Combining Texts

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

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25 ideas

2. Reason / D. Definition / 3. Types of Definition
9143 Implicit definitions must be satisfiable, creative definitions introduce things, contextual definitions build on things [Fine,K, by Cook/Ebert]
10143 'Creative definitions' do not presuppose the existence of the objects defined [Fine,K]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
18806 Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt]
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]
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]
7. Existence / A. Nature of Existence / 4. Abstract Existence
10145 Abstracts cannot be identified with sets [Fine,K]
10136 Points in Euclidean space are abstract objects, but not introduced by abstraction [Fine,K]
10144 Postulationism says avoid abstract objects by giving procedures that produce truth [Fine,K]
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]
18. Thought / E. Abstraction / 1. Abstract Thought
9144 Fine's 'procedural postulationism' uses creative definitions, but avoids abstract ontology [Fine,K, by Cook/Ebert]
18. Thought / E. Abstraction / 2. Abstracta by Selection
10141 Many different kinds of mathematical objects can be regarded as forms of abstraction [Fine,K]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10135 We can abstract from concepts (e.g. to number) and from objects (e.g. to direction) [Fine,K]
9142 Fine considers abstraction as reconceptualization, to produce new senses by analysing given senses [Fine,K, by Cook/Ebert]
10137 Abstractionism can be regarded as an alternative to set theory [Fine,K]
10138 An object is the abstract of a concept with respect to a relation on concepts [Fine,K]
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]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
8491 The Ontological Argument fallaciously treats existence as a first-level concept [Frege]