Combining Texts

All the ideas for 'General Facts,Phys Necessity, and Metaph of Time', 'Lecture on Nominalism' and 'Russell's Mathematical Logic'

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

13 ideas

2. Reason / D. Definition / 8. Impredicative Definition
10041 Impredicative Definitions refer to the totality to which the object itself belongs [Gödel]
2. Reason / F. Fallacies / 1. Fallacy
21697 The Struthionic Fallacy is that of burying one's head in the sand [Quine]
3. Truth / B. Truthmakers / 3. Truthmaker Maximalism
17962 The truth-maker principle is that every truth has a sufficient truth-maker [Forrest]
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 / E. Structures of Logic / 6. Relations in Logic
21698 All relations, apart from ancestrals, can be reduced to simpler logic [Quine]
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 / 3. Mathematical Nominalism
21696 Nominalism rejects both attributes and classes (where extensionalism accepts the classes) [Quine]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
10045 Impredicative definitions are admitted into ordinary mathematics [Gödel]