Combining Texts

All the ideas for 'Frege's Theory of Numbers', ''Ostrich Nominalism' or 'Mirage Realism'?' and 'On boundary numbers and domains of sets'

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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 / L. Paradox / 3. Antinomies
17626 The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17447 Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
8. Modes of Existence / D. Universals / 1. Universals
8502 Realism doesn't explain 'a is F' any further by saying it is 'a has F-ness' [Devitt]
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
8503 The particular/universal distinction is unhelpful clutter; we should accept 'a is F' as basic [Devitt]
8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta
8501 Quineans take predication about objects as basic, not reference to properties they may have [Devitt]