Combining Texts

All the ideas for 'On boundary numbers and domains of sets', 'Science and Hypothesis' and 'Mind and Its Place in Nature'

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5 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 / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism

10180

Mathematicians do not study objects, but relations between objects [Poincaré]

12. Knowledge Sources / B. Perception / 6. Inference in Perception

7628	Broad rejects the inferential component of the representative theory [Broad, by Maund]