Combining Texts

All the ideas for 'fragments/reports', 'Russell's Mathematical Logic' and 'Representation in Music'

expand these ideas     |    start again     |     specify just one area for these texts

16 ideas

1. Philosophy / D. Nature of Philosophy / 4. Divisions of Philosophy
20771 Six parts: dialectic, rhetoric, ethics, politics, physics, theology [Cleanthes, by Diog. Laertius]
2. Reason / D. Definition / 8. Impredicative Definition
10041 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
21716 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
10035 Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10042 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
10038 A logical system needs a syntactical survey of all possible expressions [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10046 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
10039 Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10043 Mathematical objects are as essential as physical objects are for perception [Gödel]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
10045 Impredicative definitions are admitted into ordinary mathematics [Gödel]
17. Mind and Body / A. Mind-Body Dualism / 8. Dualism of Mind Critique
6028 Bodies interact with other bodies, and cuts cause pain, and shame causes blushing, so the soul is a body [Cleanthes, by Nemesius]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
20831 The soul suffers when the body hurts, creates redness from shame, and pallor from fear [Cleanthes]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
12167 Reference without predication is the characteristic of expression [Scruton]
21. Aesthetics / B. Nature of Art / 5. Art as Language
12166 If music refers to love, it contains no predication, so it is expression, not language [Scruton]
21. Aesthetics / B. Nature of Art / 8. The Arts / a. Music
12168 Music is not representational, since thoughts about a subject are never essential to it [Scruton]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
5993 The ascending scale of living creatures requires a perfect being [Cleanthes, by Tieleman]