more from Kurt Gdel

Single Idea 9590

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

Full Idea

The vast continent of arithmetical truth cannot be brought into systematic order by laying down a fixed set of axioms and rules of inference from which every true mathematical statement can be formally derived. For some this was a shocking revelation.

Gist of Idea

Arithmetical truth cannot be fully and formally derived from axioms and inference rules


report of Kurt Gdel (On Formally Undecidable Propositions [1931]) by E Nagel / JR Newman - Gdel's Proof VII.C

Book Reference

Nagel,E/Newman,J.R.: 'Gdel's Proof' [NYU 2001], p.104

A Reaction

Good news for philosophy, I'd say. The truth cannot be worked out by mechanical procedures, so it needs the subtle and intuitive intelligence of your proper philosopher (Parmenides is the role model) to actually understand reality.