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WILL SOCRATES CROSS THE BRIDGE? A PROBLEM IN MEDIEVAL LOGIC In their treatises on insolubilia, or semantic paradoxes, medieval logicians frequently mentioned other cases in which the assumption that a proposition was true led to the conclusion that it was false, and the assumption that it was false led to the conclusion that it was true. Some of these cases were easily solved. If one considers the proposition "Socrates will enter a religious order" in relation to Socrates ' vow, "I will enter a religious order if and only if Plato does," and to Plato's vow, "I will enter a religious order if and only if Socrates does not," one sees at once that the problem stems from contradictory premises.1. But not all cases were of this sort. Consider the favourite example, "Socrates will not cross the bridge," when said by Socrates, in relation to the two premises, "All those who say what is true will cross the bridge" and "All those who say what is false will not cross the bridge."2 It is easily demonstrated that "Socrates will not cross the bridge" is true if and only if it is false, but what 1 Thomas Bricot, Tractatus Insolubilium (Parisius, 1492) sign. b. viii and sign, c i; Johannes Eckius, Bursa Pavonis (Argentine, 1507) sign, k v; John Major, Insolubilia (Parrhisiis, 1516) sign, c ii ff. Cf. Albert of Saxony, Perutilis Lógica (Venetiis, 1522) fo. 46™; Robertus de Cenali, Insolubilia in Liber Prioris Posterions (Parisius, 1510) sign, o iiii. One should note here that vows, promises and the like were treated as propositions with truth-values rather than as performative utterances with no truthvalues . This view was combined with a realization that there are certain conditions which have to be met before a vow is binding. For instance, the vower must genuinely intend to do what he vows to do, and what he vows to do must be both moral and within his power. These extra conditions were not thought relevant to the question whether "Socrates will enter a religious order" was true or false. To the slightly different question of whether Socrates would be bound by his vow, Major, for instance, held that he would not, on the grounds that his vow was conditional and that the condition, given Plato's vow, could not be fulfilled. For references to Major's text and to other discussions of vows and promises, see below, note 15. 8 Paul of Venice, Lógica Magna (Venetiis, 1499) fol. 198 and Paul of Venice, Tractatus Summularum Logice Pauli Veneti (Venetiis, 1498) sign, e ivo. The latter work which appeared in many editions, is known as the Lógica Parva. See also 76K. J. ASHWORTH is not so easily demonstrated is the source of the paradox. Certainly it is not a paradox just like "What I am now saying is false," since the key proposition does not speak of its own semantic properties, but the premises do indeed speak of truth and falsity in a way which has implications for the truth-value of "Socrates will not cross the bridge." The question thus arises whether "Socrates will not cross the bridge" is to be counted as a semantic paradox, to be dissolved in the same way as the Standard Liar is dissolved, or whether it is to be seen as needing another kind of solution, perhaps less radical in its implications for our common-sense notions about such matters as the legitimacy of self-reference or the definition of truth. I will begin by describing the two solutions offered by Paul of Venice, both of which involved treating "Socrates will not cross the bridge" as if it were a standard semantic paradox. In his Lógica Magna, Paul of Venice set out fifteen different solutions to the problem of semantic paradoxes, and it was the last of these that he applied to the proposition we are considering. The solution, which is due to Roger Swyneshed,3 was in essence that semantic paradoxes of the standard type are self-referential categorical propositions (though of course hypothetical versions can be formulated), and that they are false, because any true proposition has to satisfy not...

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