Combining Texts

All the ideas for 'Universals and Particulars', 'works' and 'On boundary numbers and domains of sets'

expand these ideas     |    start again     |     specify just one area for these texts

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6 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 / 2. Excluded Middle

15941

For intuitionists excluded middle is an outdated historical convention [Brouwer]

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 / 3. Nature of Numbers / h. Reals from Cauchy

18247

Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro]

8. Modes of Existence / D. Universals / 6. Platonic Forms / c. Self-predication

4442	Most thinkers now reject self-predication (whiteness is NOT white) so there is no Third Man problem [Armstrong]