M×Φ

Annals of Mathematics and Philosophy

What is axiomatics?

The article investigates axiomatics as a complex mathematical practice whose inquiry, while taking its cue from the analysis of some specific mathematical theories, requires an interdisciplinary approach. Axiomatics, if analyzed in detail through a study of its foundational component, of the styles with which it is associated and of the rules that govern it, performs a plurality of functions. It serves heuristic, descriptive, genetic-historical, pedagogical and architectural aims. But it can also play the role of conceptual analysis, modular analysis and coordination tool, soliciting a quest for rigor. An example taken from Peano's investigation of axiomatic systems illustrates the kind of results that this interdisciplinary approach to mathematical practice might produce, showing what can be achieved by considering axiomatics as research on the foundations of mathematics, or as a mathematical style, or as a social institution.

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Cantù, P. (2023). What is axiomatics?. M×Φ — Annals of Mathematics and Philosophy, 1(1), 1–24.

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