Single Idea 10624

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

Full Idea

The incompletability of formal arithmetic reveals, not arithmetical truths which are not truths of logic, but that logical truth likewise defies complete deductive characterization. ...Gödel's result has no specific bearing on the logicist project.

Gist of Idea

The incompletability of formal arithmetic reveals that logic also cannot be completely characterized

Source

B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], §2 n5)

Book Reference

Hale,B/Wright,C: 'The Reason's Proper Study' [OUP 2003], p.4


A Reaction

This is the key defence against the claim that Gödel's First Theorem demolished logicism.