Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'The Varieties of Necessity' and 'Lectures on the Philosophy of (World) History'

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11 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
21753 If we look at the world rationally, the world assumes a rational aspect [Hegel]
2. Reason / A. Nature of Reason / 1. On Reason
21974 The world seems rational to those who look at it rationally [Hegel]
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 / C. Sources of Modality / 1. Sources of Necessity
9216 Each area of enquiry, and its source, has its own distinctive type of necessity [Fine,K]
13. Knowledge Criteria / C. External Justification / 7. Testimony
9214 Unsupported testimony may still be believable [Fine,K]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
9215 Causation is easier to disrupt than logic, so metaphysics is part of nature, not vice versa [Fine,K]