Single Idea 8490

[catalogued under 5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic]

Full Idea

Just as functions are fundamentally different from objects, so also functions whose arguments are and must be functions are fundamentally different from functions whose arguments are objects. The latter are first-level, the former second-level, functions.

Gist of Idea

First-level functions have objects as arguments; second-level functions take functions as arguments

Source

Gottlob Frege (Function and Concept [1891], p.38)

Book Reference

Frege,Gottlob: 'Translations from the Writings of Gottlob Frege', ed/tr. Geach,P/Black,M [Blackwell 1980], p.38


A Reaction

In 1884 he called it 'second-order'. This is the standard distinction between first- and second-order logic. The first quantifies over objects, the second over intensional entities such as properties and propositions.