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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 Ref
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.
| 18806 | Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt] |
| 18899 | Frege takes the existence of horses to be part of their concept [Frege, by Sommers] |
| 4028 | Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver on Frege] |
| 9947 | Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman] |
| 9948 | Unlike objects, concepts are inherently incomplete [Frege, by George/Velleman] |
| 10319 | An assertion about the concept 'horse' must indirectly speak of an object [Frege, by Hale] |
| 4972 | I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege] |
| 8488 | A concept is a function whose value is always a truth-value [Frege] |
| 8487 | Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege] |
| 8489 | The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege] |
| 8490 | First-level functions have objects as arguments; second-level functions take functions as arguments [Frege] |
| 8491 | The Ontological Argument fallaciously treats existence as a first-level concept [Frege] |
| 8492 | Relations are functions with two arguments [Frege] |