Modern analytic philosophy is descended from a fertile if temporary union between the revived formal logic of our age and empiricist philosophy. In the last decades of the nineteenth century logic underwent, at the hands of Frege, its most important developments since Aristotle started it off as a systematic discipline. Frege’s work seemed to realize the prophetic dreams of Leibniz. With it formal logic came to cover a vastly wider field than the syllogistic logic of Aristotle had ever done. Where the logic of Aristotle was largely confined to the study of inferences owing their validity to the way the words “all,” “some,” and “not” occurred in them (as in the old favorite: all men are mortal, all Greeks are men, so all Greeks are mortal), the logic of Frege also covered inferences hinging on “and,” “or,” and “if.” Aristotle’s theory of the syllogism turned out to be a rather small, elementary segment of the second main part of Frege’s system. Frege’s logic was expressed with unprecedented rigor, and as a crowning achievement, seemed to afford a basis of indubitable certainties from which the whole of mathematics could be derived, effecting a unification of the two disciplines.

At much the same time Mach in Austria, and W. K. Clifford and Karl Pearson in England, were adapting features of the traditional empiricism of Mill to the interpretation of physics, a science that Mill knew only as an intelligent general reader. For this new philosophy of science the basis of all knowledge of fact was the reports of immediate, subjective sense-experience. All the statements of common observation and scientific theory owed their significance and truth to these basic assertions, of which they were held to be convenient abbreviations. Concepts of ordinary material things and of the theoretical entities of science were understood as shorthand for the concepts of direct perception: color patches in the visual field, felt pressures and so forth. Science in this view was an application of Mach’s principle of the economy of thought, a concise and convenient notation for the common patterns and regularities to be found in the streams of individual sense-experience.

The union of logic and empiricism was solemnized in the first really independent philosophical writings of the first man to combine the requisite logical and philosophical expertise, in Our Knowledge of the External World (1914) and Philosophy of Logical Atomism (1918) of Bertrand Russell. In these works the world is seen as an array of individual events of sense-experience, some related so as to constitute minds, some (including many of the previous group) as material things. For Russell the task of philosophy was to use the new resources of logic to analyze the stock of received knowledge, to reveal its ultimate constitution in basic empirical terms where this was possible, and to discard it as illusion where no such reduction could be effected.

WITTGENSTEIN’S Tractatus Logico-Philosophicus (1922) was the first brilliant wayward child of the marriage, but the parental lineaments were more obvious in the logical positivism of the Vienna Circle. Wittgenstein’s chief service to the tradition at this early stage of his career was to provide a congruous account of logic itself, the instrument of analysis. Formal research in the most elementary and fundamental part of the discipline led him to the view that the laws of logic are tautologies, statements that owe their necessary truth not to some unalterable structural features of the world which they might be thought to describe but to the conventions of language by which they are endowed with meaning. The central idea here is that all necessary truths are at bottom alike in nature. The most sophisticated theorems of mathematics are true for the same reason that “all bachelors are unmarried” is. That simple truism records no substantial truth about the world. It reflects a fact about language, that the same rules are in force for the distinct expressions “bachelor” and “unmarried man.” We do not discover that, as a matter of objective fact, all bachelors are unmarried men. The possibility of an exception is ruled out in advance by the meanings that are conventionally assigned to the words in question.

In its standard form, as expounded in the 1930s by Schlick and Carnap, logical positivism consisted of three main doctrines, multiply related to each other: phenomenalism—a theory of factual knowledge, conventionalism—a theory of logic or formal knowledge, and verificationism—a theory of meaning. Phenomenalism holds that all knowledge of fact is or can be reduced to knowledge of immediate experience, conventionalism that the necessary truth of logic and mathematics is due to conventions of language, verificationism that any utterance that is neither phenomenal nor conventional is beyond the pale, metaphysical, without meaning as a statement, and at best an effusion of feeling. Thus for the positivist “there is an apple here” is really a compact way of referring to a pattern of visual, tactual, and olfactory experiences that could be obtained here. “4 × 7 = 28” is made true by the meanings conventionally given to the numerals, and “God loves us all,” being neither reducible to immediate sense experience nor true in virtue of its meaning, is not really a statement at all but perhaps the expression of a subconscious wish that everything will turn out all right for us in the end.


