La Dissertatio de Arte Combinatoria de Leibniz en seconde lecture

TL;DR

This paper reexamines Leibniz's 1666 Dissertatio de Arte Combinatoria, highlighting its overlooked mathematical structure, especially the symmetric group, and its influence on Leibniz's later ideas.

Contribution

It offers a new perspective on Leibniz's work by analyzing its mathematical foundations and emphasizing the significance of the caput variationis in his thought.

Findings

Highlights the role of the symmetric group in Leibniz's combinatorial art.

Identifies the caput variationis as a fundamental concept in Leibniz's work.

Connects the Dissertatio's insights to Leibniz's subsequent philosophical ideas.

Abstract

This article considers the Dissertatio de Arte Combinatoria, published in 1666 and relatively neglected by Leibniz s scholars. However in recent times the tide seems to be changing. Our work presents three main parts (sections II, III and IV, respectively). The first one exposes the contributions of M. Serres and E. Knobloch, viewed from our stand-point. The second one emphazises the role played by the symmetric group as the underlying mathematical structure of the Opus. Finally we treat the caput variationis which, in our opinion, is the fundamental concept of the Dissertatio. Moreover, it is suggested that the importance of such a theoretical insight may be traced in many aspects of Leibniz s subsequent thought.