Permanence as a Principle of Practice

TL;DR

This paper explores the historical and philosophical significance of the principle of permanence in mathematical notation, emphasizing its role in practical rationality and its influence on the development of vector calculus and logical notation.

Contribution

It provides a historical analysis of the principle of permanence, highlighting its practical rationality aspect and its impact on mathematical notation choices.

Findings

Permanence was used to justify specific notations in vector calculus.

The principle was historically understood as a practical rationality, not just theoretical.

Hahn revived Peano's argument against Pringsheim's interpretation of permanence.

Abstract

The paper discusses Peano's argument for preserving familiar notations. The argument reinforces the principle of permanence, articulated in the early 19th century by Peacock, then adjusted by Hankel and adopted by many others. Typically regarded as a principle of theoretical rationality, permanence was understood by Peano, following Mach, and against Schubert, as a principle of practical rationality. The paper considers how permanence, thus understood, was used in justifying Burali-Forti and Marcolongo's notation for vectorial calculus, and in rejecting Frege's logical notation, and closes by considering Hahn's revival of Peano's argument against Pringsheim' reading of permanence as a logically necessary principle.