Single Idea 9004

[catalogued under 6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique]

Full Idea

We might say that set theory is not really logic, but a branch of mathematics. This would deprive 'includes' of the status of a logical word. Frege's derivation of arithmetic would then cease to count as a derivation from logic: for he used set theory.

Gist of Idea

If set theory is not actually a branch of logic, then Frege's derivation of arithmetic would not be from logic

Source

Willard Quine (Carnap and Logical Truth [1954], II)

Book Reference

Quine,Willard: 'Ways of Paradox and other essays' [Harvard 1976], p.111


A Reaction

Quine has been making the point that higher infinities and the paradoxes undermine the status of set theory as logic, but he decides to continue thinking of set theory as logic. Critics of logicism frequently ask whether the reduction is to logic.