Greek and Roman Logic

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, which are topics that might now fall under the headings of philosophy of logic or non-classical logic. This includes discussions of problems and paradoxes that connect to contemporary logic and which historically spurred developments of logical method. For example, there is great interest among ancient philosophers in the question of whether all statements have truth-values. Relevant themes here include future contingents, paradoxes of vagueness, and semantic paradoxes like the liar. We also include discussion of the paradoxes of the infinite for similar reasons, since solutions have introduced sophisticated tools of logical analysis and there are a range of related, modern philosophical concerns about the application of some logical principles in infinite domains. Our criterion excludes, however, many of the themes that Hellenistic philosophers consider part of logic, in particular, it excludes epistemology and metaphysical questions about truth. Ancient philosophers do not write treatises “On Logic,” where the topic would be what today counts as logic. Instead, arguments and theories that count as “logic” by our criterion are found in a wide range of texts. For the most part, our entry follows chronology, tracing ancient logic from its beginnings to Late Antiquity. However, some themes are discussed in several eras of ancient logic; ancient logicians engage closely with each other’s views. Accordingly, relevant publications address several authors and periods in conjunction. These contributions are listed in three thematic sections at the end of our entry

Megara and ‘the Megarians’: a City and its Philosophical School

From the late Classical to the early Hellenistic period, Megara was a vibrant centre of philosophy. The school of the so-called Megarians drew its name from the city. This paper examines the philosophical school and its leading members, Eukleides, Ichthyas, and Stilpo. The discussion of the school in the localscape of the city illustrates how ‘the Megarians’, although not necessarily united by common thought paradigms or intellectual approaches, played an integral role in the identity of place at Megara

Los condicionales y la cuantificación universal: una relación lógica y psicológica

In classical logic, it is evident that there is a clear relationship between the conditional, which is materially interpreted, and the universally quantified sentences. In this paper, I claim that this relationship is not only a requirement of that logic, but we also have important evidence that seems to prove that the human mind assumes it in a natural way by virtue of purely psychological reasons. To show this, I resort to an ancient text authored by Sextus Empiricus, in which the relationship is explained in a very precise manner, and the framework given by a current cognitive theory, the mental models theory, in which descriptions of the way it appears that human beings tend to understand both conditionals and the universally quantified sentences are included.En la lógica clásica, es evidente que existe una relación clara entre el condicional, el cual es interpretado materialmente, y las sentencias cuantificadas universalmente. En este trabajo, proponemos que tal relación no es solo una exigencia de esa lógica, sino que contamos también con importantes evidencias que parecen probar que la mente humana la asume de manera natural en virtud de razones puramente psicológicas. Para mostrar esto, recurrimos a un texto antiguo escrito por Sexto Empírico, en el que se explica la relación de un modo muy preciso, y al marco ofrecido por una teoría cognitiva actual, la teoría de los modelos mentales, en el que se incluyen descripciones de la manera en que parece que los seres humanos tendemos a entender tanto los condicionales como las sentencias cuantificadas universalmente

Harmony in diversity. On the (possible) existence of ‘the Canadian school of argumentation’

By looking at the birth and evolution of the informal logic movement, and by clarifying which kind of relations in a diversity we need in order to understand what “school” means, we would like to consider the hypothesis that there is something which could be called ‘the Canadian school of argumentation’ or, at least, of a Canadian tradition amongst those that make up the greater field of the study of argumentation

Chrysippus’ Indemonstrables and Mental Logic

Stoic logic assumes fi ve inference schemata attributed to Chrysippus of Soli. Those schemata are the well-known indemonstrables. A problem related to them can be that, according to standard propositional calculus, only one of them, modus ponens, is clearly indemonstrable. Nevertheless, I try to show in this paper that the mental logic theory enables to understand why the Stoics considered such schemata to be basic kinds of arguments. Following that theory, four of them can be linked to ‘Core Schemata’ of mental logic and the only one that is more controversial is modus tollens. However, as I also comment, some assumptions of Stoic philosophy, which can be interpreted from the mental logic theory, can explain why this last argument was included into the set of the indemonstrables as well

Heraclitus in Verse: The Poetic Fragments of Scythinus of Teos

The two fragments of Scythinus\u2019 poetic version of Heraclitus help to clarify several aspects of the philosopher\u2019s thought that are obscure in his own fragments, especially as pertains to time, \u3c7\u3c1\u3cc\u3bd\u3bf\u3c2

Stoic Trichotomies

Chrysippus often talks as if there is a third option when we might expect that two options in response to a question are exhaustive. Things are true, false or neither; equal, unequal, or neither; the same, different, or neither.. and so on. There seems to be a general pattern here that calls for a general explanation. This paper offers a general explanation of this pattern, preserving Stoic commitments to excluded middle and bivalence, arguing that Chrysippus employs this trichotomy move when he wishes to argue that apparent contradictories are only contraries, and wishes to endorse a third option. This general explanation of the pattern of trichotomies sheds light on a number of interpretive puzzles, including on Chrysippus's response to the paradox of the cone. The purpose of these trichotomies is also discussed, and it is suggested that they originate from the dialectical context in which philosophical problems were posed

The Liar Paradox as a reductio ad absurdum argument

This presentation traces an historical root of the reductio ad absurdum mode of argumentation in Greek philosophy. I propose a new understanding of the liar paradox as an instance of this mode of argumentation. I show that the paradox was crea ted as part of a refutational argument in the controversy over the justification of realism and the realists concepts of truth and certainty. The paradox was part of the dialectical style of Greek scepticism, which was characterized, inter alia, by the u se of the reductio ad absurdum. The paradox turns out to be a metaphysical and epistemological argument