Combining Texts

All the ideas for 'What is Cantor's Continuum Problem?st1=Kurt Gödel', 'Principles of Nature and Grace based on Reason' and 'Molyneux's Question'

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12 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 / 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]
7. Existence / A. Nature of Existence / 5. Reason for Existence
5062 First: there must be reasons; Second: why anything at all?; Third: why this? [Leibniz]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
19377 A monad and its body are living, so life is everywhere, and comes in infinite degrees [Leibniz]
12. Knowledge Sources / B. Perception / 1. Perception
19353 'Perception' is basic internal representation, and 'apperception' is reflective knowledge of perception [Leibniz]
12. Knowledge Sources / B. Perception / 4. Sense Data / d. Sense-data problems
7639 The Homunculus Fallacy explains a subject perceiving objects by repeating the problem internally [Evans]
15. Nature of Minds / A. Nature of Mind / 7. Animal Minds
5061 Animals are semi-rational because they connect facts, but they don't see causes [Leibniz]
21. Aesthetics / B. Nature of Art / 8. The Arts / a. Music
5063 Music charms, although its beauty is the harmony of numbers [Leibniz]