Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Letters to Russell' and 'Classes and Attributes'

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10 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
7085 The main problem of philosophy is what can and cannot be thought and expressed [Wittgenstein, by Grayling]
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]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
17894 We have no argument to show a statement is absolutely undecidable [Koellner]
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]
7. Existence / C. Structure of Existence / 6. Fundamentals / d. Logical atoms
23463 Atomic facts correspond to true elementary propositions [Wittgenstein]
8. Modes of Existence / B. Properties / 11. Properties as Sets
9783 While no two classes coincide in membership, there are distinct but coextensive attributes [Cartwright,R]
19. Language / D. Propositions / 4. Mental Propositions
23490 A thought is mental constituents that relate to reality as words do [Wittgenstein]