Combining Texts

All the ideas for 'Necessary Existents', 'On the Question of Absolute Undecidability' and 'Resurrecting Biological Essentialism'

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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 / D. Essence of Objects / 10. Essence as Species
17368 Essentialism concerns the nature of a group, not its category [Devitt]
17370 Things that gradually change, like species, can still have essences [Devitt]
19. Language / D. Propositions / 3. Concrete Propositions
19216 Propositions (such as 'that dog is barking') only exist if their items exist [Williamson]
27. Natural Reality / G. Biology / 5. Species
17369 We name species as small to share properties, but large enough to yield generalisations [Devitt]
17367 Species are phenetic, biological, niche, or phylogenetic-cladistic [Devitt, by PG]