Combining Texts

All the ideas for 'Exigency to Exist in Essences', 'Comment on Armstrong and Forrest' and 'Introduction to Zermelo's 1930 paper'

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9 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]

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

19400

Possibles demand existence, so as many of them as possible must actually exist [Leibniz]

19401

God's sufficient reason for choosing reality is in the fitness or perfection of possibilities [Leibniz]

8. Modes of Existence / D. Universals / 1. Universals

15453

The main rivals to universals are resemblance or natural-class nominalism, or sparse trope theory [Lewis]

9. Objects / C. Structure of Objects / 1. Structure of an Object

15452

We could not uphold a truthmaker for 'Fa' without structures [Lewis]

10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds

19402

The actual universe is the richest composite of what is possible [Leibniz]