Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Mathematical logic and theory of types' and 'Does moral phil rest on a mistake?'

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15 ideas

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Classes can be reduced to propositional functions [Russell, by Hanna]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
Type theory seems an extreme reaction, since self-exemplification is often innocuous [Swoyer on Russell]
Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms [Russell, by Musgrave]
Type theory means that features shared by different levels cannot be expressed [Morris,M on Russell]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
A set does not exist unless at least one of its specifications is predicative [Russell, by Bostock]
Russell is a conceptualist here, saying some abstracta only exist because definitions create them [Russell, by Bostock]
Vicious Circle says if it is expressed using the whole collection, it can't be in the collection [Russell, by Bostock]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / c. Purpose of ethics
The 'Ethics' is disappointing, because it fails to try to justify our duties [Prichard]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / c. Particularism
The mistake is to think we can prove what can only be seen directly in moral thinking [Prichard]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
Virtues won't generate an obligation, so it isn't a basis for morality [Prichard]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
23. Ethics / D. Deontological Ethics / 2. Duty
We feel obligations to overcome our own failings, and these are not relations to other people [Prichard]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
If pain were instrinsically wrong, it would be immoral to inflict it on ourselves [Prichard]