any proposition in his field even in elementary mathematics and logic, and I would not define his competence in terms of the acceptance or rejection of the proposition disputed. At any definite time there are certain tests of competence; and it is wiser to take the risk that the investigator will not urge absurdities than to insist that any particular statement is beyond challenge. Competence is best defined in terms of the methods by which a conclusion is reached rather than in terms of any particular proposition believed. If a Godel challenged the view that "greater t h a n " is always a transitive, asymmetrical relation, no one would seriously maintain he should be denied or deprived of an academic post. After all, Mill believed that 2 plus 2 might not always equal four. T h e statement of some distinguished contemporary logicians that no two words have the same meaning seems to me almost as paradoxical. I admit that one has to win the academic right, as distinct from his civil or constitutional right, to say things which his colleagues regard as absurd. But I am convinced that it is important to defend the right of those who are properly qualified in their field to talk what seems like nonsense especially in an age when the very foundations of science are shifting, and the claims of parapsychology are becoming more insistent. It seems to me that even in religion acceptance of a belief in a uniquely revealed truth does not necessitate the additional belief that dissenters and non-believers should suffer any restrictions on their intellectual and academic freedom. For such a revelation is compatible with another enjoining believers to permit others to find their path to salvation or damnation by themselves. M. Gilson has recently argued that dogmatism does not necessarily lead to intolerance but he spoils his argument by contending that tolerance necessarily rests upon some form of dogmatism. Conversely, whatever validity relativism and skepticism have as philosophical positions, they are compatible with conflicting attitudes toward academic freedom. A recent book on "the super-

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stitions" of academic freedom argues that just because there are no objective truths in the normative disciplines but only prejudices dressed up as postulates, students should be taught not the prejudices of their professors but those of the community which subsidizes the professors. Like other views on social questions, support or criticism of academic freedom can be squared with any philosophical doctrine whatsoever. II Limitations of space prevent me from taking up point by point the statements Mr. Boas makes about the state of academic and cultural freedom in the United States, and discussing his rhetorical questions. The net impact of his account is extremely misleading. I select a few key points. I. Whether one approves of Congressional investigations of education or not—and I write as one who disapproves of them— it is simply false to say that either the House or Senate Committees have sought to impose an orthodoxy of doctrine or belief on witnesses. Their faults are many and grave but they have not subpoenaed anyone because of his opinions on the economic interpretation of history or the Constitution or judicial supremacy or diplomatic representation at the Vatican. I t is not true that these Committees reject the First Amendment. Only the Supreme Court has the power to decide when a refusal to answer constitutes contempt. And far from failing to respect the Fifth Amendment, they have scrupulously observed it to a point where many now believe, including Mr. Lovejoy, that the self-incriminatory provisions of the Fifth Amendment have been so abused by gangsters, racists and members of the Communist Party that they defeat the ends of justice. As philosophers we should consider the very impressive arguments Jeremy Bentham directed more than a century ago against the privilege of refusal to give self-incriminating testimony. What is true is that hostile witnesses have always been asked whether they have been members of the Communist Party or of Soviet espionage rings or of certain Communist-front organizations. One may argue that such questions should not be asked by Congressional Committees of anyone on the mistaken view that the F . B . I , has these powers. But if inquiries of this kind are legitimate, individuals who happen to be teachers cannot be re-

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garded as a privileged class enjoying constitutional exemptions not possessed by other citizens. The revelations concerning the activities of Hiss, Remington, H . D . White, and numerous other members of the Communist P a r t y who could not be brought to trial because of the statute of limitations, seem lost on Mr. Boas. Otherwise it is hard to explain why he should imply that a question put to a person who happens to be employed as a teacher concerning his membership in the Communist Party is an invasion of academic freedom. Such persons have been questioned not because they have been identified as teachers but because they have been identified as members of the Communist Party. 2. M r . Boas makes thinly disguised references to the questioning of Owen Lattimore whose case I have elsewhere discussed with specific reference to Lattimore's articles of 1938 which were not the basis of his indictment. ("Owen Lattimore on the Moscow Trials," New Leader, 1 1 / 1 0 / 5 2 ) . But here, too, Mr. Boas misses the point. H a d Owen Lattimore been a journalist, like Frederick Field, or a business man or lawyer like others of his colleagues on the Executive staff of the Institute of Pacific Relations questioned by the Senate Committee, once he was charged with being a conscious instrument of Soviet foreign policy to the detriment of the United States, and by some leading ex-Communists as a Soviet agent, then whether the charges were true or false, it was natural that he be questioned by a Committee duly authorized by the U. S. Senate to investigate subversive activities, particularly when extremely damaging documents came to light. In what way does this involve a violation of academic freedom? Had Lattimore been a physician would questioning him have violated his medical freedom? As a matter of fact it was Mr. Lattimore who rightfully insisted that he be called as a witness. 3. T h e great mistake of the two Congressional Committees investigating subversives, aside from faults in their specific procedures exhibited even by the old Nye and LaFollette Committees, was in announcing originally that educators as a group were to be investigated, thus generating unnecessary uncertainty and alarm on the campuses of the country about their intentions. T h e educational qualifications and behavior of teachers should be no concern of Congress. Here the faculties of colleges are the only competent judges. If. on the other hand, Congress has the right to explore the pattern of conspiratorical penetration in American

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life directed by a foreign power intent upon destroying everywhere free institutions, including academic freedom, and if the Communist Party is a conspiratorial organization, then no reasonable objection can be made to uncovering the trail of infiltration wherever it leads. Reliable information and publicity about strategic positions occupied by Communist Party members may be of great importance in the defense of freedom. 4. In my book. I have considered at length charges similar to those made by Mr. Boas that American teachers are cowardly, that they have "lain down" under attack and are currently being overwhelmed by a "wave of intolerance" which "amounts to persecution." What is true is that American teachers have been subjected to more criticism than in the past but never in the history of American education have they shown more spirit and courage in defence of academic freedom. They have not been frightened and they have not been silenced. We need only contrast their indifference to academic outrages during the First World War and post-war period, when American security was not even remotely threatened, to their jealous concern for academic freedom in the present state of national emergency and undeclared war. One eloquent item. During the very week when a research scientist was charged with being the weakest link in our national security, he was unanimously elected president of the AAAS. Justified or not, was this an act of men who were frightened or who had "lain down"? 5. I must also register my astonishment at the evidence Mr. Boas cites to prove that opinion in the U.S. is so highly "regimented" that few people can make up their minds about anything outside of a narrow specialty. Will Mr. Boas tell us when Americans were better informed about public affairs or when they had more information at their disposal than to-day or when debate of the kind found in radio, television, press and forums was more vigorous and extensive? By Mr. Boas' standards American cultural life may be low but it is free, and some of its poor quality is the price of its freedom. No one is compelled to join a bookclub and Mr. Boas gives no reason for assuming that those who have joined would have read more and better books in the absence of book-clubs. The election returns over the years show that people are influenced far less by editorials than by news stories which, for all their weaknesses, are far more objective than those Nominalists, of course, differ in their views of the concrete.

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appearing in the press of more cultured peoples, e.g., the French press. N o one compels Mr. Boas or anyone else to listen to Fulton Lewis. He can tune in on Elmer Davis or turn the dial off and agitate for better commentators. 6. Despite Mr. Boas' bleak picture of American philosophy, there is more philosophical variety than ever before. We are less ridden by schools, more aware of our postulates, more interested in neighboring disciplines. And despite Mr. Boas' unfortunate experience in recommending a Catholic, there are far fewer bars to Catholics and Jews teaching philosophy to-day than in the golden age when a well-known American philosopher expressed the opinion that no one who was Jewish could properly conduct a course in the traditions of Western civilization. (I vividly recall the case of a graduate student twenty-five years ago who on the basis of his writings received seven offers of a position; five were withdrawn when it was discovered that the genealogical tree, suggested by his name, didn't have its roots in Old or New England.) True, there is less philosophical genius apparent to-day but the standards of analytical rigor are much higher. The paucity of philosophical journals is not a consequence of regimentation but of production costs, lack of interest and possibly of talent. We are free to do better but we cannot force people to live up to our conception of what is better for them especially in the light of a relativistic and pluralistic aesthetics. These lines are being written in Europe where influential sectors of public opinion are convinced that "a mood of raving totalitarian lunacy is raging in the U.S.," to quote one large newspaper. Senator McCarthy is primarily responsible for this impression. When I have tried to counter it with a more balanced picture, I have found that unbridled exaggerations by American critics of the state of American culture to-day is cited as conclusive evidence of the justice of the charge. If irresponsible exaggeration is the essence of McCarthyism, McCarthy is not the only one guilty of McCarthyism. Ill I come now to a consideration of the more strictly ethical issues of academic freedom. Note that Mr. Lovejoy's definition makes academic freedom contingent not only upon a teacher's competence but on his fulfillment of "professional ethics." Can a

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teacher be technically competent and violate professional ethics? It seems to me that the answer is affirmative. A teacher like a physician may be technically competent and still betray his trust. Some breaches of professional ethics may be construed as evidence of incompetence but it would be arbitrary to classify all of them in this way. 1. Much current discussion of academic freedom seems to revolve around legal considerations. On many occasions it is held that if a teacher exercises a legal right or does anything which is not strictly illegal, the academic community has no further concern in the matter. For example, Mr. Boas flatly characterizes as malpractice, and as a violation of the Fifth Amendment, discharge from employment of one who has invoked his constitutional right not to incriminate himself by his own testimony in a criminal case. Let us examine this more closely. Members of the academic community in virtue of the rights and privileges they enjoy are bound by certain correlative obligations, professional and moral. Among them Mr. Boas recognizes the duty "to speak the truth." I should prefer to say to seek the truth. This in turn entails a number of other obligations which explicate what is meant by seeking the truth. In addition, there are other obligations of a teacher, e.g., not to exploit his position to enroll students into political or religious organizations or to encourage them to defy the laws of a democratic society. No one can exhaustively codify these obligations any more than one can exhaustively codify the obligations of an honest man. In moral situations it is not true that everything is permitted except what is expressly forbidden. Just as a person may be legally innocent but morally or professionally blameworthy, so under certain circumstances an individual's qualifications to continue in his profession may be seriously impugned even when he exercises a constitutional right. Under the protection of the First Amendment a person may plagiarize from some writing in the public domain with complete legal immunity. But he thereby gravely compromises his position as an honest scholar. The legal question is here completely irrelevant. It is absurd therefore to argue that because certain professional penalties follow upon the assertion of a constitutional right, that the right itself has been violated, and the penalties necessarily unjustified. The issue is a moral one and as philosophers we should be the first to recognize it.

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It is precisely this failure to note the primacy of the moral issue which vitiates much of the discussion concerning the invocation of the F i f t h Amendment. Professors Sutherland and Chaffee have properly observed t h a t : "A privileged refusal to testify is not an admission of guilt for the purposes of criminal prosecution." (my italics) But our proper concern as educators is not whether an individual is legally guilty for purposes of criminal prosecution. We are not lawyers, judges, or prosecuting attorneys. Our concern is only with the question of educational integrity and professional qualifications insofar as they are affected by refusal on grounds of self-incrimination to answer inquiries bearing on vocational fitness and trust. T o this question Mr. Boas pays altogether insufficient attention. In situations where a teacher refuses to answer questions of a duly authorized committee of Congress, or of his colleagues, the crucial points are the kind of questions he refuses to answer and the grounds on which he refuses to answer them. Our moral evaluation of his action must rest on both of these considerations. T h e questions must be pertinent to his fitness to continue in his profession; and so must the implications of the grounds of his refusal to answer them. N o one will contest this in other fields. If a physician is asked: " D i d you recommend a risky operation because of a promise of a split fee?", or a lawyer: " D i d you accept a gift from the defendant on the understanding that you would throw your client's case?"—refusal to reply would lead to professional disbarment. A code of professional ethics may legitimately require an answer where the law does not. Common sense has always recognized this distinction and in moral matters, if not in epistemology, common sense is not lightly to be disregarded. If a bank teller against whom there is no evidence except that money is missing from his till invoked the F i f t h Amendment, a bank would have sufficient cause as a rule to dismiss him even if it couldn't convict him. In the interests of its depositors, it can't afford to have a teller whose honesty is in doubt and who must be watched. If in a graft-ridden city an official with an income of $5000. a year lives on a scale of $100,000. and refuses to answer questions concerning the source of his extra income on the ground that his truthful answer would incriminate him, he may keep out of jail. But why should he be kept in his job?

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For educators the sole issue posed by the invocation of the Fifth Amendment on the part of a member of the academic community, bound by the obligations of honest inquiry and teaching, is whether such invocation ever carries with it implications bearing on his moral and professional fitness to teach. An illustration will make the point clearer. Suppose a professor were charged with accepting money from a corporation "to cook" his scientific experiments, and he invoked the privileges of the Fifth Amendment. Legally he is completely justified in so doing whether he is criminally guilty or not. But morally and professionally, his refusal to answer the question which affects the whole rationale of the scientific and scholarly enterprise is highly culpable because he has struck a blow at the very foundations of the scientific community and undermined public confidence in the integrity of his institution. Although legally in the clear, his refusal to answer is morally damaging to himself and prejudicial to his colleagues. The questions asked, I repeat, must be both professionally and morally relevant. Are questions to teachers about membership in the Communist Party so relevant? No one can properly answer without studying the nature, organization, and activities of the Communist Party. M r . Boas chides the Courts for not relying upon knowledge of fact in formulating policy. But his own discussion largely ignores the authenticated facts about the Communist Party, especially the explicit instructions given its members who are teachers to violate basic tenets in the moral and professional code of honest teachers and scholars. He speaks with authority about what some religions have required of their members but about the Communist Party he relies on hearsay. " I t is said," etc. But the information is easily available. I t is unnecessary to cite here the evidence for the conclusion that membership in the Communist Party is incompatible with the honorable fulfillment of the scholar's and teacher's functions in the schools of a free society. (Cf. Chapter VIII, op. cit.) At the very least such membership establishes a prima facie presumption of unfitness to remain in the academic community. And if this is so, a question designed to elicit a truthful answer about such membership is preeminently relevant to our concern as educators even if the prima facie presumption is not ultimately sustained in any individual case.

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President Dickey of D a r t m o u t h has put the matter judiciously with respect to a teacher who refuses to answer a question a b o u t membership in the Communist P a r t y on the ground of the F i f t h Amendment. "Such a m a n , " he says, "either genuinely believes his words may incriminate him or he is using the privilege improperly. On the first assumption, he, by his own action, avows the existence of what can reasonably be regarded as disqualification for service in a position of respect and responsibility; on the other hand, if he has invoked the privilege without truly believing that he needed its protection, he has acted falsely towards his government. Either way you take it, it seems to me we must say as a matter of general policy that such a person has compromised his fitness to perform the responsibilities of higher education; and unless there is clear proof of peculiar circumstances in the particular instance which would make application of this policy unjust and unwise, the normal consequences of such disability must ensue." Since this view is an unpopular one in certain educational quarters, I should like to safeguard myself against misunderstanding. I am not saying that any individual is morally bound to answer any question put by a Congressional or a n y other committee. Nor am I saying that it is morally inadmissible to refuse to answer questions irrelevant to educational fitness and integrity on the ground of the F i f t h Amendment. N o r am I saying that it is inadmissible to refuse to answer questions which are relevant to one's educational fitness on the ground of the First Amendment, if one believes that the investigative agency has no authority to put these questions. W h a t I am saying is that it is morally and professionally inadmissible to refuse to answer questions relevant to one's educational fitness and integrity on the ground that a t r u t h f u l answer would be self-incriminating. Such a refusal should be construed as presumptive evidence of unfitness, final determination being left to faculty committees elected for that purpose. Note carefully that this in no way prevents a n y person from following the dictates of his conscience and protesting against what he believes is a violation either of his legal or moral rights. He may refuse to answer questions bearing on his educational fitness without prejudice to himself, his colleagues and his institu-

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tion, so long as he does not invoke the Fifth Amendment. In that case he is in the position of a heretic and it is up to the court to determine whether he is legally justified or not, or whether he should be punished or not. An individual whose conscience commands him to defy a legislative committee, and who refuses to answer its questions may be an honorable man, innocent of any wrongdoing, and free of presumption of educational unfitness. Although as a loyal citizen of a democracy, he has an obligation to cooperate with his government, he may regard his commitment to other values as overriding it, and is therefore prepared to face the consequences without whimpering as have genuine heretics in the past. But refusal to testify on the grounds that one's own words, if truthful, will incriminate oneself, although legal, cannot be countenanced by any standards of professional ethics. Such a procedure is presumptive evidence that a person is an educational conspirator—playing outside the rules of the game either by intent or act or both—and not an honest heretic. The issues here are grave and complex but the fundamental point was illustrated in the life and arguments of Socrates whom as philosophers we profess to honor. He insisted on telling unpalatable truths at the risk of his life yet scorned conspiratorial evasion and the easy opportunity to escape from punishment as betrayal of principles upon which the very life a free community depends. In a democracy, whose political institutions permit evils to be rectified by the processes of freely given consent, there is no right to conspiracy. What is true for the democratic community is in this respect all the more true for the academic community. The life of mind depends for its continuous functioning upon candor, openness, and the disclosure of relevant information, in the process by which truth of fact and wisdom of policy are reached. By deliberately withholding the truth on a matter which affects the very pride and honor of our vocation as scholars and teachers—particularly when other avenues of protest are open to men of conscience— those who invoke the Fifth Amendment in refusing to answer relevant inquiries about their intellectual integrity, are undermining academic freedom not defending it. The wisest policy for those who are not concealed conspirators is the policy of "clean hands and speaking out." (Cf. Westin, " D o Silent Witnesses Defend Civil Liberties?" Commentary, June 19S3)

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2. There is still another aspect of the ethics of academic freedom which comes to light when its exercise, even in its most honorable forms, conflicts with other freedoms. This exemplifies a familiar situation in which right clashes with right and in which decisions, because of the shifting perspective of consequences, cannot be generalized as valid for all times and places except in a formal manner. All of us believe, for example, both in the rights of a free press and the right to a fair trial. But sometimes the operation of a free press results in so prejudicing a community that the right to a fair trial is in effect destroyed. English law severely restricts the right of the press to comment on most criminal cases while American law gives the press much more lattitude. Every wise decision seeks to maximize both rights when the conflict is apparent but no matter what device is adopted it will impose some limitation on one or both rights. By definition academic freedom entails freedom of publication and the open interchange of ideas and discoveries. But in times when the scientist becomes "an arbiter of life and death" certain limitations upon academic freedom of research and publication may reasonably be imposed. The difficult problems, as Lise Meitner put it in her comment on the agenda of the Hamburg Congress of Science and Freedom, are to determine by whom, in respect to what, and to what degree. To avoid arbitrariness and stultification of research, it is desirable that the scientists themselves play a leading role in shaping such decisions but they cannot be the sole judges. In 1939 Einstein and other scientists voluntarily imposed an effective blanket of secrecy upon themselves in fundamental nuclear research in order to prevent the Nazis from learning about phenomena which would enable them to destroy free society and all academic freedom. In 1948, however, the same group protested the policy of secrecy even in some matters that did not involve fundamental research despite the equally serious threat to free institutions from Soviet aggression. Right or wrong, their recommendations were moral and political, and a democratic community cannot waive its responsibility for decisions of this character. Some scientists like Norbert Wiener have publicly stated that they would refuse to work on any project or disclose any scientific information that might be put to military use, or to purposes of which they do not morally approve, apparently confident that without their help those responsible for

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the defence of their freedom will ward off totalitarian aggression. Since the uses of any piece of information are incalculable, this might impose silence upon them even in the field of theory of numbers. I t is one of the glories of a democratic community that it can permit this autonomy despite the fact that its survival is at stake. But the point is that no matter who institutes this policy, it is a restriction upon academic freedom and its justification cannot be determined without reference to other moral values. Sometimes our language about academic and other freedoms betrays us into an absolutism we do not intend and which suggests that a right is unconditionally valid, i.e., irrespective of its consequences upon the complex of other rights involved. I know of no such absolute right not even the right to search for and speak the truth in all circumstances. Some of the Nazi scientists sought to discover the truth about the survival thresholds of torture by immersion. One of them in a court proceeding defended himself on the ground that important truths were thereby attained. Yet all of us would regard such a quest for truth as a moral abomination even if the results obtained might some day be useful in saving lifes—which in fact was part of the plea in extenuation. A scientist who practices upon human beings as if they were experimental animals is a stock example of insanity in popular literature. But suppose a community felt about vivisection of animals somewhat as we do about vivisection of human beings, would it be a violation of academic freedom to forbid such experiment? In a world of limited resources and opportunities would it be a limitation of academic freedom to prevent, to stretch our fancy, say publication of a discovery that would abolish death, until some provision was made for the limitation of births? On Mr. Lovejoy's definition the answer would be clearly yes, but most of us would agree that the limitations were justifiable just as we would agree that limitations on freedom of worship if such worship involves child marriage or infanticide are justifiable. This indicates that moral questions are relevant not in knowledge but to knowledge and that Mr. Boas' summary argument is overly simple. In every civilized society some restraints "other than those of logic and sound methodology" must be recognized, and about some things it is not desirable to know or disseminate the knowledge we have. Some day an international democratic authority

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may restrict the academic freedom to conduct research on new weapons of war. However, unless there is convincing reason to believe that the quest for a piece of knowledge or its publication threatens basic moral values, themselves established by intelligent inquiry, no obstacles should be placed in the path of any kind of research and the broadest dissemination of its findings. Once embarked upon inquiry, no authority should be recognized except the canons of logic and empirical evidence. This in no way weakens the case for academic freedom any more than the case for free speech is weakened by recognizing its inescapable limitations. It enables us to recognize how and why problems concerning academic freedom, like other freedoms, arise even in the most enlightened of communities, why they cannot be settled merely by slogans or the invocation of abstract principles but require specific inquiry into concrete situations. It challenges our creative intelligence to devise institutional procedures to further the advancement of knowledge in a humane society. A philosophical analysis which does not bring to light what we really mean by academic freedom and what we really are committed to in espousing it, is inadequate.

