Combining Philosophers

All the ideas for Herodotus, Euclid and Isaiah Berlin

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21 ideas

1. Philosophy / B. History of Ideas / 1. History of Ideas
7460 The great moments are the death of Aristotle, Machiavelli, and Romanticism [Berlin, by Watson]
1. Philosophy / B. History of Ideas / 5. Later European Thought
7662 Romanticism is the greatest change in the consciousness of the West [Berlin]
2. Reason / E. Argument / 6. Conclusive Proof
8623 Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / c. Derivations rules of PC
13907 If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
6297 Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
9603 An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One
9894 A unit is that according to which each existing thing is said to be one [Euclid]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
8738 Postulate 2 says a line can be extended continuously [Euclid, by Shapiro]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
22278 Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid]
8673 Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend]
10250 Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid]
10302 Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays]
14157 Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
1600 Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
7665 Most Enlightenment thinkers believed that virtue consists ultimately in knowledge [Berlin]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
7676 If we are essentially free wills, authenticity and sincerity are the highest virtues [Berlin]
23. Ethics / D. Deontological Ethics / 2. Duty
7664 The Greeks have no notion of obligation or duty [Berlin]
23. Ethics / F. Existentialism / 1. Existentialism
7677 Central to existentialism is the romantic idea that there is nothing to lean on [Berlin]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
20544 Berlin distinguishes 'negative' and 'positive' liberty, and rejects the latter [Berlin, by Swift]
29. Religion / B. Monotheistic Religion / 2. Judaism
7663 Judaism and Christianity views are based on paternal, family and tribal relations [Berlin]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
1513 The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus]