The solution John Buridan offers for the Paradox of the Liar has not been correctly placed within the framework of his philosophy of language. More precisely, there are two important points of the Buridanian philosophy of language that are crucial to the correct understanding of his solution to the Liar paradox that are either misrepresented or ignored in some important accounts of his theory. The first point is that the Aristotelian formula, ` propositio est vera quia qualitercumque significat in rebus (...) significatis ita est ', once amended, is a correct way to talk about the truth of a sentence. The second one is that he has a double indexing theory of truth: a sentence is true in a time about a time, and such times should be distinguished in the account of the truth-conditions of sentences. These two claims are connected in an important way: the Aristotelian formula indicates the time about which a sentence is true. Some interpreters of the Buridanian solution to the paradox, following the lead of Herzberger, have missed these points and have been led to postulate truth-values gaps, or surrogates of truth-value gaps, when there is nothing of this sort in his theory. I argue against this tradition of interpretation of Buridan and propose an interpretation of his solution to the Liar. (shrink)

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)

É comumente aceito, atualmente, que Aristóteles não teria enfrentado ou tentado seriamente resolver o famoso paradoxo do mentiroso, embora ele tenha sido formulado por Eubúlides de Mileto, membro da escola megárica e rival filosófico de Aristóteles. No máximo, assim reza a visão tradicional, ele parece apenas fazer uma menção desse paradoxo nas Refutações sofísticas, Capítulo 25, talvez esboçando a sua solução. O meu intento, no presente artigo, é desafiar essa opinião geral mostrando que o Estagirita fornece uma explicação implícita para (...) duas versões do paradoxo do mentiroso, a saber, a versão autorreferencial, e a versão anafórica. A minha alegação é que a solução aristotélica para essas duas versões do paradoxo encontra-se no núcleo de sua refutação de duas teses, as quais denominei como tese da synalethia e como tese da sympseudia. Tal refutação é realizada no oitavo capítulo do quarto Livro da Metafísica, um texto até agora subestimado pelos intérpretes modernos, mesmo sendo a parte final de um dos mais importantes escritos de Aristóteles. A solução aristotélica, assim defendo, é levada a cabo por meio dos seguintes princípios: toda declaração é sempre precedida por um operador de verdade da forma ‘é verdade que...’, ou seja, toda declaração, qualquer que seja o que ela possa declarar a mais, primariamente assevera a sua própria verdade; e, em conformidade com o princípio anterior, toda declaração que assevera a sua própria falsidade ou acarreta a verdade de sua contraditória é necessariamente falsa. Através desses princípios, a refutação de Aristóteles da synalethia e da sympseudia é bem-sucedida. Mostrarei que obtemos uma boa solução para as versões do mentiroso acima mencionadas, apenas aplicando esses mesmos princípios a elas. Esse tipo de solução ao mentiroso tanto quanto para as teses antes citadas é muito parecido com aquele explicitamente encontrado nas obras de diversos filósofos, a saber, Guilherme de Sherwood, Tomás Bradwardine, João Buridano, Alberto da Saxônia, Paulo Venetus, Charles S. Peirce e Arthur Prior. Assim, também defendo que essa linhagem tem as suas raízes na solução de Aristóteles. (shrink)

This book presents novel formalizations of three of the most important medieval logical theories: supposition, consequence and obligations. In an additional fourth part, an in-depth analysis of the concept of formalization is presented - a crucial concept in the current logical panorama, which as such receives surprisingly little attention.Although formalizations of medieval logical theories have been proposed earlier in the literature, the formalizations presented here are all based on innovative vantage points: supposition theories as algorithmic hermeneutics, theories of consequence analyzed (...) with tools borrowed from model-theory and two-dimensional semantics, and obligations as logical games. For this reason, this is perhaps the first time that these medieval logical theories are made fully accessible to the modern philosopher and logician who wishes to obtain a better grasp of them, but who has always been held back by the lack of appropriate ‘translations' into modern terms.Moreover, the book offers a reflection on the very nature of logic, a reflection that is prompted by the comparisons between medieval and modern logic, their similarities and dissimilarities. It is thus a contribution not only to the history of logic, but also to the philosophy of logic, the philosophy of language and semantics.The analysis of medieval logic is also relevant for the modern philosopher and logician in that, being the unifying methodology used across all disciplines at that time, logic really provided unity to science. It thus presents a unified model of scientific investigation, where logic plays the aggregating role. (shrink)

This thesis is on the history and philosophy of logic and semantics. Logic can be described as the ‘science of reasoning’, as it deals primarily with correct patterns of reasoning. However, logic as a discipline has undergone dramatic changes in the last two centuries: while for ancient and medieval philosophers it belonged essentially to the realm of language studies, it has currently become a sub-branch of mathematics. This thesis attempts to establish a dialogue between the modern and the medieval traditions (...) in logic, by means of ‘translations’ of the medieval logical theories into the modern framework of symbolic logic, i.e. formalizations. One of its conclusions is that, when properly understood within their own framework, the interest of medieval logical theories for modern investigations go beyond mere historical interest, but that a thorough conceptual analysis of such theories must be undertaken in order to avoid conceptual misprojections. While such translations of medieval into modern logic have been attempted before, the approach presented here is innovative in that attention is paid to the similarities as well as to the dissimilarities between the two traditions, and to what can be learned from the medieval masters for modern investigations in logic and semantics. (shrink)