Combining Philosophers

All the ideas for Theophrastus, Peter Auriol and Michael Hallett

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9 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 / A. Relations / 1. Nature of Relations
18528 The single imagined 'interval' between things only exists in the intellect [Auriol]
13. Knowledge Criteria / E. Relativism / 6. Relativism Critique
20921 How can we state relativism of sweet and sour, if they have no determinate nature? [Theophrastus]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / c. Purpose denied
5990 Theophrastus doubted whether nature could be explained teleologically [Theophrastus, by Gottschalk]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / b. Prime matter
16589 Prime matter lacks essence, but is only potentially and indeterminately a physical thing [Auriol]
28. God / A. Divine Nature / 4. Divine Contradictions
16651 God can do anything non-contradictory, as making straightness with no line, or lightness with no parts [Auriol]