Combining Texts

All the ideas for 'On Multiplying Entities', 'Symposium' and 'Philosophy of Mathematics'

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9 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor
In arithmetic, ratios, negatives, irrationals and imaginaries were created in order to generalise [Quine]
The quest for simplicity drove scientists to posit new entities, such as molecules in gases [Quine]
2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
7. Existence / B. Change in Existence / 4. Events / c. Reduction of events
Explaining events just by bodies can't explain two events identical in space-time [Quine]
10. Modality / A. Necessity / 11. Denial of Necessity
Necessity could be just generalisation over classes, or (maybe) quantifying over possibilia [Quine]
22. Metaethics / B. Value / 2. Values / h. Fine deeds
Niceratus learnt the whole of Homer by heart, as a guide to goodness [Xenophon]