Combining Texts

All the ideas for 'That Politics may be reduced to a Science', 'Intro to 'The Reason's Proper Study'' and 'Russell's Metaphysical Logic'

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22 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 / 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]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / c. Grelling's paradox
10631 If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10624 The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
10629 If structures are relative, this undermines truth-value and objectivity [Hale/Wright]
10628 The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright]
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 / c. Neo-logicism
10622 The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright]
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]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
10626 Objects just are what singular terms refer to [Hale/Wright]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10630 Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright]
19. Language / E. Analyticity / 2. Analytic Truths
10627 Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright]
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
21093 Friendship without community spirit misses out on the main part of virtue [Hume]
24. Political Theory / B. Nature of a State / 3. Constitutions
21091 It would be absurd if even a free constitution did not impose restraints, for the public good [Hume]
24. Political Theory / C. Ruling a State / 2. Leaders / d. Elites
21092 Nobility either share in the power of the whole, or they compose the power of the whole [Hume]