Ideas from 'Function and Concept' by Gottlob Frege [1891], by Theme Structure
[found in 'Translations from the Writings of Gottlob Frege' by Frege,Gottlob (ed/tr Geach,P. /Black,Max) [Blackwell 1980,0631129111]].
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5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
8490

Firstlevel functions have objects as arguments; secondlevel functions take functions as arguments

5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
8492

Relations are functions with two arguments

6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
8487

Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism

8. Modes of Existence / B. Properties / 10. Properties as Predicates
4028

Frege allows either too few properties (as extensions) or too many (as predicates)

9. Objects / A. Existence of Objects / 3. Objects in Thought
8489

The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place

18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
9947

Concepts are the ontological counterparts of predicative expressions

10319

An assertion about the concept 'horse' must indirectly speak of an object

8488

A concept is a function whose value is always a truthvalue

18. Thought / D. Concepts / 4. Structure of Concepts / a. Conceptual structure
9948

Unlike objects, concepts are inherently incomplete

19. Language / B. Reference / 5. Speaker's Reference
4972

I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false

28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
8491

The Ontological Argument fallaciously treats existence as a firstlevel concept
