This paper explores a currently unnoticed argument used by John Buridan to defend his analysis of modal propositions and to reject the analysis of modal propositions of necessity put forward by William of Ockham. First, I explore this argument and, by considering possible responses of Ockham to Buridan, show some of the ways in which Ockham seems to be keeping closer to Aristotle's remarks about modal propositions in Prior Analytics, 18.

In his Tractatus de Consequentiis, the 14th century logician John Buridan states a theorem, which reads like a refutation of Aristotelian Syllogistics. Syllogistics in its usual form, indeed, faces problems when propositions about the divine persons are involved, and, in some cases, when past- or future-tense propositions occur. Buridan offers different ways of overcoming some of these obstacles. The first aim of this paper is to analyse these ways, the second aim is to draw some conclusions concerning Buridan’s understanding of (...) logic and its relation to theology. (shrink)

This paper studies John Buridan's octagons of opposition for the de re modal propositions and the propositions of unusual construction. Both Buridan himself and the secondary literature have emphasized the strong similarities between these two octagons (as well as a third one, for propositions with oblique terms). In this paper, I argue that the interconnection between both octagons is more subtle than has previously been thought: if we move beyond the Aristotelian relations, and also take Boolean considerations into account, then (...) the strong analogy between Buridan's octagons starts to break down. These differences in Boolean structure can already be discerned within the octagons themselves; on a more abstract level, they lead to these two octagons having different degrees of Boolean complexity (i.e. Boolean closures of different sizes). These results are obtained by means of bitstring analysis, which is one of the key tools from contemporary logical geometry. Finally, I argue that this historical investigation is directly relevant for the theoretical framework of logical geometry, and discuss how it helps us to address certain open questions in this framework. (shrink)

In recent years modal syllogistic provided by 14th century logician John Buridan has attracted increasing attention of historians of medieval logic. The widespread use of quantified modal logic with the apparatus of possible worlds semantics in current analytic philosophy has encouraged the investigation of the relation of Buridan’s theory of modality with the modern developments of symbolic modal logic. We focus on the semantics of and the inferential relations among the propositions that underlie Buridan’s theory of modal syllogism. First, we (...) review all inferences between propositions of necessity, possibility, contingency, and non-contingency, with or without quod est locution, that are valid in Buridan’s semantics, and offer a comprehensive diagrammatic representation that includes them all. We then ask the question if there is a way to model those results in first order modal logic. Three ways of formalizing Buridan’s propositions in quantified modal logic are considered. Comparison of inferences between the quantified formulas and Buridan’s propositions reveals that, when supplied with a suitable formalization, Buridan’s semantics of categorical statements and immediate inferences among them can be fully captured by the quantified modal system T. (shrink)

O presente artigo investiga a conexão entre modalidade e tempo em dois mestres de artes Parisienses ativos na primeira metade do século 14, João Buridan (c.1290-c.1361) e João de Jandun (c.1286-c.1328). Busca-se elucidar a abordagem de ambos acerca da natureza dessa relação em um conjunto de textos pouco explorados nos debates sobre a interpretação de modalidades medievais, a saber, os comentários ao fim do primeiro livro do De Caelo de Aristóteles. A interpretação da relação entre o ‘necessário’ e o que (...) ‘sempre é’ nesse texto recebera interpretações divergentes sobre a controversa assimilação de necessidade e omnitemporalidade em concepções pré-modernas das modalidades. Por meio da análise do debate em torno das passagens Aristotélicas do De Caelo, posto por ambos os filósofos pertencentes ao milieu da Faculdade de Artes em Paris, o artigo demonstra que tal assimilação não era consensual. Através do contraste entre as análises de Jandun e Buridan, conclui-se que, embora Buridan acomode a necessidade temporal pressuposta no De Caelo enquanto necessidade condicional, ele desenvolve uma crítica da validade geral dos argumentos de Aristóteles no que tange a modalidades absolutas. (shrink)