Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'On the Concept of Number' and 'A Combinatorial Theory of Possibility'

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9 ideas

3. Truth / B. Truthmakers / 6. Making Negative Truths
15547 Negative existentials have 'totality facts' as truthmakers [Armstrong, by Lewis]
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]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
22293 Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency [Hilbert, by Potter]
10. Modality / B. Possibility / 1. Possibility
15542 All possibilities are recombinations of properties in the actual world [Armstrong, by Lewis]