Single Idea 17853

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic]

Full Idea

The intuitive proposal is the essential number theoretic truths are precisely the logical consequences of the Peano axioms, ...but the notion of consequence is a semantic one...and it is not obvious that we possess a semantic notion of the requisite kind.

Gist of Idea

Number truths are said to be the consequence of PA - but it needs semantic consequence

Source

Crispin Wright (Frege's Concept of Numbers as Objects [1983], Intro)

Book Reference

Wright,Crispin: 'Frege's Conception of Numbers' [Scots Philosophical Monographs 1983], p.-9


A Reaction

(Not sure I understand this, but it is his starting point for rejecting PA as the essence of arithmetic).