Combining Texts
Ideas for
'On the Question of Absolute Undecidability', 'Mathematical logic and theory of types' and 'Intellectual Autobiography'
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10 ideas
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
17890
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There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17887
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PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17891
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Arithmetical undecidability is always settled at the next stage up [Koellner]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
10418
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Type theory seems an extreme reaction, since self-exemplification is often innocuous [Swoyer on Russell]
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10047
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Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms [Russell, by Musgrave]
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23478
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Type theory means that features shared by different levels cannot be expressed [Morris,M on Russell]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
21718
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Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
18126
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A set does not exist unless at least one of its specifications is predicative [Russell, by Bostock]
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18128
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Russell is a conceptualist here, saying some abstracta only exist because definitions create them [Russell, by Bostock]
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18124
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Vicious Circle says if it is expressed using the whole collection, it can't be in the collection [Russell, by Bostock]
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