Combining Texts

All the ideas for 'Set Theory and related topics (2nd ed)', 'Russell's Metaphysical Logic' and 'Seven Quodlibets'

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18 ideas

2. Reason / D. Definition / 8. Impredicative Definition
21704 'Impredictative' definitions fix a class in terms of the greater class to which it belongs [Linsky,B]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / e. Equivalence classes
8920 Equivalence relations are reflexive, symmetric and transitive, and classify similar objects [Lipschutz]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
21705 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
21727 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
21719 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
21723 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
21721 Higher types are needed to distinguished intensional phenomena which are coextensive [Linsky,B]
21703 Types are 'ramified' when there are further differences between the type of quantifier and its range [Linsky,B]
21714 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
21713 Did logicism fail, when Russell added three nonlogical axioms, to save mathematics? [Linsky,B]
21715 For those who abandon logicism, standard set theory is a rival option [Linsky,B]
8. Modes of Existence / A. Relations / 1. Nature of Relations
18529 Relations are expressed either as absolute facts, or by a relational concept [William of Ockham]
8. Modes of Existence / B. Properties / 11. Properties as Sets
21729 Construct properties as sets of objects, or say an object must be in the set to have the property [Linsky,B]
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
16779 Cut wood doesn't make a new substance, but seems to make separate subjects [William of Ockham]
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
16757 Hot water naturally cools down, which is due to the substantial form of the water [William of Ockham]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
9102 If an animal approached from a distance, we might abstract 'animal' from one instance [William of Ockham]
17. Mind and Body / D. Property Dualism / 6. Mysterianism
9114 There are no secure foundations to prove the separate existence of mind, in reason or experience [William of Ockham]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
9115 To love God means to love whatever God wills to be loved [William of Ockham]