The Logical Syntax of Greek Mathematics

The aim of this monograph is to describe Greek mathematics as a literary product, studying its style from a logico-syntactic point of view and setting parallels with logical and grammatical doctrines developed in antiquity. In this way, major philosophical themes such as the expression of mathematical generality and the selection of criteria of validity for arguments can be treated without anachronism. Thus, the book is of interest for both historians of ancient philosophy and specialists in Ancient Greek, in addition to historians of mathematics.
This volume is divided into five parts, ordered in decreasing size of the linguistic units involved. The first part describes the three stylistic codes of Greek mathematics; the second expounds in detail the mechanism of "validation"; the third deals with the status of mathematical objects and the problem of mathematical generality; the fourth analyzes the main features of the "deductive machine," i.e. the suprasentential logical system dictated by the traditional division of a mathematical proposition into enunciation, setting-out, construction, and proof; and the fifth deals with the sentential logical system of a mathematical proposition, with special emphasis on quantification, modalities, and connectors. A number of complementary appendices are included as well.

Includes Greek texts with associated translation Contains several appendices and rich indices Is of interest to linguists and historians of ancient philosophy

Résumé

"This book is an English version, with expansions and improvements ... . this book is not an argument to be read cover-to-cover, but rather serves as a repository for many of the insights and views that the author developed over his years of working on these sources. ... This is an important book on the language of Greek mathematical texts, and scholars of these sources will find much that is useful in its pages." (Nathan Sidoli, MAA Reviews, March 29, 2024)

"This is a deep and detailed linguistic study of ancient Greek mathematical texts. ... This wide-ranging book exploits the resources of several disciplines including classical philology, manuscript studies, statistical analysis, and computational linguistics, as well as the history and philosophy of mathematics. It will doubtless be much used as a reference work in those disciplines." (Paul Thom, Mathematical Reviews, May, 2022)

Contenu

1. The Three Stylistic Codes of Greek Mathematics.- 2. Validation and Templates.- 3. The Problem of Mathematical Generality.- 4. The Deductive Machine.- 5. The Logical Syntax.- Appendices.- Bibliography.- Indices.