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14 results

  • 10 - Quine and Logic

  • Edited by Roger F. Gibson, Jr, Washington University, St Louis
  • Book:
    The Cambridge Companion to Quine
    Published online:
    28 May 2006
    Print publication:
    29 March 2004, pp 270-286

  • Summary

    No one since Russell has contributed so much to both philosophy and logic as Quine. No major philosopher has given anything like so much to logic, nor has any important figure in logic borne Quine’s stature as a philosopher. His work in the two fields, though distinguishable, has been very much related. He has been a pioneer philosopher of mathematical logic, while he has integrated his view of logic into the very core of his epistemology. I will discuss how logic fits with the rest of Quine’s philosophy and what motivated his choices as an expositor and teacher of logic. I will examine in particular aspects of his text Methods of Logic, now in its fourth edition.

    Logic plays a central role in Quine’s philosophy. Quine is preeminently an epistemologist. His epistemology is wedded in interlocking ways to empiricism, naturalism, and physicalism; together they lead him to see science not only as the arbiter of what is to be believed about the world but also as providing the context in which we must make our philosophy. Rather than pursue some first philosophy, we look to science for our bearings: “[I[t is within science … that reality is to be identified and described” (TPT 21). And “the basic structure of the language of science … is the predicate calculus: the logic of quantification and truth-functions” (FM 160).

  • In Memoriam: Nelson Goodman 1906–1998

  • Joseph S. Ullian
  • Journal:
    Bulletin of Symbolic Logic / Volume 5 / Issue 3 / September 1999
    Published online by Cambridge University Press:
    15 January 2014, pp. 392-394
    Print publication:
    September 1999
    • Article
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  • Is Any Set Theory True?

  • Joseph S. Ullian
  • Journal:
    Philosophy of Science / Volume 36 / Issue 3 / September 1969
    Published online by Cambridge University Press:
    14 March 2022, pp. 271-279
    Print publication:
    September 1969

  • This paper draws its title from the recent symposium of which it was part; it attempts to respond to the question raised by that title, taking current work in set theory into account. To this end the paper contrasts set theory with number theory, examines a severe brand of set-theoretic realism that is suggested by a passage from Gödel, and sketches a first-order way of looking at the results about competing extensions of Zermelo-Fraenkel set theory. A formalistic sentiment may be detectable in some portions of the paper.

  • Peirce, Gambling, and Insurance

  • Joseph S. Ullian
  • Journal:
    Philosophy of Science / Volume 29 / Issue 1 / January 1962
    Published online by Cambridge University Press:
    14 March 2022, pp. 79-80
    Print publication:
    January 1962

  • Peirce writes “It is an indubitable result of the theory of probabilities that every gambler, if he continues long enough, must ultimately be ruined … if he plays long enough he will be sure some time to have such a run against him as to exhaust his entire fortune. … The same thing is true of an insurance company. Let the directors take the utmost pains … according to the doctrine of chances, the time must come, at last, when their losses will bring them to a stop.” This note shows that under the most plausible interpretation of the quoted passage Peirce is committed to a mathematical untruth.