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Buridan's Bridge

Published online by Cambridge University Press:  30 January 2009

Dale Jacquette
Dale Jacquette
Affiliation:
The Pennsylvania State University
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Extract

John Buridan's Sophismata contains some of the most interesting puzzles and paradoxes of any of the many surviving medieval informal logic manuals. Buridan's purpose is not only to illustrate and challenge Aristotelian syllogistic with difficulties of interpretation, but also in part to lay logical philosophical foundations for a radically nominalistic ontology in the tradition of William of Ockham.

Type
Articles
Information
Philosophy , Volume 66 , Issue 258 , October 1991 , pp. 455 - 471
Copyright
Copyright © The Royal Institute of Philosophy 1991

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References

1 Buridan, John, Sophismata [Paris, c. 1496]Google Scholar, translated as Sophisms on Meaning and Truth by Scott, Theodore Kermit (New York: Appleton-Cen-tury-Crofts, 1966), p. 219.Google Scholar An alternative translation of Buridan's Chapter VIII, including Sophism 17, is found in Hughes, G. E., John Buridan on Self-Reference: Chapter Eight of Buridan's ‘Sophismata’, Translated with an Introduction, and a Philosophical Commentary (Cambridge University Press, 1982), pp. 74–75; commentary, pp. 157–162. See note 9 below.Google Scholar

2 I have been unable to locate any prior published source for this sophism; nor does Buridan, as he sometimes does in other cases, attribute to it any earlier origin. The paradox as such in Buridan's formulation or recognizable alteration also does not appear in the most popular later compendia of sophisms, such as Saxonia's, Albertus deSophismata [Paris, 1502] (Hildesheim: Georg Olms Verlag, 1975).Google Scholar There are seven surviving manuscripts and five printed editions of Buridan's text. The most complete and authoritative manuscript seems to be the Paris 1496 document. But as Buridan died around 1358, the work could not have been written later than the middle of the 14th Century. A version of the paradox was sufficiently well-known to find its way into Miguel de Cervantes' Don Quixote. The occasion is Sancho Panza's brief tenure as Governor of the ‘island’ of Barataria, when he is called on to settle some difficult problems of jurisprudence (translated by Peter Motteux, revised (New York: Airmont Publishing Company, Inc., 1967), p. 671): ‘My Lord, said he, a large River divides in two Parts one and the same Lordship. I beg your Honour to lend me your Attention, for’ tis a case of great importance, and some Difficulty—Upon this River there is a Bridge; at one End of which there stands a Gallows, and a kind of Court of Justice, where four Judges use to sit, for the Execution of a certain Law made by the Lord of the Land and River, which runs thus. Whoever intends to pass from one End of this Bridge to the other, must first upon his Oath declare whither he goes, and what his Business is. If he swear Truth, he may go on; but if he swear false, he shall be hang'd, and die without Remission upon the Gibbet at the End of the Bridge. After due Promulgation of this Law, many People, notwithstanding its Severity, adventur'd to go over this Bridge, and as it appear'd they swore true, the Judges permitted 'em to pass unmolested. It happen'd one Day that a certain Passenger being sworn, declar'd, that by the Oath he had taken, he was come to die upon that Gallows, and that was all his Business. This put the Judges to a Nonplus; for, said they, if we let this Man pass freely, he is forsworn, and according to the Letter of the Law he ought to die: If we hang him, he has sworn Truth, seeing he swore to die on that Gibbet; and then by the same Law we should let him pass.’ Cervantes is evidently a better novelist than logician, since his restatement of Buridan's bridge, similar as it is in some details, involves no real antinomy. The obvious way out is to hold that the passenger spoke truly in saying it was his business to be hanged on the gallows, but that nevertheless his business, expressed only by a statement of intent, remains unfulfilled or unaccomplished when the judges acting consistently in accord with the conditional law decide he swore truly as to his intended business, and so permit him freely to cross the bridge. Sancho gives an alternative philosophically less satisfactory resolution in this strange but no less edifying History, which it were now tedious to relate.