Symposium:

ON T H E ONTOLOGICAL SIGNIFICANCE OF T H E LOWENHEIM-SKOLEM THEOREM GEORGE D . W . BERRY AND J O H N R .

I . GEORGE D . W .

MYHILL

BERRY

1. Preliminary considerations. The Lowenheim-Skolem theorem in effect states that every formal system with a model has a denumerable model. The term "model" is here used in that broad sense under which "possession of a model" and "consistency" are synonymous. We may accordingly take the theorem as asserting that every consistent formal system has a denumerable model. Now a given collection of objects forms a model of a given system if the system can be so interpreted that the collection is the system's universe of discourse and the system is in fact true of the objects in the collection. A collection is denumerable if it contains no more members than the set of all positive integers. Thus a denumerable collection is one such that the number of its members is either some finite cardinal or the smallest infinite cardinal, usually designated by the Hebrew letter aleph with an inferior 'o', but hereafter called A„. In view of these considerations, the gist of the Lowenheim-Skolem theorem can be rephrased as follows: every consistent formal system can be so interpreted that its truth presupposes the existence of at most A0 entities. The bearing of this theorem on the ontological question "What exists?" forms the subject of the present paper. A bewildering variety of answers to the ontological question have, of course, been proposed. But any such answer that is both comprehensive and thorough has included a theory of abstract objects and on the basis of this theory each can be classified as some form of nominalism or conceptualism or platonism. Whatever ontological 39

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significance the Lowenheim-Skolem theorem possesses would seem to lie in its reference to these three types of metaphysics. But when is a theory nominalistic? Or conceptualistic, or platonistic? Its classification will perhaps present few difficulties when the theory in question explicitly states some doctrine characteristic of nominalism or conceptualism or platonism. But if he is to be consistent and thoroughgoing, the ontologist must not only enunciate his ontology; he must also, at least in principle, interpret all his rational beliefs in a fashion compatible with it. These will presumably include at least fragments of logic, of mathematics and of the natural sciences. Ideally, they will constitute a powerful, interpreted formal system. Let us call such a broad, interpreted system a general language or, when there is no danger of confusion, simply a language. What is wanted, then, is some criterion by which we can determine the ontological commitments of such a language or of any of its component theories. The most adequate such criterion suggested to date has been proposed by W. V. Quine in his papers "Designation and Existence" (Journal of Philosophy, Vol. 36 [1939]) and "On Universals" (Journal of Symbolic Logic, Vol. 12 [1947]). First, if the language to be examined is not already in such a form, it must be recast so that bound variables occur within it and play there the same roles that they play, for instance, within the functional calculi of first and higher orders. Then under Quine's criterion any theory within the language, from a single statement to the entire language itself, attributes existence to exactly those objects which the bound variables of the theory must take as values if the theory is to be true. Thus determined, the property of existence would seem to be the broadest possible, including as it does both the existence of concrete objects and, if such there be, abstract objects as well. Existence so defined is, nonetheless, only defined relative to some given language. We can, however, fix an absolute sense to the term 'existence' and so answer the unqualified question "What exists?" by adopting some language and accepting its ontological presuppositions as true. Viewed in this light the question 'What bearing has the Lowenheim-Skolem theorem on the question "What exists?"?' can be rephrased as 'What reason does the Lowenheim-Skolem theorem give us for preferring one general language—nominalist, conceptualistic or platonistic—to others?'

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2. Nominalism. Traditionally, nominalism is described as that metaphysical doctrine t h a t denies existence to abstract universals and attributes it to concrete particulars. Nominalistic discourse may permit ostensible references to the abstract via words which like 'circularity' or 'beauty' Plato would have held to be names of eternal Ideas. But the nominalist must interpret all such references as specious only: he must hold t h a t the locutions embodying them are merely circumlocutions, referring in a roundabout way to a solid world of concrete, particular things. W h a t is more, whenever the nominalist admits such an oblique expression to his language, he must be able to so explain its meaning as to eliminate therefrom all references to the abstract; wherever he cannot do this, he is in all conscience bound to reject the oblique term as according to his lights literally meaningless. In this way, the nominalist is committed to an actual "reduction of the abstract to the concrete." It is not enough that he believe such a reduction theoretically possible: with respect to the contents of his own language, he must also carry out the reduction in full detail. In the light of Quine's criterion, the gist of the foregoing description is clear. T h e language of the nominalist m a y contain expressions which appear to be names of abstract objects; it may even contain expressions that appear to be bound variables taking abstract entities as values. But all such apparent names and bound variables enter the language via definition only; each is introduced as a compact or otherwise convenient device for discussing concrete objects. T h u s when in a n y sentence containing such an apparent name or bound variable all defined expressions are replaced by their defining expressions and this process of replacement continued until only primitive notation remains, the resulting primitive transcription of the original sentence will contain no name not the name of a concrete object and no bound variables taking anything except concrete objects as values. Now it should be noted that, while the process of definition adds new terms to a language's vocabulary, it a d d s no new entities to its universe of discourse, for a sentence and its primitive transcription refer to exactly the same things. F r o m first to last the nominalist grants existence only to the concrete objects he begins with; for him, their number is the number of all the objects there are. Nominalists, of course, differ in their views of the concrete.

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Some are physicalists, holding that all cognitively significant discourse can be reduced to a description of physical entities. These entities may in turn be identified with atoms of matter or actual spatio-temporal volumes or points. But whatever they are, it is characteristic of physicalism to hold that once they are identified their properties are to be established not by a priori stipulation but by the empirical investigations of physical science. In particular, any theory ascribing a number to the totality of concrete objects or asserting or denying some upper limit beneath which such a number must lie enjoys, for the physicalist, the status of an empirical hypothesis, a fragment of that part of cosmic physics that deals with the magnitude of the physical universe. Such a hypothesis must, like any physical theory, be anchored—though perhaps by a chain of inferences that is both long and fragile— to some body of observational data. Thus in seeking to determine the number of concrete objects, the physicalist must consult contemporary physical theories and the evidence that supports them. Direct observation naively interpreted testifies, as Descartes and preceding theologians pointed out, to the existence of only finite collections. When the physicalist turns to the physicist in an effort to take advantage of the latter's indirect observational methods and sophisticated theoretical interpretations, the physicalist finds himself face to face with relativity-theory, which holds the total number of points in space-time to be finite. Now if the number of such points is finite, so is the number of their combinations and this second number surely forms an upper limit which the number of concrete objects under any physicalistic interpretation cannot exceed. If the physicalist accepts relativityphysics he must assume the number of all entities finite. True, he might not accept it. He might, for instance, adopt some alternative brand of physics that maintains the cosmos infinitely extended. But on what evidence? By some standards the desirability of a full arithmetic of positive integers might in itself justify the recognition of infinite collections. Not, however, by the standard of the physicalist: his existence-criteria are those of the physicist and in these observation plays a crucial role. At this point the physicalist is apt to feel either (a) that in presuming to arbitrate between competing systems of physics he has passed beyond the sphere of his own competence or (b) that within these systems neither the doctrine that the universe is finite

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nor its contradictory is firmly enough grounded in evidence to serve as one of the foundation-stones of his entire philosophy of mathematics. In either event, the outcome is the same: the physicalist will g r a n t the existence of this or that finite assemblage b u t he will p r u d e n t l y refrain from assuming either t h a t all assemblages are finite or t h a t some are not. In practice, he will recognize only w h a t is finite. T h e nominalist, of course, need not be a physicalist: instead, he m a y be a phenomenalist. If he is he will, like all nominalists, be committed to 'reducing the abstract to the concrete" b u t he will identify this last not with the entities of physical science b u t rather with directly perceived objects inhabiting immediate experience—sensa or sense-data, for instance, or collections or sequences of such. For him, they will comprise all existence a n d their number will be the number of all the things there are. If psychology h a d attained to the authority of physics, t h e phenomenalist might, in seeking to fix this number or to determine a t least its order of magnitude, turn for advice to the psychologist, so becoming a psychologicalist. Even if he is loath to be so labeled, he can hardly ignore the evidence which the specialists in the theory of sensation have amassed. Such evidence points unmistakably in the direction of finitude. Consider, for instance, a single sense, say vision, and of the immediate objects perceived through this sense a single property, say color. Color itself varies along at least three dimensions—intensity, saturation and hue; consider the last of these. T h i s varies with the frequency of t h e radiation forming the usual stimulus. But of the total range of frequencies a t which radiant energy is emitted, only a narrow band provokes a visual response. Radiation of one set of frequencies elicits red sensa, radiation of another set yields violet sensa. These constitute the threshold and lintel of hue: all the remainder of the visual spectrum is provided by intervening frequencies; below red a n d above violet lie the vast domains of the invisible. F r o m threshold to lintel frequency varies continuously. N o t so, however, the corresponding hues perceived: a change in frequency m a y be too slight to evoke a n y change in the hue perceived, a n d there are least noticeable differences in frequency each of which corresponds to a pair of a d j a c e n t hues. T h u s although he m a y be capable of perceiving hues provoked by an infinite n u m b e r of frequencies, the totality of hues perceivable

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by a given perceiver, even when in a state of optimal visual acuity, is finite in number. With respect to intensity and saturation, the other colordimensions, the situation is similar: in the case of each dimension, there is a threshold and a lintel of perception, and least noticeable differences divide the intervening strip into a finite number of intensities or saturations. Indeed, the situation is similar with respect to any dimension of any sensory property. Since the number of human senses, if not five, is at least finite, since the number of distinct sensory properties directly perceived by any sense is also finite, and since the number of dimensions possessed by each property is finite too, it follows that the totality of hues, saturations, intensities, pitches, loudnesses, timbres and atomic sensa in general is for any given perceiver itself finite. Any attempt to generate from the finite totality of atomic sensa possible within the immediate awareness of a single subject an infinite totality of molecular sensa seems faced with obstacles which remain insurmountable as long as the would-be generator remains both a nominalist and a phenomenalist. He might take all atomic sensa as comprising not just those falling within the awareness of a single individual but those directly perceived by all individuals past, present or future. So conceived, the number of atomic sensa would still be finite unless he were willing to assume the existence of infinitely many perceivers—an assumption for which there is no tittle of evidence. If he identifies molecular sensa with combinations of atomic sensa, the number of the former and hence of the former plus the latter will still be finite. He might take molecular sensa as not simply combinations but rather as sequences of atomic sensa; still the number of such sequences will be finite unless there is no upper limit to their length. The absence of such a limit would seem to involve once more the fanciful conjecture that there are infinitely many perceivers. If the nominalist seeks to accommodate an infinite number of sensa by admitting to his universe of discourse unperceived sensa or unperceived combinations or sequences of sensa, he has abandoned nominalism; for all such are theoretical constructs, abstractions as distinct from any concrete object as the eternal platonistic entities the nominalist eschews. I t would seem, then, that the nominalist, whether he subscribes to physicalism or phenomenalism, dares recognize the existence

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of only a finite number of things. In limiting his world to the concrete, he has made it in toto the subject matter of the empirical sciences, and the findings of these are not such as to justify any overall assumption of infinitude. Even if he finds the contradictory assumption virtually as groundless and so refrains from making it, he will have no recourse but to proceed in other connections as if it were true, recognizing as the need arises this or that finite number of objects but never an infinite number. It is this commitment to finitude that the relevance of the Lowenheim-Skolem theorem to nominalism must, if it lies anywhere, lie. Under the theorem, every consistent formal system has an interpretation which presupposes the existence of at most the smallest possible infinity of objects. Every nominalistic interpretation, moreover, assumes the existence of a finite number of objects only. Now the difference between the finite and the smallest infinite, however great that difference is, is still smaller than the difference between the finite and the larger infinites. Thus the Lowenheim-Skolem theorem assures us in the case of any consistent formal system that there is an interpretation nearer than might otherwise have been supposed in the number of objects it assumes to the kind of interpretation that a nominalistic ontology can accommodate. Thus, it might be argued, in showing that the notion of any but the smallest infinity is in an obvious sense dispensable, the Lowenheim-Skolem theorem carries the nominalist that much closer to one of his principal goals—the goal, that is, of showing that the notion of an infinity of any magnitude is likewise dispensable. This argument is considerably less convincing at second sight than at first. No doubt it achieves much of its initial plausibility by suggesting that some variant of the Lowenheim-Skolem argument can be used to establish a much stronger theorem, viz. that every system with a model has a finite model. But this theorem, at least in the broad sense of 'model' which is used in the Lowenheim-Skolem theorem and which justifies interpreting 'possession of a model' as 'consistency', is known to be false. Thus, if the Lowenheim-Skolem theorem carries the nominalist to a point nearer to his goal than any he has hitherto gained, it also once and for all abandons him there. Unfortunately for the nominalist, it is the part of his journey lying between this point and his goal which is the most important

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and difficult. If he could assume the existence of even the smallest infinity, it would lie within his power to provide interpretations for the arithmetic of natural and rational numbers and perhaps for a segment of real number theory sufficient to explain the computations of engineers. Since he is barred from making any such assumption, his is the titanic task of either showing that these disciplines have no interpretations, and are therefore literally meaningless, or of providing for these disciplines some effective substitutes. On methods of achieving either of these results the Lowenheim-Skolem theorem sheds no faintest gleam of light. 3. Platonism and Conceptualism. With respect to the existence of abstract entities, the platonist stands at the opposite pole from the nominalist. The latter denies their existence altogether; when his language is reduced to primitive notation, they are not mentioned at all. The platonist, on the contrary, believes that abstract objects do exist and that discussion of them is genuinely what it seems, not merely a compact manner of talking about concrete things only. His language accordingly is shot through and through with ineliminable references to the abstract; even when his sentences are reduced to primitive notation, some of them will contain names of abstract entities or bound variables taking abstract entities as values. So far, the platonist and the conceptualist agree. But in describing the nature of the abstract objects, the existence of at least some of which they jointly accept, the conceptualist and the platonist differ. Whereas the platonist believes abstract objects exist independently of the mind, the conceptualist holds them to be products of mental activity. Now the mind is an organ of proven fallibility, prone to confusion and liable to overestimate its own powers. Particularly is this so in any region in which the mind escapes that control by objective fact exemplified in empirical science. But according to the conceptualist, the domain of the abstract is just such a region: here, he says, we are not describing a pre-existing world the evidence of whose actual character will eventually enable us to correct our initial report of it; rather, we are ourselves freely creating the world we describe. Accordingly when faced with the issue of what abstract entities should be granted existence, the conceptualist proceeds with caution. He feels the need of some orderly master program to prevent the mind from issuing con-

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flicting directives. H e is apt thus to begin by conferring existence upon a limited set of abstract entities whose compatibility seems guaranteed by intuition, thereafter admitting additional abstract entities at least, if not one by one, in companies no one of which is permitted to take the field beside its predecessor until it too has passed the reviewing stand of his mind's eye. I f the question of which abstract entities exist engenders in the platonist any such feelings of caution, they are much fainter ones. T h e platonist holds abstract entities irreducible constituents of the universe, constituents that are not mind-created but instead antedate mind and, indeed, creation itself. Holding as he does that they comprise an eternal domain such that he can by taking thought add to it or remove from it no single member, the platonist feels no need for anything corresponding to the conceptualist's overall production-schedule. He is not, the platonist maintains, responsible for the abstract; his only duty is to describe it truly. Here the platonist must fall back on intuition: he begins by ascribing existence to entities whose properties and relations seem evident. These include at least the simpler objects of classical mathematics. In order to unify his theory and render it more comprehensive, however, he soon finds himself impelled to postulate the existence of additional abstract entities, some of a complexity that baffles intuition. T h e postulates admitting these he feels justified in believing as long as the consequences he derives from them are intuitively acceptable. As their consequences become less intuitively acceptable, his confidence in the postulates decreases, and with the appearance of a contradiction—which is the most intuitively unacceptable of statements—his confidence vanishes, so that he modifies a postulate or rejects it altogether. On the other hand, deduction may disclose unsuspected weaknesses in the postulates; the platonist will then strengthen his assumptions. T h e working methods of the platonistic logician thus bear a striking resemblance to those methods of hypothesis and verification employed within the empirical sciences. W h a t sorts of formalized languages will the conceptualist and platonist prefer and, consistently with their respective ontological viewpoints, be capable of employing? With respect to the platonist, the answer is easy: he will naturally prefer and find himself free to select for his own usage the most powerful languages not known

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to be inconsistent. These are the languages usually identified with that viewpoint within the philosophy of mathematics known as logicism, a point of view which regards classical mathematics as literally meaningful and in its entirety deducible from purely logical assumptions. Various methods of constructing such systems are known. Wherever the systems contain bound variables, at least some of the latter will take abstract objects as values. The platonist's desire to incorporate within his system all or almost all of classical mathematics leads him to admit, perhaps by adopting axioms of infinity and choice and other existence-principles, as great a variety of entities as he dares. The resulting system will be capable of accommodating arithmetics of both denumerably and indenumerably infinite cardinals. Indeed, its universe of discourse need be limited only by those ad hoc restrictions imposed under set-theory or type-theory to protect the system against the familiar logical antinomies. The conceptualises confidence in the mind's ability to contrive complex entities consistently may be strong or weak and his belief as to what constitutes a permissible master plan of production will be optimistic or the reverse accordingly. It is the latitude allowed the mind by such a production-plan that determines the strength of the conceptualist's system. Here we find the greatest variety, a spread that begins with the relatively weak intuitionistic languages suggested by Brouwer and, in part, formalized by Heyting, a spread that continues through the stronger "definite" Language I of Carnap's The Logical Syntax of Language, and includes in its upper reaches the relatively strong constructivist language sketched by Quine in his "On Universals." Of these three languages, none is capable of providing a theory of the larger infinities: even the most optimistic versions of conceptualism appear to regard the cardinals past A„ as too complex to be safely produced. The intuitionistic and definite languages achieve this exclusion of larger infinities by banning reductio ad absurdum arguments involving the refutation of a universally quantified sentence, a type of argument on which the existenceproof of any cardinal greater than A0 depends. The intuitionistic language secures this result by adopting a drastic course: it abandons the law of excluded middle. The definite language is more moderate: it accepts thé law of excluded middle, thus per-

