Single Idea 10071

[catalogued under 5. Theory of Logic / K. Features of Logics / 2. Consistency]

Full Idea

Second Incompleteness Theorem: roughly, nice theories that include enough basic arithmetic can't prove their own consistency.

Gist of Idea

Second Incompleteness: nice theories can't prove their own consistency

Source

report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Peter Smith - Intro to Gödel's Theorems 1.5

Book Reference

Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.6


A Reaction

On the face of it, this sounds less surprising than the First Theorem. Philosophers have often noticed that it seems unlikely that you could use reason to prove reason, as when Descartes just relies on 'clear and distinct ideas'.