Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Paradoxes of the Infinite' and 'Comments on a Certain Broadsheet'

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11 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
9987 An aggregate in which order does not matter I call a 'set' [Bolzano]
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 / a. The Infinite
10856 A truly infinite quantity does not need to be a variable [Bolzano]
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]
12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
2602 What experience could prove 'If a=c and b=c then a=b'? [Descartes]
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
2600 The mind's innate ideas are part of its capacity for thought [Descartes]
2601 Qualia must be innate, because physical motions do not contain them [Descartes]