Combining Texts

All the ideas for 'Function and Concept', 'Letter to Frege 29.12.1899' and 'The Big Book of Concepts'

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38 ideas

3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt]
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 [Frege]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
Relations are functions with two arguments [Frege]
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 [Frege]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
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
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
The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege]
12. Knowledge Sources / B. Perception / 5. Interpretation
Research shows perceptual discrimination is sharper at category boundaries [Murphy]
14. Science / C. Induction / 1. Induction
Induction is said to just compare properties of categories, but the type of property also matters [Murphy]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
The main theories of concepts are exemplar, prototype and knowledge [Murphy]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman]
An assertion about the concept 'horse' must indirectly speak of an object [Frege, by Hale]
A concept is a function whose value is always a truth-value [Frege]
18. Thought / D. Concepts / 4. Structure of Concepts / a. Conceptual structure
Unlike objects, concepts are inherently incomplete [Frege, by George/Velleman]
18. Thought / D. Concepts / 4. Structure of Concepts / c. Classical concepts
The classical definitional approach cannot distinguish typical and atypical category members [Murphy]
Classical concepts follow classical logic, but concepts in real life don't work that way [Murphy]
Classical concepts are transitive hierarchies, but actual categories may be intransitive [Murphy]
The classical core is meant to be the real concept, but actually seems unimportant [Murphy]
The theoretical and practical definitions for the classical view are very hard to find [Murphy]
18. Thought / D. Concepts / 4. Structure of Concepts / d. Concepts as prototypes
There is no 'ideal' bird or dog, and prototypes give no information about variability [Murphy]
Prototypes are unified representations of the entire category (rather than of members) [Murphy]
The prototype theory uses observed features, but can't include their construction [Murphy]
The prototype theory handles hierarchical categories and combinations of concepts well [Murphy]
Prototypes theory of concepts is best, as a full description with weighted typical features [Murphy]
Learning concepts is forming prototypes with a knowledge structure [Murphy]
18. Thought / D. Concepts / 4. Structure of Concepts / e. Concepts from exemplars
The exemplar view of concepts says 'dogs' is the set of dogs I remember [Murphy]
Children using knowing and essentialist categories doesn't fit the exemplar view [Murphy]
Exemplar theory struggles with hierarchical classification and with induction [Murphy]
Conceptual combination must be compositional, and can't be built up from exemplars [Murphy]
The concept of birds from exemplars must also be used in inductions about birds [Murphy]
The most popular theories of concepts are based on prototypes or exemplars [Murphy]
18. Thought / D. Concepts / 4. Structure of Concepts / f. Theory theory of concepts
We do not learn concepts in isolation, but as an integrated part of broader knowledge [Murphy]
Concepts with familiar contents are easier to learn [Murphy]
Some knowledge is involved in instant use of categories, other knowledge in explanations [Murphy]
People categorise things consistent with their knowledge, even rejecting some good evidence [Murphy]
19. Language / B. Reference / 5. Speaker's Reference
I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
The Ontological Argument fallaciously treats existence as a first-level concept [Frege]