The Logical Syntax of Greek Mathematics

This monograph explores Greek mathematics as a literary product, comparing it to logical and grammatical doctrines from antiquity. It describes the three stylistic codes, validation mechanism, mathematical object status, deductive machine, and sentential logical system. It is of interest to historians of ancient philosophy, specialists in Ancient Greek, and historians of mathematics.

Format: Hardback
Length: 396 pages
Publication date: 23 June 2021
Publisher: Springer Nature Switzerland AG

This monograph aims to present Greek mathematics as a literary product, analyzing its style from a logical and syntactic perspective, drawing parallels with logical and grammatical doctrines developed in antiquity. By doing so, it can address significant philosophical themes, such as the expression of mathematical generality and the selection of criteria for valid arguments, without resorting to anachronistic approaches. This book appeals to a wide range of scholars, including historians of ancient philosophy, specialists in Ancient Greek, and historians of mathematics.

The volume is organized into five parts, each progressively focusing on smaller linguistic units. The first part introduces the three stylistic codes of Greek mathematics, the second delves into the mechanism of validation, the third explores the status of mathematical objects and the problem of mathematical generality, the fourth analyzes the main features of the deductive machine, which is governed by the traditional division of a mathematical proposition into enunciation, setting-out, construction, and proof, and the fifth examines the sentential logical system of a mathematical proposition, with a particular emphasis on quantification, modalities, and connectors. Additionally, several complementary appendices are included to provide further insights.

By examining Greek mathematics through the lens of logic and syntax, this monograph offers a fresh perspective on the subject, shedding light on its literary qualities and its philosophical implications. It contributes to our understanding of the development of mathematics and its relationship to other fields of study in antiquity.

Weight: 776g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030769581
Edition number: 1st ed. 2021