more from Gottlob Frege

### Single Idea 10013

#### [catalogued under 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers]

Full Idea

Summary: numerical terms are singular terms designating objects; numerical predicates are level 1 concepts and relations; quantification over mathematics is referential; hence arithmetic has first-order form, and mathematical objects exist, non-spatially.

Gist of Idea

Numerical statements have first-order logical form, so must refer to objects

Source

report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §55?) by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.123

Book Reference

-: 'Journal of Philosophy' [-], p.123

A Reaction

[compressed] So the heart of Frege is his translation of 'Jupiter has four moons' into a logical form which only refers to numerical objects. Commentators seem vague as to whether the theory is first-order or second-order.