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mitting some rcductio ad absurdum arguments, but excludes (unlimited) universal and existential quantifiers, thus barring those rcductio ad absurdum arguments with conceptualistically unacceptable conclusions. Abandonment of the law of excluded middle and omission of unlimited quantifiers both result in serious curtailments of power. Quine's constructivist language, which employs neither device, is by far the strongest of the three conceptualistic systems. Quine conceives the guiding principle of his production-plan as simply this: no class is to be granted existence unless its members either exist ab initio or have been previously constructed. T h u s concrete objects are assumed to exist prior to t h e date of the system's origin; classes of concrete objects can accordingly be constructed straightway. Only then can we construct classes having such classes or such classes plus concrete objects as members. Similarly classes of the third level can have only concrete objects or these plus classes of such or both of these plus classes of concrete objects as members. And so on: each class will have its level a n d as members only classes of lower level or concrete objects. Moreover, this process of constructing classes of higher a n d higher level is to be envisaged as continued indefinitely so t h a t there is no class of highest finite level. If the existence of denumerably infinite classes is to be proved within this system, a t least as the system is formalized b y Quine in the article cited, an axiom of infinity must be added. T h e justification of such an axiom on conceptualistic g r o u n d s presents a certain problem. One solution would begin by boldly assuming the class of concrete objects ( d e n u m e r a b l y ) infinite. T h e conceptualist might then justify this assumption by claiming t h a t , if it does not create concrete objects outright, the mind does a t least determine their number; in particular, he might urge, the mind is capable of making the number of concrete objects infinite simply by conceiving every concrete object as composed of smaller concrete objects. Alternatively, the conceptualist might assume the n u m b e r of abstract objects infinite. H e might then j u s t i f y this assumption by arguing t h a t the mere adoption of a rule, such as Quine's, for constructing entities brings simultaneously into existence all objects in theory constructible by repeated applications of the rule, even when the number of applications a n d hence of entities is, as in the case of Quine's rule, infinite. And there are

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doubtless still other alternatives, some as acceptable at least as either of the two mentioned. Whichever method of justifying the addition of an axiom of infinity to Quine's system is adopted, the upshot will be to render provable within the system the existence of denumerably infinite collections. We may thus consider the system so supplemented and hence regard conceptualism in its strongest formulation as accommodating classes of A c members. In turning to the relevance of the Lowenheim-Skolem theorem to conceptualism and platonism, it is well first of all to banish two misconceptions which, if not prevalent in the literature, are at least commonly encountered in informal discussion. The first misconception is that the conceptualist cannot accept the LowenheimSkolem theorem because its proof requires non-constructivist principles, which he rejects. The second misconception is that the platonist must reject the Lowenheim-Skolem theorem because it proves that indenumerable collections need not be recognized and so contradicts the Cantorian indenumerability-proofs, which he accepts. The first misconception has a factual basis: it is true that the published proof of the Lowenheim-Skolem theorem is nonconstructive in character and that, as a result, the conceptualist cannot consistently accept this proof. But it is after all a commonplace of logic that the truth of a statement does not depend upon the validity of any one proof of it: the statement may be true in virtue of some other proof which is valid. Such a proof of the Lowenheim-Skolem theorem is immediately forthcoming from the conceptualist's ontology. Under the latter, the universe contains at most a denumerable infinitude of objects, so that all models are denumerable and any system with a model has a denumerable one. Thus the very motives which lead the conceptualist to reject the proof of the Lowenheim-Skolem theorem constrain him to accept the theorem itself as true. The second misconception can be formulated as follows: "The staunch platonist accepts as true and hence consistent a system in which Cantor's theorem to the effect that indenumerable collections exist can be proved. The staunch platonist also accepts the Lowenheim-Skolem theorem which asserts that any consistent system can be so interpreted that its truth presupposes the existence of at most a denumerable infinitude of entities. There is

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here somewhere an inconsistency." One suspects that it is some form of this misconception that has led authors ordinarily cautious to term the Lowenheim-Skolem theorem "the Lowenheim-Skolem paradox." Actually, of course, no contradiction is involved. Cantor's theorem says that there are more than A 0 entities but, when translated into the notation of some formalized system, says so only when this notation is given the platonistic interpretation intended by the theorem's author. There is, on the face of it, at least, no contradiction involved in maintaining that under a different interpretation the formal transcription of Cantor's theorem will have a quite different meaning, that as construed under this different interpretation it will not assert that more than A„ objects exist. The Lowenheim-Skolem theorem merely assures us that if the system in which this transcription is provable is consistent then that system is susceptible of an interpretation under which neither Cantor's theorem nor any other theorem of the system asserts that the totality of all things exceeds the denumerable. The Lowenheim-Skolem theorem thus does not show the strong platonistic system inconsistent: what it does show is that the axioms of the latter, if consistent, form a non-categorical set (i.e., admit of more than one interpretation) and have a non-standard model. It is here that we come within the area of what has been conjectured to be the Lowenheim-Skolem theorem's major ontological significance. This conjecture might be put into the form of an argument as follows: By the Lowenheim-Skolem theorem, every consistent system—even the strong platonistic one—can be so interpreted that it does not assert the existence of the indenumerable. Thus in the case of any consistent system we can adopt such an interpretation of it and, without thereby being forced to reject any consistent system as meaningless, dispense with the notion of indenumerability altogether. Now conceptualism is fully capable of accommodating the denumerable; it is only with the admission of the indenumerable that a given interpretation of a system proves itself unavoidably platonistic. Hence in dispensing with the indenumerable we can also abandon all platonistic interpretations, adopting conceptualistic ones in their stead. But this is only another way of saying that we can dispense with platonism itself and become conceptualists. The force of this argument may be justly estimated if we

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imagine the case of a nominalist who after extended meditation becomes convinced that the full arithmetic of positive integers is, under some interpretation of it, true. He examines this arithmetic and finds therein an axiom of infinity. He recognizes, of course, that his own philosophy justifies belief in no such axiom. Therefore he tries to reinterpret the arithmetic in such a way that the axiom of infinity will no longer, under its new interpretation, require the existence of more objects than his philosophy can admit. He soon finds this impossible; he finds that, by their structure alone, systems containing an axiom of infinity exclude finite and therefore nominalistic models. He must therefore either renounce nominalism or the full arithmetic of positive integers. "This kind of thing" the conceptualist might confess, "might once have happened to me. I might have become convinced that strong platonistic systems are, when correctly interpreted, true. Failing to find any interpretation that would not require the existence of indenumerable collections, I might have concluded that no such interpretation existed and that conceptualism was thus doubtful. In showing that any consistent system has such an interpretation, the Lowenheim-Skolem theorem removes this temptation from my path." But should it? The conceptualist can have but two reasons for believing the Lowenheim-Skolem theorem: (1) he takes it as a trivial corollary of conceptualism, which holds all models denumerable, or (2) he grants the validity of its published proof, which is non-constructive in character. Under alternative (1), it is conceptualism which supports the Lowenheim-Skolem theorem, not the converse; under alternative (2) the conceptualist becomes a platonist, and will construe the Lowenheim-Skolem theorem, not as supporting conceptualism, but rather as merely furnishing one more evidence of the capacious power of platonistic logic. I t should be noted that in his "Arithmetic Models for Formal Systems" (Methodos, Vol. 3 [1951]) Wang has given directions for the construction of denumerable models and indeed within the domain of elementary arithmetic, but only for consistent systems whose axioms, above and beyond quantification theory, are finite in number. If the Lowenheim-Skolem theorem could be rendered similarly constructive for systems in which such axioms are infinite in number, the above argument would, of course, fail.

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Then the conceptualist could justifiably cite the LowenheimSkolem theorem as substantiating his own position. There are considerations, however, of a type other than those previously adduced which, while they do not imply that the conceptualist may not or should not cite the Lowenheim-Skolem theorem in his own support, at least indicate that he will gain little by doing so. Nor is the weight of considerations of this type liable to be decreased by any foreseeable discovery within the field of logic. Imagine a geography book, filled with true sentences describing the sizes and physical contours of the continents, the chief economic activities of the various nations, the populations of major cities, and so on. These sentences can be translated into a language consisting solely of the familiar notation of quantification-theory plus a stock of constant empirical and logical predicates. The sentences so translated may be taken as a formal system, either by choosing from them a selection which implies the rest or simply by adopting the entire set of translated sentences as axioms. Since the axioms are finite in number and, because they are true, are consistent, the previously cited result of Wang's will enable us to construct an arithmetic interpretation of them, an interpretation under which the geographer's original discussion of continents, cities, and populations is transformed into a description of integers and the relations in terms of addition and multiplication that they bear to one another. But would the mere existence of this interpretation tempt the geographer, or any of us, to prefer it to his original one? Would the fact that the original theory can be arithmetically interpreted lead anyone to claim that it should be, that the land-masses and peoples presupposed by the initial interpretation can justifiably be rejected and the whole earth considered, Pythagoras-wise, as a congeries of numbers? The existence of a given interpretation provides in itself no justification for preferring that interpretation to another; the grounds for such preference must stem from considerations which look beyond the mere existence of the preferred interpretation to criteria by reference to which the competing interpretations can be judged. What are the criteria which might lead one to prefer for any given system a conceptualistic rather than a platonistic interpretation? One such is economy. But this is of little impor-

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tance in the eyes of the platonist, and the conceptualist cannot hold it the crucial consideration; if he did, he would be a nominalist. Another criterion is consistency. But consistency is a property of a system's structure alone, so that a system with a conceptualistic and a platonistic interpretation is either consistent under both or inconsistent under both. The conceptualist might argue that under the Lowenheim-Skolem theorem every consistent system with a platonistic interpretation has a true conceptualistic one and that if we cannot find such a conceptualistic interpretation we have good reason to suspect the system of inconsistency. This, he might add, provides ample grounds for confining ourselves to conceptualistic interpretations. But even if the Lowenheim-Skolem theorem guarantees the existence of this conceptualistic interpretation where the system is consistent, it does not tell us how to find it and Wang's extension tells us this only when the system's supra-quantificational axioms are finite in number. In other cases the conceptualist faced with the strong platonistic system and unable to find for it a model within his own universe of discourse will not know whether to attribute his failure to the system's inconsistency or on the contrary to blame it on his own lack of ingenuity. Also, the platonist might contend, such excessive concern for consistency represents a failure of nerve and forms as effective an obstacle to the progress of knowledge as would the attitude of empirical scientists if none of them dared to advance a new hypothesis for fear that future observation would prove him wrong. Consistency and economy, moreover, are not the sole criteria relevant. The geographical example given makes this evident, for here consistency under either interpretation is assured and the arithmetic interpretation, presupposing abstract objects only rather than both abstract and concrete, is if anything the more economical of the two. We retain the geographical interpretation because it meshes with a wide background of belief connected with the given interpretation but not part of it and so not reflected in the system interpreted. The arithmetic interpretation might match with one of its own every distinction and relation embodied in the geographical but it would not fit the hole left in the wider context by the latter's elimination. Now the philosophy of the conceptualist and that of the platonist each forms such a broad context, a context of which the interpretation of any given formal

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system that is likely to be proposed constitutes only a part. One context requires one sort of interpretation, the other another. In showing that systems of a previously unsuspected variety are open to interpretations of either sort, the Lowenheim-Skolem theorem is not apt to lead anyone to abandon the interpretation that he prefers in favor of another. It is for this reason that conceptualism and platonism are each so largely immune to the weapons of the other: they stand facing each other like two mediaeval fortresses, each so strong in its defenses and so weak in its means of attack that neither can conquer the other. Viewed in the perspective of the conceptual framework of the present investigation, the ontological significance of the Lowenheim-Skolem theorem would thus seem to be meagre indeed. The theorem is irrelevant to nominalism and whatever support it offers conceptualism against platonism is slight in comparison with the forces, on both sides, already in the field. This largely negative conclusion may show the inadequacy of the conceptual framework adopted or it may arise from deficiencies in the proposed analysis of nominalism, conceptualism and platonism in terms of it or it may stem from still other sources. Still, if it has done no more than open what is by no means a simple topic to general discussion, the present investigation will have served its major purpose.

Symposium:

ON THE ONTOLOGICAL SIGNIFICANCE OF T H E LOWENHEIM-SKOLEM THEOREM GEORGE D . YV. B E R R Y AND J O H N R .

I I . JOHN R .

MYHILL

MYHILL

I share with the previous speaker the conviction that the Lôwenheim-Skolem theorem has no direct philosophical implications. T h i s phrase should be clarified. W h a t is implied is a proposition and to say there are philosophical implications implies that there are philosophical propositions. This runs counter to the idea that philosophy is an activity rather than a doctrine, an idea to which with reservations I subscribe. However part if not all of this activity consists in the assertion of propositions, which are not however philosophical propositions in themselves, but become philosophical in virtue of being asserted in the course of philosophical activity. Hence no proposition has philosophical implications in the strict sense, but perhaps every proposition may with propriety be asserted in the course of philosophical activity. Almost any proposition may I suppose initiate philosophical activity, and I take the invitation to contribute the present paper as a request to perform a philosophical activity initiated (after those introductory remarks) by the assertion of the Lôwenheim-Skolem theorem. T h e assertions made by me subsequently to this assertion I shall call indirect implications of the Lôwenheim-Skolem theorem, using the word 'implication' in its colloquial rather than its technical sense. M y initial remark that the theorem has no direct philosophical implications is therefore a direct consequence of my view that philosophy is an activity rather than a doctrine. I do not maintain that philosophy is wholly or primarily an activity of clarification. In particular I cannot see that clarification is the principal goal of ethics, though it might be an important 57

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instrument in achieving that goal. None the less clarification is part of philosophy, or at least the clarification of certain issues is. Much of the activity which I will perform in this paper will be clarificatory, that is, it will be devoted to stating in non-technical terms what the Lowenheim-Skolem theorem is. Why is this a philosophical activity? Would a clarification of say the binomial theorem be philosophical? Clearly not; more exactly, it seems highly dubious that the assertion of the binomial theorem could profitably initiate a philosophical discourse, except perhaps by way of illustration of some general aspect of mathematics for which purpose a good many other theorems would have served equally well. T h e reason why the Lowenheim-Skolem theorem seems a fruitful proposition with which to begin a philosophical discourse, while the binomial theorem does not, is that we are inclined to ask " W h a t does the Lowenheim-Skolem theorem really mean?" while we are not inclined to ask " W h a t does the binomial theorem really mean?" I take such questions seriously. A question is an expression of intellectual anxiety and an answer is an attempt at resolution of that anxiety. I distinguish formal from informal questions, and within the latter I distinguish subjective and objective. A formal question carries with it the form of its answer, that is, the social context is such that the criterion of acceptability for the answer is known and agreed upon by both questioner and answerer in abstraction from the answer itself. The purest kind of formal question is the question of the truth or falsity of a mathematical theorem within a known system. For the criteria of being a proof or not being a proof within that system are capable of exact specification and are in the ideal case specifically agreed upon by questioner and answerer. Questions in the empirical sciences are a less pure kind of formal question, since the criteria of confirmation are less exactly specifiable than those of mathematical proof. An informal question is one the form of whose answer is not known either by questioner or answerer in abstraction from the answer itself. The dictum that the meaning of a proposition is the method of its verification does not apply to propositions which answer informal questions, for part of the meaning of such a question is to question what the form of its answer would be. Thus part of the meaning of the question "How shall I face the prospect of my death?" is "What form of answer (psychoanalytic,

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theological, semantical) would resolve the anxiety expressed by the question 'How shall I face the prospect of my death?'?" More simply; if and in proportion as a question is formal, the questioner is prepared to state precisely what kind of evidence would convince him of the truth of any proposed answer. A formal question asks for the matter of its answer but provides the form; an informal question asks for both. Any question, therefore, which asks after the general features of formalism, must be itself informal, for if the form of the answer were known to the questioner, he would already presuppose or regard as unquestioned a certain form as appropriate to answering his question, and so in questioning the nature of formalism would already be operating in the framework of a formalism which was unquestioned. Hence metamathematics must be in the final analysis informal; for the process of discussing formalisms by means of other formalisms must either terminate in a formalism which is not discussed, or be informal. But in the first case we would be doing mathematics and not in the strict sense metamathematics. Anyone familiar with the writings of Hilbert can provide illustrations for himself of this phenomenon. I shall try to show that anxiety concerning the Lowenheim-Skolem theorem originates partly in a desire to consider formal objects outside of the formalism in which they are imbedded, and so presents in a specifically acute way the informality characteristic of metamathematical anxiety. T h e opinions that this anxiety results from a confusion of different formalisms or from a confusion between internal and external questions, or from a self-contradictory desire that an object be at once formal and non-formal, I dismiss because of my contention that anxiety can frequently be resolved by verbal answer even when it does not provide the form of that answer. A question does not have to be precise in order to express a genuine anxiety and thus be a genuine question. I distinguish within informal questions between objective and subjective, according as there is or is not agreement as to the effectiveness of the answer in resolving the anxiety which prompted the question. Hence there is no way of knowing whether an informal question is objective or subjective until the question is answered. Even in that case, there is usually the possibility that a subjectively satisfying answer may later be replaced by an objectively satisfying one. Evidently the distinction between sub-

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jective and objective informal questions is relative, dependent on social conditions. A question which is informal, but close to objectivity is "What is the meaning of the definite article?" At the other extreme are questions expressive of neurotic anxiety which can be resolved only by special treatment in each case. Philosophical activity is the activity of resolving anxiety expressed by objective informal questions. Because what is at one time informal may later become formal, the philosophical area shrinks progressively, yielding place to science. Because few if any informal questions are entirely objective, there is diversity of philosophical systems. I repeat that the anxiety expressed in feeling the Lowenheim-Skolem theorem as a paradox results in part from the desire to grasp a formal object apart from its setting in a formal system; thus this anxiety concerns formalism in general and so can be resolved only informally. On the other hand, I am optimistic enough to hope that at least part of my comments will provoke agreement; hence the clarificatory part of them and a certain amount of the motivational analysis may claim to be philosophical in the sense I have explained. I shall now state the theorem roughly and exhibit the proximate grounds for anxiety concerning its 'real meaning.' The theory states that every formal system expressed in the first order functional calculus has a denumerable model. In particular the general theory of sets as axiomatized e.g. by von Neumann and Godel has a denumerable model; yet this theory was designed in part in order to formalize in a consistent and rigorous manner the arguments of Cantor's theory of infinite cardinals, one of the main results of which is that the continuum is more than denumerably infinite. One can state the perplexity arising from this circumstance in various ways; e.g. that the attempt to formalize the notion of a non-denumerable infinity is forever doomed to failure, and that this is an essential and unanticipated limitation of formalism. This perplexity we shall resolve incidentally later. Simpler to handle now and nearer the spirit of the foregoing discussion is the following statement: the continuum is according to formalized set-theory non-denumerable; i.e. its non-denumerability is a thesis of that theory. This thesis however asserts that no one-toone correlation between the continuum and the integers exists; for in this way is nondenumerability defined. On the other hand, since formalized set-theory possesses a denumerable model, it

