Combining Texts

All the ideas for 'Tractatus', 'Introduction to Zermelo's 1930 paper' and 'De arcanus motus'

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7 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

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The first-order ZF axiomatisation is highly non-categorical [Hallett,M]

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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

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The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M]

8. Modes of Existence / C. Powers and Dispositions / 1. Powers

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Because of the definitions of cause, effect and power, cause and effect have the same power [Leibniz]

9. Objects / E. Objects over Time / 10. Beginning of an Object

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Generation is when local motions aggregate to become a single subject [Nicholas of Autrecourt]

10. Modality / A. Necessity / 2. Nature of Necessity

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Every necessary proposition is demonstrable to someone who understands [Leibniz]