Combining Texts

All the ideas for 'Extrinsic Properties', 'On Euclidean Geometry' and 'What is Cantor's Continuum Problem?'

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10 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
8679 We perceive the objects of set theory, just as we perceive with our senses [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
9942 Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
16886 The truth of an axiom must be independently recognisable [Frege]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
18062 Set-theory paradoxes are no worse than sense deception in physics [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10868 The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
13517 If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
10271 Basic mathematics is related to abstract elements of our empirical ideas [Gödel]
8. Modes of Existence / B. Properties / 4. Intrinsic Properties
14979 Being alone doesn't guarantee intrinsic properties; 'being alone' is itself extrinsic [Lewis, by Sider]
15454 Extrinsic properties come in degrees, with 'brother' less extrinsic than 'sibling' [Lewis]
9. Objects / A. Existence of Objects / 5. Individuation / b. Individuation by properties
15455 Total intrinsic properties give us what a thing is [Lewis]