Combining Texts

All the ideas for 'Philosophical Fragments', 'Philosophical Implications of Mathematical logic' and 'Introduction to Zermelo's 1930 paper'

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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]

5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic

22329

Logic is highly general truths abstracted from reality [Russell, by Glock]

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]

7. Existence / A. Nature of Existence / 5. Reason for Existence

16007

I assume existence, rather than reasoning towards it [Kierkegaard]

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

16013

Nothing necessary can come into existence, since it already 'is' [Kierkegaard]

15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind

21569

It is good to generalise truths as much as possible [Russell]