The Liar Paradox: medieval and modern approaches

The subject of the research is the Liar paradox, probably the best known and one of the oldest paradoxes in logic. It borrows its name from Eubulides? Liar Riddle: ?Does the man who says ?I am lying? lie?? If he is lying, then what he says is the case, therefore what he says is true (and thus he is not lying); but if what he says (i.e. that he is lying) is true, then he is lying. Over the last decades, the Liar paradox has been an immensely popular philosophical topic ? a search in any database listing works in philosophy will yield at least a couple hundred titles. But the Liar paradox is not only popular among 20th and 21st century philosophers; it was also very fashionable among medieval philosophers. Nonetheless, in spite of the major relevance of the Liar Paradox as a philosophical topic in both periods, few comparisons between modern and medieval solutions have been carried out, and none of them aimed at providing a thorough comparative assessment of the two traditions. In order to fill this gap in the literature, this research has three distinctive aims: ● A comprehensive assessment of the similarities and dissimilarities between modern and medieval treatments of the Liar Paradox, in order to obtain a wide-ranging chart of both traditions. I intend to offer a comparative taxonomy of both traditions, comparing also the arguments in favor and against the different proposals in each of the two traditions. I will focus on the similarities as well as on the dissimilarities between the two traditions. What is innovative in this approach is precisely the emphasis on the clarifying power of weighing a given paradigm against another. ● The evaluation of the quarrel concerning the Liar Paradox opposing the two medieval logicians J. Buridan and T. Bradwardine, and the repercussions of their solutions for a general semantic theory. Bradwardine?s and Buridan?s solutions seem to resemble each other at first sight: both maintained that, besides implying their falsity, Liar sentences implied their own truth as well, and therefore were simply false (since they implied an absurdity). But while Buridan went as far as claiming that all sentences, paradoxical or not, imply their own truth, Bradwardine proved that this property was exclusive to Liar-like sentences. ● A formalization of medieval treatments of the Liar Paradox (which specific treatment(s) will be determined in due course). In effect, insofar as medieval semantics is primarily token-based -- that is, actually formed sentence-tokens are the bearers of truth-values --, a promising starting point are modern formal treatments of the Paradox where tokens are truth-value bearers. But, since some of the basic assumptions of medieval semantics are unlike and even incompatible with those of most modern theories, adjustments will be necessary in the application of the latter to formalize aspects of the former.