Single Idea 23444

[catalogued under 5. Theory of Logic / K. Features of Logics / 1. Axiomatisation]

Full Idea

Mathematics investigates the deductive consequences of axiomatic theories, but it also needs its own foundational axioms in order to provide models for its various axiomatic theories.

Gist of Idea

To investigate axiomatic theories, mathematics needs its own foundational axioms

Source

Øystein Linnebo (Philosophy of Mathematics [2017], 4.1)

Book Reference

Linnebo,Øystein: 'Philosophy of Mathematics' [Princeton 2017], p.56


A Reaction

This is a problem which faces the deductivist (if-then) approach. The deductive process needs its own grounds.