more from Kurt Gdel

Single Idea 10867

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

Full Idea

An approximation of Gdel's Theorem imagines a statement 'This system of mathematics can't prove this statement true'. If the system proves the statement, then it can't prove it. If the statement can't prove the statement, clearly it still can't prove it.

Gist of Idea

'This system can't prove this statement' makes it unprovable either way


report of Kurt Gdel (On Formally Undecidable Propositions [1931]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.15

Book Reference

Clegg,Brian: 'Infinity' [Robinson 2003], p.202

A Reaction

Gdel's contribution to this simple idea seems to be a demonstration that formal arithmetic is capable of expressing such a statement.