Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'A Puzzle Concerning Matter and Form' and 'The Language of Thought'

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9 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]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
16755 The possible Aristotelian view that forms are real and active principles is clearly wrong [Fine,K, by Pasnau]
18. Thought / B. Mechanics of Thought / 4. Language of Thought
8090 Since the language of thought is the same for all, it must be something like logical form [Fodor, by Devlin]
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
11143 If concept-learning is hypothesis-testing, that needs innate concepts to get started [Fodor, by Margolis/Laurence]