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The number of unknown paradoxes

Published online by Cambridge University Press:  17 April 2020

Roy Sorensen  and
Mark Sainsbury
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Extract

‘A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science’.

How many paradoxes are there? By 1920, Bertrand Russell's star student had concluded that there are few or zero paradoxes in philosophy. Most philosophical propositions ‘are not false but nonsensical’.

Type
Research Article
Information
Philosophy , Volume 95 , Issue 2 , April 2020 , pp. 155 - 159
Copyright
Copyright © The Royal Institute of Philosophy 2020

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References

1 Russell, Bertrand ‘On denoting’ Mind 14 (1905) 479–93CrossRefGoogle Scholar.

2 Wittgenstein, LudwigTractatus Logico-Philosophicus (London: Trench, Trubner & Co., Ltd., 1922), 4.003Google Scholar. Almost all contemporary definers of ‘paradox’ agree that a paradox is composed of meaningful statements. An outlier is Roy Sorensen who ‘allows for the possibility of meaningless paradoxes’; Sorensen, Roy, A Brief History of the Paradox (Oxford: Oxford University Press, 2003)Google Scholar.

3 The number of paradoxes discussed in general books on paradoxes varies. For example, Clark, MichaelParadoxes from A to Z, 3rd ed. (London: Routledge, 2012) discusses 93CrossRefGoogle Scholar; Rescher, NicholasParadoxes: Their Roots, Range, and Resolution (Chicago: Open Court, 2001) discusses 146Google Scholar; Sainsbury, MarkParadoxes, 3rd ed. (Cambridge: Cambridge University Press, 2009) discusses 34CrossRefGoogle Scholar; Roy Sorensen, op. cit. note 1, discusses 29. Of course, these authors do not claim that the paradoxes they discuss are all there are, and they make no claims for what the future holds.

4 This proposal is similar to, though distinct from, Rescher's, op. cit. note 1, 6. ‘Minimal’ is to prevent inflating the count of paradoxes by adding irrelevant sentences to a paradoxical set.

5 The graveyard includes paradoxes that now count as scientific corpses such as the Copernican paradox that the earth orbits the sun. Russell thought progress in ‘philosophy’ is disguised by the requirement that philosophy be speculative rather than settled. We leave the body count to historians.

6 Peirce, C.S., The Collected Papers of Charles Sanders Peirce, ed. Hartshorne, Charles and Weiss, Paul, 8 vols. (Harvard University Press: Cambridge MA, 1935) vol VI: 122Google Scholar.

7 Eve, Arthur Stewart, Rutherford: Being the life and letters of the Rt. Hon. Lord Rutherford, O. M. (Cambridge: Cambridge University Press, 1939)Google Scholar.

8 Carnap, Rudolf, Scheinprobleme in der Philosophie (Berlin: Weltkreis-Verlag, 1928)Google Scholar; translated as Pseudoproblems in Philosophy by George, R. A. (Berkeley and Los Angeles: University of California Press, 1967)Google Scholar.

9 Carnap, Rudolf, Logical Foundations of Probability (Chicago: University of Chicago Press, 1950)Google Scholar.

10 Efron, Bradley and Thisted, Ronald ‘Estimating the Number of Unseen Species: How Many Words Did Shakespeare Know?’ Biometrika 63:3 (1976) 435–447Google Scholar.

11 Roy Sorensen, op. cit. note 1, xi.