In his Outlines of Pyrrhonism 2.110–113, Sextus Empiricus presents four different accounts of the conditional, presumably all from the Hellenistic period, in increasing logical strength. While the interpretation and provenance of the first three accounts is relatively secure, the fourth account has perplexed and frustrated interpreters for decades or longer. Most interpreters have ultimately taken a dismissive attitude towards the fourth account and discounted it as being of both little historical and logical interest. We argue that this attitude is unwarranted (...) and demonstrate that the conditional expressed in the fourth account can profitably be understood as a precursor of analytic entailment, familiar from containment logics such as those developed by Parry and Angell. Exploiting recent work by Fine, we present a formal truthmaker semantics for this conditional and show how it sheds light on a number of longstanding issues in the interpretation of this passage. (shrink)

O presente trabalho foi elaborado com o objetivo de apresentar de maneira introdutória o que é a lógica estoica e qual papel ela desempenha dentro da escola estoica. Nela deixaremos de lado o que chamamos de a teoria estoica dos argumentos e nos deteremos apenas naquilo que se refere ao que poderíamos, por enquanto, chamar de sentenças e suas moléculas. O que será exposto aqui é fruto de dois anos de estudo acerca da lógica estoica.

This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. Much of Stoic (...) logic appears surprisingly modern: a recursively formulated syntax with some truth-functional propositional operators; analogues to cut rules, axiom schemata and Gentzen’s negation-introduction rules; an implicit variable-sharing principle and deliberate rejection of Thinning and avoidance of paradoxes of implication. These latter features mark the system out as a relevance logic, where the absence of duals for its left and right introduction rules puts it in the vicinity of McCall’s connexive logic. Methodologically, the choice of meticulously formulated meta-logical rules in lieu of axiom and inference schemata absorbs some structural rules and results in an economical, precise and elegant system that values decidability over completeness. (shrink)

ABSTRACT: Alexander of Aphrodisias’ commentaries on Aristotle’s Organon are valuable sources for both Stoic and early Peripatetic logic, and have often been used as such – in particular for early Peripatetic hypothetical syllogistic and Stoic propositional logic. By contrast, this paper explores the role Alexander himself played in the development and transmission of those theories. There are three areas in particular where he seems to have made a difference: First, he drew a connection between certain passages from Aristotle’s Topics and (...) Prior Analytics and the Stoic indemonstrable arguments, and, based on this connection, appropriated at least four kinds of Stoic indemonstrables as Aristotelian. Second, he developed and made use of a specifically Peripatetic terminology in which to describe and discuss those arguments – which facilitated the integration of the indemonstrables into Peripatetic logic. Third, he made some progress towards a solution to the problem of what place and interpretation the Stoic third indemonstrables should be given in a Peripatetic and Platonist setting. Overall, the picture emerges that Alexander persistently (if not always consistently) presented passages from Aristotle’s logical œuvre in a light that makes it appear as if Aristotle was in the possession of a Peripatetic correlate to the Stoic theory of indemonstrables. (shrink)

For many recent readers of Hegel, Wilfrid Sellars’s 1956 London lectures on the “Myth of the Given” have signaled an important rapprochement between Hegelian and analytic traditions in philosophy. Here I want to explore the ideas of another philosopher, also active in London in the 1950s, who consciously pursued such a goal: John N. Findlay. The ideas that Findlay brought to Hegel—sometimes converging with, sometimes diverging from those of Sellars—had been informed by his earlier study of the Austrian philosopher Alexius (...) Meinong, and transformations of Meinong’s ideas by his student, the logician Ernst Mally. These ideas that Findlay found Hegel-friendly are ones that have had a particular bearing on more recent analytic modal metaphysics, especially via the work of Findlay’s own former student, Arthur Prior. Given this, we might not be surprised at the similarities between the type of actualist interpretation of modal logic that Prior offered in opposition to David Lewis’s variant on Leibnizian possibilism, and Hegel’s approach to the category of “Actuality” [Wirklichkeit] at the end of the Objective Logic of The Science of Logic. But the similarities, I suggest, do not end there, as elements of Hegel treatment of predication in the Subjective Logic parallel similar elements found in the work of Mally and, more recently, “modal actualists” such as Prior and Stalnaker. In this paper I explore some puzzling features of Hegel’s treatment of predication in the Subjective Logic from the point of view of the need for a logic for thought about the modally complex actual world, as Hegel conceived it. (shrink)