Combining Philosophers

All the ideas for Anaxarchus, John Dupr and Michael Hallett

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22 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
The first-order ZF axiomatisation is highly non-categorical [Hallett,M]
Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M]
7. Existence / E. Categories / 1. Categories
All descriptive language is classificatory [Dupré]
7. Existence / E. Categories / 2. Categorisation
We should aim for a classification which tells us as much as possible about the object [Dupré]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
Natural kinds don't need essentialism to be explanatory [Dupré]
9. Objects / D. Essence of Objects / 10. Essence as Species
A species might have its essential genetic mechanism replaced by a new one [Dupré]
It seems that species lack essential properties, so they can't be natural kinds [Dupré]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]
14. Science / A. Basis of Science / 4. Prediction
The possibility of prediction rests on determinism [Dupré]
18. Thought / C. Content / 5. Twin Earth
Presumably molecular structure seems important because we never have the Twin Earth experience [Dupré]
26. Natural Theory / B. Natural Kinds / 1. Natural Kinds
Phylogenetics involves history, and cladism rests species on splits in lineage [Dupré]
Kinds don't do anything (including evolve) because they are abstract [Dupré]
26. Natural Theory / B. Natural Kinds / 7. Critique of Kinds
Natural kinds are decided entirely by the intentions of our classification [Dupré]
Borders between species are much less clear in vegetables than among animals [Dupré]
Even atoms of an element differ, in the energy levels of their electrons [Dupré]
Ecologists favour classifying by niche, even though that can clash with genealogy [Dupré]
Wales may count as fish [Dupré]
Cooks, unlike scientists, distinguish garlic from onions [Dupré]
27. Natural Reality / G. Biology / 5. Species
Species are the lowest-level classification in biology [Dupré]
The theory of evolution is mainly about species [Dupré]