Combining Texts

All the ideas for 'Beitrage', 'The Modularity of Mind' and 'Russell's Metaphysical Logic'

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13 ideas

2. Reason / D. Definition / 8. Impredicative Definition
'Impredictative' definitions fix a class in terms of the greater class to which it belongs [Linsky,B]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
Reducibility says any impredicative function has an appropriate predicative replacement [Linsky,B]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
Definite descriptions theory eliminates the King of France, but not the Queen of England [Linsky,B]
5. Theory of Logic / I. Semantics of Logic / 5. Extensionalism
Extensionalism means what is true of a function is true of coextensive functions [Linsky,B]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
The task of logicism was to define by logic the concepts 'number', 'successor' and '0' [Linsky,B]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
Higher types are needed to distinguished intensional phenomena which are coextensive [Linsky,B]
Types are 'ramified' when there are further differences between the type of quantifier and its range [Linsky,B]
The ramified theory subdivides each type, according to the range of the variables [Linsky,B]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Did logicism fail, when Russell added three nonlogical axioms, to save mathematics? [Linsky,B]
For those who abandon logicism, standard set theory is a rival option [Linsky,B]
8. Modes of Existence / B. Properties / 11. Properties as Sets
Construct properties as sets of objects, or say an object must be in the set to have the property [Linsky,B]
18. Thought / B. Mechanics of Thought / 3. Modularity of Mind
Mental modules are specialised, automatic, and isolated [Fodor, by Okasha]
18. Thought / E. Abstraction / 2. Abstracta by Selection
We form the image of a cardinal number by a double abstraction, from the elements and from their order [Cantor]