Philosophy Paradoxes
by
Michael Clark
  • LAST REVIEWED: 08 October 2015
  • LAST MODIFIED: 24 July 2013
  • DOI: 10.1093/obo/9780195396577-0201

Introduction

Many paradoxes are best construed as inferences from plausible premises to an implausible conclusion. The sorites paradox, or paradox of the heap, is like this: A pile of 10,000 grains is a heap. For any number n greater than 1, if a pile of n grains is a heap then so is a pile of n – 1 grains. So one grain is a heap. Even if all paradoxes can be forced into this mold, they are not naturally presented in this way. Semantic paradoxes like the liar and set-theoretic paradoxes like Russell’s typically yield contradictions. In some paradoxes, we are faced with a dilemma. Which of two ships, for example, is identical with Theseus’s original ship, the ship with its planks replaced or the ship reconstituted from the old planks? In other paradoxes, there are parallel arguments for conflicting verdicts. But a common theme is the conflict with our ordinary belief.

The Nature of Paradoxes

Quine 1966 is a classic. Clark 2012 on paradox is a general discussion. Sainsbury 2009 characterizes paradox as “an apparently unacceptable conclusion derived by apparently acceptable reasoning from apparently acceptable premises,” and recognizes degrees, some paradoxes being deeper than others. Passeau 2013 offers a precise treatment of such degrees. Both Lycan 2010 and Rescher 2001 treat paradoxes as, in Lycan’s words, “inconsistent sets of propositions, each of which is very plausible.” Whereas Sainsbury 2009 picks out certain propositions as premises, the latter treat Sainsbury’s premises and conclusion on a par. Logically, the accounts are equivalent, but Sainsbury’s account is often more natural (say for the sorites). Sorensen 1988 aims to show how many paradoxes, like the unexpected examination, exhibit a “master cognitive flaw.” Sorensen 2003 contains a technical criticism of Sainsbury 2009.

  • Clark, Michael. Paradoxes from A to Z. 3d ed. London: Routledge, 2012.

    E-mail Citation »

    The entry on paradox is a general discussion.

  • Lycan, William. “What, Exactly, Is a Paradox?” Analysis 70 (2010): 615–622.

    DOI: 10.1093/analys/anq069E-mail Citation »

    An alternative account to Sainsbury 2009, and similar to Rescher 2001. Available online for purchase or by subscription.

  • Passeau, Alexander. “An Exact Measure of Paradox.” Analysis 73.1 (2013): 17–26.

    DOI: 10.1093/analys/ans142E-mail Citation »

    The paper is a precise treatment of degrees of paradoxicality, given in formal symbolic terms, with a sensitive discussion. Available online for purchase or by subscription.

  • Quine, W. V. “The Ways of Paradox.” In The Ways of Paradox and Other Essays. By W. V. Quine, 3–20. New York: Random House, 1966.

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    This is a classic paper, which distinguishes “veridical” from “falsidical” paradoxes.

  • Rescher, Nicholas. Paradoxes: Their Roots, Range, and Resolution. Chicago: Open Court, 2001.

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    This gives an alternative account to Sainsbury 2009, and is similar to Lycan 2010. See especially chapter 1.

  • Sainsbury, R. M. “Introduction.” In Paradoxes. 3d ed. By R. M. Sainsbury, 1–2. Cambridge, UK: Cambridge University Press, 2009.

    DOI: 10.1017/CBO9780511812576.002E-mail Citation »

    This is an influential account. It recognizes degrees, so that some paradoxes are deeper than others.

  • Sorensen, Roy. Blindspots. Oxford: Clarendon, 1988.

    E-mail Citation »

    The book illustrates the “master cognitive flaw” in such examples as the unexpected examination and similar paradoxes of the author’s own invention.

  • Sorensen, Roy. A Brief History of the Paradox: Philosophy and the Labyrinths of the Mind. Oxford: Oxford University Press, 2003.

    E-mail Citation »

    These few pages criticize Sainsbury 2009. The criticism, though sound, does not show that Sainsbury is fundamentally wrong. See pp. 104–107.

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