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possesses a model in the integers; and so there is a one-to-one correlation between all the sets of formalized set-theory and the integers, namely the correlation which correlates each set with the integer representing it in the model. A fortiori there is a correlation between those particular sets in the formal system which constitute the continuum and a subset of the integers. It appears to follow that the continuum dealt with in formal set-theory is denumerable, hence not a true continuum; moreover, that the thesis of formal set-theory to the effect that (this) 'continuum' is non-denumerable actually asserts merely that it is not capable of enumeration by any correlation appearing amongst the objects of that theory, i.e. appearing as a value of its variables. For the thesis asserts "there is no R which is a one-to-one correlation between (this) continuum and the integers''; and since there does appear in the light of the Lowenheim-Skolem theorem to be such a correlation, we seem forced to conclude that this correlation is not amongst the range of values of the variable R, i.e. not amongst the objects of formal set-theory. Hence we infer that we cannot adequately express the notion of indenumerability and of the continuum within formalized set-theory, in the sense that all we can assert is the absence of a correlation within the set-theory itselj between the continuum and the integers, whereas to do justice to our intuitive idea of a non-denumerable continuum we would wish to assert the absence of any correlation whatsoever. Here 'any correlation whatsoever' is an informal notion, for as soon as it is formalized we have once more only those correlations which one represented in a particular formal system, and the whole argument could be repeated concerning this system. Hence we suspect the existence of a non-formalizable notion, and that on a very low level of mathematics. The 'paradox' thus concerns the inadequacy of formalism to its supposed informally conceived object, and is therefore, in line with our previous discussion, a paradigm of the eventually informal and philosophical character of metamathematical anxiety. Naturally this whole argument is unprecisely formulated and probably contains outright fallacies; this is unimportant if it has served its purpose of directing attention to the proximate grounds of anxiety surrounding the Lowenheim-Skolem theorem. The exhibition of the fallacies would in any case not resolve the anxiety. As a first step to this resolution we state the theorem again

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with pedantic lucidity; we use this to pass to a discussion of the relation between formalism and its object. The theorem deals in its usually stated form only with systems framed in the notation of the first-order functional calculus: recent extensions to higherorder calculi by Henkin offer no essential further problem from our present point of view. We now explain what the first-order functional calculus is. By an atomic matrix will be meant a property of or a relation between a finite number of variables, e.g. 'x is a woman', 'x hates y', 'x takes z from y'. Here the variables 'x', 'y', 'z' are without meaning, hence the matrix as a whole is without meaning. The English words 'woman', 'hates', 'takes', etc. however retain their ordinary meanings. The variables are not to be regarded as names or abbreviations. We can abbreviate the English words denoting properties or relations by so-called predicate letters; thus 'x is a woman' might be 'Wx', 'x hates y' might be 'Hxy' and so forth. As abbreviations of English words these letters have a meaning: we repeat that the variables, as mere place-holders for meanings, have in themselves no meaning, and so the entire matrix has no meaning. From atomic matrices we form other matrices by the following two operations. (1) Quantification. The variables occurring in atomic matrices, along with certain other variables to be explained presently, are called free (i.e. meaningless) variables. We consider a certain domain of objects U which we call the universe of discourse; it may be any non-empty domain whatever. In order to specify the interpretation of a system in which quantifiers are used we have to state not only the interpretation of the predicate letters (e.g. that 'W' means woman, 'H' means hate and so forth) but also the universe of discourse U. Now take any matrix containing a free variable (it may or may not be atomic). Take for example the matrix 'Wx' read 'x is a woman'. We take the free variable and place it in parentheses before the matrix, thus (x) Wx. The variable then becomes so-called bound or meaningful, and the meaning is that when the variable x in the matrix is interpreted as any element whatever of U, the result is true. Thus (x)Wx means that every element of U is a woman. Suppose now that the matrix contains other free variables besides x and that we prefix the quantifier (x). For example, consider the matrix (x) Hxy. This 'means' that every element of U hates y; but y is still

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meaningless and free, whereas the x has become meaningful and bound. Hxy needs either interpretation or quantification of both its variables to make it meaningful; (x)Hxy only needs interpretation or quantification of the y. If we further quantify the y we get (y) (x) Hxy which means in view of the interpretation of the quantifiers and of H that every element of U hates every element of U (including incidentally itself; distinct variables do not have to refer to distinct elements of U ) . If free variables occur in a matrix it is meaningless pending interpretation or quantification of those variables. As soon as and not before all the variables have been bound it becomes a meaningful assertion, true or false provided that the interpretation of the quantifiers (i.e. the universe of discourse) and that of the letters 'H', 'W', etc., have been specified, as we assume they have. I must apologize for boring you with this somewhat pedantic explanation of the first-order functional calculus. I claim, however, that it is necessary for my purpose to do this, and that even those who are familiar with the technique of proof in that calculus may perhaps profit from the semantical remarks made in the course of this exposition. The aim of the exposition is to clarify the notion of 'model', which plays such an important role in the Lowenheim-Skolem theorem. Confused ideas about 'non-standard' models are rife today, and the lay reader is not entirely to blame. If this paper explains what models and non-standard models are, it will perhaps forestall confusion in philosophical circles. (2) The other means by which complex matrices are built up from simpler and ultimately from atomic matrices is truth-functional composition. Given two matrices like 'x hates z' and ' ( y ) (y is a woman)' we can form their conjunction, disjunction, implication, and so on: and given a single matrix we can form its negation. The variables which are free and meaningless in an element of a truth-functional compound are still free and meaningless, awaiting quantification, in the compound itself; similarly for the bound variables. Thus in 'x hates z or (y) (y is a woman)' x and z are free while y is bound; the matrix is meaningless until the x and z become bound also. A matrix in which all variables are bound is the only meaningful kind of matrix. We shall speak of it as a (formal) sentence. Thus (supposing U specified e.g. as the class of people) the

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matrix 'not (x) (x hates x ) ' is equivalent to the English sentence 'not every person hates himself,' and this is true. Formal properties of relations and properties (in this case the non-reflexivity of h a t e ) are expressed by matrices without free variables, otherwise called ( f o r m a l ) sentences or closed matrices. B y a system framed within the first order functional calculus is m e a n t a set of sentences (not necessarily finite or even axiomatizable, though it will aid understanding to concentrate for the nonce on the case of axiomatizability). W e give an example of a system: 1. (x) ( y ) (if x hates y, then y does not h a t e x ) . 2. (x) ( y ) (z) (if x hates y and y hates z, then x hates z ) . These two statements together (we could have conjoined t h e m into a single s t a t e m e n t ) assert (falsely if U means all people) t h a t U is partially ordered by hatred. Now let us m a k e the notational change of writing Hxy for 'x hates y'. W e get 1'. (x) ( y ) (if Hxy, then not H y x ) . 2'. (x) (y) (z) (if H x y and Hyz, then H x z ) . Let us now consider the system consisting of these two sentences in abstraction from our interpretation of U as all people and H as hatred. We now have an uninterpreted formal system; it ' m e a n s ' t h a t the (unspecified) relation H is a partial ordering of U. Pending specification of H and U, it has no real meaning; it is true of some choices of H and U, false of others. T h a t is, some relations are partial orderings of some classes, some not. Hence we define an uninterpreted formal system f r a m e d within t h e first order functional calculus as a set of sentences exactly like those of an interpreted formal system except t h a t U is unspecified and so are the predicate letters (as H in the present instance). T o any such uninterpreted system we m a y assign a vastly infinite number of interpretations. An interpretation consists of a specification of U (i.e. a [partial] interpretation of the quantifiers) together with an interpretation of each predicate letter appearing. T h u s a possible interpretation of the uninterpreted formal system (1', 2') is: U (i.e. the range of the variables) is people, H is hatred. This interpretation m a k e s false each of V, 2' and a fortiori their conjunction. On the other hand if we specify U as integers and H as 'less t h a n ' we get a true interp r e t a t i o n ; we get the truism that the relation 'less t h a n ' partially orders the integers.

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A true interpretation of a system is called a model of t h a t system. T h u s the relation 'less than' and the universe of discourse consisting of the integers forms a model of the uninterpreted system (1', 2') a n d in a derivative sense a model (this time a reinterpretation) of the interpreted system (1, 2). A system is called syntactically inconsistent if a contradiction is formally derivable f r o m it; semantically inconsistent if it has no model. It is a f u n d a m e n t a l theorem of (classical) metamathematics t h a t these two notions and hence the corresponding notions of consistency are equivalent. I take this opportunity of criticizing a remark of the previous speaker that for the conceptualist t h e Lowenheim-Skolem theorem was a trivial consequence of his conceptualism. T h e r e are four propositions to be considered: A. Every syntactically consistent system possesses a model. B. Every system which possesses a model possesses a denumerable model. C. Every model is denumerable. D. Every syntactically consistent system possesses a denumerable model. T h e previous speaker maintained correctly that for the conceptualist the Lowenheim-Skolem theorem B was a trivial consequence of the conceptualistic dogma C. D is also a form of the theorem, which from the classical standpoint (which is expressed in A) is equivalent to B. But unless the conceptualist accepts A, he cannot get D out of B. But the only grounds that he can have for accepting A are the grounds on which we usually believe the Lowenheim-Skolem theorem itself. Hence only an uninteresting form of the Lowenheim-Skolem theorem is a trivial consequence of conceptualism; no reason has been offered by t h e speaker w h y the conceptualist should accept the interesting form D. B u t this is a digression. T h e Lowenheim-Skolem theorem may now be stated precisely as follows. Let 'system' here and henceforth mean interpreted or uninterpreted formal system framed within the first order functional calculus. If a system has a model it has a denumerable model, hence (for a platonist) if a system is syntactically consistent it has a denumerable model. Uneasiness concerning this result m a y now be expressed more precisely than before: it seems t h a t we cannot ensure by means of a n y formal system that a n y of t h e sets, or the fields of any of the relations, referred to in the

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(interpreted) system are non-denumerable. For there will always exist relations satisfying all the theorems of such systems, whose fields are included in a denumerable universe of discourse U . Hence there is an elementary mathematical notion which escapes formalization within the first order functional calculus. (Notice that the sense of 'escapes formalization' is here much more farreaching than that in which, according to Godel's theorem, the arithmetic of natural numbers escapes formalization. For here we place no restriction on the system from the point of view of axiomatizability or recursive enumerability.) In order to understand the reasons why this is felt to be paradoxical, it will be illuminating to reflect on just what properties of relations are formalizable within the first order functional calculus. First we define this phrase more precisely. A property of relations is said to be formalizable within the first order functional calculus if there exists a consistent system framed in that calculus and a predicate letter, say R', appearing in t h a t system, such that in every model of that system the relation assigned as interpretation to ' R ' has the given property. T h u s the property of being a partial ordering of its field is formalizable in the first-order functional calculus while the property of having a non-denumerable field is not. T h e problem of characterizing in a simple fashion the set of all properties of relations which are in this sense formalizable within the first order functional calculus is one which the literature barely touches upon in its generality. For our present purposes we concentrate upon those properties of relations which involve only the cardinality of their fields. As an example of a system restricting this cardinality consider the system having as its sole member the following sentence: N o t (y) (x) not (Hxy and Gx and not Gy) T h i s says that H relates a G to a non-G; hence its field must contain a t least two members. Similarly we can put any desired finite lower bound on the cardinality of the field of a relation. Also by means with which you must be familar, we can compel H to have a field (at least denumerably) infinite. Finally, we can trivially by means of the axiom: (x) ( y ) not Hxy assure that H has an empty field. T h e following conditions upon the cardinality of the field of a

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relation are thus expressible within the first order functional calculus: A. T h e condition of being void. B. For each finite integer n, the condition of having at least n members. C. The condition of being infinite. I t can be shown that no conditions other than these can be imposed by systems formalized within the first order functional calculus upon the cardinality of the field of a relation. In particular we cannot impose in this manner the restriction of having an indenumerably infinite field, nor the condition of having a field of at most n elements for any positive integer n. T h e same holds for restrictions on the cardinality of the universe U, except that for trivial technical reasons we cannot compel it to be void. For every consistent system S there exists a number n less than or equal to A 0 (the number sometimes designated by the first letter of the Hebrew alphabet with an inferior 'o') such that S has models in all sizes greater than or equal to n. T h u s we may place any desired finite or denumerably infinite lower bound on the size of U by means of an axiomatization in the first order functional calculus, but we cannot impose any upper bound nor a non-denumerable lower one. I t will bear on our problem if we now consider how we would " n a t u r a l l y " impose an upper bound on the size of U. Clearly the sentence: 4. N o t (x) (y) not (z) (z is x or z is y) where 'is' is taken in the sense of identity imposes the upper bound 2 on the size of U. Yet is not this couched within the first order functional calculus? For surely we could just as easily write it: 4'. N o t (x) (y) and (z) (Izx or Izy) But in this form, where we do not insist on any particular interpretation of I, we no longer impose any upper bound whatever on the size of U. I t is only when we interpret I as identity that the intended effect is achieved. For instance 4' has an infinite model, if we take U for example as the set of integers and I as congruence modulo 2. We therefore see that if certain interpretations are specified in advance, we can say more about an unspecified relation H than we can if no interpretation is specified in advance. For instance if

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4' appears in some formal system along with other sentences containing 'H', and if I is interpreted as identity, then neither U nor a fortiori the field of H can contain more than two elements; but in the light of our previous discussion this restriction could not have been put upon H if the interpretation of I had been left free. We are thus led to the conception of a standard model, which we define as follows. Let there be given a system S formalized within the first-order functional calculus, and let there be given preassigned interpretations to certain of the predicate letters appearing therein, and possibly also to U. Then by an (arbitrary) model will be meant any interpretation of U and of the predicate letters appearing in S which makes all the sentences in S come out true, regardless of whether or not the interpretations coincide with the preassigned ones. Those models which accord with the preassigned interpretation are called standard (relative to that preassigned interpretation); the others non-standard. Thus we can say that, relative to the interpretation of I as identity, no standard model of a system containing 4' has more than two elements in its U, but that non-standard models of arbitrarily great cardinality exist. We can now deal formally with the so-called 'Skolem paradox'. Let the interpretation 'x is a member of y' be given to the Greek letter epsilon. Then by the Lówenheim-Skolem theorem, denumerable models for set-theory exist; that is, there exist relations having all the formal properties assigned to class-membership by the axioms of (any consistent) set-theory, and also having denumerable fields. But none of these relations is class-membership; for class-membership certainly has a vastly non-denumerable field. Hence all the Skolem-Lowenheim models of set-theory are non-standard, relative to the given interpretation. Indeed there is evidently only one standard model of set-theory, because the predicate-letter epsilon, the only one which appears, is already preassigned on interpretation. The insight we get into the relation between formalism and its object is therefore as follows: Formalism can determine its object with varying degrees of specificity. The more determination we bring to the interpretation of the formalism, the more formalism will determine its object. Thus any finite relation can be determined to within an isomorphism by a system in which a

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symbol I for identity occurs, provided this symbol is antecedently given a standard interpretation: but if the interpretation of I is left free, the other relations of the system are determined only to within a 'homomorphism'. This remark sounds trivial, however, if we take the limiting case that all the symbols have been preassigned on interpretation, as is in particular the case with the set-theoretic situation which prompted the original anxiety. For then it seems to say only that if we fix the interpretation of epsilon, the set-theory has but one model, namely the one which interprets epsilon in the way we fixed it, and U as the field of epsilon thus interpreted; and that this model is indenumerable. But then it seems after all that the indenumerability arose in the (informal, external) interpretation and not in the formalism itself; so that after all there is a good sense in which formalism is inadequate to express indenumerability. This difficulty can I think be resolved by distinguishing a private and a public aspect of formalism. Formalism in its private aspect is a computational device for avoiding 'raw thought'—we operate with symbols which keep their shape rather than with ideas which fly away from us. All real mathematics is made with ideas, but the formalism is always ready in case we grow afraid of the shifting vastness of our creations. Ultimately formalism in its private aspect is an expression of fear. But fear can lend us wings and armor, and formalism can penetrate where intuition falters, leading her to places where she can again come into her own. The Skolem 'paradox' thus proclaims our need never to forget completely our intuitions. We could shift to a formalism indistinguishable from set-theory and it could be something other than set-theory. It only remains set-theory as long as the intuition of membership has not slipped away from us. It could be formally the same and have a grotesquely different meaning. The astonishing thing is perhaps less the Skolem "paradox" that formalism apart from prior interpretation does not completely determine its object, than the fact that an uninterpreted formalism can determine its object at all. At least, even if our intuition of membership perishes entirely, we can rely on set-theory not to turn overnight into the theory of some finite group, even though we cannot guarantee that it will not turn into a theory about some complicated arithmetical relation.

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If it did it would look the same in print, though the motivation would puzzle the reader. This brings us to the public aspect of formalism. In those cases (e.g. the setting of a lower bound on the cardinality of the universe) where formalism adequately delimits its object, we may consider that communication has been established. (But really even this is a matter of degree; for we presuppose a standard interpretation of truth-functional connectives even in arbitrary models, and perhaps a good deal more.) But (ignoring this point) there seem to be no formal means of assuring that our conception of membership any more than our perception of a particular sense-quality is the same as another person's. For no finite or even infinite number of formal assertions agreed on by us both could be evidence that his set-theory was not in my sense denumerable. Of course it would not be denumerable in his sense, but I would not know if he meant by 'denumerable' what I meant by 'denumerable' unless I knew that he meant the same as I meant by 'membership'. The second philosophical lesson of the Lowenheim-Skolem theorem is that the formal communication of mathematics presupposes an informal community of understanding. A formalism constrains and limits its objects in certain ways. If we preassign an interpretation to some of these objects, we thereby restrict the interpretation of the rest. A formalism which is completely uninterpreted (i.e. even in regard to truth-functional connectives, the part of the meaning of quantifiers which is independent of the specification of U, and the juxtaposition of symbols) imposes no restriction on its object. If we fix these three interpretations, there is still room for some latitude. In particular, a formalism interpreted only in these respects cannot force the interpretation of any of its predicate-letters as a relation with a non-denumerable field. Such is the burden of the Lowenheim-Skolem theorem. The constraint exerted by a formalism on its objects is therefore a resultant of the formalism itself and the preassigned interpretation of its symbols. T h e theorem places before us in a striking fashion the role of the second factor.

