If, then, therefore? Neoplatonic Exegetical Logic between the Categorical and the Hypothetical

Marije Martijn

doi:10.30965/26664275-bja10043

Abstract

Abstract 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.

Highlights

Neoplatonic Logic?One of the debates in the history of logic, is if there is such a thing as (Neo)Platonic logic
I will argue that the views on the differences and relation between categorical and hypothetical syllogisms is a point in case, as they are determined by underlying Neoplatonic epistemological considerations
He points out that some categorical syllogisms are demonstrated by reductio, and require the use of hypothetical syllogisms, but does not think this implies a reduction of categorical to hypothetical, because the demonstrative power of the reductio lies in its categorical element. Another interesting topic is the variety we find in ancient explanations of reductio arguments as consisting of categorical and/or hypothetical syllogisms

Summary

Introduction

One of the debates in the history of logic, is if there is such a thing as (Neo)Platonic logic. Socratic elenchus or refutation does typically use mixed arguments, including reductio ad absurdum; categorical syllogisms are used to present demonstrative knowledge; the wholly hypothetical syllogisms work as a preparatory dialectical stage. These two give a Platonic angle to late ancient syllogistic, as being founded, the first upon the logic of the intelligible, and the role of definitions in scientific demonstrations, and the second upon the dialectical method of division, with its assumption of exhaustive dichotomies They help explain why on occasion the commentators’ syllogisms may seem invalid, but turn out to be valid if we assume co-extension and dichotomy. Let us turn to the commentaries for some examples of Neoplatonic uses of and reflections on categorical and hypothetical syllogisms

Introductory Remarks – Commentary on the Republic and Platonic Theology

Conclusion