Peano's Conception of a Single Infinite Cardinality

TL;DR

This paper explores Peano's lesser-known views on the infinite and his conception of a single infinite cardinality, reconstructing his evolving ideas and underlying motivations.

Contribution

It provides a detailed reconstruction of Peano's ideas on the infinite and offers hypotheses about his motivations, which are less documented in existing literature.

Findings

Peano's conception of a single infinite cardinality evolved over time.

Hypotheses about Peano's motivations for his views on the infinite.

Reconstruction of Peano's ideas contributes to historical understanding of mathematical infinity.

Abstract

While Peano's negative attitude towards infinitesimals, in particular, geometric infinitesimals, is widely documented, his conception of a single infinite cardinality and, more generally, his views on the infinite, are a lot less known. The paper reconstructs the evolution of Peano's ideas on these questions, and formulates several hypotheses about their underlying motivations.