Combining Philosophers

All the ideas for Anaxarchus, Isaiah Berlin and R Kaplan / E Kaplan

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15 ideas

1. Philosophy / B. History of Ideas / 1. History of Ideas
The great moments are the death of Aristotle, Machiavelli, and Romanticism [Berlin, by Watson]
1. Philosophy / B. History of Ideas / 5. Later European Thought
Romanticism is the greatest change in the consciousness of the West [Berlin]
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]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]
14. Science / C. Induction / 3. Limits of Induction
The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
Most Enlightenment thinkers believed that virtue consists ultimately in knowledge [Berlin]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
If we are essentially free wills, authenticity and sincerity are the highest virtues [Berlin]
23. Ethics / D. Deontological Ethics / 2. Duty
The Greeks have no notion of obligation or duty [Berlin]
23. Ethics / F. Existentialism / 1. Existentialism
Central to existentialism is the romantic idea that there is nothing to lean on [Berlin]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
Berlin distinguishes 'negative' and 'positive' liberty, and rejects the latter [Berlin, by Swift]
29. Religion / B. Monotheistic Religion / 2. Judaism
Judaism and Christianity views are based on paternal, family and tribal relations [Berlin]