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Burleigh's Paradox

Published online by Cambridge University Press:  03 September 2007

Dale Jacquette
Dale Jacquette
Affiliation:
The Pennsylvania State University, Netherlands Institute for Advanced Study (NIAS)
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Abstract

Walter Burleigh in his c. 1323 De Puritate Artis Logicae Tractatus Longior considers a counterexample to hypothetical syllogism. The paradox implied by Burleigh's inference has come to be known as the problem of the ass (asinum), or, more prosaically, ‘You are an ass’. The argument states: ‘If I call you an ass, then I call you an animal; if I call you an animal, then I speak truthfully; therefore, if I call you an ass, then I speak truthfully’. Burleigh's paradox is reconstructed and formalized for purposes of critical analysis, in which the putative counterexample is ultimately shown to involve a fallacy of equivocation.

Type
Research Article
Information
Philosophy , Volume 82 , Issue 3 , July 2007 , pp. 437 - 448
Copyright
Copyright © The Royal Institute of Philosophy 2007

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References

1 Burleigh, Walter, De Puritate Artis Logicae Tractatus Longior, with a Revised Edition of the Tractatus Brevior. Edited by Boehner, Philotheus (St. Bonaventure, NY: The Franciscan Institute, 1955), 203Google Scholar.

2 Burley, Walter, On the Purity of the Art of Logic, The Shorter and the Longer Treatises, translated by Spade, Paul Vincent (New Haven: Yale University Press, 2001), 7Google Scholar.

3 See Nuchelmans, Gabriel, ‘Walter Burleigh on the Conclusion that You Are an Ass’, Vivarium, 32, 1994, 90–101CrossRefGoogle Scholar. A useful source on Burleigh's philosophy of logic, life and works, is the special issue of Vivarium, 37, 1999, 1–100, Studies on Walter Burley 1989–1997, edited by Gerhard Krieger. Burleigh's logic of consequentiae is translated into modern Polish notation and evaluated by Prior, A.N., ‘On Some Consequentiae in Walter Burleigh’, The New Scholasticism: Journal of the American Catholic Philosophical Association, 27, 1953, 435–446CrossRefGoogle Scholar. See Boh, Ivan, ‘Walter Burleigh's Hypothetical Syllogistic’, Notre Dame Journal of Formal Logic, 4, 1963, 241–269CrossRefGoogle Scholar. Compare Boh, in his prior, ‘A Study in Burleigh: Tractatus de Regulis Generalibus Consequentiarum’, Notre Dame Journal of Formal Logic, 3, 1962, 83–101. Boh in both sources follows Prior's use of Polish notation in characterizing Burleigh's inference schemata.

4 It might be objected that Burleigh's argument is unsound because the assumption in the original reconstruction, that ‘If a calls b a swine, then a calls b an animal’, is false. The objection could be upheld on the grounds that calling something F is narrowly intensional, so that it does not follow from the fact that someone calls something F and that being F implies being G that therefore the person calls the thing G. The point is well-taken, as far as it goes, depending on what is supposed to be meant by ‘calling’ something this or that. I have relied on the standard exposition of Burleigh's paradox, which might be rephrased on a de re interpretation of ‘predicates’ in order to avoid the objection while preserving the same conclusions, as ‘If a (de re) predicates of b the property of being a swine, then a (de re) predicates of b the property of being an animal’ (similarly for the second assumption and conclusion).

5 Alternatively, an equivocation can be identified in the two uses of the phrase ‘I speak truly’. It might be said that the proper expansion of this phrase in the argument's second assumption and conclusion refer to different things about which the truth is spoken. In the second assumption, the phrase refers to speaking the truth in saying that the person is an animal, while in the conclusion it refers instead to speaking the truth in saying that the person is a swine (ass). Properly expanded, these clauses should then read, respectively: ‘… I speak truly in saying that you are an animal’ and ‘I speak truly in saying that you are a swine (ass)’. Here the equivocation is explicit since only the first expansion is true, the second is false, and the inference from the assumptions to the conclusion thereby rendered deductively invalid.

6 I am grateful to the Netherlands Institute for Advanced Study in the Humanities and Social Sciences (NIAS), Royal Netherlands Academy of Arts and Sciences (KNAW), for support of this and related topics in philosophical logic and philosophy of mathematics during my visit as Resident Research Fellow in 2005–2006. A version of the central argument of this paper was presented under the title. Deductional and the Informal Fallacies at the Sixth International Conference on Argumentation, International Society for the Study of Argumentation (ISSA). University of Amsterdam, Amsterdam, The Netherlands, June 27–30, 2006, and under the present title at the Society for Exact Philosophy, University of British Columbia, Vancouver, British Columbia, Canada, May 17, 2007.