Combining Texts

All the ideas for 'The Scope and Language of Science', 'Introduction to Zermelo's 1930 paper' and 'Precepts for Advancing Science and Arts'

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8 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]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
8463 Maths can be reduced to logic and set theory [Quine]
8. Modes of Existence / B. Properties / 1. Nature of Properties
8461 The category of objects incorporates the old distinction of substances and their modes [Quine]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
19392 I don't recommend universal doubt; we constantly seek reasons for things which are indubitable [Leibniz]
17. Mind and Body / E. Mind as Physical / 6. Conceptual Dualism
8462 A hallucination can, like an ague, be identified with its host; the ontology is physical, the idiom mental [Quine]