The pressure of history brought most leading European positivists to the United States at the end of the 1930s, notably Carnap and Reichenbach. They got an intellectual welcome over and above the political asylum open to them as refugees from fascism. To start with, there is a certain broad affinity between positivism and pragmatism, in Dewey’s version at any rate, since both are pro-scientific and anti-theological. Peirce, who was preeminently a logician and a philosopher of science, shared the leading interests of the positivists and his version of pragmatism closely anticipated the verification principle. For Peirce the meaning of a statement lay in the observable difference that would result from its being true rather than false. Such a view is remote from the pragmatism of folklore, the idea that the true is what works, which is not all that much of a travesty of the position of William James. Then there is a strongly pragmatic flavor to the idea that all concepts but those of immediate sensory qualities are abbreviative constructions to be chosen on grounds of convenience and economy. The leading American theorist of knowledge of the interwar period, C. I. Lewis, had come, from a pragmatic starting point, very close to positivism by 1929 when the European movement was only just under way. Always a phenomenalist, he was at that time a conventionalist and he was an anti-metaphysician in practice if not by profession.

BUT JUST AS TRANSPLANTATION seemed to be giving new life to the most developed form of the union between logic and empiricism, the union itself was coming apart. Logic was withdrawing itself from philosophy and assimilating itself to mathematics. A good theoretical reason for this was Gödel’s proof, in his epoch-making paper of 1931, that the Frege-Russell ideal of constructing a complete system of logic and mathematics was incapable of completion. So the interest of logicians turned from the construction of one ideal system to the disciplined study of deductive systems of all kinds from outside. Another reason was the increasing bulk and sophistication of logic itself which converted its skilled practitioners into an autonomous profession, one that had a direct technical application in the theory of electrical circuits and computer engineering.

On the other side, philosophy of a broadly empiricist, non-edifying kind was undergoing a revolt against formalism, that is against the conviction that discourse achieves its ideal form in the propositions of mathematics and natural science and against the connected principle of method which takes translation into the notation of formal logic to be the proper way to distill the substantial content from any kind of thought or speech. The uncharitable explain this revolt by the fact that philosophers in Britain, where it began, ordinarily know a good deal of classics and rather little mathematics or science. But this was more the fertilizer than the seed of the new development.

At any rate since 1945 analytic or empirical philosophy has become less and less formal, more and more grammatical, at first in Britain, more recently in the United States. It has not tried to solve the traditional problems of philosophy in the manner of positivism by a formalistic regimentation of language but has aimed rather to undermine the problems, to expose them as the outcome of hidden, seductive deviations from the ordinary use of words by close study of the way in which language is actually employed. Mathematics and natural science, the ideal forms of thought for positivism, are viewed by linguistic philosophers, usually pretty much out of the corners of their eyes, as just two out of the many going concerns within the whole field of discourse. Wittgenstein, in the later part of his career, and J. L. Austin, the most influential linguistic philosophers, laid great stress on the many other purposes that language can serve over and above the communication of knowledge. For them statement is not the prime function of language but is on a level with advice, incitement, the expression of feeling, and a host of others. Secondly, they dismissed the claims of formal logic to be a canon of rationality. For them it is not a display of the essential structure of rational discourse, but is rather a diagram or even caricature of properly conducted intellectual processes, a highly selective, not a literal, representation of them. Their philosophical method does not pursue economy and system but seeks to make explicit in all their complex variety the rules which govern established uses of words. This informal logic is a conservative undertaking, for it does not judge the forms of discourse it examines by a formal ideal of the communication of truth. It seeks simply to understand the different kinds of generally prevailing discourse and to codify them only to the extent that is necessary for the relief of philosophical perplexity and is possible in view of the complexity of language. Positivism, by contrast, is radical and critical. It dismisses metaphysics and theology altogether and looks down on common speech and the everyday beliefs it is used to express as first crude approximations to the language and the theories of science.


From a distance the two schools may seem as hard to distinguish as are Stalinists and revisionists to the eye of a stockbroker but there is no love lost between them. To their opponents the positivists look rigid and unenlightened followers of Procrustes, the linguistic philosophers look desultory, amateurish, and constitutionally inconclusive. An example may help to convey the difference between their procedures. Both are interested in the concept of cause. But where the positivist seeks for a single defining formula in logical notation for the sense of the word central to science, the linguistic philosopher compiles an open-ended album of its possible uses, registering every nuance and inflection with taxonomical dedication.

