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)

In ‘Logical Consequence (Slight Return)’, Gillian Russell asks ‘What is logical consequence?’, a question which has vexed logicians since at least the twelfth century, when people first began to wonder what it meant for one sentence (or proposition) to follow from another sentence (or proposition, or set of sentences, or set of propositions), or whether it was possible to put down rules determining when the relation of ‘follows from’ (or ‘is antecedent to’) holds. Her aim is threefold: (1) to explain (...) what an answer to the question ‘What is logical consequence?’ would need to be able to do in order to be a satisfying answer; (2) to identify previous answers to the question; and (3) to demonstrate why these previous answers are inadequate to do what the answer needs to be able to do, and to offer a new answer. In the present paper, I respond to these aims in two ways. The first is to say something about where Russell’s central question even comes from, because this is not a topic that is often discussed by twentieth- and twenty-first-century logicians, and even historians of logic tend to not have had much to say about when—and why—this question even comes about in the first place. The second is to evaluate the accounts proposed and discussed by Russell, including her new proposal. In the end, I will argue that she has reached the right account of the nature of logical consequence, but not necessarily for the right reasons. (shrink)

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)

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)