In this paper we look at the suitability of modern interval-based temporal logic for modeling John Buridan’s treatment of tensed sentences in his Sophismata. Building on the paper, we develop Buridan’s analysis of temporal logic, paying particular attention to his notions of negation and the absolute/relative nature of the future and the past.We introduce a number of standard modern propositional interval temporal logics to illustrate where Buridan’s interval-based temporal analysis differs from the standard modern approaches. We give formal proofs of (...) some claims in, and sketch how the standard modern systems could be defined in terms of Buridan’s proposals, showing that his logic can be taken as more basic. In diesem Aufsatz betrachten wir das Geeignetsein einer modernen intervallbasierten temporalen Logik für die Modellierung von John Buridans Behandlung zeitabhängiger Sätze in seinen Sophismata. Aufbauend auf den Aufsatz stellen wir Buridans Analyse der temporalen Logik dar, mit besonderer Berücksichtigung seiner Begriffe der Negation und der absoluten/relativen Natur der Zukunft und der Vergangenheit. Wir führen einige standardmäßige moderne intervallbasierte temporale Aussagenlogiken ein, um zu illustrieren, wo Buridans intervallbasierte temporale Analyse von den standardmäßigen modernen Zugangsweisen abweicht. Wir geben formale Beweise einiger Behauptungen in an und skizzieren, wie die standardmäßigen modernen Systeme im Sinne der Vorschläge Buridans definiert werden könnten; wir zeigen damit, dass seine Logik als die grundlegendere aufgefasst werden kann. (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)

The recovery of Aristotle’s logic during the twelfth century was a great stimulus to medieval thinkers. Among their own theories developed to explain Aristotle’s theories of valid and invalid reasoning was a theory of consequence, of what arguments were valid, and why. By the fourteenth century, two main lines of thought had developed, one at Oxford, the other at Paris. Both schools distinguished formal from material consequence, but in very different ways. In Buridan and his followers in Paris, formal consequence (...) was that preserved under uniform substitution. In Oxford, in contrast, formal consequence included analytic consequences such as ‘If it’s a man, then it’s an animal’. Aristotle’s notion of syllogistic consequence was subsumed under the treatment of formal consequence. Buridan developed a general theory embracing the assertoric syllogism, the modal syllogism and syllogisms with oblique terms. The result was a thoroughly systematic and extensive treatment of logical theory and logical consequence which repays investigation. (shrink)

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)

In this paper, we provide a historical exposition of John Buridan's theory of divided modal propositions. We then develop a semantic interpretation of Buridan's theory which pays particular attention to Buridan's ampliation of modal terms. We show that these semantics correctly capture his syllogistic reasoning.

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)