BUT ALTHOUGH THE UNION of logic and empiricism is no longer the height of philosophical fashion it was thirty years ago, it is by no means extinct. In Britain its orthodox form is skillfully defended by Ayer, the Hannibalic figure who first brought the elephants of positivism over the Alpine barrier of British intellectual insularity. Sir Karl Popper, never a member of the Vienna Circle but from early days a critical and highly independent associate, is active and influential. And there is Professor W. V. Quine of Harvard, who is at once the most elegant expounder of systematic logic in the older, pre-Gödelian style of Frege and Russell, the most distinguished American recruit to logical empiricism, probably the contemporary American philosopher most admired in the profession, and an original philosophical thinker of the first rank.

Readers of The New York Review who know him only through his contributions to it may have thought him a geographer, since most of them have been reviews of atlases. (But this taste is not peculiar to him among philosophers. Hobbes, Aubrey reports, “took great delight to go to the bookbinders’ shops and lie gaping on mappes.”) What such readers will not have failed to notice is that he is an extremely witty and felicitous writer. Some great philosophical books are very badly written indeed, those of Kant being unrivaled for their combination of eminence and ugliness. Philosophers who are also logicians at least write lucidly on the whole but they can be fairly dull, as witness the greatest of their number, Aristotle and Frege. But many logicians are entertaining as well as clear. Lewis Carroll and Bertrand Russell have contributed to laughter as well as to understanding.

There are several reasons for the fact that logical writings can be funny with no loss of relevance. A relatively superficial one is that the high abstractions with which they deal can be illustrated with any sort of subject-matter, in a way the odder the better. A deductive argument is valid provided that its conclusion must be true if its premises are but it is not required that its premises actually be true (hence the striking rationality of some cranks and madmen). The distinction is instructively enforced by examples in which they are not. A more substantial reason is that logic deals in surprises. If all rules of inference were obvious it would not be worth codifying them. Furthermore the discovery and prevention of paradoxes has been one of the chief engines of logical progress and a paradox is, among other things, a joke in the full Bergsonian sense, the outcome of mechanical reliance on an ordinarily trustworthy instrument. The title essay of Quine’s The Ways of Paradox is a beautifully concise survey of the nature and significance of paradoxes and the following delightful proof that 2 = 1 will give some idea of its attractions. Suppose that x = 1. Then, multiplying by x, x2=x and, subtracting 1 from both sides, x2—1=x—1. But x2—1=(x+1) (x—1). So divide both sides of x2—1=x—1 by x—1. The result is x+1=1. But since x=1, 2=1. QED.

In general Quine’s style combines a certain rotundity of utterance with a verbal wit that exploits the submerged associations and resonances of technical terms. But there are also bonuses of straightforward humor. It is characteristic that Quine should replace those traditional bores X and Y in one of his essays by McX and Wyman. Or consider this passage which needs a small glossary. “(Ξ x)” may be read here as “there is something of which it is true that,” the x’s following this symbol as “it” and “.” as “and.”

The incorrectness of reading “Ctesias is hunting unicorns” in the fashion: (Ξ x) (x is a unicorn. Ctesias is hunting x) is conveniently attested by the non-existence of unicorns, but it is not due simply to that zoological lacuna. It would be equally incorrect to render “Ernest is hunting lions” as: (1) (&926; x) (x is a lion. Ernest is hunting x), where Ernest is a sportsman in Africa. The force of (1) is rather that there is some individual lion (or several) which Ernest is hunting; stray circus property, for example. The contrast recurs in “I want a sloop.” The version (2) (&926; x) (x is a sloop. I want x) is suitable insofar only as there may be said to be a certain sloop that I want. If what I seek is mere relief from slooplessness, then (2) gives the wrong idea.

I dare say there are low-spirited people who would regard this passage as merely jocose. But it makes an important point with memorable economy that statements like “I want a sloop” are ambiguous: the sloop desired may be a particular sloop or any old sloop. The entertaining elements are not detachable incrustations stuck on to the bare bones of the exposition. Some proper name had to be chosen for the lion-hunting example (1); it was a happy thought to pick Ernest as the subject for such a virile predicate.

THIS SPECIAL GIFT of running the workaday virtues of lucidity and concision in harness with the ability to produce audible laughter makes Quine’s more strictly logical books unique of their kind. It is displayed in the more important, comprehensive, and full-dress of them—Mathematical Logic and Set Theory and Its Logic,—as well as in his Elementary Logic, an introduction to the rudiments of the subject that goes with particular thoroughness into the business of converting ordinary speech into logical notation and vice versa, and in his Methods of Logic, to my mind the best of all comparatively introductory books on the subject, in which the hard formal core is buttressed with philosophical commentary on one side and practical hints for the aspiring ratiocinator on the other.

