An eleventh-century Greek text, in which a fourth-century patristic text is discussed, gives an outline of a solution to the Liar Paradox. The eleventh-century text is probably the first medieval treatment of the Liar. Long passages from both texts are translated in this article. The solution to the Liar Paradox, which they entail, is analysed and compared with the results of modern scholarship on several Latin solutions to this paradox. It is found to be a solution, which bears some analogies (...) to contemporary game semantics. Further, an overview of other Byzantine scholia on the Liar Paradox is provided. The findings and the originality of the discussed solution to the Liar Paradox suggest a change in the way in which Byzantine Logic is traditionally regarded in contemporary scholarship. (shrink)

Two periods in the history of logic and philosophy are characterized notably by vivid interest in self-referential paradoxical sentences in general, and Liar sentences in particular: the later medieval period (roughly from the 12th to the 15th century) and the last 100 years. In this paper, I undertake a comparative taxonomy of these two traditions. I outline and discuss eight main approaches to Liar sentences in the medieval tradition, and compare them to the most influential modern approaches to such sentences. (...) I also emphasize the aspects of each tradition that find no counterpart in the other one. It is expected that such a comparison may point in new directions for future research on the paradoxes; indeed, the present analysis allows me to draw a few conclusions about the general nature of Liar sentences, and to identify aspects that would require further investigation. (shrink)

Jean Buridan has offered a solution to the Liar Paradox, i.e. to the problem of assigning a truth-value to the sentence ‘What I am saying is false’. It has been argued that either this solution is ad hoc since it would only apply to self-referencing sentences [Read, S. 2002. ‘The Liar Paradox from John Buridan back to Thomas Bradwardine’, Vivarium, 40 , 189–218] or else it weakens his theory of truth, making his ‘a logic without truth’ [Klima, G. 2008. ‘Logic (...) without truth: Buridan on the Liar’, in S. Rahman, T. Tulenheimo and E. Genot, Unity, Truth and the Liar: The Modern Relevance of Medieval Solutions to the Liar Paradox, Berlin: Springer, 87–112 ; Dutilh Novaes, C. 2011. ‘Lessons on truth from mediaeval solutions to the Liar Paradox’, The Philosophical Quarterly, 61 , 58–78]. Against , I will argue that Buridan's solution by means of truth by supposition does not involve new principles. Self-referential sentences force us to handle supposition more carefully, which does not warrant the accusation of adhoccery. I will also argue, against (2), that it is exaggerated to assert that this solution leads to a ‘weakened’ theory of truth, since it is consistent with other passages of the Sophismata, which only gives necessary conditions for the truth of affirmative propositions, but sufficient conditions for falsity. (shrink)