Ideas from 'works' by Gottlob Frege [1890], by Theme Structure
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4. Formal Logic / F. Set Theory ST / 1. Set Theory
13455

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
16895

The null set is indefensible, because it collects nothing

4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
3328

Frege proposed a realist concept of a set, as the extension of a predicate or concept or function

5. Theory of Logic / C. Ontology of Logic / 2. Platonism in Logic
13473

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
3319

Frege gives a functional account of predication so that we can dispense with predicates

6076

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
9871

Frege always, and fatally, neglected the domain of quantification

5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
16884

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
3331

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
16880

Frege aimed to discover the logical foundations which justify arithmetical judgements

8689

Eventually Frege tried to found arithmetic in geometry instead of in logic

7. Existence / A. Nature of Existence / 3. Being / i. Deflating being
5657

Frege's logic showed that there is no concept of being

9. Objects / F. Identity among Objects / 5. SelfIdentity
3318

Frege made identity a logical notion, enshrined above all in the formula 'for all x, x=x'

11. Knowledge Aims / A. Knowledge / 2. Understanding
16885

To understand a thought, understand its inferential connections to other thoughts

12. Knowledge Sources / A. A Priori Knowledge / 2. SelfEvidence
16887

Frege's concept of 'selfevident' makes no reference to minds

12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
16894

An apriori truth is grounded in generality, which is universal quantification

14. Science / B. Scientific Theories / 1. Scientific Theory
16882

The building blocks contain the whole contents of a discipline

18. Thought / D. Concepts / 6. Abstract Concepts / h. Abstractionism critique
5816

Frege said concepts were abstract entities, not mental entities

19. Language / A. Language / 1. Language
9179

Frege frequently expressed a contempt for language

19. Language / B. Meaning / 6. Meaning as TruthConditions
7307

A thought is not psychological, but a condition of the world that makes a sentence true

19. Language / C. Semantics / 2. Fregean Semantics
7309

Frege's 'sense' is the strict and literal meaning, stripped of tone

7312

'Sense' solves the problems of bearerless names, substitution in beliefs, and informativeness

19. Language / F. Analytic/Synthetic / 2. Analytic Propositions
7725

'P or notp' seems to be analytic, but does not fit Kant's account, lacking clear subject or predicate

19. Language / F. Analytic/Synthetic / 3. Analytic Truths
7316

Analytic truths are those that can be demonstrated using only logic and definitions

28. God / C. Proofs of Reason / 1. Ontological Proof
3307

Frege put forward an ontological argument for the existence of numbers
