Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Roman Law' and 'Metaphysics: a very short introduction'

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11 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]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
18617 Substances, unlike aggregates, can survive a change of parts [Mumford]
10. Modality / B. Possibility / 3. Combinatorial possibility
18618 Maybe possibilities are recombinations of the existing elements of reality [Mumford]
18619 Combinatorial possibility has to allow all elements to be combinable, which seems unlikely [Mumford]
18620 Combinatorial possibility relies on what actually exists (even over time), but there could be more [Mumford]
25. Social Practice / D. Justice / 3. Punishment / a. Right to punish
7294 No crime and no punishment without a law [Roman law]