Aristotle was the founder not only of logic but also of modal logic. In the Prior Analytics he developed a complex system of modal syllogistic which, while influential, has been disputed since antiquity--and is today widely regarded as incoherent. Combining analytic rigor with keen sensitivity to historical context, Marko Malink makes clear that the modal syllogistic forms a consistent, integrated system of logic, one that is closely related to other areas of Aristotle's philosophy. Aristotle's modal syllogistic differs significantly from modern (...) modal logic. Malink considers the key to understanding the Aristotelian version to be the notion of predication discussed in the Topics--specifically, its theory of predicables and the ten categories. The predicables introduce a distinction between essential and nonessential predication. In contrast, the categories distinguish between substantial and nonsubstantial predication. Malink builds on these insights in developing a semantics for Aristotle's modal propositions, one that verifies the ancient philosopher's claims of the validity and invalidity of modal inferences. While it acknowledges some limitations of this reconstruction, Aristotle's Modal Syllogistic brims with bold ideas, richly supported by close readings of the Greek texts. (shrink)

As regards the issue of futura contingentia, Aquinas's interpretation turns on a phrase that has sometimes been dismissed as irrelevant or even confused: "...non tamen haec vel illa determinatae...". It is shown that this clause is in complete conformity with Aquinas's interpretation of the principles of non-contradiction and of excluded middle. According to this interpretation the meaning of propositional negation derives from the first two principles considered collectively but is not presupposed by them. With respect to time-relative modalities this implies (...) that at the time of announcement, say, of a sea battle both parts of the contradiction could be true, provided one understands "could" in the sense of a counterfactual possibility with respect to the final outcome. It is also shown that Aquinas's interpretation allows one to avoid some perplexities in connection with the controversial beginning of Met. IX, 4. Some final considerations are meant to show the rationale of that interpretation. (shrink)

Two main claims are defended. The first is that negative categorical statements are not to be accorded existential import insofar as they figure in the square of opposition. Against Kneale and others, it is argued that Aristotle formulates his o statements, for example, precisely to avoid existential commitment. This frees Aristotle's square from a recent charge of inconsistency. The second claim is that the logic proper provides much thinner evidence than has been supposed for what appears to be the received (...) view, that is, for the view that insofar as they occur in syllogistic negative categoricals have existential import. At most there is a single piece of evidence in favor of the view?a special case of echthesis or the setting out of a case in proof. (shrink)

Jan Lukasiewicz's treatise on Aristotle's Syllogistic, published in the 1950s, has been very influential in framing contemporary understanding of Aristotle's logical systems. However, Lukasiewicz's interpretation is based on a number of tendentious claims, not least, the claim that the syllogistic was intended to apply only to non-empty terms. I show that this interpretation is not true to Aristotle's text and that a more coherent and faithful interpretation admits empty terms while maintaining all the relations of the traditional square of opposition.

The prevailing truth-functional logic of the twentieth century, it is argued, is incapable of expressing the subtlety and richness of Aristotle's Principle of Excluded Middle, and hence cannot but misinterpret it. Furthermore, the manner in which truth-functional logic expresses its own Principle of Excluded Middle is less than satisfactory in its application to mathematics. Finally, there are glimpses of the "realism" which is the metaphysics demanded by twentieth century logic, with the remarkable consequent that Classical logic is a particularly inept (...) instrument to analyze those philosophies which stand opposed to the "realism" it demands. (shrink)