Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Practical Necessity' and 'Essays on Intellectual Powers 1: Preliminary'

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11 ideas

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]
10. Modality / A. Necessity / 10. Impossibility
23283 Necessity implies possibility, but in experience it matters which comes first [Williams,B]
12. Knowledge Sources / E. Direct Knowledge / 1. Common Sense
23633 Many truths seem obvious, and point to universal agreement - which is what we find [Reid]
18. Thought / C. Content / 2. Ideas
23630 Only philosophers treat ideas as objects [Reid]
19. Language / A. Nature of Meaning / 9. Ambiguity
23629 The ambiguity of words impedes the advancement of knowledge [Reid]
26. Natural Theory / C. Causation / 1. Causation
23632 Similar effects come from similar causes, and causes are only what are sufficient for the effects [Reid]