Combining Texts

All the ideas for 'reports', 'What is Cantor's Continuum Problem?' and 'Aesthetica'

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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 / 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]

10. Modality / A. Necessity / 8. Transcendental Necessity

3016	Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius]

21. Aesthetics / A. Aesthetic Experience / 1. Aesthetics

8063	Baumgarten founded aesthetics in 1750 [Baumgarten, by Tolstoy]

21. Aesthetics / B. Nature of Art / 2. Art as Form

8118	Beauty is an order between parts, and in relation to the whole [Baumgarten, by Tolstoy]

22. Metaethics / C. The Good / 1. Goodness / b. Types of good

8117	Perfection comes through the senses (Beauty), through reason (Truth), and through moral will (Good) [Baumgarten, by Tolstoy]