Combining Texts

All the ideas for 'Introduction to Russell's Theory of Types', 'Mechanisms' and 'Introduction to Zermelo's 1930 paper'

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12 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 / 4. Axioms for Sets / p. Axiom of Reducibility
18170 The Axiom of Reducibility is self-effacing: if true, it isn't needed [Quine]
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]
14. Science / B. Scientific Theories / 2. Aim of Science
17488 Empiricist theories are sets of laws, which give explanations and reductions [Glennan]
14. Science / D. Explanation / 2. Types of Explanation / i. Explanations by mechanism
17493 Modern mechanism need parts with spatial, temporal and function facts, and diagrams [Glennan]
17487 Mechanistic philosophy of science is an alternative to the empiricist law-based tradition [Glennan]
17489 Mechanisms are either systems of parts or sequences of activities [Glennan]
17490 17th century mechanists explained everything by the kinetic physical fundamentals [Glennan]
17491 Unlike the lawlike approach, mechanistic explanation can allow for exceptions [Glennan]
26. Natural Theory / C. Causation / 4. Naturalised causation
17494 Since causal events are related by mechanisms, causation can be analysed in that way [Glennan]