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Single Idea 10073

[from 'Intro to Gödel's Theorems' by Peter Smith, in 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets ]

Full Idea

By Gödel's First Incompleteness Theorem, there cannot be a negation-complete set theory.

Gist of Idea

There cannot be a set theory which is complete

Source

Peter Smith (Intro to Gödel's Theorems [2007], 01.3)

Book Reference

Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.5

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A Reaction

This means that we can never prove all the truths of a system of set theory.