Permanence as a principle of practice

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's reading of permanence as a logically necessary principle.