Symposium:

ARE RELIGIOUS DOGMAS COGNITIVE AND MEANINGFUL? RAPHAEL DEMOS AND C . J. DUCASSE

I. RAPHAEL DEMOS

Although in this paper I am solely concerned with the cognitive elements of religion, I do not of course assume that cognition is all that is important in religion. In this paper, by religion I will mean chiefly the Christian religion; this is the one I know best by far and it is the one in whose truth I believe. I will first discuss religious belief and then I will explore religious meaning. My study of religious cognition will also involve extended digressions into general epistemology. We may tentatively distinguish the following systems of belief: common sense, science, animism, religion and philosophy. In this scheme common sense stands to science as animism to religion, the first member of the pair representing a relatively undeveloped version of the second. Later on, I will make a similar distinction of philosophical levels. It is generally taken for granted that the appeal to faith is a uniquely distinguishing feature of religious belief. Certainly religious thinkers do not hesitate to declare that faith is a valid source of belief in religion; thus, the author of the Epistle to the Hebrews speaks of faith as the 'evidence' of things unseen. In this passage faith means belief not resting on the evidence of the senses; but the word has for me a wider meaning; namely, as belief which rests on no evidence whatever, whether empirical or a priori. Of the other systems of belief it is popularly assumed that scientific beliefs rest on empirical evidence exclusively; and that so do those of common sense, although with a lesser degree of firmness. It is also believed that philosophers at any rate intend 71

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to ground their doctrines rationally, by appealing to experience or to self-evidence, and more vaguely, to intelligent speculation. Religion seems to stand, then, apart from these other systems, by unashamedly resting its beliefs on faith—standing not only apart from, but behind these systems so to speak; and thus remaining in the rear of the progress of the human mind. Now I will try to show that religion is not alone, but that all the systems of belief I have cited are in the same boat, all floating on the infirm waters of faith. Putting the matter more cautiously, I will say that all the above-mentioned systems of belief rest on ultimate commitments. For instance, why do I, as a man of common sense, believe in the existence of independent physical objects? Because I believe it. Why do I believe that other people exist? Because I believe it. Perhaps for both cases I should add that I believe as I do because other people believe likewise; because these beliefs are part of common sense. (The circle in this 'argument' should be noted). And this is what I call faith. One reason why in the case of both science and philosophy the element of faith is unnoticed is because the commitments are unconscious. These are, to a considerable extent, commitments as to what is a valid way of knowing. T h e air of important demonstration in science and philosophy is dissipated as soon as we notice that both make basic assumptions as to what constitutes evidence; for instance as to the meaning and validity of 'experience,' as to the validity of memory, as to the criteria of valid theory—and so forth. Let me dwell on memory for a moment. Memory, it is agreed, is of the past which, because it is past cannot be given to the mind; thus memory is contrasted with experience—and in a wider sense of 'experience,' with rational intuition in Descartes' sense of the word, when he opposed it to deduction. T h a t science must rely on memory is obvious; we are obliged to remember the evidence of the senses obtained in the past, on which we base our present theories. It is true that most scientific observations are preserved in records; but in order that such records be authentic and not fairy tales, they must at some point be connected with memory. Possibly even so-called report-sentences or protocols depend on a memory of the sensory given; for the latter has a very brief duration and it takes time to write, utter, or even think the protocol sentences.

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I submit that reliance on memory is a sheer trust or faith. For, let us agree that there are many good reasons—proofs, if you like —for believing that memory is veridical. I will not go into these reasons, since it does not matter here what they are. But these reasons are not now present in my mind; I only remember them, and in so doing, I am using memory to support memory. Of course, I may once more and now go through these reasons. So now I know that memory is trustworthy. But so long as I have these reasons present to my mind I cannot engage in remembering. The business of justifying memory is self-defeating. While actually involved in memory, I cannot be also intuiting the reasons which justify it; and, as we have just noted, so long as I am contemplating the reasons, I am unable to engage in remembering. I t is as though an instrument invariably disintegrated in the very process of performing its function. So far as I know, Descartes was the first philosopher to point up the relevance of memory not only for science but for mathematics. He showed that trust in memory was involved in the carrying out of any extended mathematical proof. Descartes realized that the reliance of mathematicians on memory is a matter of sheer trust or faith; he therefore tried to correct the situation by proving the existence of God who, being perfect, will not deceive man in the various faculties with which he endows men—faculties inclusive of memory and our disposition to believe in the existence of physical objects. Nevertheless Descartes, too, is obliged to remember the proofs of God and so must trust the memory which justifies the trust. As distinct from mathematics, science relies on sense-experience. But for science too memory is more important than sense-experience. Immediacy functions in science in a Pickwickian sense; it is remembered immediacy. Both immediacy and inference function as materials for memory. As scientists and as plain men we live in the past. What of the assumed relevance of sense-data for the purpose of confirming predictions in science? Here we are forced to distinguish between sense-data and images, for images have no confirmatory value. But how distinguish the one from the other? Not surely by the criterion of voluntary control, for there are compulsive images, not subject to the conscious will. Berkeley suggested that sense-data are regular, obeying laws. But surely images obey laws too? Surely a scientist would not deny that there are causes

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even for images, physiological or psychological or both, even when he cannot point to these causes. Berkeley only evaded the issue when he asserted that sense-data, as distinct from images, obey 'natural' laws; natural laws are simply those laws which sensedata obey and images do not. Thus science is able to verify generalizations by rigorously selecting as data just those elements in experience which do, in principle, verify generalizations in science. I t is said that religious belief in the existence of God rests on faith. But natural science too entails an undemonstrated belief in something like the uniformity of nature—a belief, that is to say, that nature has the kind of structure which justifies our taking its behavior in the past as a clue to its behavior in the future. Thus, not only in their source, but in their content too, the two systems of belief seem to me to be analogous, in that both seem to be beliefs in the existence of something like an order of nature. To be more specific, the belief in God is equivalent to the view that things make 'moral' sense in the universe; that, although there is evil in nature, this evil will somehow be overcome by good. The natural scientist has his evil too, which is chance; yet he too believes that somehow there is an explanation for everything that happens. But to return to the question of justification—I would say that the religious belief is no more of a faith than is the belief that nature is uniform. They are both acts of faith, not only in that they go beyond the evidence but in that, at least up to a point, they go against the evidence. Job said: "Though he slay me, yet will I trust in him." And the scientists' position may be caricatured by putting these words in his mouth: "I will find an explanation even if it kills m e ; " more accurately; " I will go on believing that there is an explanation, even though I cannot find one." It may be urged that modern science, in recognizing the so-called Heisenberg principle of uncertainty has correspondingly limited the range of the principle of explanation. To this I might answer that there is an analogous phenomenon in modern doctrines of religion in so far as they recognize a limited God. But I prefer to dispute the truth of the above interpretation of the impact of the principle of uncertainty on the principle of explanation. Heisenberg himself views his principle merely as an extension of the doctrine of secondary qualities. He writes:

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"According to D e m o c r i t u s , a t o m s h a v e lost the qualities like colors, taste, etc., t h e y only occupied space, b u t geometrical assertions a b o u t a t o m s were admissible a n d required no f u r t h e r a n a l ysis. In m o d e r n physics, a t o m s lose this last p r o p e r t y , t h e y possess geometrical qualities in no higher degree t h a n color, taste, etc. . . . O n l y the experiment of a n observer forces the a t o m to indicate a position, (italics m i n e ) a color a n d a q u a n t i t y of h e a t . " (Philosophic Problems of Nuclear Physics, p. 3 8 ; see also pp. 1 0 5 - 6 ) . I h a v e referred earlier to the religious belief t h a t e v e n t s in n a t u r e m a k e " m o r a l ' ' sense. T h e r e is here a notion of m e a n i n g f u l ness which requires elucidation. F o r the scientist, too, a s w a s noted, the universe is m e a n i n g f u l , t h o u g h in a different sense of the t e r m . M e a n i n g f u l n e s s as a religious notion m a y be a p p r o a c h e d b y its application to c o n d u c t . Echoing K a n t , we speak t o d a y of action being rational (or reasonable) in t h e sense t h a t it is n o t self-inconsistent, or not self-defeating. W h a t I h a v e in m i n d , however, is something different, a l t h o u g h it too h a s connections with K a n t , n a m e l y with w h a t he was reaching out for w h e n a r g u i n g for his postulates. T h e notion of m e a n i n g f u l n e s s in religious language is essentially a common sense one a n d u n t e c h nical. W e say t h a t life is m e a n i n g f u l when it achieves values in some s t a b l e fashion. M e r e action and change are meaningless, we s a y ; t h e y m u s t aim a t something; a n d a t something worthwhile. B u t striving w i t h o u t a c h a n c e of a c c o m p l i s h m e n t is also deemed meaningless. And ends, once accomplished, m u s t be c a p a b l e of preservation, for the a c t i v i t y to be m e a n i n g f u l . T h i s is m e a n i n g f u l n e s s in living. N o w , we say, derivatively, t h a t t h e real world is m e a n i n g f u l in so far as it m a k e s such acc o m p l i s h m e n t possible, probable, n a y p e r h a p s certain. Religion is the belief t h a t the world is m e a n i n g f u l in this fashion. F o r such a belief the senses provide no evidence—certainly not a n y conclusive evidence; a n d the scientifically-minded see no reason for a d o p t i n g this belief. C e r t a i n l y such a belief is f o u n d e d on f a i t h , b u t no more so t h a n the scientist's own belief t h a t n a t u r e is m e a n ingful in his sense, n a m e l y t h a t n a t u r e is such t h a t it enables us to m a k e successful predictions and generalizations. T h e reader will recall Spinoza's doctrine t h a t God's a t t r i b u t e s are infinite. B y this Spinoza m e a n t t h a t each a t t r i b u t e is self-

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contained and complete, never intersecting with another attribute. I wish to say that in some sense both the scientific and the religious accounts are, like Spinoza's attributes, infinite, that is to say, autonomous. Or, to use Prof. Tillich's phrase for theology (Systematic Theology, I, p. 8), each system is a circle, in other words a closed system. Let us, for instance, compare the scientific account of thunder with the magical account. The scientist will of course reject the latter; but he cannot refute it. The animist will introduce, let us say, evidence from a dream; but dream images are irrelevant for the scientist. Each system has its own definition of fact. Each system carries a lantern by which to illuminate the darkness. While what is thereby seen is seen indeed, the lantern itself is not illuminated, or rather the lantern shines both on itself and other things. T h e lanterns are different, and each is checked by its own light. It may be thought that science is able to crash into the animistic circle by an appeal to pragmatic considerations. Science 'works.' Our own kind of medical men can cure diseases which the witchdoctors cannot; also we can produce crops as the magician cannot. But the fact is that pragmatism is an appeal to values, and that the values, too, are part of the system. T h e religious believer, for instance, may say that his values are not material primarily, that what he is concerned with is the salvation of his soul and with blessedness. There are also differences involving factual matters. Where the scientist may claim that his system provides greater satisfaction for life on this earth, the religious believer might retort that he is concerned with what happens to him in the life after death. And for the scientist to say that there is no life after death is to beg the (factual) question. The formalization of religious belief is theology; the formalization of natural science is naturalism. We may legitimately call both naturalism and theology exhibitions of philosophical thinking, provided we understand that neither goes beyond formalization, that neither attempts to justify its correlative system of belief. They both rest on faith. Thus, in the passage cited earlier Prof. Tillich admits, nay asserts, that he founds his theology on the authority of the Bible. So the naturalistic philosopher accepts all the premises of natural science, and simply formalizes them. His professed rules of evidence are the scientist's rules of evidence.

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Verification, he says, must be (sense-) empirical; also a concept has a meaning only to the extent that, in principle, it may be verified or falsified by sense-experience. Naturalism may be defined as the theology of natural science. Does the philosopher concerned offer any arguments in support of these views about validation and meaning? Not so far as I know. He simply borrows the practice of the natural scientist and erects it into a formal principle. His meta-scientific statements then are precisely personal declarations of faith, professions of belief, not assertions but expressions of the form 'I believe that p.' In both the theologian and the philosopher of the naturalistic school (along with his brother the positivist) we find operating a modified version of St. Augustine's principle ''believe in order to understand" (your experience, or the world). In calling religion and science systems of belief, in describing naturalism and theology as professions of belief, I do not, of course, imply that they are false. Neither do I imply that they are not knowledge; I am only asserting that they are not known to be knowledge. Nor do I regard faith as the last word for either of these systems. Naturalism and theology are unself-criticized philosophies. I will call this level Philosophy A. ' T r u e ' philosophy (Philosophy B ) begins with the Socratic query: why do I believe as I do?; with the Socratic knowledge, which is knowledge of one's ignorance—the awareness that one's beliefs rest on faith. Then there is Philosophy C, which (in the way of Plato's dialectic) criticizes, modifies or justifies fundamental beliefs; or even adds wider speculations of its own. For myself, I take the basic beliefs of both science and religion to be 'insights'—instances of knowledge, in the sense in which Plato opposed knowledge to opinion. T h e question is how I , or anyone else, would be justified in regarding these systems of belief as valid, while at the same time rejecting others. T h e r e must be an implicit reference to some fundamental criteria, but if so, would not these criteria constitute but another set of premises, that is to say, of beliefs, and therefore of 'commitments.'? Any attempt to justify premises would appear to be a self-defeating task. Perhaps then the very question is a pseudo-question. T h u s we might take a position like that indicated by Spinoza's words: "when I am asleep and dreaming I think I am awake; when I am awake, I know that I am awake

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and that I was dreaming." I have no solution for this most vital problem. But I would strongly insist that any view which regards premise-adopting as arbitrary commitment, as irrational, as relative to person, place, and time is excluded. For such a view itself claims to be non-arbitrary, non-relative and rational. Is argument in religion of a different sort than in any other field, say science? That there are vital differences between religious and scientific cognition surely is obvious from the fact that considerations which are held as conclusive in religious discussion for the most part make not the slightest impression on the scien tist. In so far as their differing basic premises include validating forms of inference, then the respective modes of argument are different. I refer the reader back to what was said about the different senses of meaningfulness in science and in religion. There is a corresponding difference as to conceptions and categories of description and explanation. A scientist thinks in terms of spatio-temporal conceptions, and of physical events which are determined. An animist or a religious believer thinks of the world in terms of agencies, of persons, of minds; he posits non-temporal, eternal entities; he thinks of agencies which are free and creative; of entities which act purposively, which strive. A physical object is something which can only act here and now, but a mind can reach out of the present into the past through memory; and indeed, can think of, intend, or 'mean' anything anywhere. Thus in religion we encounter the notion of spirit, of something immaterial in that intrinsically it is not limited by spatio-temporal conditions and does not act according to the principle of physical causation. From the fact that the world (or part of it) is categorized by religion (at least the Christian religion) in personal terms, certain consequences follow. In science one event or substance is like another except in so far as its description is different; particulars qua particulars don't count. Conversely, in the Christian doctrine, certain historical events and times are vested with special significance. Whereas, in the scientific view, similar substances or events function simply as illustrations of laws, in the Christian view, of such two numerically different but descriptively similar entities one may have a special significance which the other may lack. In the scientific view, the particular is nothing more than a carrier of a description or an essence; thus all science is Platoniz-

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ing. B u t in the religious view, t h e individual f u n c t i o n s in its uniqueness. T i m e flows e q u a b l y b u t persons observe b i r t h d a y s , a n d for C h r i s t i a n s , D e c e m b e r 25 is C h r i s t m a s . N o w , when p a r ticular e v e n t s are vested with special significance, such e v e n t s a r e a p p r o p r i a t e l y termed miracles. T h e y a r e miraculous because their special significance is inexplicable in terms of their n a t u r a l p r o p erties; in the physical order, they do not differ f r o m other events. I come now to the p r o b l e m of religious meaning. T a k e such a p p a r e n t l y descriptive p h r a s e s as the following: God is a Spirit; God is a P e r s o n ; God is E t e r n a l L i f e ; G o d is L o v e ; the L o r d God A l m i g h t y ; the L o r d M o s t H i g h ; O u r F a t h e r in H e a v e n . W h a t is the w a y to view such representations of G o d ? ( a ) I t is possible to t h i n k of t h e m as literal descriptions of G o d ; this is the position of f u n d a m e n t a l i s t Christianity. I t is n o t s a t i s f a c t o r y because it leads to i d o l a t r y : i d e n t i f y i n g God with w h a t is a t best an image of God. ( b ) A t a n other extreme is the view t h a t these are not descriptions a t all, b u t p u r e l y m y t h i c a l or symbolic. B y 'symbol' I m e a n a word whose m e a n i n g is exclusively emotive. A symbol does n o t refer to a n y t h i n g in the o b j e c t ; its f u n c t i o n is to arouse a p p r o p r i a t e a t t i t u d e s , feelings a n d responses. (c) T h i s view in t u r n leads to a still more extreme d o c t r i n e — t h a t we can know n o t h i n g of God's a t t r i b u t e s . T h i s is the alternative of nescience. I a m rejecting b o t h b a n d c. Against the l a t t e r , I m a i n t a i n t h a t we can k n o w G o d ; against the former, t h a t in using a t t r i b u t e - w o r d s for God we are referring to p r o p e r t i e s in the object. Nevertheless I d e n y the first a l t e r n a t i v e ; I do n o t t h i n k t h a t the descriptions of God are literal. ( d ) B u t if a t t r i b u t e - w o r d s in religion are neither literal nor emotive, m i g h t they be m e t a p h o r s ? I use this word in the sense of allegory; although a m e t a p h o r has emotive overtones like a symbol, I distinguish it f r o m the latter because a m e t a p h o r is descriptive. A m e t a p h o r m a y be defined as condensed literal m e a n ing, a n d w h e n the m e a n i n g is spread out, the m e t a p h o r e v a p o r a t e s . A d o p t i n g then the view t h a t a m e t a p h o r is potentially descriptive (literally) as distinguished from w h a t might be called ordin a r y prose (which is an a c t u a l literal description) I would d e n y t h a t religious a t t r i b u t e - w o r d s like ' p e r s o n ' 'love' 'spirit' are m e t a -

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phors; I take this position because I do not think that the descriptions into which a metaphor could be translated apply to God literally. Religious attribute-words, while descriptive, are not literal; they are, in fact, analogical. To sum up the above diversities of meaning and arranging them in an ascending order: 1. Words with zero meaning, as in nescience. 2. Symbols—terms with emotive meaning only. 3. Metaphors—literal, quasi-descriptive. 4. Analogical terms—descriptive but not literal. 5. 'Prose' terms—both descriptive and literal. Before defining what I mean by analogical terms, I will explain why I believe that the descriptive terms in religious discourse are not literal. This is not at all because of any assumption on my part that God has no essence, or that, if he has an essence such an essence is intrinsically un-intelligible. God can certainly comprehend his own nature. It is only that man, because of the finite nature of his mind, cannot comprehend God's nature in terms of his (God's) intrinsic properties. Hence man must have recourse to terms of comparison; he can understand God's nature by comparing it with properties which he knows literally. Take the familiar statement that man is (created as) an image of God. Therefore, God can be thought of in the image of man. Moreover, this relation of analogy between God and man is known literally. While, if I say that God is a person in an analogical sense, I am not ascribing the attribute of personality to God in a literal sense, yet I am ascribing literally a certain analogical relation between personality in man and personality in God. It is sometimes said that although we cannot literally know what God is we can literally know that God is. The similarity to Kant's doctrine of things-in-themselves is obvious here; there are things in themselves but we cannot literally know what they are. Against Kant's view, the valid question has been raised: "If you cannot know what the noumena are, how can you even know that they are? Surely the reasons preventing you from knowing their essence would operate equally to prevent you from knowing their existence." So with God. The statement that while we can know that God exists, we cannot know what he is, is facile. In fact, just as we can ascribe personality to God analogically only, so do we ascribe existence to God in an analogical—and in no other—sense.

