Combining Texts

All the ideas for 'What is Cantor's Continuum Problem?st1=Kurt Gödel', 'On the Concept of Number' and 'Utilitarianism and the Virtues'

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14 ideas

3. Truth / A. Truth Problems / 3. Value of Truth
We should speak the truth, but also preserve and pursue it [Foot]
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]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency [Hilbert, by Potter]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
Consequentialists can hurt the innocent in order to prevent further wickedness [Foot]
Why might we think that a state of affairs can be morally good or bad? [Foot]
Good outcomes are not external guides to morality, but a part of virtuous actions [Foot]
The idea of a good state of affairs has no role in the thought of Aristotle, Rawls or Scanlon [Foot]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
Morality is seen as tacit legislation by the community [Foot]
23. Ethics / E. Utilitarianism / 5. Rule Utilitarianism
For consequentialism, it is irrational to follow a rule which in this instance ends badly [Foot]