Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'The Ages of the World' and 'Protrepticus (frags)'

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8 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / d. Philosophy as puzzles
17949 Inquiry is the cause of philosophy [Aristotle]
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]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
20957 We don't choose our characters, yet we still claim credit for the actions our characters perform [Schelling]