Scattered logical writings not incorporated in previous books make up the bulk of Selected Logic Papers. Its contents are pretty strictly for the initiated, even the article “Logic, Symbolic” reprinted from an encyclopedia. This is an amazing feat of condensation with something solid to say in its brief scope about every major topic of interest in modern formal logic. But it must surely daunt all but the cleverest of technically innocent inquirers. The Ways of Paradox is made up of twentyone more generally accessible pieces showing a much higher ratio of prose to logical symbolism. Quine describes the first five as “semi-popular pieces on logic and the foundations of mathematics.” The remainder comprises all of Quine’s philosophical work that has not been either collected into From a Logical Point of View or worked into Word and Object, his general treatise on the philosophy of language.

Earlier I boiled the standard, Viennese, form of logical empiricism down to three main theses: phenomenalism, conventionalism, and verificationism. Quine dissents from all three but remains in the tradition because his main problems are those of his positivist predecessors, because he employs the same touchstones of rationality, namely mathematics and physical science, and because he follows the same philosophical method, the interpretation of discourse with the apparatus of modern formal logic. Quine is not exactly a postivist then, but he is a continuator of the positivist mode of analytic philosophy. He is the most productive and distinguished of those who have continued in that mode and resisted the informality and desultoriness of linguistic philosophy à la Austin and the later Wittgenstein.

Quine’s rejection of phenomenalism rests partly on the irreducibility of ordinary statements of objective fact to immediate sensory terms and partly on the inadequacies of such language as we have for the reporting of private, sensory events. There is, in his view, no unique pattern of immediate experience associated with each empirical statement as its certifier. Language does not mirror experienceable fact but stands in a much more complex relation to it. The relation of a belief to the facts that confirm or undermine it is always mediated through other beliefs. So when the facts are contrary to expectation it is not the belief in the forefront of our attention that has to be dropped. The surprise can be accommodated just as well by dropping one of the other beliefs with which the first belief is connected. In an odd situation I do not have to give up my belief that this is a chicken; I can drop the conviction that no chicken has three legs instead.

QUINE’S POSITION HERE is not peculiar to him, though his way of presenting it is. Others, for example Popper, have taken the fallibilist line that all empirical discourse stands to extra-linguistic reality in the loose-fitting kind of relation that for positivism was the feature distinguishing statements of theory from statements of observation. What is special to Quine is the very general conception of the interconnectedness of our beliefs that he derives from it. In his view the entire body of our beliefs is up for judgment each time an observation is made, no element of it has a privileged immunity from revision. Pragmatic considerations of simplicity and convenience must decide which of the defendants is to be the victim sacrificed to accommodate an unexpected experience. According to positivism the system of our beliefs is bounded at either end, so to speak, by two kinds of incorrigibly certain truths: at one end by reports of immediate experience, at the other by the necessary propositions of logic and mathematics. These are indubitable and all other beliefs must be manipulated into consistency with them. Quine denies any difference of principle as far as corrigibility is concerned between these pampered darlings of epistemology and other beliefs.

This adventurous kind of holism had been applied before in a partial way, to theories but not to statements of observation by the French philosopher of science, Duhem. Quine accepts his doctrine about theories but rejects the theory-observation distinction by which Duhem limited its scope. Taking a step further Quine includes in the total range of revisable belief the principles of inter-connection themselves, the truths of logic and mathematics. This is one facet of his most notorious deviation from orthodoxy, his anti-conventionalist denial of any basic difference of kind or principle between that which is analytically true in virtue of meaning and that which is synthetically true in virtue of experience. The positivist tradition saw a sharp discontinuity between (1) descriptive statements about the world and (2) linguistic statements expressing logical relations between descriptive statements. The relations expressed by statements of type (2) were taken to be identities of meanings and to have been established by conventions of language rather than to reflect the objective nature of things. Quine sees only a difference of degree. For him what is called analytic is only more general and less readily revised than what is called synthetic. He contends that the arguments by which the distinction has been defended all turn on a set of words—“analytic,” “contradictory,” “necessary,” “synonymous”—each of which requires one of the others for its explanation and none of which is clear in itself. Like the terms of theology these terms fit together logically well enough; the hard question is how any of them is to be related to the actual world. Even those least convinced by his arguments must admit that they are deployed with admirable resource and ingenuity. Any doctrine as far-reaching as the dualism of analytic and empirical discourse draws its strength from a wide variety of considerations. Quine’s polemic against it has something worth examination to say about all of them. The Ways of Paradox contains his first assault on conventionalism, which came out in 1935, as well as two recent variations on the theme.

