Combining Texts

All the ideas for 'Function and Concept', 'The Value of Knowledge and the Pursuit of Understanding' and 'Begriffsschrift'

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34 ideas

1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
22270 Frege changed philosophy by extending logic's ability to check the grounds of thinking [Potter on Frege]
2. Reason / B. Laws of Thought / 1. Laws of Thought
8939 We should not describe human laws of thought, but how to correctly track truth [Frege, by Fisher]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
18806 Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt]
4. Formal Logic / C. Predicate Calculus PC / 1. Predicate Calculus PC
4971 I don't use 'subject' and 'predicate' in my way of representing a judgement [Frege]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / d. Universal quantifier ∀
17745 For Frege, 'All A's are B's' means that the concept A implies the concept B [Frege, by Walicki]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
7728 Frege has a judgement stroke (vertical, asserting or judging) and a content stroke (horizontal, expressing) [Frege, by Weiner]
16881 The laws of logic are boundless, so we want the few whose power contains the others [Frege]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
7622 In 1879 Frege developed second order logic [Frege, by Putnam]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
7729 Frege replaced Aristotle's subject/predicate form with function/argument form [Frege, by Weiner]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
8490 First-level functions have objects as arguments; second-level functions take functions as arguments [Frege]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
8492 Relations are functions with two arguments [Frege]
5. Theory of Logic / G. Quantification / 1. Quantification
9950 A quantifier is a second-level predicate (which explains how it contributes to truth-conditions) [Frege, by George/Velleman]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
9991 For Frege the variable ranges over all objects [Frege, by Tait]
10536 Frege's domain for variables is all objects, but modern interpretations first fix the domain [Dummett on Frege]
5. Theory of Logic / G. Quantification / 3. Objectual Quantification
7730 Frege introduced quantifiers for generality [Frege, by Weiner]
7742 Frege reduced most quantifiers to 'everything' combined with 'not' [Frege, by McCullogh]
5. Theory of Logic / H. Proof Systems / 1. Proof Systems
13824 Proof theory began with Frege's definition of derivability [Frege, by Prawitz]
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
13609 Frege produced axioms for logic, though that does not now seem the natural basis for logic [Frege, by Kaplan]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
17855 It may be possible to define induction in terms of the ancestral relation [Frege, by Wright,C]
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 [Frege]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
10607 Frege's logic has a hierarchy of object, property, property-of-property etc. [Frege, by Smith,P]
7. Existence / A. Nature of Existence / 1. Nature of Existence
11008 Existence is not a first-order property, but the instantiation of a property [Frege, by Read]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
18899 Frege takes the existence of horses to be part of their concept [Frege, by Sommers]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
4028 Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver on Frege]
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 [Frege]
11. Knowledge Aims / A. Knowledge / 2. Understanding
19261 Understanding is seeing coherent relationships in the relevant information [Kvanvig]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
9947 Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman]
10319 An assertion about the concept 'horse' must indirectly speak of an object [Frege, by Hale]
8488 A concept is a function whose value is always a truth-value [Frege]
18. Thought / D. Concepts / 4. Structure of Concepts / a. Conceptual structure
9948 Unlike objects, concepts are inherently incomplete [Frege, by George/Velleman]
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 [Frege]
19. Language / C. Assigning Meanings / 4. Compositionality
22280 Frege's account was top-down and decompositional, not bottom-up and compositional [Frege, by Potter]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
7741 The predicate 'exists' is actually a natural language expression for a quantifier [Frege, by Weiner]
8491 The Ontological Argument fallaciously treats existence as a first-level concept [Frege]