Single Idea 18111

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

Full Idea

If logic is neutral on the number of objects there are, then logicists can't construe numbers as objects, for arithmetic is certainly not neutral on the number of numbers there are. They must be treated in some other way, perhaps as numerical quantifiers.

Gist of Idea

Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality

Source

David Bostock (Philosophy of Mathematics [2009], 5.5)

Book Reference

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.159