For the entire Islamic tradition, the crowning glory of Aristotelian logic is the syllogistic theory outlined in the Prior and Posterior Analytics, especially the latter. The purpose of logic is to provide the means whereby knowledge is to be acquired, and the most valuable type of knowledge is that which is certain and necessary, that is, knowledge gained according to the paradigm of demonstra...

"Lesniewski defined ontology, one of his three foundational systems, as 'a certain kind of modernized 'traditional logic' [On the foundations of mathematics (FM), p. 176]. In this respect it is worth bearing in mind that in the 1937-38 academic year Lesniewski taught a course called "Traditional 'formal logic' and traditional 'set theory' on the ground of ontology"; cf. Srzednicki and Stachniak...

'Aristotelian logic', as it was taught from late antiquity until the 20th century, commonly included a short presentation of the argument forms modus (ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens, and modus tollendo ponens. In late antiquity, arguments of these forms were generally classified as 'hypothetical syllogisms'. However, Aristotle did not discuss such arguments, no...

In the present article we attempt to show that Aristotie's syllogistic is an underlying logie which includes a natural deductive system and that it is not an axiomatic theoryas had previously been thought. We construct a mathematical model which reflects certain structural aspects of Aristotle's logic and we examine both the mathematical properties of the model and the relation of the model to ...

Ever since Łukasiewicz, it has been opinio communis that Aristotle’s modal syllogistic is incomprehensible due to its many faults and inconsistencies, and that there is no hope of finding a single consistent formal model for it. The aim of this paper is to disprove these claims by giving such a model. My main points shall be, first, that Aristotle’s syllogistic is a pure term logic that does no...

A semantics is presented for Storrs McCalΓs separate axiomatizations of Aristotle's accepted and rejected polysyllogisms. The polysyllogisms under discussion are made up of either assertoric or apodeictic propositions. The semantics is given by associating a property with a pair of sets: one set consists of things having the property essentially and the other of things having it accidentally. A...

Abstract The rich body of physical theories defines the foundation our understanding world. Its mathematical formulation is based on classical Aristotelian (binary) logic. In philosophy science ambiguities, paradoxes, and possibility subjective interpretations facts have challenged binary logic, leading, among other developments, to Gotthard Günther’s theory polycontexturality (often also terme...

The present paper deals with the semantics of all, some and not in English and related languages. Since these semantics imply a logic, it also deals with the logic of quantification in natural language. To the extent that the linguistic findings are universally valid, the results are relevant to the study of human cognition in general. Since standard quantification theory (SQT) replaced Aristot...

-