Combining Texts

All the ideas for 'What is Cantor's Continuum Problem?st1=Kurt Gödel', 'Being You' and 'Hilbert's Programme'

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16 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 / 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 / a. The Infinite
17809 Gödel showed that the syntactic approach to the infinite is of limited value [Kreisel]
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 / 1. Foundations for Mathematics
17810 The study of mathematical foundations needs new non-mathematical concepts [Kreisel]
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 / 8. Brain
23513 Single neurons can carry out complex functions [Seth]
23514 The cerbellum has a huge number of neurons, but little involvement in consciousness [Seth]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / e. Cause of consciousness
23516 Maybe a system is conscious if the whole generates more information than its parts [Seth]
16. Persons / C. Self-Awareness / 2. Knowing the Self
23519 The self is embodied, perspectival, volitional, narrative and social [Seth, by PG]
18. Thought / B. Mechanics of Thought / 6. Artificial Thought / a. Artificial Intelligence
23518 Modern AI is mostly machine-based pattern recognition [Seth]
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
23517 Volition is felt as doing what you want, with possible alternatives, and a source from within [Seth]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / d. Biological ethics
23515 Human exceptionalism plagues biology, and most other human thinking [Seth]
27. Natural Reality / C. Space / 3. Points in Space
17811 The natural conception of points ducks the problem of naming or constructing each point [Kreisel]