Combining Philosophers

All the ideas for H.Putnam/P.Oppenheim, R Kaplan / E Kaplan and Antisthenes (Ath)

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12 ideas

2. Reason / B. Laws of Thought / 3. Non-Contradiction
Contradiction is impossible [Antisthenes (I), by Aristotle]
2. Reason / D. Definition / 13. Against Definition
Some fools think you cannot define anything, but only say what it is like [Antisthenes (I), by Aristotle]
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]
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]
22. Metaethics / C. The Good / 3. Pleasure / f. Dangers of pleasure
I would rather go mad than experience pleasure [Antisthenes (I)]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
Antisthenes said virtue is teachable and permanent, is life's goal, and is like universal wealth [Antisthenes (I), by Long]
28. God / C. Attitudes to God / 2. Pantheism
Antisthenes says there is only one god, which is nature [Antisthenes (I), by Cicero]