Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Mathematical logic and theory of types' and 'Against the Professors (six books)'

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20 ideas

3. Truth / A. Truth Problems / 5. Truth Bearers
6021 It is only when we say a proposition that we speak truly or falsely [Sext.Empiricus]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
17884 Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
17893 'Reflection principles' say the whole truth about sets can't be captured [Koellner]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
11064 Classes can be reduced to propositional functions [Russell, by Hanna]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
6020 'Man is a rational mortal animal' is equivalent to 'if something is a man, that thing is a rational mortal animal' [Sext.Empiricus]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
17894 We have no argument to show a statement is absolutely undecidable [Koellner]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
6407 The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
17890 There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17887 PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17891 Arithmetical undecidability is always settled at the next stage up [Koellner]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
10418 Type theory seems an extreme reaction, since self-exemplification is often innocuous [Swoyer on Russell]
10047 Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms [Russell, by Musgrave]
23478 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
21718 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
18126 A set does not exist unless at least one of its specifications is predicative [Russell, by Bostock]
18128 Russell is a conceptualist here, saying some abstracta only exist because definitions create them [Russell, by Bostock]
18124 Vicious Circle says if it is expressed using the whole collection, it can't be in the collection [Russell, by Bostock]
14. Science / A. Basis of Science / 1. Observation
6026 How can you investigate without some preconception of your object? [Sext.Empiricus]
23. Ethics / B. Contract Ethics / 9. Contractualism
6032 Right actions, once done, are those with a reasonable justification [Sext.Empiricus]
26. Natural Theory / A. Speculations on Nature / 4. Mathematical Nature
1517 The tektraktys (1+2+3+4=10) is the 'fount of ever-flowing nature' [Sext.Empiricus]