Single Idea 10309

[catalogued under 9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta]

Full Idea

Frege's argument for abstract objects is: 1) singular terms in true expressions must denote objects, 2) numerals function as singular terms, 3) there must exist numbers denoted by those expressions.

Gist of Idea

Frege says singular terms denote objects, numerals are singular terms, so numbers exist

Source

report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Bob Hale - Abstract Objects Ch.1

Book Reference

Hale,Bob: 'Abstract Objects' [Blackwell 1987], p.11


A Reaction

[compressed] Given that most of the singular term usages can be rephrased adjectively, this strikes me as a weak argument, though Hale pins his whole book on it.