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In this connection I would like to quote from Prof. Stace's recent and important work Time and Eternity. "Religion is the desire to break away from being and existence altogether. . . ." (p. 5). "The nothingness of God finds expression in other phrases having the same sense. God is Non-Being, Nothing, Emptiness, the Void, the Abyss. Silence and darkness, used as privative terms importing the absence of sound, the absence of light, are also used as metaphors of his Non-Being." (p. 8). Nevertheless Mr. Stace denies that the statement that God is Nothing is equivalent to the statement that there is no God. For the proposition "God does not exist" is false too. (pp. 7, 61). Thus in some sense of existence it is false that God exists, but in another sense it is true that God exists; the former is the literal, the latter the analogical sense. (1 am not in any way suggesting that Mr. Stace would accept the interpretation I put on his statements. Nevertheless, as the reader will gather from my later remarks, my debt to his book in this essay is considerable.) Now for the reasons why an appeal to analogy is necessary. In attempting to describe God, theologians seem compelled to make contradictory statements. Thus God is said to be transcendent, yet also immanent; eternal yet also temporal; personal, yet also impersonal. The Kingdom of Heaven is within us; yet also forever beyond us. Such assertion of contradictory statements superficially suggests that God is intrinsically unintelligible and that theological truth is irrationalistic. Of course, Hegel has made a logic out of anti-logic through his formulation of the dialectic. But Christian theology need not be Hegelian. The descriptions of God cited above are not in fact inconsistent because, to take one example, the sense in which time is denied of God and that in which time is ascribed to God are not the same senses; yet they are not different either; the senses are analogical. As we know, the mystics have proclaimed that God is ineffable. St. Chrysostom wrote five sermons on the incomprehensibility of God, in which he rises to flights of sublime eloquence. St. Chrysostom quotes St. Paul to show that God is unapproachable as well as inconceivable. Yet St. Paul also writes: "The invisible things of him (of God) from the creation of the world are clearly seen, being understood by the things that are made, even his eternal power and Godhead." (Romans 1,2). What is the answer to the paradox? The nature of God cannot be known intrinsically; it

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can be known by comparison with other things. Now, anyone would be rash to contradict the mystics; but in fact, the mystics are inconsistent, like St. Paul. Of course when the mystics assert that God is incomprehensible they do not mean that God is uncognizable. What they mean is that God is cognizable by a mode of cognition which is unique—different from sense-perception and from conception. The real question is whether what is cognized in the mystical mode can be translated into the language of some other mode. And here mystics divide themselves into two groups: those who maintain that the language of the mystic is not translatable into any other, and those who assert that it is. Of the second group are those mystics who regard nature as the manifestation of God ("the heavens declare the glory of God") and who regard natural events as 'symbolic' of divine meanings. When I say that both Smith and Jones are men, the sense in which I use the term man in the two cases is exactly the same. Thus, as the schoolmen would say, the sense of man in this example is univocal. When I use the word post for the mail and also to designate a pillar I am using the word in two different senses. This is what the schoolmen called the equivocal use of a term. Now I submit that identity of sense and difference of sense do not exhaust the meaning of sense; there is a third alternative, namely that the sense of a term is analogical—neither the same nor different. Some scholastic philosophers have tried to define analogy as part-identity and part-difference. I regard this view as wrong; analogy is an irreducible relation, other than both identity and difference. When religious analogy is misconstrued as difference, we are liable to get the extreme forms of mysticism, merging with the doctrine of nescience. When analogy is misconstrued as identity (that is to say, taken as literally descriptive) we find anthropomorphism. Of course, the doctrine of analogy is taken from Aristotle, although in a modified version. Compare analogy with likeness. In its ordinary sense (which I will call conceptual likeness) this relation is always reducible, and reducible to identity and difference together. Thus when I say that Smith is like Jones, you can always ask me: in what respect? and I can answer: in intelligence or in height; both Smith and Jones are smart or they are both tall. Here, likeness between two things means that A and B have a common property. Thus conceptual likeness is reducible to identity in a certain re-

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spect, and is the same as Aristotle's generic identity—for instance, that men and dogs are both animals. Now analogy is not, a t all, that kind of likeness (if likeness it be). I t is likeness perhaps in that we are comparing two things; but it is not a likeness which is reducible to the possession of a common property; it is not likeness in this or that 'respect'; it is just likeness. It is reported that Wittgenstein said something as follows: " T o propose to think in violation of the law of contradiction is like proposing to play chess without the queen; and that is all one can say about the comparison." Now this would be an instance of analogical likeness: A is to B, as C is to D . T o return to theology: God exists; God has or is a mind; God is a living God; God is love; God has designs and purposes—in all these sentences the attributions must be taken analogically. T h u s God loves, but his love is not the sort of thing we mean when we say, man loves; when we ascribe purposiveness to God, we must not be taken to mean that he proceeds by the route of means and ends, as when man acts purposively. Now, these are negative statements; and there have been mystics according to whom the only statements we can make about God are negations. Yet this is half the story; the senses of 'love' and 'design' are analogical. T h u s affirmative statements about God are available. I will now make the further proposal that the concept of analogy is applicable also outside theological thought, and within philosophical discourse. I will consider the remarks by Margaret Macdonald on " T h e Philosopher's Use of Analogy" (Logic and Language, First Series, ed. by Antony Flew, pp. 80-100), especially because they are typical of widely accepted views among members of the school of philosophical analysis. In a very acute discussion, among other things, of Aristotle's concepts of matter and form and of Descartes' famous example of the piece of wax, Miss Macdonald makes the following point. Both Aristotle and Descartes speak of stripping matter of all secondary qualities, and Aristotle of all qualities whatever. Miss Macdonald concedes that they do not mean " t h a t qualities are taken from objects as skins from an onion" (p. 87). Philosophers who use such language have in mind abstraction or intellectual analysis. But her point is precisely that when philosophers use these words, they are using them in a different sense from their ordinary usage—and therefore in a misleading sense. For instance, in its ordinary sense, 'analysis'

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is an operation by which we decompose a complex object into its parts; and for such an operation we have sensible criteria by which to identify it. But "it is logically impossible to apply any such criteria to the separation of matter from its qualities" (Ibid). Again, by Aristotle's own admission matter is that which receives all predicates, and "since nothing which is known can be described except by ascribing predicates, no description or knowledge of matter is possible . . . obviously, therefore, it is logically impossible to apply any sensible criteria whatever for the distinction of material and design. But such criteria are part of what we mean by such words; they give the words their use and philosophers who attempt to apply them by analogy without indicating similar criteria, or indeed any sensible criteria whatever are not using an analogy but simply misusing these ordinary words. . . ." (p. 94). And on the next page she states that philosophical 'theories' are not theories at all, because they are not testable as scientific theories are. May I point out an 'analogy' between Miss Macdonald's argument and Mr. Stace's? For instance, Mr. Stace insists cogently that the religious infinite is wholly different from the conceptual or mathematical infinite. "We must understand that the word 'infinite' in the religious sense, has nothing at all to do with that sense of the word in which it is applied to space, time, and the number series." {Ibid p. 47). In the same fashion Mr. Stace argues that when we ascribe love and existence to God, these terms are not used in their ordinary meanings. Nevertheless, Mr. Stace also asserts that the proposition 'God is Not-Being' is not equivalent to the proposition 'There is no God.' In some sense, he agrees, God exists, and also that God is love. Now, Miss Macdonald's contribution is certainly important as showing that the philosophers' use of such terms as matter, form, abstraction, analysis, is not the same as those of science or common sense. Traditional philosophers, I think, must be convicted of not having been sufficiently aware of these distinctions. What I would dispute however is Miss Macdonald's conclusion that philosophers are giving a new and simply different sense to these words while pretending to use them in the old one; and that so far the philosophers' language is misleading. I would urge, in opposition, that the philosopher's use of these terms has an analogical relation to that of science and common sense. I t is note-

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worthy that Miss Macdonald is herself setting the problem as I would have done: she is raising the question whether the philosopher's use of analogy is justified. She denies that it is justified because—so she implies—analogy involves similarity of criteria. Now by similarity she means what I have called conceptual likeness, possession of a common genus, or identity of sense. But I submit that there is, at any rate, another sort of analogy irreducible to identity 'in respect of x'; and this sort does exist between philosophical, scientific and common sense discourse. By their arguments, members of the school of philosophical analysis have intended to show that philosophical 'theorizing,' or philosophical argument, or philosophical 'rational discourse' is nothing of the sort. My own conclusion from their arguments is just the reverse. It is true that ethical discourse, scientific discourse, theological discourse, philosophical discourse are not rational in the same sense. There is no definition of rationality which applies in the same sense to these various operations. Shall we therefore say that 'rationality' is simply an equivocal word? Yet surely it is not equivocal as the word 'kind' is, when referring both to genus and to willingness to help: I maintain that it is the case both that rationality has not the same meaning, and that it has not a different meaning in these various descriptions. A case in point is the current controversy about ethical sentences. In the earlier phase of their discussion, analytical philosophers had tended sharply to oppose ethical sentences to scientific and other factual sentences. The meaning of the former, it was then pointed out, is emotive, while the meaning of the latter is empirical. But more recently, without at all blurring this distinction, analytical philosophers have come to agree that there is such a thing as ethical reasoning, no less than scientific reasoning, and that consequently, considerations of validity are no less pertinent in ethical sentences than in those of science. My own interpretation of the fact of both difference and similarity is that ethical discourse is analogous to scientific discourse, and that rationality is an analogous term; so is meaning also; so is meaningfulness. In conclusion, it is relevant to indicate how similar the contrast between philosophy and science (and common sense) on the one hand is to the contrast between mysticism and conceptual thought on the other. A fundamental objection by the analytical school against traditional philosophers has been that the latter has

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abused linguistic usage in that they have taken a term with limited meaning and have then applied it to everything. For instance, in every day life, the term existence has a definite limited meaning. We say that men and horses exist but centaurs and hobgoblins do not. But a traditional philosopher uses the same term so as to ask the question whether the whole physical world exists. T h e objection raised is that the word existence has now been forced into another meaning, or rather it is meaningless because it has been given an absolutely general application which allows of no contrast. For instance—the analyst will ask—what would the nonexistence of the physical world mean? Now, an objection of this sort challenges the very concept of philosophy as it has been traditionally employed; at least metaphysics has meant the attempt to make general statements about the totality of things. And now let us turn to the complaints of the mystics concerning theological-conceptual formulations. I will refer again to Mr. Stace's account of religious knowledge. Mr. Stace asserts that the mystical intuition cannot be given a conceptual expression for the reason that concepts are limited. " I t is being this or that which is the disease of things." (p. 5). "The discursive, discriminating, conceptual intellect cannot apprehend the divine." (p. 39) "For, to conceptualize is to divide and relate" (p. 45) . . . "the infinity of God means that than which there is no other." (p. 47) Indeed we know from Spinoza, the philosopher-mystic, that particular modes exist by negation, whereas God exists by inclusion. When, therefore, a Christian of the common garden variety says that God loves man, the mystic accuses him of taking an attribute which in everyday experience has an opposite (love as contrasted with hate) and applying it to God whose attributes admit of no opposites. I suggest that the respective complaints, on the one hand, of the mystic addressed to the ordinary Christian and, on the other, of the philosophical analyst addressed to the ordinary philosopher, have the same import. Both the mystic and the traditional philosopher employ terms which designate what I may call 'total' properties—properties which have no opposites. The mystic complains that the ordinary Christian takes terms which designate limited properties and then wrongly applies them to God where their application is unlimited. And the philosophical analyst complains

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that the traditional philosopher takes terms which have only a partial application and applies them in an unlimited fashion. Now, I believe that the 'ineffabilist' variety of mystic to be wrong. Despite differences I hold t h a t there are analogies between God a n d human experience. So I would urge t h a t despite differences there are analogies between philosophical discourse a n d the language of common sense, justifying the transfer of terms from one language to the other. N o man is an island, said J o h n D o n n e . T o d a y , the Christian neo-fundamentalists, with their insistence t h a t God is an absolute ' O t h e r ' are trying to place God on an inaccessible island where no influences from common experience might pollute him. So do the philosophical analysts t r y to isolate traditional philosophy from common sense and science by a kind of q u a r a n t i n e during which after proper t h e r a p y it will be purified of all infection. T h e motives are different b u t they lead to t h e same result—isolation. Now, I believe in islands, including Shakespeare's 'scepter'd isle' in which the Oxford School of Analysis is flourishing today. Yet I hope we shall construct causeways f r o m the islands to the mainland, or, at least, establish a ferry service to the continent of common experience; and this m a y be done by what I have called analogical relations and analogical terms.

Symposium:

ARE RELIGIOUS DOGMAS COGNITIVE AND MEANINGFUL? R A P H A E L D E M O S AND C . J . D U C A S S E

II. C. J.

DUCASSE

The considerations set forth in Professor Demos's paper have to do only with the purportedly cognitive aspect of religion, not with its emotional or pragmatic aspects. Furthermore, the only religion he considers is Christianity, which he tells us is the one he believes to be true. His paper apparently aims to show that the beliefs distinctive of Christianity, and more particularly those about God, are true. The beliefs about God specifically mentioned in the paper are that God exists, has or is a mind, is a living God, is love, is a person, is a spirit, and has designs and purposes. To show that these beliefs represent knowledge about God, two things would be necessary. One is that the attribute-terms predicated of God in the statements of those beliefs should have some definite meaning, and that we should be told what it is. The other is that evidence should be presented, sufficient to show that the attributes meant by those terms are in fact possessed by God. As regards the first of these two requisites, philosophical reflection leads Professor Demos to assert (as against the fundamentalists) that those statements about God are not true if the attribute-terms predicated in them are taken literally; i.e., are taken in the sense they have when predicated of human beings. He asserts also that the function of the attribute-terms in those statements is not emotive, or at least not solely or essentially emotive, but is descriptive; and hence he rejects the view that God is incomprehensible and unknowable. He maintains, however, that those attribute-terms are not descriptive in the sense in which metaphorical terms are so; for metaphorical terms are capable 89

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of being translated into literal terms, and he thinks that the literal terms into which such religious words as "person," " l o v e , " "spirit," and the rest could be translated would not apply to God literally. W h a t Professor Demos maintains is that those predicates are descriptive neither literally nor metaphorically but "analogically." W h a t then is analogical description? Professor Demos says a good many things about analogy, as follows: (a) T h a t analogy is not analyzable as part-identity and partdifference; (b) T h a t analogy is not conceptual likeness, which always reduces to possession of a common property; (c) T h a t "the doctrine of analogy is taken from Aristotle, although in a modified version," which version, however, Professor Demos does not so far as I can find state explicitly but only illustrates, by saying that there is "analogical likeness: A is to B as C is to D " between proposing to think in violation of the law of contradiction, and proposing to play chess without the queen; (d) T h a t analogy is "an irreducible relation;" (e) T h a t " i t is not likeness in this or that respect," but is " j u s t likeness." In a portion of his typescript omitted because of space limitations from his paper as printed, he also stated: ( f ) T h a t "analogy cannot be analyzed; it is known by being seen, b y being recognized immediately;" and (g) T h a t "there are no definite criteria for deciding whether there is analogy or not." I must confess that I am unable to extract from these seven statements any conception, consistent with all of them, of w h a t Professor Demos means by " a n a l o g y . " T h e ordinary meaning of the term is likeness of relationship; i.e., that the relation between A and B is similar to the relation between C and D . Hence the only terms that can be analogical in this sense are terms that designate relationships. But some at least of the attribute-terms predicated of God, which Professor Demos mentions, are prima facie not relational terms at all; and he makes no attempt to show them to be relational. Y e t , that ordinary meaning of the term " a n a l o g y " seems to be the one he adopts at the place where he illustrates analogy b y citing the likeness between proposing to

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think in violation of the law of contradiction, and proposing to play chess without the queen. But if this is an example of what he means by analogy, then analogy is not unanalyzable, and is reducible to possession of a generic character; for, in that example, there is a generic character which the two proposals share. It is the paradoxical one that both are proposals to engage in activity of a kind defined specifically as activity in modes conforming to all of certain rules, and yet are proposals not to conform to some of those rules. This is the only clear-cut example I can find in Professor Demos's paper of what he means by analogy; and, as we have just seen, this example is analyzable into predication of literal sameness in respect of a generic character. It therefore refutes the very contention it is intended to prove, namely, that, unlike metaphorical predications, analogical predications are not so analyzable. The paper thus brings forth no reason to believe that any predications are analogical in a sense other than that of metaphorical. Professor Demos's insistence nonetheless that analogy is unanalyzable, seems explicable only as expression of a deep wish that the attribute-terms which Christian theologians predicate of the God they define should somehow be descriptive, although they are not descriptive either literally or metaphorically. But since no meaning for those predicates is actually offered in the paper, belief that God has certain characters, which in fact are specified only by those vacuous predicates, would seem to be itself vacuous. This does not augur well for the possibility that the statements which apply those predicates to God are cognitive, i.e., represent knowledge. The argument of the part of the paper which appears intended to establish that they are cognitive is not too clear. I t seems to be in essence that even those things commonly accounted as the most certainly known are not really known a t all but ultimately are matters of pure faith—"faith" being defined (correctly I think) as "belief which rests on no evidence whatever, whether empirical or a priori;" for the paper describes as equally "floating on the infirm waters of faith," two systems of belief. One consists of common sense, of science, and of philosophy of science, or more specifically, naturalistic philosophy of science. T h e other system consists of animism, of religious beliefs, and of theology. As examples of beliefs belonging to the first group, Professor

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Demos mentions belief in the validity of memory, belief that independent physical objects exist and that other people exist, belief "as to what constitutes evidence," belief "as to the criteria of valid theory," belief in the uniformity of nature. As belonging to the second group, on the other hand, he cites belief in God; belief—to which he declares the belief in God equivalent—"that things make 'moral' sense in the universe," i.e., that in the universe valuable ends can be attained and preserved; and, belief that certain individual things, events, and persons function in their uniqueness and are "vested with special significance;" such events—for example, the birth of Jesus—being "then appropriately termed miracles" because their special significance "is inexplicable in terms of their natural properties;" whereas "in the scientific view, the particular is nothing more than a carrier of description or an essence." To dissect exhaustively such truth as there is in these various contentions from what seem to me fatal errors in them would be too lengthy a task for the space at my disposal. I shall therefore be able to call attention only to a few of the graver mistakes I think I see. (a) T o begin with the last item of the second group of beliefs just listed, I submit that the religious view of individual events and persons is mistakenly identified there with what in fact is only the historical view of them. The birth of George Washington on February 22, or indeed that of John Doe on a particular other day, is, as truly as that of Jesus on December 25, a historical and therefore unique event, and one vested (for some persons, many or few,) with special significance of one kind or another. But Washington is not on this account reckoned as divine or even as a saint, nor his birth as a miracle. Hence, that an individual person or event functions to some extent "in its uniqueness" and is "vested with special significance," is not sufficient to confer religious status on either. Moreover, so far as I can see, the special significance of Jesus and of Washington, however different in kind and magnitude, is, if indeed inexplicable, then inexplicable in both cases only in the sense in which are so the historical repercussions of any historical event, which, qua historical, are, like the event itself, unique and therefore in some degree novel. Those repercussions are inexplicable in the sense that the inexhaustible detail and specificity of

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any concrete event is never totally predictable, even theoretically. On the other hand, the special significance which any given past historical event has turned out to have is explicable to some extent in the sense of traceable to causes—to the extent, namely, that the "natural properties" of the event and of its historical context happen to resemble those of other events and of their contexts, that had been observed earlier. (b) I turn next to Professor Demos's statement that 'religion is the belief that the world is meaningful" in the sense that, in it, valuable ends can be attained and preserved; and that "for such a belief the senses provide no evidence." T h a t the world, up to the present, has been such as to make achievement and preservation of valuable ends possible to some extent is, I submit, evidenced by the fact that such achievement and preservation has been observed again and again by each of us. Belief that the world will continue to be such is due to the psychological momentum called habit, which automatically extrapolates to the future the regularities or approximate regularities we have observed in the past. As so generated, this belief is no more intrinsically religious than is the belief that tomorrow water will continue to run downhill as usual. Moreover, even if it were religious, it would not be essentially Christian or even theistic, since Buddhism and Jainism, which are non-theistic religions— and indeed, contemporary Humanism, not to mention atheists and agnostics, also hold that belief. (c) The subject of extrapolation to the future brings me to Professor Demos's most radical contention, namely, that the basic beliefs of science and of the naturalistic or, I assume, of any other philosophy of science are, exactly as much as those of religion, matters of pure faith; that is, rest on no evidence whatever, of any kind; so that there is not the slightest reason to regard them as true rather than as false. How then, Professor Demos asks, would one be justified in regarding the basic beliefs of both science and religion "as valid, while at the same time rejecting others." For this, he says, it would be necessary to appeal "to some fundamental criteria." But would not these likewise be matters of pure faith? Professor Demos declares that he has "no solution for this most vital problem." The solution, I would suggest, lies in noticing that, in the defi-

