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INCONSISTENCY AND PARADOX IN MEDIEVAL DISPUTATIONS: A DEVELOPMENT OF SOME HINTS IN OCKHAM The Liar Paradox is well-known, as is the way it calls into doubt some of our most basic semantic assumptions. In this paper, I intend to consider a more modest group of paradoxes, that is, propositions which seem puzzling, absurd or even inconsistent whether because of some feature of the proposition itself or some feature of the situation in which it is uttered.1 Examples from ordinary English include the familiar cases "I have nothing to say to you," "My lips are sealed," "I have no comment to make." They also include such sentences as "I'm sorry, I don't speak any English," "I'm quite incapable of uttering a grammatically correct sentence," "I never generalize," "Don't talk to me, I'm asleep," or even "I do not exist." Such pragmatic paradoxes will turn out to have certain features in common with the Liar Paradox. Some ofthem give rise to logical contradictions, some ofthem are selfreferential , some ofthem seem to include a reference to their own truth or falsity. But there are also important differences, as I hope to demonstrate . Hints of a solution to some of these problems are to be found in Ockham; but my main discussion will be based on the work ofseveral later medieval logicians, notably John Buridan, Albert ofSaxony and William Buser, all of whom were active at the University of Paris in the middle years of the fourteenth century. To be precise, Buridan taught there from about 1320 to about 1360, Albert taught there from 1 For some twentieth century discussion and further references see A. Pap, Semantics and Necessary Truth (New Haven and London: Yale University Press, 1958) 259-267; C. L. Hamblin, Fallacies (London: Methuen &. Co., 1970) 301. 130E. J. ASHWORTH 1351 to 1362, and Buser taught there from 1357 until after 1364.2 I shall also draw on the work of Paul of Venice, who wrote his Lógica Magna in 1397-1398. These writers all had a very strong interest in pragmatic paradoxes. The reason for this has to do with the nature ofthe university curriculum. Virtually all undergraduate students were in the Arts Faculty, and at least the first two years of the four year course were largely devoted to the study oflogic. As we all know, logic is most effectively taught by means of frequent assignments and tests; and the set-work in a medieval university was oral. It consisted in taking part in debates or disputations. Some disputations involving senior students, Masters and Doctors, were about matters of substance, and it is these that have been recorded in, for instance, the works of St. Thomas Aquinas. Beginning logic students, however, took part in socalled obligational disputations, which a sixteenth-century author (Domingo de Soto) described as "games for boys."3 These games had two players. The opponent put forward a proposition called a positum which was usually false. The other player, the respondent, had to admit the positum if it was logically possible. He then had to grant it. The opponent now put forward a series of further propositions, and at each step the respondent had to reply "I grant it" or "I deny it" or "I doubt it."4 The point of the game was for the opponent to induce the respondent to grant both parts of a logical contradiction. The 2 For information about Buser, see C. H. Kneepkens, "The Mysterious Buser Again: William Buser of Heusden and the Obligationes Tract Ob rogatum " in English Logic in Italy, edited by A. Maierù (Naples: Bibliopolis, 1982) 147-166. 3 Domingo de Soto, Summulae (Salmanticae, 1554: Reprinted Hildesheim , New York, 1980) fol. 156rb: "Est enim ars haec velut puerorum Iudus . . . ." For further discussion of obligational disputations and a full bibliography, see E. J. Ashworth, editor and translator, Paul of Venice. Lógica Magna Part 11. Fascicule 8. Tractatus de Obligationibus. (British Academy: Classical and Mediaeval Logic Texts; forthcoming.) 4 The fourth response, "I distinguish it," is mentioned by Ockham: see Ockham, Summa Logicae, pars HI—3, c.41 (OPh I, 737). However, it is not mentioned by any of the other fourteenth...


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