Buridan's solution of the semantic paradoxes

Abstract

This thesis is an investigation of the methods used to resolve semantic paradoxes by John Buridan, a 14th century logician at the University of Paris. We investigate specifically chapter 8 of his "Sophismata". Our investigation is based on the translation by G. E. Hughes of this chapter. The purpose of this investigation is to specify precisely what these methods were, and assess the degree to which they were successful. In the Introduction we distinguish between the problem encountered by modern inventors of artificial languages, who wish to prevent self-reference from occurring, and the problem with which Buridan was concerned, of devising a method of classifying the self-referential statements of natural languages as true or false. Only the latter problem will be dealt with here. This definition of our problem is followed in chapter 1 by a discussion of Buridan's notion of "proposition" which differs importantly from those of many others who have discussed the problem, and is essential to the success of his solution. Chapter 2 concerns Buridan's criteria of valid inference. The occurrence of self-referential propositions requires much more care than is usual in defining validity. In chapter 3 we discuss Buridan's treatment of liar paradoxes, and his "truth-entailment rule" (as G. E. Hughes calls it), which concerns the relation between a proposition, another saying that the first exists, and a third saying that the first is true. We discuss how the rule can be consistent with Buridan's criteria of valid inference and suggest three alternative interpretations of it consistent with the text. In chapter 4 we attempt to shed further light on the "existence" premiss in the rule, and its probable origins by considering what Buridan has to say (in his "Consequentiae") about "ut nunc" consequences and their reduction to simple ones. In chapter 5 we offer an interpretation of Buridan's method and terminology in terms of modern speech-act theory, as developed by Austin, Searle, and Vanderveken. This gives us a basis for preferring one of our three alternative interpretations and leads to an improvement in the clarity of the terminology (from a modern point of view). Finally, in our conclusion, we claim that Buridan's solution is satisfactory, on the basis of our speech-act interpretation, and draw the moral that to understand semantic paradoxes we should consider the pragmatic features of utterance of a paradoxical proposition to be part of the semantics, contrary to the usual practice of separating the two.