Logic: The “Megarics” (Cambridge History of Hellenistic Philosophy) (original) (raw)
Related papers
Classics, 2019
In ancient philosophy, there is no discipline called “logic” in the contemporary sense of “the study of formally valid arguments.” Rather, once a subfield of philosophy comes to be called “logic,” namely in Hellenistic philosophy, the field includes (among other things) epistemology, normative epistemology, philosophy of language, the theory of truth, and what we call logic today. This entry aims to examine ancient theorizing that makes contact with the contemporary conception. Thus, we will here emphasize the theories of the “syllogism” in the Aristotelian and Stoic traditions. However, because the context in which these theories were developed and discussed were deeply epistemological in nature, we will also include references to the areas of epistemological theorizing that bear directly on theories of the syllogism, particularly concerning “demonstration.” Similarly, we will include literature that discusses the principles governing logic and the components that make up arguments...
Chrysippus' Modal Logic and Its Relation to Philo and Diodorus
Döring/Ebert (eds), Dialektiker und Stoiker , 1993
ABSTRACT: The modal systems of the Stoic logician Chrysippus and the two Hellenistic logicians Philo and Diodorus Cronus have survived in a fragmentary state in several sources. From these it is clear that Chrysippus was acquainted with Philo’s and Diodorus’ modal notions, and also that he developed his own in contrast of Diodorus’ and in some way incorporated Philo’s. The goal of this paper is to reconstruct the three modal systems, including their modal definitions and modal theorems, and to make clear the exact relations between them; moreover, to elucidate the philosophical reasons that may have led Chrysippus to modify his predessors’ modal concept in the way he did. It becomes apparent that Chrysippus skillfully combined Philo’s and Diodorus’ modal notions, with making only a minimal change to Diodorus’ concept of possibility; and that he thus obtained a modal system of modalities (logical and physical) which fit perfectly fit into Stoic philosophy.
Ancient Logic and Its Modern Interpretations,
This book treats ancient logic: the logic that originated in Greece by the Peripatetics and the Stoics, mainly in the hundred year period beginning about 350 BCE. Ancient Logic and Its Modern Interpretations is based on the 1973 Buffalo Symposium on Modernist Interpretations of Ancient Logic, the first conference devoted entirely to critical assessment of the state of ancient logic studies. Contributors: Corcoran, Garver, Gould, Kretzmann, Mueller, the Mulherns, Zirin.
The Development of Modus Ponens In Antiquity: From Aristotle to the 2nd Century AD
Phronesis, 2002
"ABSTRACT: This paper traces the earliest development of the most basic principle of deduction, i.e. modus ponens (or Law of Detachment). ‘Aristotelian logic’, as it was taught from late antiquity until the 20th century, commonly included a short presentation of the argument forms modus (ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens, and modus tollendo ponens. In late antiquity, arguments of these forms were generally classified as ‘hypothetical syllogisms’. However, Aristotle did not discuss such arguments, nor did he call any arguments ‘hypothetical syllogisms’. The Stoic indemonstrables resemble the modus ponens/tollens arguments. But the Stoics never called them ‘hypothetical syllogisms’; nor did they describe them as ponendo ponens, etc. The tradition of the four argument forms and the classification of the arguments as hypothetical syllogisms hence need some explaining. In this paper, I offer some explanations by tracing the development of certain elements of Aristotle’s logic via the early Peripatetics to the logic of later antiquity. I consider the questions: How did the four argument forms arise? Why were there four of them? Why were arguments of these forms called ‘hypothetical syllogisms’? On what grounds were they considered valid? I argue that such arguments were neither part of Aristotle’s dialectic, nor simply the result of an adoption of elements of Stoic logic, but the outcome of a long, gradual development that begins with Aristotle’s logic as preserved in his Topics and Prior Analytics; and that, as a result, we have a Peripatetic logic of hypothetical inferences which is a far cry both from Stoic logic and from classical propositional logic, but which sports a number of interesting characteristics, some of which bear a cunning resemblance to some 20th century theories."
A simple semantics for Aristotelian apodeictic syllogistics
Advances in Modal Logic, 2010
The first systematic study of reasoning and inference in the West was done by Aristotle. However, while his assertoric theory of syllogistic reasoning is provably sound and complete for the class of models validating the inferences in the traditional square of opposition [5, p. 100], his modal syllogistic, developed in chapters 3 and 8–22 of the Prior Analytics [1], has the rather dubious honor of being one of the most difficult to understand logical systems in history. Starting with some of his own students, many have considered Aristotle's modal ...
Some notes on the Aristotelian doctrine of opposition and the propositional calculus
Disputatio. Philosophical Research Bulletin , 2023
We develop some of Williamson's ideas regarding how propositional calculus aids in comprehending Aristotelian logic. Specifically, we enhance the utilisation of truth tables to examine the structure of opposition diagrams. Using 'conditioned truth tables', we establish logical dependency relationships between the truth values of different propositions. This approach proves effective in interpreting various texts of the Organon concerning the doctrine of opposition.
2017
This article examines the main characteristics of the concepts of implication in relevant, connexive and paraconsistent logics and discusses the origins of these concepts in Antiquity. It is made a comparative analysis between the meaning of this connective in the three logics in regard to their correspondence to the conditional “if...., then....” used in natural language and presents arguments that the notion of implication, proposed by relevant logic, provides the most adequate formal explication of the conditional connective in the mentioned sense.