Combining Philosophers

All the ideas for Bernard Linsky, Averroes (Ibn Rushd) and James Baillie

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15 ideas

2. Reason / D. Definition / 7. Contextual Definition
Contextual definitions eliminate descriptions from contexts [Linsky,B]
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 / D. Assumptions for Logic / 4. Identity in Logic
In logic identity involves reflexivity (x=x), symmetry (if x=y, then y=x) and transitivity (if x=y and y=z, then x=z) [Baillie]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
Definite descriptions, unlike proper names, have a logical structure [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]
7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing
Prime matter is halfway between non-existence and existence [Averroes]
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]