Combining Texts

All the ideas for 'What is Cantor's Continuum Problem?st1=Kurt Gödel', 'Individuals:Essay in Descript Metaphysics' and 'Maths as a Science of Patterns'

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20 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
7920 Descriptive metaphysics aims at actual structure, revisionary metaphysics at a better structure [Strawson,P]
1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
7922 Descriptive metaphysics concerns unchanging core concepts and categories [Strawson,P]
1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
7921 Close examination of actual word usage is the only sure way in philosophy [Strawson,P]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
6299 Axioms are often affirmed simply because they produce results which have been accepted [Resnik]
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 / 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 / 1. Mathematics
6304 Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik]
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 / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
6300 Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik]
6303 Sets are positions in patterns [Resnik]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
6295 There are too many mathematical objects for them all to be mental or physical [Resnik]
6296 Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik]
6301 Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik]
6302 Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik]
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]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / d. Other minds by analogy
9282 I can only apply consciousness predicates to myself if I can apply them to others [Strawson,P]
16. Persons / B. Nature of the Self / 7. Self and Body / a. Self needs body
9263 A person is an entity to which we can ascribe predicates of consciousness and corporeality [Strawson,P]
19. Language / C. Assigning Meanings / 3. Predicates
9281 The idea of a predicate matches a range of things to which it can be applied [Strawson,P]