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nition of faith as "belief which rests on no evidence whatever," the term "evidence" enters; and hence that we are entitled to ask what is that thing, called Evidence, upon which that definition tacitly postulates that some beliefs rest, and prescribes that those to be termed " f a i t h " do not rest. Either this negation is wholly devoid of meaning, or else some definition of what the term "evidence" is to be taken to mean is implicit in the very notion of faith as defined. But definitions and defining postulates are neither true nor false and neither believed nor disbelieved, but only respected or disregarded by this or that person. Their status is thus essentially that of rules of a game—a game, in the broad sense, being an activity whose modes one makes conform to certain rules—those, namely, which together define the nature of the particular game concerned. Of course, the rules of a given game—say, chess—are binding only on persons who elect to play that particular game— chess rather than perhaps checkers. But if a person violates them either deliberately or unawares, then in so doing he is in fact playing a different game, which may resemble chess to some extent, but is not chess itself. Now, there is a game called Pursuit of Knowledge, and the rules which define its nature and differentiate this game from others are those called The Rules of Evidence—specifically, the rules of observational, experimental, inductive, deductive, circumstantial, and testimonial evidence. Nobody is obligated to obey these rules, but whoever flouts them is automatically then playing a different game; and, if he nevertheless continues to employ the words which have meaning only in terms of those rules—words, namely, such as "true", "false", "valid", "fallacious", "proof", "probability", "knowledge", etc.—then the game he is actually playing is that of cheating at the pursuit of knowledge; just as purporting to play chess but making the king move two steps at a time instead of only one is not playing chess but cheating at chess. The game of thinking loosely, inconsistently, incongruously, of arguing illogically, and of believing irresponsibly, may be more fun and is certainly easier and far more popular than that of thinking precisely, logically and scientifically, that is, of thinking in the manners that yield knowledge as distinguished from erroneous or groundless beliefs; but it is not the same game. Yet the knowledge-producing game is the one which

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those unconscious cheaters too intend and purport to be playing. For they too intend their statements to communicate their thoughts; intend their arguments to prove or disprove something; and intend their assertions to represent ¡acts, not fictions or groundless opinions. That is, the rules by which they intend and purport to be playing, but which they are breaking unawares, are those of the game of communication—one of which is that statements shall not be ambiguous; or those of the game of logical inference; or those of the game of ascertaining facts. Now, Professor Demos's initial and most radical contention was, we noted, that the basic beliefs of science are, like those of religion, matters of pure faith. This contention, however, and all that he rests upon it, is, I submit, disposed of at one sweep by the fact, which the preceding remarks have made clear, that what he calls the basic beliefs of science are really not beliefs at all, but are the rules of the game of pursuit of knowledge; and that it is only within this game, i.e., in terms of its rules, that the question whether a given belief is erroneous or true, groundless or well-grounded, valid or invalid, has any meaning at all. This game, however, is the one which the theologian too intends and purports to be playing; but he cheats at it when he takes, as starting point for his inferences of fact, assertions merely known to be contained in the Bible, instead of—as the rules of that game require—assertions known to be true by observation, whether physical, psychological, sociological, or other. The automatic consequence of such cheating is that the beliefs reached through it put into the hands of the cheater no verifiable power to predict events, nor any verifiable power to control them. This pragmatic difference is not, as Professor Demos asserts, a matter of values, but is a matter of plain fact, independent of such positive or negative values as power of prediction or of control may have. The theologian, of course, claims these powers for his beliefs, but hides from himself and from others his incapacity to substantiate the claim by making the further and equally unsubstantiated claim that his predictions will be verified and the efficacy of his beliefs proved, in a life after death. There is thus a radical difference between the scientific and the theological systems of belief. It is that difference which constitutes the first a system of knowledge, but the second a system only of faith, that is, according to Professor Demos's own definition, a system of beliefs

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"which rests on no evidence whatever." And it is that difference which justifies the characterization of theology—by Michelet, I believe—as "the art of befuddling oneself methodically." This conclusion must not be thought to ignore the possibility of kinds of experience other than the traditional five species of sensation; for example, perhaps, clairvoyant or telepathic impressions, or the here more directly relevant kind of experience which the mystics report. The mystical experience is sometimes regarded —plausibly, I think—as religious experience par excellence, which all other religious experiences but approximate or adumbrate in various degrees. In paranormal or mystical experiences, however, just as in ordinary sense-experiences, it is essential to distinguish between the experience itself, and what the person who has it takes it to signify. He may, for example, declare that he hears a bell, or that he tastes sugar; whereas the auditory sensation he experiences may in fact be caused not by a bell but by a phonograph and the sweet taste he tastes not by sugar but by saccharin. The distinction between what an experience is, and what it means, applies to the mystical ecstasy also: its literally experienced psychological characters are one thing; and what the experience is taken to signify is quite another thing—for instance, as believed by theistic mystics, that is signifies union with God. No doubt is possible, I think, that the extraordinary state termed mystical ecstasy has been aspired after and sometimes experienced by certain men and women; that the intrinsic value of this state is found by them far greater than that of any other human experience; and that the traces left by it on those who have experienced it have sometimes infused their subsequent life with notable energy, courage, and devotion to noble work. Moreover, they testify that the experience is not only one of intense bliss, but also one of great insight. Greatness of insight, however, is not necessarily insight into something great. T h a t the feeling of insight, like some other feelings, is capable of being generated, and with great intensity, by subjective physiological or psychological causes, was shown by Wm. James's experiments with the inhaling of nitrous oxide. Other persons who, like the present writer, have repeated the experiment, have likewise sometimes obtained what James called the "anaesthetic revelation," in which great insight is obtained into something; usually, however, into

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something very trivial, such as the casual words being uttered at the moment by the anaesthetist. This suggests that consciousness of insight, whether generated thus by drugs or by peculiar psychological exercises, will automatically attach itself to any idea that happens to be occupying attention at the time. In the mystic, the idea which occupies it is virtually certain to be that of unity, for all-encompassing love is the feeling the mystic cultivates, and love, like other emotions, tends to generate in the person experiencing it the ideas and beliefs congruous with it; specifically in the case of love, the idea and belief of unity between lover and beloved. To this, the feeling of insight or conviction, which is a feature of the mystical as well as of the anaesthetic trance, automatically adheres. And it is this psychological adhesion which the mystic reports as "insight" or "revelation" that such unity is a cosmic fact; or, if he happens to be a theist, that he has been united with God. For, as Professor Coe has memorably pointed out, the mystic acquires his cosmological or theological ideas in the very same ordinary and observable ways as do other persons. He does not derive them from the mystical experience, but brings them with him to the experience. They are what determines whether the beloved object, to which the mystic feels himself united in the ecstasy, is conceived by him impersonally as the whole universe; or on the contrary, personalistically, as some divine being—Jesus, for St. Teresa; or Kali the world-mother, for Ramakrishna; etc. The actual fact thus is only that when, or in so far as, anybody harbors intense and limitless love, then, or in so far, such love unites him with whatever real or imaginary object he bestows it upon. The mystic trance does not discover, but institutes, this unity.

Symposium:

JUSTIFICATION IN SCIENCE FREDERIC B . F I T C H AND A R T H U R W .

I.

FREDERIC B .

BURKS

FITCH

It is often asserted that some scientific theory is justified by some set of observed facts. In this paper we will be concerned with the nature of this justification. If one wished to take a purely psychological view it might be maintained that there are no genuine principles of justification but simply a tendency to believe a given theory in the face of certain facts. According to this standpoint there would be merely beliefs of various degrees in various theories and these beliefs would be simply the psychological consequences of experiences of observation. There would be no genuine justification of the theories concerned because one person's psychological processes might be different from another's, and so one person would tend to believe a certain theory under the same conditions that would cause another person not to believe that theory. There would be no objective criterion as to whether a particular theory should be believed in the light of given evidence. But in science it does seem that certain theories are really justified by given evidence, and that this is more than simply saying that individuals tend to believe certain kinds of theories when presented with certain kinds of evidence. T h e following account of the nature of justification is offered with the realization that it may require serious revision and improvement. T h e topic is generally recognized as containing many difficulties. It is hoped that the present approach meets most of the usual difficulties, and perhaps even all of them. I begin by discussing briefly propositions and theories. A proposition may be described as being the meaning of a sentence, or what a sentence expresses. It may also be described as

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a logically possible state of affairs (in case the sentence expressing it is not self-contradictory) or a logically impossible state of affairs (in case the sentence expressing it is self-contradictory). True sentences express facts, that is, they express true propositions or true states of affairs. Self-consistent false sentences express possible states of affairs that logically might have been realized but in fact are not realized. Self-inconsistent sentences express states of affairs that cannot consistently be realized. The propositions expressed by false sentences are of course said to be false, just as those expressed by true sentences are said to be true. A popular attitude is to be very puzzled as to exactly what sort of things propositions are, and to express great doubt as to whether there are such things as propositions at all, especially false propositions. The suggestion is that to admit there are such things as propositions is to populate the universe with a lot of superfluous entities, very much as the ancients populated the universe with demons, angels, and mysterious essences. We should instead be featherless bipeds, it is said, and keep both feet on the ground. But in order to be rational animals as well as featherless bipeds, and in order to be scientists and produce such contrivances as jet planes and cyclotrons, there seems to be essential need to assume the existence of many sorts of abstract entities, such as the number ir, and unobservable entities, such as neutrons, and there seems to be need to deal with possible "states'' of physical systems. These "states" are not unlike the possible (and impossible) states of affairs which I am here identifying with propositions. The assumption that there are propositions and other socalled "abstract entities" is really fully in accord with the spirit of the actual procedures of advanced work in physics and mathematics. Arguments of the following sort can also be adduced in favor of the hypothesis (or proposition) that there are propositions: If some one defends the view that there are no propositions, then what is he defending but a proposition to the effect that there are no propositions? Similarly if some one denies that there are any false propositions, what is the view he is attacking if it is not something that he believes to be a false proposition? Surely he is attacking something more than a mere sentence or string of symbols. The founders of our Republic were said to have been

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dedicated to the proposition that all men are created equal. Are we to suppose that this means that they were really dedicated to the string of symbols, "All men are created equal," and to all other strings of symbols into which this string of symbols can be transformed by some special rules? I doubt that they would have said so themselves. Granting that there are such things as propositions, we can treat each scientific theory as a class of propositions, namely those propositions which are expressed by the theorem-sentences of the theory if the theory is formalized by use of axioms and rules of procedure. If the formalization is "finitary" in the sense that only a finite number of axioms or axiom schemata are used, and only a finite number of rules of procedure, each of which refers to only a finite number of previously established theoremsentences, then the class of theorem-sentences is "recursively enumerable," that is to say, the class of Godel numbers of the theorem-sentences is recursively enumerable in the sense described on page 306 of S. C. Kleene's book, Introduction to Metamathematics. Furthermore, if the class of theorem-sentences is recursively enumerable, we will say that the class of propositions expressed by them is also recursively enumerable. Indeed we could think of the Godel numbers as assigned directly to the propositions themselves, instead of to the corresponding sentences. Let us go a step further and say that we regard every recursively enumerable class of propositions as being a "theory." We could even include among theories each class (of propositions) which is "arithmetical" in the sense that the class of Godel numbers of its propositions is arithmetical as this concept is defined on page 239 of Kleene's cited book. Systems of logic and systems of mathematics, viewed as theories, may often be conveniently treated in this way as being recursively enumerable (or even arithmetical) classes of propositions. Empirical theories, on the other hand, are probably better viewed as relations between propositions than as classes of propositions. This is because an empirical theory (that is, a theory concerned with the empirical world) is used to relate one fact with another. For example, given the fact that a baseball of a specified mass, shape and size is struck a blow of a specified amount of force in a specified direction, we can predict that the baseball will move in a certain path and with a certain velocity

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through the air. Thus the former complex fact enables us, by use of a theory, to predict the latter complex fact. If several antecedent facts must be ascertained to enable us to predict some consequent fact by means of a theory, these antecedent facts can usually be treated as conjoined to form a single complex fact, and the theory will relate this single antecedent fact to the predicted fact. Thus an empirical theory serves as a two-place relation between facts, or rather between propositions, since only true propositions are facts. Just as we do not wish to regard every class of propositions as being a theory, but only recursively enumerable classes of propositions (and perhaps certain other classes, e.g. arithmetical classes of propositions), so also we do not regard every two-place relation between propositions as a theory, but only recursively enumerable two-place relations between propositions (and some others perhaps, such as arithmetical relations between propositions). Thus we have two kinds of theories, those which are classes and those which are relations. We will call the former "classai theories" and the latter "relational theories." A classai theory does not have the effect of saying, " I f this is a fact then that is a fact," as a relational theory does. Instead it has the effect of saying categorically that such and such propositions (those that are members and hence theorems of it) are facts. A relational theory, on the other hand, enables us to predict facts from other facts. Of course even a classai theory may enable us to predict facts from other facts, but to do this it must introduce some concept of causation, or if it is restricted to dealing with abstract truths of mathematics or logic, then at least it must introduce some sort of implication according to which some abstract truths "follow from" others. A relational theory does not require concepts of causation or implication to relate empirical fact with empirical fact, or abstract truth with abstract truth, because the theory itself performs this relating function. It might even be argued that the concepts of causation and implication are pseudo-concepts that seem required when we insist on having a classai theory perform the relating function that properly belongs to a relational theory. Hence the difficulties connected with the concepts of causation and implication. This is merely a suggestion, and I would not wish to insist on it.

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Consider next the concept of "explanation." Suppose that B is the class of all propositions that are known to be true at some particular time by some particular person or persons, or at least are highly believed by such a person or persons. Let p be a member of B, and let C be some classai theory. I will say that C is an explanation of p, relative to the "evidence" B, provided that the following four conditions are satisfied: Condition 1. T h e proposition p is a member of C. In other words, the theory C classifies the proposition p as true. (The members of a classai theory are essentially the theorems of the theory, and so they are regarded as classified as true by the theory.) Condition 2. No member of C has its contradictory in the evidence B. In other words, C is not contradicted by the evidence B. Condition 3. There is no proposition, class, relation, or other entity involved in the definition of C in such a way that it could be replaced at will by any other proposition, class, etc., without destroying the membership of p in C. In other words, no factor involved in the definition of C is irrelevant to p's membership in C. For example this condition is violated if q is any proposition and if C is defined as the class of propositions each of which is identical with p or with q. In this case the choice of q could be varied at will without affecting the membership of p in C. On the other hand the condition would not be violated if C were defined as the class of all propositions of the form, "x is black," where x is a crow, and where p is the specific proposition "a is black," where a is a specific crow. In this case the theory C says in effect that all crows are black. I t is clear that p is a member of C, but there is no factor in the definition of C that can be varied at will in such a way as to leave p still a member of C. This third condition, incidentally, is incompatible with a thoroughgoing axiom of extensionality for classes since reference is here made in an essential way to the mode of definition of a class, and classes defined in different ways are assumed to be different even if they have the same members. Condition 4. Some proposition in C is not in B. In other words, the theory C asserts the truth of at least one proposition not in the given evidence. This condition prevents C from being simply an ad hoc explanation.

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The above four conditions are, then, the conditions under which C will be said to explain p relatively to evidence B. I now turn to the concept of justification. C will be said to be justified by the evidence B if C explains (relatively to B) at least one proposition belonging to the evidence B. It is clear from the foregoing that if C is justified by B, then C is consistent with all of B and is a relevant explanation of part of B. It is also possible to introduce the notion of "comparative justification" as follows: If Ci and C2 are classal theories both of which are justified by B, and if the class of propositions that are explained by C 2 relatively to B is a proper subclass of the class of propositions that are explained by C 2 relatively to B, then Ci will be said to be more justified by B than C 2 is by B. In other words, the theory with the greater explanatory power is the more justified theory, as between two theories each of which is justified by the evidence. Of course if the two theories explain different parts of the evidence, then they are not comparable in this way. According to this view of justification, a theory as a whole is justified, rather than justified part by part, because if one part of a theory serves as an explanation of some fact p, then the whole theory does not usually also serve as an explanation of p, since the remaining part of the whole would usually be irrelevant to p, and condition 3 would be violated. Nevertheless, if each of several theories Ci, C 2 , . . . , C„, explains some different part of the evidence B, so that each is separately justified by the evidence B, we still can say that in a secondary sense of "justification" the logical sum of the classes C 1 ; C 2 , . . . , C„, is also a theory justified by B, even though no one fact of B is "explained" by this theory in the strict sense demanded by condition 3. I turn next to a consideration of explanation and justification in connection with relational theories. If 72 is a relational theory, and therefore a two-place relation among propositions, R will be supposed to hold among propositions in such a way that if q bears R to p, then p is to be regarded as predicted or asserted by R on the basis of q. Thus if q is some fact in the evidence class B, and if q bears R to p, then theory R is to be conceived as predicting p from q. For each q belonging to B, there is therefore a class of propositions predicted by R on the basis of q. I call this class the class of i?-predictions from q, and write it as R (q). The class R(q) is the class of those propositions to which q bears R.

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The fact p, which is a member of the evidence class B, will be said to be explained by the relational theory R, relatively to evidence B, if the following four conditions are satisfied. These four conditions are closely analogous to the previously stated four conditions that apply to classai theories. Condition 1'. There is a member q of B such that p is a member of R(q). Condition 2'. There are no propositions q and s such that q is a member of B, s is a member of R(q), and the contradictory of s is a member of B. Condition 3'. There is no entity involved in the definition of R in such a way that, for some member q of B, the membership of p in R(q) remains unaffected while that entity is varied at will. Condition 4'. For some member q of B, there is some proposition that is a member of R(q) but not of B. Just as in the case of a classai theory, if a relational theory R explains (relatively to B) at least one proposition of the evidence B, then R will be said to be justified by the evidence B. Also, if and R2 are relational theories that are justified by B, and if the class of propositions explained by R2 relatively to B is a proper subclass of the class of propositions explained by Ri relatively to B, then Rx will be said to be more justified by B than J?2 is justified by B. This completes my general account of justification. Notice that by treating theories as recursively enumerable classes or recursively enumerable relations we avoid some of the more troublesome "paradoxes of confirmation," particularly the following one that was called to my attention by my colleague Professor Hempel: If a theory is "confirmed" by each true proposition that it implies, if q is any true proposition, and if p is any proposition implied by a theory T, then the proposition "p or q" is both true and implied by T. Hence we can always find a confirmation for any theory. In the approach used in the present paper, however, we do not employ a concept of implication in connection with theories in this way. We would permit a classai theory, for example, to have p as one of its members (or asserted propositions) without having the proposition "p or q" as one of them. It might be supposed that the class of all true propositions would serve as a "theory" which would explain all propositions

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belonging to any evidence class B. This is avoided, however, by the requirement that theories must be recursively enumerable, or at least arithmetical. It can be shown by methods due to Godel that the class of all true propositions is neither recursively enumerable nor arithmetical. I wish to conclude with some brief remarks about counterfactual conditionals and about probability propositions. Suppose I say, "If q were the case, then p would be the case." I take this to mean that q is false and that there is some true relational theory R and some true proposition t such that p is explained by R(q&it) relatively to all the known evidence B. (In saying that a relational theory R is true, I mean that every member of R(u) is true, for every u that is a true proposition.) By a "probability proposition" I mean a proposition of the form, "The probability is x that a fact of kind K is of kind L." I abbreviate such a proposition as [x,K,L], For example, the proposition, "The probability is J/2 that a penny when tossed will come up heads," is a probability proposition [x,K,L], where z is ]/ï, K is the class of all those facts that consist of the tossing of individual pennies, and L is the class of all those facts that consist of the tossing of individual pennies that come up heads in the tosses concerned. Now what sort of evidence can justify a probability proposition? Of course no amount of evidence can rejute a probability proposition. If I were to contend that the chance of a penny's coming up heads were only no number of tosses, however great, would be sufficient to refute this, because the reply could be that if the penny were tossed enough more times, it would be seen to come up heads in only one third of the total number of tosses. As far as the justification of probability propositions is concerned, I think we must be satisfied with comparative justification. If the following condition is satisfied, it can be said that with respect to the evidence B the probability proposition [x,K,L] is more justified than the probability proposition [y,K,L] : The number x is nearer than the number y to the actual ratio of members of L in B to members of K in B. Here the number of members of K in B would have to be finite, but this would ordinarily be the case in all practical situations, such as tossings

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of a coin. We assume furthermore that probability propositions do not themselves appear among the members of an evidence class B. The concept, " a t least as justified as," among probability propositions, can be defined analogously to the concept "more justified than." In this case x would have to be at least as near as y to the actual ratio. So far we have supposed that probability propositions are not among the members or predicted propositions of the theories whose justification we have been concerned with. Let us therefore suppose now that two classal theories Ci and C 2 have probability propositions among their members, as well as having propositions that are not probability propositions. It will be said that Ci is at least as justified by evidence B as C 2 is by evidence B, under the following condition: Ci and C 2 are both justified by B, and the class of propositions explained by C 2 relatively to B is a subclass of those explained by Cx relatively to B, and corresponding to every probability proposition j 2 belonging to C 2 there is a probability proposition belonging to C\ such that ^ is at least as highly justified by B as s->. Analogously we can define what we mean by saying that Ci is more justified by evidence B than Co is by evidence B. In a similar way an account can be given of comparative justification of relational theories that are concerned with probability predictions. Theories of quantum mechanics seem to be of this sort. It is hoped that the account of justification that has been outlined here can be applied to the problem of justifying theories of logic and mathematics and philosophy, as well as theories of empirical science. For example, we often assume some logical principle to be true even though we do not have any certain insight that it is true. We test it by its consequences, very much as in the case of an empirical principle. An example of such a principle is the axiom of choice. The so-called inductive procedures of empirical science are used in logic and mathematics more extensively than is often realized. A sound theory of justification should have applications in non-empirical as well as empirical realms, and should itself be justified in widely diverse fields of thought.

