The ‘Dialectical school’ denotes a group of early Hellenistic philosophers that were loosely connected by philosophizing in the — Socratic — tradition of Eubulides of Megara and by their interest in logical paradoxes, propositional logic and dialectical expertise. . Its two best known members, Diodorus Cronus and Philo the Logician, made groundbreaking contributions to the development of theories of conditionals and modal logic. Philo introduced a version of material implication; Diodorus devised a forerunner of strict implication. Each developed a system (...) of modal notions that satisfies the basic logical requirements laid down by modern standard modal theories. In antiquity, Diodorus Cronus was famous for his so called Master Argument, which aims to prove that only the actual is possible. (shrink)

Essays on Aristotle's Sea-Battle, Lazy Argument, Argument Reaper, Diodorus' Master Argument -/- The book is devoted to the ancient logical theories, reconstruction of their semantic proprieties and possibilities of their interpretation by modern logical tools. The Ancient arguments are frequently misunderstood in modern interpretations since authors usually have tendency to ignore their historical proprieties and theoretical background what usually leads to a quite inappropriate picture of the argument’s original form and mission. Author’s primary intention was to draw attention to the (...) complexity of some historical arguments and to the theoretical context in which arguments were created, circulated, developed, and finally tuned. Four well-known ancient arguments – with a common central subject related to the future contingencies problem – are reconstructed from available historical sources: “The Sea Battle”, which is drawn from Aristotle’s treatise De Interpretatione; two arguments, usually ascribed to the Stoics, “The Lazy Argument” and “The Reaper”; “The Master Argument” of the Megarian philosopher Diodorus. Arguments are linguistically and semantically detaily analyzed, formally presented by reflecting some relevant corresponding hypotheses based on physical or logical theories of their ancient authors, and finally covered by appropriate logical tools familiar to a modern reader. Two appendices are added at the closing part of the book. One covering some assumptions relevant for understanding of rival streams in ancient theories of meaning related to the nature of names and naming; the other is devoted to the ancient understanding of logical proposition and attempts to find an adequate Latin translation of the Greek delicate philosophical term “ἀξίωμα”. (shrink)

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)

Philodemus’ De signis is one of the classical texts of greatest semiotic interest. It reports the debate which arose between the Epicureans and an opposing school, usually identified as the Stoics, concerning semiotic inference. The Epicureans proposed to construct semiotic inferences based on generalizations resting on similarity, ultimately configuring their method as a form of induction. Their opponents attacked the Epicurean proposal in a twofold way: on the one hand, they argued that the Epicureans’ method intrinsically lacked cogency, invalidating their (...) inferences from a logical point of view. On the other, they criticized the notion of similarity, arguing that it is generally a vague notion, and in some cases impossible to implement, as when one is faced with unique cases. The debate is very complex and is divided into replies and rejoinders. The ultimate impression one gets is that the Epicureans were able, for the first time in antiquity, to propose a real method to construct semiotic inferences, even though the latter were subject to fallibility, while their opponents did not propose a method, but a test, “elimination,” able only to check the logical soundness of semiotic inferences. In doing so, they placed themselves in a tradition extending back to the theory of signs formulated – albeit in a significantly different way – by Aristotle. (shrink)

Controversy has surrounded the interpretation of the so-called 'Diodorean' and 'Chrysippean' conditionals of the Stoics. I critically evaluate and reject two interpretations of each of them: as expressing natural laws, and as strict conditionals. In doing so I engage with the work of authors such as Frede, Gould, Hurst, the Kneales, Mates, and Prior. I conclude by offering my own proposal for where these Stoic conditionals should be located on a 'ladder' of logical strength.

ABSTRACT This paper offers an account of the early career of Martha Kneale, née Hurst, and of the five papers she published between 1934 and 1950. One on metaphysical and logical necessity, from 1938, is particularly interesting. In it she considers the metaphysics of time and offers an explanation of ‘the necessity of the past’, which has some resemblance to Kripke’s ideas about metaphysical necessities, in that it assigns an important role to experience in how we come to know them. (...) But Kneale’s view is very different from Kripke’s, depending not on doctrines about rigid designation but rather on recognition of the failure of the atomist/empiricist account of ‘simple’ and ‘complex’ concepts. That account cannot deal with such things as the relations of the determinates of a determinable like colour. A plausible corollary of this, which Kneale exploits, is that some of our experience reveals to us that there are phenomena which are intrinsically complex in having multiple distinguishable aspects, but where those aspects are inseparable. Other of the papers show Kneale to have been pursuing interesting lines of thought about McTaggart’s argument against the reality of time and on the mind-body problem. (shrink)

The main issue of the present Article is a discussion about the conditional proposition in Stoic- Megarian Logic. There were, in Stoic-Megarian school, many theories of meaning to interpret these propositions. Since conditional propositions made the structure’s core of their Logic, so for the understanding of the key concept of their thought, we need searching, prior to anything, in the semantics of these propositions. We will, in the first place and much survey, compare between Stoic-Megarian Logic and Aristotelian Logic and (...) present where is the state of conditional propositions in the Stoic-Megarian Logic; then, in the second place, we explore all kinds of conditional proposition and their conditions of truth values in Stoic-Megarian Logic and compare them with the concept of implication in modern logic and reinterpret them with new instruments in modern logic. Most logicians, in this field, evaluate and compare Stoic-Megarian conditional propositions with definitions of Material implication, strict implication, and Natural laws and we, in this Article, evaluate and analyze these propositions with this perspective and ideas. (shrink)