Combining Texts

All the ideas for 'fragments/reports', 'On Multiplying Entities' and 'Remarks on axiomatised set theory'

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9 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor

8208	In arithmetic, ratios, negatives, irrationals and imaginaries were created in order to generalise [Quine]

8207	The quest for simplicity drove scientists to posit new entities, such as molecules in gases [Quine]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

17879

Axiomatising set theory makes it all relative [Skolem]

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

17878

If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem]

6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics

17880

Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem]

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism

17881

Mathematician want performable operations, not propositions about objects [Skolem]

7. Existence / B. Change in Existence / 4. Events / c. Reduction of events

8205	Explaining events just by bodies can't explain two events identical in space-time [Quine]

10. Modality / A. Necessity / 11. Denial of Necessity

8206	Necessity could be just generalisation over classes, or (maybe) quantifying over possibilia [Quine]

21. Aesthetics / C. Artistic Issues / 7. Art and Morality

468	Musical performance can reveal a range of virtues [Damon of Ath.]