Combining Texts

All the ideas for 'An Introduction to Hegel', 'Relations' and 'Russell's Mathematical Logic'

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

17 ideas

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]
8. Modes of Existence / A. Relations / 1. Nature of Relations
21339 We want the ontology of relations, not just a formal way of specifying them [Heil]
21349 Two people are indirectly related by height; the direct relation is internal, between properties [Heil]
21340 Maybe all the other features of the world can be reduced to relations [Heil]
8. Modes of Existence / A. Relations / 2. Internal Relations
21348 In the case of 5 and 6, their relational truthmaker is just the numbers [Heil]
21351 Truthmaking is a clear example of an internal relation [Heil]
21344 If R internally relates a and b, and you have a and b, you thereby have R [Heil]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
21350 If properties are powers, then causal relations are internal relations [Heil]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / b. Defining ethics
21788 The moral will is self-determining, but the ethical will is met in society [Houlgate]