So far I have mentioned two distinction-eroding doctrines of Quine’s, those in which continuities replace hard-and-fast frontiers between observation and theory in the field of empirical discourse and between the empirical and the analytic within the field of methodically establishable statements in general. Quine’s third main heresy is his denial of a distinction between science in the most inclusive sense, and metaphysics; or, at any rate, between science and a rather temperately conceived ontology. He shares more than a fondness for maps with Hobbes. Both are logician-philosophers with a special respect for mathematics and physics and with powerfully idiosyncratic prose styles. It is clear that Quine has a strong leaning towards Hobbes’s minimal ontology, which says that nothing exists but material bodies. In an essay “On Mental Entities” in The Ways of Paradox he propounds a very general version of Hobbes’s materialist denial of an ultimate distinction between the mental and the physical. He identifies the mental state of a subject with the physical condition of the organism in question at the time, leaving it to neurophysiology to discover the precise details of the relevant physical states. He is not worried by the possibility that two organisms could truly report different states of mind, although there was no physical difference but position in space between them. If such a possibility seemed to be realized, he would either deny that both reports are true or put forward the irrefutable hypothesis that there is a physical difference between the two that has not been detected.

THERE IS EVIDENCE that Quine would like to be a nominalist with Hobbes too and to deny the independent existence of abstract as well as of mental entities, leaving concrete physical things as the only ultimate constituents of the world. What frustrates him here is his conviction that mathematics is true (or if, like everything else, it is in principle revisable, as true as anything is), that classes are abstract entities, and that mathematics makes irreducible reference to classes. Carnap, the main repository of the positivist tradition, has claimed that whereas “there are molecules” and “there are black swans” are assertions of empirical fact, such general statements about whole categories of things as “there are numbers” or “there are classes” are either truistic consequences of the adoption of a language in which the names of numbers and classes occur, or else disguised ways of proposing that such a language be adopted. True to form, Quine replies by arguing that such reasons as are given for interpreting “there are numbers” as a linguistic proposal show “there are molecules” to be one too.

Quine’s three main philosophical innovations add up to a coherent theory of knowledge of great boldness and originality which he has for the most part constructed single-handed. He has arrived, by an entirely new route, at a position which has some general affinities of outline with the absolute idealism of F. H. Bradley, another philosophical stylist given to disconcerting negations. But the spirit of the two philosophies could hardly be more different. Quine’s aim is to show the essential continuity of all forms of rational discourse. Taking science as ordinarily conceived to be the central form of rationality, he seeks to connect it with direct observation of the world on the one hand and with logic, mathematics, and ontology on the other. Bradley of course had no such aim. He saw all discursive thought as inadequate to the apprehension of reality, which could be grasped only by a kind of mystical immersion in its undivided flow. Science, in his view, was not the paradigm of rationality but a crude practical instrument.

The final upshot of Quine’s philosophy is an assertion of the essential unity of science and, even more, of the ultimate identity of science with all rational thought. He emphasizes its unity in opposition to a long tradition of dualism, distinguishing pure mathematics as the achievement of unaided reason from natural knowledge derived from the senses, that stretches back, through Hume and Leibniz, to Plato’s separation of knowledge and opinion. The other point could be expressed in a quasi-Paterian formula: All thought aspires to the condition of science. To Quine the devotion of linguistic philosophers to ordinary language and common sense has a Luddite flavor. Science, with its inextricably mathematical and observational aspects, as the most precise and most firmly established body of human beliefs, is the criterion by which all our convictions must be judged.

Quine’s theory of knowledge has had a good deal of piecemeal discussion, but it needs and deserves a fuller and more systematic exposition than its creator has yet been able to give it. In this respect Word and Object was something of a disappointment since Quine’s views about knowledge took a fairly recessive place in it. In Britain at any rate, some of the steam appears to have gone out of the anti-formalist movement. Wittgenstein and Austin are not so reverently regarded now as they were ten years ago, and the philosophical atmosphere is more hospitable than it has been for a long time to Quine’s style of philosophising. In the United States the most effective and penetrating critic of anti-formalist linguistic philosophy is Professor Hilary Putnam, who, if not a disciple, is sympathetic to many of Quine’s ideas. Most universities teach formal logic to their philosophy students as they have done since the universities of Paris and Oxford came into being in the twelfth century. Quine’s work proves that the subject is still of the most direct relevance to the epistemological core of philosophy.

This Issue

January 12, 1967