La contribución de Ricardo Salles se centra en la interpretación peripatética de Alejandro en contra de la tesis estoica de que la lógica no es “instrumento”, sino “parte” de la filosofía. Según Alejandro, si la lógica fuera parte de la filosofía, como pretenden los estoicos, la filosofía no podría ocupar el lugar más elevado en la jerarquía del conocimiento; pero esto sería, en cierto modo, paradójico, argumenta Salles, pues todos –tanto estoicos como peripatéticos– consideran, por diversas razones, que la filosofía (...) es, por su objeto, la disciplina más elevada. De acuerdo con Salles, sin embargo, esta aguda crítica no es lo suficientemente penetrante para poner de manifiesto una verdadera inconsistencia en el estoicismo. Salles cree que esto sería paradójico, pues todos –tanto estoicos como peripatéticos– consideran, por diversas razones, que la filosofía es, por su objeto, la disciplina más elevada. De acuerdo con Salles, sin embargo, la aguda crítica de Alejandro no es lo suficientemente penetrante para poner de manifiesto una verdadera inconsistencia en el estoicismo. Su principal debilidad, en su opinión, radica en el hecho de que el razonamiento sobre el cual descansa depende de supuestos aristotélicos que los estoicos rechazan. (shrink)

While there is now considerable experimental evidence that, on the one hand, participants assign to the indicative conditional as probability the conditional probability of consequent given antecedent and, on the other, they assign to the indicative conditional the “defective truth-table” in which a conditional with false antecedent is deemed neither true nor false, these findings do not in themselves establish which multi-premise inferences involving conditionals participants endorse. A natural extension of the truth-table semantics pronounces as valid numerous inference patterns that (...) do seem to be part of ordinary usage. However, coupled with something the probability account gives us—namely that when conditional-free ϕ entails conditional-free ψ, “if ϕ then ψ” is a trivial, uninformative truth—we have enough logic to derive the paradoxes of material implication. It thus becomes a matter of some urgency to determine which inference patterns involving indicative conditionals participants do endorse. Only thus will we be able to arrive at a realistic, systematic semantics for the indicative conditional. (shrink)

In late antiquity, logic developed into what Ebbesen calls the LAS, the Late Ancient Standard. This paper discusses the Neoplatonic use of LAS, as informed by epistemological and metaphysical concerns. It demonstrates this through an analysis of the late ancient debate about hypothetical and categorical logic as manifest in the practice of syllogizing Platonic dialogues. After an introduction of the Middle Platonist view on Platonic syllogistic as present in Alcinous, this paper presents an overview of its application in the syllogizing (...) practice of Proclus and others. That overview shows that the two types were considered two sides of the same coin, to be used for the appropriate occasions, and both relying on the methods of dialectic as revealing the structure of knowledge and reality. Pragmatics, dialectic, and didactic choices determine which type or combination is selected in syllogizing Plato. So even though there is no specific Neoplatonic logic, there is a specific Neoplatonic use of LAS. (shrink)

Greek antiquity saw the development of two distinct systems of logic: Aristotle’s theory of the categorical syllogism and the Stoic theory of the hypothetical syllogism. Some ancient logicians argued that hypothetical syllogistic is more fundamental than categorical syllogistic on the grounds that the latter relies on modes of propositional reasoning such asreductio ad absurdum. Peripatetic logicians, by contrast, sought to establish the priority of categorical over hypothetical syllogistic by reducing various modes of propositional reasoning to categorical form. In the 17th (...) century, this Peripatetic program of reducing hypothetical to categorical logic was championed by Gottfried Wilhelm Leibniz. In an essay titledSpecimina calculi rationalis, Leibniz develops a theory of propositional terms that allows him to derive the rule ofreductio ad absurdumin a purely categorical calculus in which every proposition is of the formA is B. We reconstruct Leibniz’s categorical calculus and show that it is strong enough to establish not only the rule ofreductio ad absurdum, but all the laws of classical propositional logic. Moreover, we show that the propositional logic generated by the nonmonotonic variant of Leibniz’s categorical calculus is a natural system of relevance logic known as RMI$_{{}_ \to ^\neg }$. (shrink)

Aristotle presents a formal logic in the Prior Analytics in which the premises and conclusions are never conditionals. In this paper I argue that he did not simply overlook conditionals, nor does their absence reflect a metaphysical prejudice on his part. Instead, he thinks that arguments with conditionals cannot be syllogisms because of the way he understands the explanatory requirement in the definition of a syllogism: the requirement that the conclusion follow because of the premises. The key passage is Prior (...) Analytics I.32, 47a22–40, where Aristotle considers an argument with conditionals that we would consider valid, but which he denies is a syllogism. I argue that Aristotle thinks that to meet the explanatory requirement a syllogism must draw its conclusion through the way its terms are predicated of one another. Because arguments with conditionals do not, in general, draw their conclusions through predications, he did not include them in his logic. (shrink)

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)

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)