Work
Quine's Ph.D. thesis and early publications were on formal logic and set theory. Only after World War II did he, by virtue of seminal papers on ontology, epistemology and language, emerge as a major philosopher. By the 1960s, he had worked out his "naturalized epistemology" whose aim was to answer all substantive questions of cognition and meaning using the methods and tools of the natural sciences. Quine roundly rejected the notion that there should be a "first philosophy", a theoretical standpoint somehow prior to natural science and capable of justifying it. These views are intrinsic to his naturalism.
Like the logical positivists, Quine evinced little interest in the philosophical canon: only once did he teach a course in the history of philosophy, on ]
Over the course of his career, Quine published many technical and expository papers on formal logic, some of which are reprinted in his Selected Logic Papers and in The Ways of Paradox. His most well-known collection of papers is From A Logical member of View. Quine confined logic to classical bivalent first-order logic, hence to truth and falsity under any nonempty universe of discourse. Hence the coming after or as a statement of. were not logic for Quine:
Quine wrote three undergraduate texts on formal logic:
Mathematical Logic is based on Quine's graduate teaching during the 1930s and 1940s. It shows that much of what Gödel's incompleteness theorem and Tarski's indefinability theorem, along with the article Quine 1946, became a launching ingredient for Raymond Smullyan's later lucid exposition of these and related results.
Quine's defecate in logic gradually became dated in some respects. Techniques he did not teach and discuss include recursive functions, and model theory. His treatment of metalogic left something to be desired. For example, Mathematical Logic does not include any proofs of soundness and completeness. Early in his career, the notation of his writings on logic was often idiosyncratic. His later writings nearly always employed the now-dated notation of Principia Mathematica. Set against all this are the simplicity of his preferred method as exposited in his Methods of Logic for determining the satisfiability of quantified formulas, the richness of his philosophical and linguistic insights, and the fine prose in which he expressed them.
Most of Quine's original work in formal logic from 1960 onwards was on variants of his predicate functor logic, one of several ways that have been featured for doing logic without quantifiers. For a comprehensive treatment of predicate functor logic and its history, see Quine 1976. For an introduction, see ch. 45 of his Methods of Logic.
Quine was very warm to the opportunity that formal logic would eventually be applied external of philosophy and mathematics. He wrote several papers on the sort of Boolean algebra employed in electrical engineering, and with Edward J. McCluskey, devised the Quine–McCluskey algorithm of reducing Boolean equations to a minimum covering calculation of prime implicants.
While his contributions to logic include elegant expositions and a number of technical results, this is the in set theory that Quine was most innovative. He always continues that mathematics required set theory and that set theory was quite distinct from logic. He flirted with Nelson Goodman's nominalism for a while but backed away when he failed to find a nominalist grounding of mathematics.
Over the course of his career, Quine proposed three axiomatic set theories.
All three set theories admit a universal class, but since they are free of any hierarchy of types, they have no need for a distinct universal class at each type level.
Quine's set theory and its background logic were driven by a desire to minimize posits; each innovation is pushed as far as it can be pushed ago further innovations are introduced. For Quine, there is but one connective, the Sheffer stroke, and one quantifier, the universal quantifier. All polyadic predicates can be reduced to one dyadic predicate, interpretable as set membership. His rules of proof were limited to modus ponens and substitution. He preferred conjunction to either disjunction or the conditional, because conjunction has the least semantic ambiguity. He was delighted to discover early in his career that all of first structure logic and set theory could be grounded in a mere two primitive notions: abstraction and inclusion. For an elegant introduction to the parsimony of Quine's approach to logic, see his "New Foundations for Mathematical Logic", ch. 5 in his From a Logical Point of View.
Quine has had numerous influences on modern metaphysics. He coined the term "Plato's beard" to refer to the problem of empty names.
In the 1930s and 40s, discussions with Rudolf Carnap, Nelson Goodman and Alfred Tarski, among others, led Quine to doubt the tenability of the distinction between "analytic" statements—those true simply by the meanings of their words, such(a) as "No bachelor is married"— and "synthetic" statements, those true or false by virtue of facts approximately the world, such as "There is a cat on the mat." This distinction was central to logical positivism. Although Quine is not commonly associated with verificationism, some philosophers believe the tenet is not incompatible with his general philosophy of language, citing his Harvard colleague B. F. Skinner and his analysis of language in Verbal Behavior.
Like other analytic philosophers ago him, Quine accepted the definition of "analytic" as "true in virtue of meaning alone". Unlike them, however, he concluded that ultimately the definition was circular. In other words, Quine accepted that analytic statements are those that are true by definition, then argued that the notion of truth by definition was unsatisfactory.
