Ideas from 'Mathematical logic and theory of types' by Bertrand Russell [1908], by Theme Structure

[found in 'Logic and Knowledge' by Russell,Bertrand (ed/tr Marsh,Robert Charles) [Routledge 1956,0-415-09074-1]].

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4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Classes can be reduced to propositional functions
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
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
Type theory seems an extreme reaction, since self-exemplification is often innocuous
Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms
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 is a conceptualist here, saying some abstracta only exist because definitions create them
Vicious Circle says if it is expressed using the whole collection, it can't be in the collection