Combining Texts

All the ideas for 'fragments/reports', '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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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 / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers

3338	Numbers have been defined in terms of 'successors' to the concept of 'zero' [Peano, by Blackburn]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic

5897	0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew]

25. Social Practice / E. Policies / 5. Education / b. Education principles

13304

Learned men gain more in one day than others do in a lifetime [Posidonius]

27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure

20820

Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]