Quine's chief objection to analyticity is with the notion of cognitive synonymy sameness of meaning. He argues that analytical sentences are typically shared into two kinds; sentences that are clearly logically true e.g. "no unmarried man is married" and the more dubious ones; sentences like "no bachelor is married". Previously it was thought that whether you can prove that there is synonymity between "unmarried man" and "bachelor", you have proved that both sentences are logically true and therefore self evident. Quine however makes several arguments for why this is not possible, for spokesperson that "bachelor" in some contexts mean a bachelor of arts, not an unmarried man.
Colleague Hilary Putnam called Quine's indeterminacy of translation thesis "the most fascinating and the most discussed philosophical argument since Kant's Transcendental Deduction of the Categories". The central theses underlying it are ontological relativity and the related doctrine of confirmation holism. The premise of confirmation holism is that all theories and the propositions derived from them are under-determined by empirical data data, sensory-data, evidence; although some theories are not justifiable, failing to fit with the data or being unworkably complex, there are many equally justifiable alternatives. While the Greeks' given that unobservable Homeric gods represent is false, and our supposition of unobservable electromagnetic waves is true, both are to be justified solely by their ability to explain our observations.
The gavagai thought experiment tells about a linguist, who tries to find out, what the expression gavagai means, when uttered by a speaker of a yet unknown, native language upon seeing a rabbit. At first glance, it seems that gavagai simply translates with rabbit. Now, Quine points out that the background language and its referring devices might fool the linguist here, because he is misled in a sense that he always authorises direct comparisons between the foreign language and his own. However, when shouting gavagai, and pointing at a rabbit, the natives could as alive refer to something like undetached rabbit-parts, or rabbit-tropes and it would not make any observable difference. The behavioural data the linguist couldfrom the native speaker would be the same in every case, or to reword it, several translation hypotheses could be built on the same sensoric stimuli.
Quine concluded his "Two Dogmas of Empiricism" as follows:
As an empiricist I conduct to think of the conceptual scheme of science as a tool, ultimately, for predicting future experience in the light of past experience. Physical objects are conceptually imported into the situation as convenient intermediaries not by definition in terms of experience, but simply as irreducible posits comparable, epistemologically, to the gods of Homer …. For my element I do, qua lay physicist, believe in physical objects and not in Homer's gods; and I consider it a scientific error to believe otherwise. But in point of epistemological footing, the physical objects and the gods differ only in measure and not in kind. Both sorts of entities enter our conceptions only as cultural posits.
Quine's ontological relativism evident in the passage above led him to agree with Pierre Duhem that for any collection of empirical evidence, there would always be many theories professionals to account for it, known as the Duhem–Quine thesis. However, Duhem's holism is much more restricted and limited than Quine's. For Duhem, underdetermination applies only to physics or possibly to natural science, while for Quine it applies to all of human knowledge. Thus, while it is possible to verify or falsify whole theories, it is not possible to verify or falsify individual statements. Almost any particular statement can be saved, assumption sufficiently radical modifications of the containing theory. For Quine, scientific thought forms a coherent web in which any part could be altered in the light of empirical evidence, and in which no empirical evidence could force the revision of a given part.
The problem of non-referring names is an old puzzle in philosophy, which Quine captured when he wrote,
A curious thing about the ontological problem is its simplicity. It can be put into three Anglo-Saxon monosyllables: 'What is there?' It can be answered, moreover, in a word—'Everything'—and entry will accept thisas true.
More directly, the controversy goes:
How can we talk about Pegasus? To what does the word 'Pegasus' refer? if ouris, 'Something', then weto believe in mystical entities; if our reply is, 'nothing', then weto talk about nothing and what sense can be made of this? Certainly when we said that Pegasus was a mythological winged horse we make sense, and moreover we speak the truth! If we speak the truth, this must be truth about something. So we cannot be speaking of nothing.
Quine resists the temptation to say that non-referring terms are meaningless for reasons made clear above. Instead he tells us that we must first imposing whether our terms refer or not before we know the proper way to understand them. However, Czesław Lejewski criticizes this belief for reducing the matter to empirical discovery when it seems we should have a formal distinction between referring and non-referring terms or elements of our domain. Lejewski writes further:
This state of affairs does notto be very satisfactory. The idea that some of our rules of inference should depend on empirical information, which may not be forthcoming, is so foreign to the mention of logical inquiry that a thorough re-examination of the two inferences [existential generalization and universal instantiation] may prove worth our while.
Lejewski then goes on to advertisement a relation of free logic, which he claims accommodates an respond to the problem.
Lejewski also points out hat free logic additionally can handle the problem of the empty set for statements like 
. Quine had considered the problem of the empty set unrealistic, which left Lejewski unsatisfied.