Combining Texts

All the ideas for 'In Metaphysics', 'Russell's Mathematical Logic' and 'Utopia'

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16 ideas

2. Reason / D. Definition / 8. Impredicative Definition
Impredicative Definitions refer to the totality to which the object itself belongs [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
Reference to a totality need not refer to a conjunction of all its elements [Gödel]
5. Theory of Logic / K. Features of Logics / 8. Enumerability
A logical system needs a syntactical survey of all possible expressions [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Mathematical objects are as essential as physical objects are for perception [Gödel]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
Impredicative definitions are admitted into ordinary mathematics [Gödel]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Are things distinct if they are both separate, or if only one of them can be separate? [Duns Scotus, by Pasnau]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
Substance is only grasped under the general heading of 'being' [Duns Scotus]
24. Political Theory / D. Ideologies / 3. Conservatism
All modern social systems seem to be conspiracies of the rich [More,T]
24. Political Theory / D. Ideologies / 5. Democracy / d. Representative democracy
If you try to get elected, you should be permanently barred from seeking office [More,T]
25. Social Practice / E. Policies / 1. War / a. Just wars
Only Utopians fail to see glory in warfare [More,T]
25. Social Practice / F. Life Issues / 2. Euthanasia
In Utopia, legal euthanasia is considered honourable [More,T]
28. God / C. Attitudes to God / 2. Pantheism
In Utopia, the Supreme Being is identical with Nature [More,T]