Combining Texts

All the ideas for 'On Body and Force, Against the Cartesians', 'Against the Mathematicians' and 'Introduction to Zermelo's 1930 paper'

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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]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
20795 Some things are their own criterion, such as straightness, a set of scales, or light [Sext.Empiricus]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
20794 How can sceptics show there is no criterion? Weak without, contradiction with [Sext.Empiricus]
14. Science / D. Explanation / 2. Types of Explanation / h. Explanations by function
13195 To explain a house we must describe its use, as well as its parts [Leibniz]
15. Nature of Minds / C. Capacities of Minds / 10. Conatus/Striving
13193 Active force is not just potential for action, since it involves a real effort or striving [Leibniz]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
13194 God's laws would be meaningless without internal powers for following them [Leibniz]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
13196 All qualities of bodies reduce to forces [Leibniz]
13192 Power is passive force, which is mass, and active force, which is entelechy or form [Leibniz]