Combining Texts

All the ideas for 'On boundary numbers and domains of sets', 'The Foundations of Mathematics' and 'Isolation and Non-arbitrary Division'

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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 / D. Assumptions for Logic / 2. Excluded Middle

18844

You would cripple mathematics if you denied Excluded Middle [Hilbert]

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 / a. Units

17435

Objects do not naturally form countable units [Koslicki]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

17433

We can still count squares, even if they overlap [Koslicki]

17439

There is no deep reason why we count carrots but not asparagus [Koslicki]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts

17434

We struggle to count branches and waves because our concepts lack clear boundaries [Koslicki]

7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff

17436

We talk of snow as what stays the same, when it is a heap or drift or expanse [Koslicki]