The only passage from Aristotle's works that seemsto discuss the paradox of the liar is within chapter 25 of Sophistici Elenchi (180a34–b7). This passage raises several questions: Is it really about the paradox of the liar? If it is, is it addressing a strong version of the paradox or some weak strain of it? If it is addressing a strong version of the paradox, what solution does it propose? The conciseness of the passage does not enable one to answer these (...) questions beyond doubt, and commentators have offered very different replies. However, a reasonable case can be made for claiming, first, that the passage in question is about the paradox of the liar, second, that it addresses a strong version of the paradox, and, third, that it attempts to solve it by assuming that someone uttering 'I am speaking falsely' (or whatever sentence-type the paradox turns on) is neither speaking truly nor speaking falsely absolutely. (shrink)

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)

This paper discusses ancient versions of paradoxes today classified as paradoxes of presupposition and how their ancient solutions compare with contemporary ones. Sections 1–4 air ancient evidence for the Fallacy of Complex Question and suggested solutions, introduce the Horn Paradox, consider its authorship and contemporary solutions. Section 5 reconstructs the Stoic solution, suggesting the Stoics produced a Russellian-type solution based on a hidden scope ambiguity of negation. The difference to Russell’s explanation of definite descriptions is that in the Horn Paradox (...) the Stoics uncovered a hidden conjunction rather than existential sentence. Sections 6 and 7 investigate hidden ambiguities in “to have” and “to lose” and ambiguities of quantification based on substitution of indefinite plural expressions for indefinite or anaphoric pronouns, and Stoic awareness of these. Section 8 considers metaphorical readings and allusions that add further spice to the paradox. (shrink)