Combining Philosophers

All the ideas for Vassilis Politis, R Kaplan / E Kaplan and Archimedes

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11 ideas

2. Reason / D. Definition / 1. Definitions
The Pythagoreans were the first to offer definitions [Politis, by Politis]
3. Truth / A. Truth Problems / 4. Uses of Truth
'True of' is applicable to things, while 'true' is applicable to words [Politis]
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]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing
Maybe 'What is being? is confusing because we can't ask what non-being is like [Politis]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
Necessary truths can be two-way relational, where essential truths are one-way or intrinsic [Politis]
14. Science / C. Induction / 3. Limits of Induction
The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]