Combining Philosophers

All the ideas for Rescher,N/Oppenheim,P, Richard T.W. Arthur and R Kaplan / E Kaplan

expand these ideas     |    start again     |     specify just one area for these philosophers

---

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]

9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts

12887

A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim]

10. Modality / B. Possibility / 1. Possibility

19378

Early modern possibility is what occurs sometime; for Leibniz, it is what is not contradictory [Arthur,R]

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

15713

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

17. Mind and Body / A. Mind-Body Dualism / 4. Occasionalism

19380

Occasionalism contradicts the Eucharist, which needs genuine changes of substance [Arthur,R]