Combining Texts

All the ideas for 'fragments/reports', 'Russell's Metaphysical Logic' and 'The Problem of Knowledge'

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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]
2. Reason / F. Fallacies / 1. Fallacy
19463 Induction assumes some uniformity in nature, or that in some respects the future is like the past [Ayer]
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 / 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]
11. Knowledge Aims / B. Certain Knowledge / 5. Cogito Critique
19461 Knowing I exist reveals nothing at all about my nature [Ayer]
19459 To say 'I am not thinking' must be false, but it might have been true, so it isn't self-contradictory [Ayer]
19460 'I know I exist' has no counterevidence, so it may be meaningless [Ayer]
14. Science / A. Basis of Science / 6. Falsification
19464 We only discard a hypothesis after one failure if it appears likely to keep on failing [Ayer]
14. Science / C. Induction / 2. Aims of Induction
19462 Induction passes from particular facts to other particulars, or to general laws, non-deductively [Ayer]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]