Single Idea 21647

[catalogued under 6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism]

Full Idea

Frege's tying the objectivity of arithmetic to the objectivity of logic makes sense of the fact that can find out about arithmetic by thinking alone.

Gist of Idea

Logicism makes sense of our ability to know arithmetic just by thought


Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 06.1.1)

Book Reference

Hofweber,Thomas: 'Ontology and the Ambitions of Metaphysics' [OUP 2018], p.154

A Reaction

This assumes that logic is entirely a priori. We might compare the geometry of land surfaces with 'pure' geometry. If numbers are independent objects, it is unclear how we could have any a priori knowledge of them.