Combining Texts

All the ideas for 'What is Cantor's Continuum Problem?st1=Kurt Gödel', 'Letter to Bramhall' and 'Natural Theology'

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13 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
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
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
Set-theory paradoxes are no worse than sense deception in physics [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
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
Basic mathematics is related to abstract elements of our empirical ideas [Gödel]
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
A chair is wood, and its shape is the form; it isn't 'compounded' of the matter and form [Hobbes]
9. Objects / D. Essence of Objects / 15. Against Essentialism
Essence is just an artificial word from logic, giving a way of thinking about substances [Hobbes]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
Unlike a stone, the parts of a watch are obviously assembled in order to show the time [Paley]
From the obvious purpose and structure of a watch we must infer that it was designed [Paley]
Even an imperfect machine can exhibit obvious design [Paley]
All the signs of design found in a watch are also found in nature [Paley]
No organ shows purpose more obviously than the eyelid [Paley]