3 Sophisms on Meaning and Truth, p. 220.Google Scholar

4 Ibid. Buridan refers to Aristotle, De Interpretatione 9, 19a27–29.Google Scholar

5 Sophisms on Meaning and Truth, p. 220.Google Scholar

6 Kant, Immanuel, Critique of Pure Reason (1787), translated by Smith, Norman Kemp (New York: St. Martin's Press, 1965), A548/B576Google Scholar: ‘The action to which the “ought” applies must indeed be possible under natural conditions.’ Kant, , Foundations of the Metaphysics of Morals, translated by Beck, Lewis White, edited by Wolff, Robert Paul (Indianapolis: Bobbs-Merrill Company, Inc., 1969), pp. 76–81.Google Scholar

7 Whitehead, Alfred North and Russell, Bertrand, Principia Mathematica, second [1927] edition (Cambridge University Press, 1963), Vol. I, Part II, Section B, pp. 386–417.Google Scholar The ramified rather than simple theory of types is the version needed to solve informal semantic paradoxes that arise within ordinary language. Whitehead and Russell rejected the theory in the second edition of Principia bcause of difficulties in formulating definitions of real numbers within its limitations. Tarski, Alfred, ‘The Concept of Truth in Formalized Languages’, translated by Woodger, J. H., in Tarski, Logic, Semantics, Metamathematics: Papers from 1923 to 1938, second edition, edited by Corcoran, John (Indianapolis: Hackett Publishing Company, 1983), pp. 152–278Google Scholar; ‘The Establishment of Scientific Semantics’, ibid., pp. 401–408; ‘The Semantic Conception of Truth and the Foundations of Semantics’, Philosophy and Phenomenological Research, 4, 1944, pp. 341–376.Google Scholar

8 See Carnap, Rudolf, ‘The Logicist Foundations of Mathematics’, translated in Philosophy of Mathematics: Selected Readings, edited by Benacerraf, Paul and Putnam, Hilary, second edition (Cambridge University Press, 1983), pp. 41–52.Google Scholar

9 This is Hughes' interpretation of Buridan's solution, which also influences his English translation of this part of the text (John Buridan on Self-Reference, pp. 161–162Google Scholar). In his introduction, p. 31, Hughes explains: ‘What I have tried to do … is simply to assemble a version [of Buridan's text] that seemed to me to make the best philosophical sense at each point.’ For these and other reasons I have preferred to adopt Scott's translation, which, as Hughes admits, attempts to give a more literal rendering of Buridan's medieval Latin. For independent reasons, I am reluctant to lean heavily on Kant's principle, especially in resolving moral dilemmas. See Jacquette, Dale, ‘Moral Dilemmas, Disjunctive Obligations, and Kant's Principle that “Ought” Implies “Can”’, forthcoming in Synthese.Google Scholar

10 Buridanus, Johannes, Sophismata: Critical Edition with an Introduction, edited by Scott, Theodore Kermit (Stuttgart: Frommann-Holzboog, 1977), p. 156.Google Scholar Note that inflected endings do not prohibit reordering the Latin words of the sentence in some ways that preserve a proper first propositional fragment, such as the equivalent form: ‘In aquam tuproiicies me.’

11 This is the burden of Buridan's Sophism 4, Sophisms on Meaning and Truth, pp. 187–188.Google Scholar See Hughes, , John Buridan on Self-Reference, p. 91Google Scholar: ‘… in Sophism 4 Buridan's main contention is that a “part of a proposition” is never itself a proposition, even though it has the structure appropriate to a proposition and could be a proposition if it were not embedded in a larger one.’

12 I have benefited from the comments and criticism of Hector-Neri Castañeda and other participants in the International Symposium on ‘Zeichen und Zeit’, Académie du Midi—Institut für Philosophie‘, L'Abbaye Lagrasse, Lagrasse, France, June 3–9, 1990, where this argument was first presented. I am grateful to the Alexander von Humboldt-Stiftung for supporting this and related projects during my research year as Forschungsstipendiat in the Federal Republic of Germany, 1989–1990.