Combining Texts

All the ideas for 'Clitophon', 'On boundary numbers and domains of sets' and 'Concepts without Boundaries'

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9 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]
7. Existence / D. Theories of Reality / 10. Vagueness / b. Vagueness of reality
8983 If 'red' is vague, then membership of the set of red things is vague, so there is no set of red things [Sainsbury]
7. Existence / E. Categories / 2. Categorisation
8986 We should abandon classifying by pigeon-holes, and classify around paradigms [Sainsbury]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
8982 Vague concepts are concepts without boundaries [Sainsbury]
8984 If concepts are vague, people avoid boundaries, can't spot them, and don't want them [Sainsbury]
8985 Boundaryless concepts tend to come in pairs, such as child/adult, hot/cold [Sainsbury]
22. Metaethics / B. Value / 2. Values / f. Altruism
1590 The just man does not harm his enemies, but benefits everyone [Plato]