Single Idea 23446

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic]

Full Idea

If the 2nd Incompleteness Theorem undermines Hilbert's attempt to use a weak theory to prove the consistency of a strong one, it is still possible to prove the consistency of one theory, assuming the consistency of another theory.

Gist of Idea

You can't prove consistency using a weaker theory, but you can use a consistent theory

Source

Øystein Linnebo (Philosophy of Mathematics [2017], 4.6)

Book Reference

Linnebo,Øystein: 'Philosophy of Mathematics' [Princeton 2017], p.71


A Reaction

Note that this concerns consistency, not completeness.