Combining Texts

All the ideas for 'Realism in Mathematics', 'On Multiplying Entities' and 'Good and Evil'

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9 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor
The quest for simplicity drove scientists to posit new entities, such as molecules in gases [Quine]
In arithmetic, ratios, negatives, irrationals and imaginaries were created in order to generalise [Quine]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
A natural number is a property of sets [Maddy, by Oliver]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins]
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 / C. The Good / 1. Goodness / a. Form of the Good
'Good' is an attributive adjective like 'large', not predicative like 'red' [Geach, by Foot]