Combining Philosophers

All the ideas for Anaxarchus, Catherine Z. Elgin and R Kaplan / E Kaplan

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10 ideas

2. Reason / A. Nature of Reason / 6. Coherence

8616	How can multiple statements, none of which is tenable, conjoin to yield a tenable conclusion? [Elgin]

8617	Statements that are consistent, cotenable and supportive are roughly true [Elgin]

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]

13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification

8618	Coherence is a justification if truth is its best explanation (not skill in creating fiction) [Elgin]

13. Knowledge Criteria / D. Scepticism / 1. Scepticism

3061	Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, 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]