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 1980,0-631-12911-1]].

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5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
First-level functions have objects as arguments; second-level functions take functions as arguments
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
Relations are functions with two arguments
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism
8. Modes of Existence / B. Properties / 10. Properties as Predicates
Frege allows either too few properties (as extensions) or too many (as predicates)
9. Objects / A. Existence of Objects / 3. Objects in Thought
The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place
18. Thought / D. Concepts / 2. Ontology of Concepts / c. Fregean concepts
Concepts are the ontological counterparts of predicative expressions
An assertion about the concept 'horse' must indirectly speak of an object
A concept is a function whose value is always a truth-value
18. Thought / D. Concepts / 3. Structure of Concepts / a. Conceptual structure
Unlike objects, concepts are inherently incomplete
19. Language / D. Theories of Reference / 5. Speaker's Reference
I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false
28. God / C. Proofs of Reason / 2. Ontological Proof critique
The Ontological Argument fallaciously treats existence as a first-level concept