Combining Philosophers

All the ideas for H.Putnam/P.Oppenheim, R Kaplan / E Kaplan and Jenny Teichmann

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11 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
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
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
The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan]
'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan]
8. Modes of Existence / B. Properties / 1. Nature of Properties
Not only substances have attributes; events, actions, states and qualities can have them [Teichmann]
14. Science / C. Induction / 3. Limits of Induction
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
Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson]
17. Mind and Body / A. Mind-Body Dualism / 2. Interactionism
Body-spirit interaction ought to result in losses and increases of energy in the material world [Teichmann]
29. Religion / D. Religious Issues / 2. Immortality / b. Soul
No individuating marks distinguish between Souls [Teichmann]
The Soul has no particular capacity (in the way thinking belongs to the mind) [Teichmann]