Combining Philosophers

All the ideas for Michael Hallett, Richard Tuck and Anjan Chakravarrty

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11 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
17833 The first-order ZF axiomatisation is highly non-categorical [Hallett,M]
17834 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
17837 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
17836 The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M]
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
15148 Powers give explanations, without being necessary for some class membership [Chakravartty]
9. Objects / D. Essence of Objects / 5. Essence as Kind
15145 A kind essence is the necessary and sufficient properties for membership of a class [Chakravartty]
9. Objects / D. Essence of Objects / 15. Against Essentialism
15147 Cluster kinds are explained simply by sharing some properties, not by an 'essence' [Chakravartty]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
7413 Without confidence in our beliefs, how should we actually live? [Tuck]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
15144 Explanation of causal phenomena concerns essential kinds - but also lack of them [Chakravartty]
26. Natural Theory / B. Natural Kinds / 4. Source of Kinds
15146 Some kinds, such as electrons, have essences, but 'cluster kinds' do not [Chakravartty]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
15151 Many causal laws do not refer to kinds, but only to properties [Chakravartty]