Journal of the History of Philosophy

An ImprovedPons Asinorum? C. L. HAMBLIN THE PONS ASINORUMor "bridge of asses" is a diagram embodying Aristotle's rules of argument-finding in Prior Analytics 43a20-45b12. These rules were elaborated by Alexander of Aphrodisias, xwho speaks of a "diagram" and may reasonably be credited with having invented it3 The diagram itself is given by John Philoponus. a It is discussed by Averroes.4 In the thirteenth century Albert the Greats gave a diagram labelled with the Latin equivalent of Aristotle's letters, and these later gave rise to the code-names ]ecana, cageti, and so on for syllogistic moods. The result was a theory of the syllogism paralleling, and in some respects simpler than, the better-known theory embodied in the Barbara Celarent verse. It is not much discussed by major logicians in the thirteenth and fourteenth centuries, but Bochefiski finds it in Thomas Bdeot'se commentary on the work of George of Brussels. In the fifteenth century it appears in John Dorp's commentary on Buridan, 7 and in Peter Tartaret, a who is the first to use the name ports asinorum and gives an elaborately drawn diagram with an allegory about an ass (= logical beginner?) crossing one of a number of bridges between a major and a minor term? By the time of Rabelaisx~the name has become proverbial: it is also sometimes applied to the fifth proposition of the first book of Euclid, concerning the equality of the angles at the base of an isosceles triangle, which is the first difficult theorem in that work and has a figure slightly reminiscent of the logical diagram. Bayle11 speculates that the name ports asinorum, French pont aux dries, arises from a pun between dne and an, x Alexander of Aphrodisias, In Aristotelis Analyticorum Priorum Librum I Commentarium, ed. M. Wallies (Berlin, 1883). Commentaria in Aristotelem Graeca, vol. 2, part 1, 290-322. 2 William and Martha Kneale, The Development o] Logic (Oxford: Clarendon Press, 1962), p. 186. a John Philoponus, In Aristotelis Analytica Priora Commentaria. ed. M. Wallies (Berlin, 1905). Commentaria in Aristotelem Graeca, vol. 13 part 2, 270-300. See p. 274. I. M. Bochenski, A History o/Formal Logic, ed. and trans. I. Thomas (Notre Dame, Ind.: University of Notre Dame Press, 1961), 24.35. Hereafter referred to as B. 4 Averroes, Aristotelis opera cure Averrois commentariis (Frankfurt/Main: Minerva, 1962 [Venice, 1562-1574]). C. Prantl, Geschichte der Logik im Abendlande (Leipzig, 1927 [18551870 ]), 2, 393. Hereafter referred to as P. 5 Albert the Great, Opera quae hactenus haberi potuerunt (Lyons, 1651), vol. 11: Liber I priorum Analyticorum, tract VI, chap. 3. Also B, 32.36. Thomas Bricot, Cursus optimarum quaestionum super philosophiam Aristotelis . . . (Freiburg i. B.? 14907). P, 4, 200. B, 32.38. T Jean Buridan, Perutile compendium totiits logice . . . cure preclarissima solertissimi viri Joannis Dorp expositione (Frankfurt/Main: Minerva, 1965 [Venice: P. de Quarengis, 1499]). s Peter Tarteret, Commentarii in Isagogas Porphyrii et libros logicorum Aristotelis... (Basel: Johann Froben, 1517). 9 See B. 32.38. lo Francois Rabelais, Gargantua and Pantagruel, 11, oh. 28. 11 Pierre Bayle, Dictionary, Historical and Critical, Des Maizeaux trans., 2nd ed. (London, 1735), Article "Buridaa." [131] 132 HISTORY OF PHILOSOPHY "whether," and refers to the choice between alternative middle terms; he also proposes a link with the fable of Buridan's ass, which could not choose between equally distant heaps of hay. Others1-"have connected the doctrine of the pans with Buridan, but the section De arte inveniendi medium at the end of tract 5 in printed editions of Buridan's Compendium appears to be the work of Dorp. (Little, actually, is known of Dorp. FatalTM quotes the explicit of a manuscript of his commentary with the date 1426; and his name is listed among those of masters expelled from the University of Paris for nominalism by order of Louis XI in 1474.14 But with so great an interval one suspects a mistake. In any case Dorp lived a century later than Buridan.) The standard diagram is shown in figure 1: Let us suppose we are interested in establishing, by means of a syllogistic argument, a conclusion connecting two given terms as subject and predicate, and let us...