Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'A Plea for Excuses' and 'Contextualism Defended (and reply)'

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12 ideas

1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
21960 Ordinary language is the beginning of philosophy, but there is much more to it [Austin,JL]
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 / C. External Justification / 6. Contextual Justification / a. Contextualism
19558 Our own intuitions about whether we know tend to vacillate [Cohen,S]
19561 We shouldn't jump too quickly to a contextualist account of claims to know [Cohen,S]
19563 The context sensitivity of knowledge derives from its justification [Cohen,S]
19560 Contextualism is good because it allows knowledge, but bad because 'knowing' is less valued [Cohen,S]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
19559 Contextualists slightly concede scepticism, but only in extremely strict contexts [Cohen,S]