Combining Philosophers

All the ideas for Giordano Bruno, R Kaplan / E Kaplan and Otto Neurath

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10 ideas

1. Philosophy / G. Scientific Philosophy / 3. Scientism

7081	Philosophy is not separate from or above empirical science [Neurath]

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 / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique

10486

If we are rebuilding our ship at sea, we should jettison some cargo [Boolos on Neurath]

8485	We must always rebuild our ship on the open sea; we can't reconstruct it properly in dry-dock [Neurath]

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

15713

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

29. Religion / A. Polytheistic Religion / 2. Greek Polytheism

9287	Bruno said that ancient Egyptian magic was the true religion [Bruno, by Yates]