Combining Philosophers

All the ideas for H.Putnam/P.Oppenheim, James Van Cleve and R Kaplan / E Kaplan

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9 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]

13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma

8840	There are five possible responses to the problem of infinite regress in justification [Cleve]

13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism

8841	Modern foundationalists say basic beliefs are fallible, and coherence is relevant [Cleve]

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

15713

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

14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction

20653

Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson]