Willard Van Orman Quine


Willard Van Orman Quine was an American philosopher and logician in the analytic tradition, recognized as "one of the most influential philosophers of the twentieth century". He was the Edgar Pierce Chair of Philosophy at Harvard University from 1956 to 1978.
Quine was a teacher of logic and set theory. He was famous for his position that first-order logic is the only kind worthy of the name, and developed his own system of mathematics and set theory, known as New Foundations. In the philosophy of mathematics, he and his Harvard colleague Hilary Putnam developed the Quine–Putnam indispensability argument, an argument for the reality of mathematical entities. He was the main proponent of the view that philosophy is not conceptual analysis, but continuous with science; it is the abstract branch of the empirical sciences. This led to his famous quip that "philosophy of science is philosophy enough". He led a "systematic attempt to understand science from within the resources of science itself" and developed an influential naturalized epistemology that tried to provide "an improved scientific explanation of how we have developed elaborate scientific theories on the basis of meager sensory input". He also advocated holism in science, known as the Duhem–Quine thesis.
His major writings include the papers "On What There Is", which elucidated Bertrand Russell's theory of descriptions and contains Quine's famous dictum of ontological commitment, "To be is to be the value of a variable", and "Two Dogmas of Empiricism", which attacked the traditional analytic-synthetic distinction and reductionism, undermining the then-popular logical positivism, advocating instead a form of semantic holism and ontological relativity. They also include the books The Web of Belief, which advocates a kind of coherentism, and Word and Object, which further developed these positions and introduced Quine's famous indeterminacy of translation thesis, advocating a behaviorist theory of meaning.

Biography

Quine's parents were Robert Cloyd Quine and Harriet Ellis Van Orman. Quine grew up in Akron, Ohio, where he lived with his parents and older brother Robert Cloyd. His father was a manufacturing entrepreneur and his mother was a schoolteacher and housewife. Quine became an atheist around the age of 9 and remained one for the rest of his life.

Education

Quine received his B.A., summa cum laude, in mathematics from Oberlin College in 1930, and his Ph.D. in philosophy from Harvard University in 1932. His thesis supervisor was Alfred North Whitehead. He was then appointed a Harvard Junior Fellow, which excused him from having to teach for four years. During the academic year 1932–33, he travelled in Europe thanks to a Sheldon Fellowship, meeting Polish logicians and members of the Vienna Circle, as well as the logical positivist A. J. Ayer. It was in Prague that Quine developed a passion for philosophy, thanks to Carnap, whom he called his "true and only maître à penser".

World War II

Quine arranged for Tarski to be invited to the September 1939 Unity of Science Congress in Cambridge, for which the Jewish Tarski sailed on the last ship to leave Danzig before Nazi Germany invaded Poland and triggered World War II. Tarski survived the war and worked another 44 years in the US. During the war, Quine lectured on logic in Brazil, in Portuguese, and served in the United States Navy in a military intelligence role, deciphering messages from German submarines, and reaching the rank of lieutenant commander. Quine could lecture in French, German, Italian, Portuguese, and Spanish as well as his native English.

Personal

He had four children by two marriages. Guitarist Robert Quine was his nephew.
Quine was politically conservative, but the bulk of his writing was in technical areas of philosophy removed from direct political issues. He did, however, write in defense of several conservative positions: for example, he wrote in defense of moral censorship; while, in his autobiography, he made some criticisms of American postwar academics.

Harvard

At Harvard, Quine helped supervise the Harvard graduate theses of, among others, David Lewis, Gilbert Harman, Dagfinn Føllesdal, Hao Wang, Hugues LeBlanc, Henry Hiz and George Myro. For the academic year 1964–1965, Quine was a fellow on the faculty in the Center for Advanced Studies at Wesleyan University. In 1980
Quine received an honorary doctorate from the Faculty of Humanities at Uppsala University, Sweden.
Quine's student Dagfinn Føllesdal noted that Quine suffered from memory loss towards his final years. The deterioration of his short-term memory was so severe that he struggled to continue following arguments. Quine also had considerable difficulty in his project to make the desired revisions to Word and Object. Before dying, Quine noted to Morton White: "I do not remember what my illness is called, Althusser or Alzheimer, but since I cannot remember it, it must be Alzheimer." He died from the illness on Christmas Day in 2000.

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 knowledge 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 majority of analytic philosophers, who were mostly interested in systematic thinking, Quine evinced little interest in the philosophical canon: only once did he teach a course in the history of philosophy, on David Hume, in 1946.

Logic

Over the course of his career, Quine published numerous 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 Point of View. Quine confined logic to classical bivalent first-order logic, hence to truth and falsity under any universe of discourse. Hence the following were not logic for Quine:
  • Higher-order logic and set theory. He referred to higher-order logic as "set theory in disguise";
  • Much of what Principia Mathematica included in logic was not logic for Quine.
  • Formal systems involving intensional notions, especially modality. Quine was especially hostile to modal logic with quantification, a battle he largely lost when Saul Kripke's relational semantics became canonical for modal logics.
Quine wrote three undergraduate texts on formal logic:
  • Elementary Logic. While teaching an introductory course in 1940, Quine discovered that extant texts for philosophy students did not do justice to quantification theory or first-order predicate logic. Quine wrote this book in 6 weeks as an ad hoc solution to his teaching needs.
  • Methods of Logic. The four editions of this book resulted from a more advanced undergraduate course in logic Quine taught from the end of World War II until his 1978 retirement.
  • Philosophy of Logic. A concise and witty undergraduate treatment of a number of Quinian themes, such as the prevalence of use-mention confusions, the dubiousness of quantified modal logic, and the non-logical character of higher-order logic.
Mathematical Logic is based on Quine's graduate teaching during the 1930s and 1940s. It shows that much of what Principia Mathematica took more than 1000 pages to say can be said in 250 pages. The proofs are concise, even cryptic. The last chapter, on Gödel's incompleteness theorem and Tarski's indefinability theorem, along with the article Quine, became a launching point for Raymond Smullyan's later lucid exposition of these and related results.
Quine's work in logic gradually became dated in some respects. Techniques he did not teach and discuss include analytic tableaux, 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 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 proposed for doing logic without quantifiers. For a comprehensive treatment of predicate functor logic and its history, see Quine. For an introduction, see ch. 45 of his Methods of Logic.
Quine was very warm to the possibility that formal logic would eventually be applied outside 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 sum of prime implicants.

Set theory

While his contributions to logic include elegant expositions and a number of technical results, it is in set theory that Quine was most innovative. He always maintained 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.
  • New Foundations, NF, creates and manipulates sets using a single axiom schema for set admissibility, namely an axiom schema of stratified comprehension, whereby all individuals satisfying a stratified formula compose a set. A stratified formula is one that type theory would allow, were the ontology to include types. However, Quine's set theory does not feature types. The metamathematics of NF are curious. NF allows many "large" sets the now-canonical ZFC set theory does not allow, even sets for which the axiom of choice does not hold. Since the axiom of choice holds for all finite sets, the failure of this axiom in NF proves that NF includes infinite sets. The consistency of NF relative to other formal systems adequate for mathematics is an open question, albeit that a number of candidate proofs are current in the NF community suggesting that NF is equiconsistent with Zermelo set theory without Choice. A modification of NF, NFU, due to R. B. Jensen and admitting urelements, turns out to be consistent relative to Peano arithmetic, thus vindicating the intuition behind NF. NF and NFU are the only Quinean set theories with a following. For a derivation of foundational mathematics in NF, see Rosser ;
  • The set theory of Mathematical Logic is NF augmented by the proper classes of von Neumann–Bernays–Gödel set theory, except axiomatized in a much simpler way;
  • The set theory of Set Theory and Its Logic does away with stratification and is almost entirely derived from a single axiom schema. Quine derived the foundations of mathematics once again. This book includes the definitive exposition of Quine's theory of virtual sets and relations, and surveyed axiomatic set theory as it stood circa 1960.
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 before 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 order 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.