Combining Philosophers

All the ideas for Michael Burke, R Kaplan / E Kaplan and Pittacus

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15 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX

15717

Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number

15712

1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

15711

The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic

15714

'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan]

15715

'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan]

9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind

16235

Persistence conditions cannot contradict, so there must be a 'dominant sortal' [Burke,M, by Hawley]

14753

The 'dominant' of two coinciding sortals is the one that entails the widest range of properties [Burke,M, by Sider]

9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates

16072

'The rock' either refers to an object, or to a collection of parts, or to some stuff [Burke,M, by Wasserman]

9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail

14751

Tib goes out of existence when the tail is lost, because Tib was never the 'cat' [Burke,M, by Sider]

9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay

16071

Sculpting a lump of clay destroys one object, and replaces it with another one [Burke,M, by Wasserman]

16234

Burke says when two object coincide, one of them is destroyed in the process [Burke,M, by Hawley]

13278

Maybe the clay becomes a different lump when it becomes a statue [Burke,M, by Koslicki]

9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects

14750

Two entities can coincide as one, but only one of them (the dominant sortal) fixes persistence conditions [Burke,M, by Sider]

10. Modality / A. Necessity / 8. Transcendental Necessity

3016	Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius]

14. Science / C. Induction / 3. Limits of Induction

15713

The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]