more from Robert S. Wolf

Single Idea 13535

[catalogued under 5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic]

Full Idea

The 'completeness' of first order-logic does not mean that every sentence or its negation is provable in first-order logic. We have instead the weaker result that every valid sentence is provable.

Gist of Idea

First-order logic is weakly complete (valid sentences are provable); we can't prove every sentence or its negation


Robert S. Wolf (A Tour through Mathematical Logic [2005], 5.3)

Book Reference

Wolf,Robert S.: 'A Tour Through Mathematical Logic' [Carus Maths Monographs 2005], p.174

A Reaction

Peter Smith calls the stronger version 'negation completeness'.