Combining Texts

All the ideas for 'fragments/reports', 'Induction' and 'Mathematical logic and theory of types'

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14 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]
13. Knowledge Criteria / C. External Justification / 8. Social Justification
If you would deny a truth if you know the full evidence, then knowledge has social aspects [Harman, by Sosa]
19. Language / F. Communication / 3. Denial
Contradiction is impossible, since only one side of the argument refers to the true facts [Prodicus, by Didymus the Blind]
28. God / B. Proving God / 3. Proofs of Evidence / c. Teleological Proof critique
People used to think anything helpful to life was a god, as the Egyptians think the Nile a god [Prodicus]
28. God / C. Attitudes to God / 5. Atheism
The gods are just personified human benefits [Prodicus]
He denied the existence of the gods, saying they are just exaltations of things useful for life [Prodicus]