### Single Idea 10006

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

Full Idea

Representing arithmetic formally we do not primarily care about semantic features of number words. We are interested in capturing the inferential relations of arithmetical statements to one another, which can be done elegantly in first-order logic.

Gist of Idea

First-order logic captures the inferential relations of numbers, but not the semantics

Source

Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.3)

Book Reference

-: 'Philosophical Review 114' [Phil Review 2005], p.217

A Reaction

This begins to pinpoint the difference between the approach of logicists like Frege, and those who are interested in the psychology of numbers, and the empirical roots of numbers in the process of counting.