Ideas from 'works' by Gottlob Frege [1890], by Theme Structure

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4. Formal Logic / F. Set Theory ST / 1. Set Theory
Frege did not think of himself as working with sets
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
The null set is indefensible, because it collects nothing
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
Frege proposed a realist concept of a set, as the extension of a predicate or concept or function
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Frege frequently expressed a contempt for language
5. Theory of Logic / C. Ontology of Logic / 2. Platonism in Logic
Frege thinks there is an independent logical order of the truths, which we must try to discover
5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic
Frege gives a functional account of predication so that we can dispense with predicates
For Frege, predicates are names of functions that map objects onto the True and False
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
Frege always, and fatally, neglected the domain of quantification
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Basic truths of logic are not proved, but seen as true when they are understood
6. Mathematics / B. Foundations for Mathematics / 4. Definitions of Number / c. Fregean numbers
If '5' is the set of all sets with five members, that may be circular, and you can know a priori if the set has content
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Frege aimed to discover the logical foundations which justify arithmetical judgements
Eventually Frege tried to found arithmetic in geometry instead of in logic
7. Existence / A. Nature of Existence / 3. Being / i. Deflating being
Frege's logic showed that there is no concept of being
9. Objects / F. Identity among Objects / 5. Self-Identity
Frege made identity a logical notion, enshrined above all in the formula 'for all x, x=x'
11. Knowledge Aims / A. Knowledge / 2. Understanding
To understand a thought, understand its inferential connections to other thoughts
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
Frege's concept of 'self-evident' makes no reference to minds
12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
An apriori truth is grounded in generality, which is universal quantification
14. Science / B. Scientific Theories / 1. Scientific Theory
The building blocks contain the whole contents of a discipline
18. Thought / E. Abstraction / 8. Abstractionism Critique
Frege said concepts were abstract entities, not mental entities
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
A thought is not psychological, but a condition of the world that makes a sentence true
19. Language / B. Assigning Meanings / 5. Fregean Semantics
Frege's 'sense' is the strict and literal meaning, stripped of tone
'Sense' solves the problems of bearerless names, substitution in beliefs, and informativeness
19. Language / E. Analyticity / 1. Analytic Propositions
'P or not-p' seems to be analytic, but does not fit Kant's account, lacking clear subject or predicate
19. Language / E. Analyticity / 2. Analytic Truths
Analytic truths are those that can be demonstrated using only logic and definitions
28. God / C. Proofs of Reason / 1. Ontological Proof
Frege put forward an ontological argument for the existence of numbers