Symposium:

JUSTIFICATION IN SCIENCE F R E D E R I C B . F I T C H AND A R T H U R W .

I I . ARTHUR W .

BURKS

BURKS

I Professor Fitch begins his discussion of justification with a defense of a Platonic theory of propositions. While I am sympathetic to such a theory, I do not think his arguments for it are valid. Nor do I think that his Platonism is really required for his theory of justification. His query, " I f some one defends the view that there are no propositions, then what is he defending but a proposition to the effect that there are no propositions?" seems to me to be on a par with Johnson's kicking of the stone. In the ordinary sense of "physical objects" the Berkeleyan believes there are physical objects, and in the ordinary sense of "proposition" the nominalist believes there are propositions. Using the phrase "physical object" in its ordinary sense we can roughly formulate the issue between the realist and the phenomenalist as follows: Is a physical object an irreducible kind of ontological entity or is it a compound of more basic ontological entities such as sense data? Similarly, using the word "proposition" in its ordinary sense we can roughly formulate the issue between the Platonist and the nominalist by: Is a proposition an irreducible kind of ontological entity, or is it constructible out of more ontologically basic entities such as sentences? This formulation shows that the nominalist will grant that there are propositions in the sense required by Fitch's theory of justification, so we need not pursue the issue further. II Since justification in science is verification, and verification involves probability as well as deduction, a few preliminary re109

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marks on these topics are in order. We will assume throughout that if the probability of p relative to q is 1 then q logically implies p. We then distinguish two kinds of cases in which p justifies q. In the first, the probability of q on p is one; we shall call cases of this kind deductive justifications. In the second, which admits of degrees, the probability of q on p is x and x is neither zero nor one; we shall call justifications of this kind probabilistic justifications. Of course these conditions do not completely characterize the justification situation—they do not exclude, for example, a proposition justifying itself—but they are the ones I should like to discuss in this paper. Whenever we use "probability" without qualification we mean it in the sense of inductive probability (Carnap's "probabilityi") as contrasted to frequency probability (Carnap's "probability 2 "). It is important to note that our usage here is different from that of Fitch, who uses "probability" only in the latter sense; hence his discussion of the justification of what he calls "probability propositions" is not a discussion of what we have called "probabilistic justification." We shall discuss Fitch's theory of justification in terms of the following example. Let / / a be the hypothesis that a certain box contains 1 white and 2 black balls, and H b the hypothesis that it contains 1 black and 2 white balls. Let g be such that the probability of each hypothesis relative to g is one-half and let t be the "prediction" that of 10 "fair" draws with replacement 6, 7, or 8 are black. Now it seems to me that this is an instance, though admittedly a somewhat artificial one, of probabilistic justification: the probability of Z/a on t & g is .90 and hence t & g justifies Ha to degree .90. Similarly, the probability of t on / / a is .68, and Ha explains t to degree .68. It is therefore of interest to see how this example may be dealt with in terms of Fitch's patterns of justification. T h e following somewhat clumsy formulation seems to fit his pattern for relational theories. Let s be the assertion that the probability of Ha and the probability of Hh are each equal to onehalf, and let B a consist of J and t. Further, let Ra(q,p) mean that q logically implies that the probability of p on H„ is greater than one-half and that the probability of p on Hh is less than one-half. Then it seems to follow by Fitch's Conditions 1', 2', 3', and 4' that t is explained by i? a relative to B a and that is justified by the evidence B e . I shall make two criticisms of Fitch's theory of justification,

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using this example as a point of departure. The first is that Condition 3' is too vague for me to be certain that it is satisfied in this example. The purpose of Conditions 3 and 3' is clear enough: they require that the class of propositions called the theory have that kind of unity which distinguishes what is ordinarily called a scientific theory from any arbitrary aggregate of propositions. This requirement is a non-extensional one, and, like most nonextensional requirements, is difficult to formulate precisely. While the rough formulations of Conditions 3 and 3' seem correct as far as they go, they are not very fully developed. This lack is important because so many of Fitch's results depend on these conditions. His conclusion that a theory as a whole is justified makes explicit use of Condition 3. And Condition 4 excludes an ad hoc explanation only in the presence of Condition 3, else C could consist of the members of B plus some arbitrary, unrelated proposition. My second criticism of Fitch's theory of justification is the following. It is of the very essence of probabilistic justification that it admits of degrees, whereas in the example under consideration Fitch's pattern gives us a result which is not qualified by a degree. Perhaps Fitch intended such an example as this to be dealt with in terms of his discussion of the justification of (frequency) probability propositions. That would involve construing H& and Hb to mean that the frequency probability of white draws is one-third and two-thirds respectively so that the observed frequency would justify Ha more than Hh. There are a number of objections to this, however. In the first place the degree to which Ha is justified by t & g is omitted. Second, and Hb are not frequency probability propositions, since they describe the directly observable contents of the box. Finally, even if the present example were subject to this interpretation, there are many examples of probabilistic justification in science which are clearly not so interpretable. In the next paragraph we will give an example which is not, and in Section 4 we will give some examples of probabilistic justification which involve theories (e.g., Newton's theory of gravitation) that are clearly not interpretable as frequency probability propositions. That Fitch's patterns of justification do not adequately accommodate probabilistic justifications is shown by the fact that they admit of Hempel's paradox of confirmation. (I refer here to the

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paradox usually called by this name, not to the one mentioned by Fitch in his paper.) Let C 8 be the theory containing all substitution instances of "All swans are white" and let Dg contain "a is a swan" and "If a is a swan then a is white." Then D s justifies C 8 ; this amounts to saying that " a is a white swan" justifies "All swans are white." In a similar way we can derive in Fitch's system the result that "b is a non-white non-swan" justifies "All swans are white." This result is unqualified in Fitch's pattern, and therefore paradoxical, because Fitch's pattern does not distinguish the different degrees to which "a is a white swan" and "b is a nonwhite non-swan" justify "All swans are white." To resolve the paradox we must observe that "a is a white swan" appreciably increases the probability of "All swans are white" while "b is a black shoe" increases it by a trivially small amount. But this is a difference of degree which does not appear in Fitch's pattern. (This resolution of the "paradox" was proposed by Janina Hosiasson-Lindenbaum in "On Confirmation," Journal of Symbolic Logic, Vol. 5, pp. 133-48. She explains the difference in degrees of confirmation here on the basis of such facts as there being more non-white things than swans. Her explanation is correct in the case of everyday examples of induction by simple enumeration, which make implicit use of such facts. However, the text-book patterns of induction by simple enumeration do not involve such facts, so for them the explanation is different. I suggest that it involves the fact that "swan" has a smaller logical width in Carnap's sense than "non-swan.") Ill Professor Fitch also discussed the following question, which was suggested by the Program Committee: " I s the process of justification one which inevitably brings us to justify total systems of knowledge rather than isolated statements?" The remainder of this paper will be devoted to a further discussion of that question. The thesis that the process of empirical verification necessarily involves whole groups of theories is as old as absolute idealism and the coherence theory of truth, though today its defenders are to be found mostly among pragmatists. Since it says in effect that not a theory alone, but a theory together with its context, is the irreducible unit from the point of view of justification, we will

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refer to it as the contextnalist thesis of justification. Now the concepts justify and isolated, and hence the contextualist thesis itself, are highly vague and ambiguous, so a more careful and precise formulation of the issues is in order. To this end I will, during the course of this paper, formulate five theses (called Theses 1, 2, 3, 4, and 5) which express my own viewpoint on various of these issues. The contextualist would accept only Thesis 1 and would reject the others, so this procedure should help to localize some of the points of controversy. Since the contextualist thesis is often advanced in connection with crucial experiments, we will begin with an examination of this notion. There are undoubtedly experiments crucial in the weak sense of markedly changing the probability status of the theory being tested; for example, the results of measuring the bending of light as it passed the sun greatly increased the probability of the General Theory of Relativity. The debatable question is: Are there any experiments crucial in the strong sense of determining the probability of a theory to be zero or one? It is sometimes maintained that there are, on the ground that in some instances of justification a scientist deduces an observation statement from a theory, refutes that statement by an experiment, and thus establishes that the theory in question is definitely false. Foucault's experiment has been mentioned as a case in point. It is argued that the Newtonian corpuscular theory of light entails that light will travel more rapidly in water than in the less dense medium air, that Foucault's experiment showed that the velocity of light in water is less than in air, and that hence this experiment showed that the Newtonian corpuscular theory is false. (F. M. Chapman and Paul Henle, The Fundamentals of Logic, pp. 327-28.) It is not held that this result shows the wave theory to be true, though of course it increases its probability, but rather that testing a scientific theory is like testing a proposition of the form "All A's are B's": a single instance may falsify it, but a single instance cannot establish its truth. The standard objection to the foregoing argument brings us back to the contextualist thesis of justification. This objection, which seems to me correct, is that the prediction which is tested is not deducible from the main theory under test, but only from the main theory together with auxiliary theories, and hence that the falsity of the prediction does not logically imply the falsity of

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the main theory but only that the main theory or one of the auxiliary theories is false. We may illustrate this point with the Foucault example. Let H c be Newton's corpuscular theory, which is the main theory under test in this example. Hc alone does not entail that light will travel more rapidly in the denser of two media, but only Hc in conjunction with Newton's gravitational theory, the auxiliary theory As. Foucault measured the relative velocities of light in air and in water with a complicated apparatus composed of a rapidly revolving mirror, some stationary mirrors, a lens, etc. Let rt be a complete description of Foucault's experimental set-up and of his observed results. Clearly not-r f cannot be deduced from H c and A g alone; rather, other auxiliary theories are required: the laws of reflection and refraction of light ( / i r ) , statements about the density of water and air (Aa), etc. I t will be noted that these last two auxiliary theories deal with the experimental arrangements employed to test the main theory, being theories about the physical processes exemplified in the instruments used. Thus in the Foucault example the hypothesis being investigated was not deductively refuted in isolation but only in the context of various auxiliary theories. This seems to be generally the case, so that subject to the qualification that "main theory" and other key terms be appropriately defined, we offer THESIS 1: Directly verifiable experimental predications are not deducible from the main theory under test alone, but only from this theory together with auxiliary theories. I suggest that Thesis 1 is part of what is intended by the contextualist thesis of justification. Thesis 1 does not settle all the issues raised by contextualism, however. Note first that though Thesis 1 implies that isolated theories cannot be shown to have a probability of zero, it does not imply that a group of theories can be shown to have a probability of zero, for people make mistakes in setting up and reporting the results of experiments, so there is a non-zero probability, albeit very low, that the observation report is false. Hence Thesis 1 does not imply that the justificatory status of a group of theories is any different from that of an isolated theory in this important respect. Now if we cannot establish a zero (or unity) probability for a theory or a group of theories, we are left with the possibility of establishing non-zero non-unit probabilities; that is, we are left with prob-

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abilistic justification. Thus Thesis 1 does not cover this very important type of scientific justification. IV Before discussing the question of whether or not isolated theories can be justified probabilistically we need to dispose of some preliminary matters. We will use "theory" and "observation statement" as names of distinct types of statements, regardless of their truth status. Galileo's law of falling bodies and Kepler's planetary laws are examples of theories. We will consider only theories that do not have a probability of zero or one relative to any finite number of direct observational reports, i.e., only those to which Thesis 1 is applicable. The report of an observation of the orbit of Mars together with a description of the apparatus used (or any non-analytic—i.e., neither logically true nor logically false—truth-function of these statements) is an observation statement, as is a description of one of Galileo's experiments of rolling balls down an inclined plane. We stipulate that, as in these examples, all observation statements are physical object statements, even though our usage here excludes some reports (e.g., from psychology) normally called observation statements. The contextualist thesis of justification presupposes that theories can be counted, i.e., that there are identity criteria for them, so that "isolated" theories can be distinguished from "groups" of theories. Presumably something like the following is intended. Galileo's law of falling bodies and Kepler's planetary laws are different theories, and while the conjunction of the two is a single proposition it does not have sufficient unity to be called a single theory. Newton's theory of gravitation is a single theory which (together with other statements) entails both Galileo's and Kepler's theories. Our conventions for symbolizing theories and observation statements will be as follows. Upper-case letters refer to theories, lower-case letters to observation statements. Letters with and without numerical subscripts are variables, letters with alphabetic subscripts are constants. Individual upper-case letters represent only "single" theories, but individual lower-case letters may represent non-analytic truth-functions of any arbitrary finite number of direct observational reports.

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T h e claim is often made by contextualists in discussions of crucial experiments that one can explain the phenomenon in question by giving up one of the auxiliary theories rather than the main theory. For example, one could explain Foucault's result by saying that the theory of gravitation is false. According to Thesis 1, it is logically possible to keep Newton's corpuscular theory and reject his gravitational theory on the basis of Foucault's result. But what is merely logically possible must be sharply distinguished from what is a reasonable inductive procedure. There was tremendous evidence in Foucault's time for the theory of gravitation, and an adequate theory of justification must take this evidence into account. Indeed, by the principle of total information all relevant information must be taken into account in determining the complete justificatory status of the theory. To show the role of such evidence let us analyze one pattern of argument that is often employed in scientific justification. Let H be the main theory under test, Alt . . . , As auxiliary theories, and r the main observation statement used in testing H. These auxiliary theories have been adopted on the basis of considerable evidence, which is part of the total evidence relevant to H which is available at the time. Other available evidence relevant to H is of at least two kinds. First, that used to support accepted theories that are special cases of the main theory. Since these accepted theories constitute the "background of knowledge" from which an extension to H is made, we will call them the background theories, Bi, . . . , BM. Second, there may be available evidence relevant to the main theory which is not used to support either the auxiliary theories or the background theories; this will appear simply as a (complicated) general observation statement g. We can now state the pattern of inference in question, which is based on Bayes' theorem of inverse probabilities. The probability of H relative to Ax . . . As & Bi, . . . B^ & g is x, which is neither zero nor one. The probability of r relative to H and A-i . . . As & Bx . . . •Bm & g is greater than the probability of r relative to not-.// and Ai . . . An & . . . 5m & g. Therefore, the probability of H relative to r and Ax . . . As & Bx . . . Bu & g is greater than x.

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Obviously m a n y minor variations of this pattern are possible, some of which m a k e explicit the approximate values of the probabilities involved, but this form will suffice for our purpose. Since it a n d similar patterns are often used in justifying scientific hypotheses we will refer to it as the pattern of hypothesis. T h i s pattern, without the background theories, is clearly applicable to Foucault's experiment. An example in which the background theories play an important role is the test of N e w t o n ' s theory of gravitation by the determination of the gravitational constant at various places on the surface of the earth. In this case H becomes the theory of gravitation; r becomes an observation s t a t e m e n t involving reports on measurements of the gravitational constant at various latitudes and data used in determining the size a n d shape of the earth (put in appropriate conditional f o r m ) ; Ai, . . . , Ay become the auxiliary theories related to the instruments used to get the observations given in r; B1: B2 become Galileo's law of falling bodies and Kepler's planetary laws; a n d g contains information relevant to determining the periods a n d distances of the planets from the earth and the diameter of the earth. N o t e that in this case Bi and B > are, in accordance with our general requirement, "special cases" of H (g is required for the deduction of these two theories from Newton's gravitational t h e o r y ) , and that even before the test Newton's theory was wellconfirmed by these two theories. A final preliminary matter must be disposed of before we return to the contextualist thesis of justification. Since Ai . . . .4 N & Bi . . . .BM & g is generally known prior to the experimental testing of r, the probability of H relative to Ax . . . /1N- & Bx . . . Bu & g is in one sense an a priori probability. We shall call it a relative a priori probability (it is sometimes called an antecedent p r o b a b i l i t y ) , to distinguish it from the probability of H prior to any empirical information, which we shall call an absolutely a priori probability. ( T h e concept of an absolutely a priori probability, though not the name, is due to C a r n a p ; in his system it is a probability relative to a tautology or logical truth.) T h e concept of an absolutely a priori probability will be used in the following section in describing certain ways in which theories can be justified in isolation. However, the very introduction of this concept marks an issue with the contextualist, who would deny its

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meaningfulness. We will, however, postpone our discussion of this issue to the section following the next one. V The conclusion of the pattern of hypothesis states essentially that the probability of 11 on r and A i . . . /4N & Br . . . BM & g is greater than the probability of H on Aj . . . & B\ . . . B^ & gIn this case H is justified by r only in the context of the auxiliary and background theories. This does not preclude there being a justification of H relative to r merely (and hence in isolation from the auxiliary and background theories) and I think such justification is possible. Its existence is asserted by the following thesis. THESIS 2: For some r and H, the probability oj II relative to r is unequal to the absolutely a priori probability of H. (I believe this thesis holds for every verifiable hypothesis H , but the weaker form above is sufficient for present purposes. According to the direction of the inequality r will justify H or not-//.) Thesis 2 does not, however, take into account all the available information used in the pattern of hypothesis. As a consequence the probability effect of r on H in Thesis 2 will in general be very small. We are thus led to the question: Is there a pattern by which H may be justified in isolation from any other theories and which takes proper account of all the information available? It seems to us that there is. Associate with each auxiliary theory An a conjunction an which includes all known observation statements inductively relevant to An, and associate with each background theory Bm a conjunction bm which includes all known observation statements inductively relevant to Bm. We shall call each an an auxiliary observation statement and each bm a background observation statement. The following thesis then states that H may sometimes be justified by observation statements merely: THESIS 3: For some r and II, the probability oj H on r and