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.