Combining Texts

All the ideas for 'works', 'On boundary numbers and domains of sets' and 'There Are No Abstract Objects'

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7 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
17832 Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13028 Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy]
5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
10121 Contradiction is not a sign of falsity, nor lack of contradiction a sign of truth [Pascal]
5. Theory of Logic / L. Paradox / 3. Antinomies
17626 The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo]
8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta
14596 Call 'nominalism' the denial of numbers, properties, relations and sets [Dorr]
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
14597 Natural Class Nominalism says there are primitive classes of things resembling in one respect [Dorr]
10. Modality / A. Necessity / 11. Denial of Necessity
14598 Abstracta imply non-logical brute necessities, so only nominalists can deny such things [Dorr]