Combining Texts

All the ideas for 'On Certainty', 'On the Question of Absolute Undecidability' and 'Epistemic Justification'

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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]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
19679 'Access' internalism says responsibility needs access; weaker 'mentalism' needs mental justification [Kvanvig]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
3597 Foundations need not precede other beliefs [Wittgenstein]
19678 Strong foundationalism needs strict inferences; weak version has induction, explanation, probability [Kvanvig]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
3596 Total doubt can't even get started [Wittgenstein, by Williams,M]
19. Language / A. Nature of Meaning / 10. Denial of Meanings
4721 If you are not certain of any fact, you cannot be certain of the meaning of your words either [Wittgenstein]