Combining Texts

All the ideas for 'Philosophy of Nature (Encylopedia II)', 'Notes on Comments by Fardella' and 'What is Cantor's Continuum Problem?'

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10 ideas

1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
22077 Metaphysics is the lattice which makes incoming material intelligible [Hegel]
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]
9. Objects / B. Unity of Objects / 1. Unifying an Object / c. Unity as conceptual
13160 To exist and be understood, a multitude must first be reduced to a unity [Leibniz]
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
13161 Substances are everywhere in matter, like points in a line [Leibniz]
24. Political Theory / C. Ruling a State / 4. Changing the State / c. Revolution
21756 All revolutions result from spirit changing its categories, to achieve a deeper understanding [Hegel]