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Contra Buridanum

Published online by Cambridge University Press:  01 January 2020

Allen Hazen
Allen Hazen*
Affiliation:
University of Melbourne, Parkville, Victoria, Australia3052
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Extract

The French philosopher Jean Buridan's work on the logical paradoxes is currently attracting more attention than it has for several centuries. In part this is due to a general resurgence of interest in the paradoxes, but the immediate occasion is the recent publication of G. E. Hughes's edition, translation, and commentary on the chapter of Buridan's Sophismata most immediately concerned with the paradoxes. (This despite the fact that an English version of the whole of the Sophismata cheaper than even the paper back edition of Hughes's has been available for some years, as has an excellent account of Buridan's theory by A. N. Prior.) It is worth noting, therefore, that Buridan's theory fails, and in a way that makes it seem unlikely that it can be developed into a serious rival of more modern theories.

Type
Research Article
Information
Canadian Journal of Philosophy , Volume 17 , Issue 4 , December 1987 , pp. 875 - 880
Copyright
Copyright © The Authors 1987

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References

1 Hughes, G.E. John Buridan on Self-Refernce: Chapter eight of Buridan's Sophismata, with a translation, an introduction, and a philosophical commentary (Cambridge: Cambridge University Press 1982)Google Scholar. (Paperback edition does not contain Latin text.)

2 Scott, T.K. John Buridan: Sophisms on Meaning and Truth (New York: AppletonCentury- Crofts 1966)Google Scholar. (Hughes says his translation differs from Scott's on some points; Scott's, however, seems quite useable.)

3 Findlay, J.N. ed., Studies in Philosophy (London: Oxford University Press 1966) 241–59Google Scholar

4 Tarski, in a footnote in the Wahrheitsbegriff. makes a bow to nominalism, suggesting that his syntactic axioms (which imply the existence of infinitely many formulas) may have a nominalistic interpretation if we are willing to count formula-shaped regions of space as formulas whether or not they are linked in (a suggestion taken up by Goodman and Quine a decade later, and already implicitly rejected a decade earlier by Hilbert because of its presuppositions about physical space).

5 I have known about this counterexample to Buridan's analysis since I was a student, in the late 1960s. I would not be surprised to learn that it was originally advanced by one of Buridan's contemporaries.

6 Church's ‘Comparison of Russell's Resolution of the Semantical Antinomies with that of Tarski’ (Journal of Symbolic Logic 41 [1976] 747-60; reprinted in Martin, R.L. ed., Recent Essays on Truth and tile Liar Paradox [Oxford: Clarendon Press 1984] 289–306)Google Scholar gives an elegant introduction to the Russellian approach. Russell's own best statement is his widely reprinted ‘Mathematical Logic as Based on the Theory of Types,’ American Journal of Mathematics 30 (1908) 222-62.

7 Most twentieth-century approaches can be thought of either as following Russell in distinguishing types (or levels of language, or some related notion), or as proposing a type-free theory based on a nonclassical logic. In the concluding section of my article ‘Predicative Logics’ (in Guenthner, F. and Gabbay, D. eds., Handbook of Philosophical Logic, vol. I [Dordrecht: Reidel 1983)331–407)Google Scholar, I suggested that some of Russell's own remarks could be seen as foreshadowing a theory of the latter sort.

8 Burge, T. ‘Semantical Paradox,’ Journal of Philosophy 76 (1979) 169–98CrossRefGoogle Scholar; reprinted in Martin, 83-117

9 Perhaps the most insightful recent essay on the topic is Charles Parsons's ‘The Liar Paradox,’ Journal of Philosophical Logic 3 (1974) 381-412; reprinted in Martin, 7-45, and in Parsons's own Mathematics in Philosophy (Ithaca: Cornell University Press 1983), 221-67. The ‘Postscript’ written for its reprinting in Mathematics in Philosophy contains, inter alia, a clearer exposition of Burge's view than Burge's own paper.