more from Peter Koellner

Single Idea 17887

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic]

Full Idea

To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem].

Gist of Idea

PA is consistent as far as we can accept, and we expand axioms to overcome limitations


Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1)

Book Reference

-: 'Philosophia Mathematica' [-], p.4

A Reaction

Each expansion brings a limitation, but then you can expand again.