Combining Texts

All the ideas for 'works', 'Elements of Geometry' and 'The DhammaPada'

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21 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
7893 Our life is the creation of our mind [Anon (Dham)]
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]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / a. Idealism
7898 The world is just the illusion of an appearance [Anon (Dham)]
22. Metaethics / B. Value / 2. Values / g. Love
7894 Hate is conquered by love [Anon (Dham)]
22. Metaethics / C. The Good / 3. Pleasure / f. Dangers of pleasure
7899 Even divine pleasure will not satisfy the wise, as it is insatiable, and leads to pain [Anon (Dham)]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
7896 The foolish gradually fill with evil, like a slowly-filled water-jar [Anon (Dham)]
7897 The wise gradually fill with good, like a slowly-filled water-jar [Anon (Dham)]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
20239 Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche]
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
7895 Don't befriend fools; either find superior friends, or travel alone [Anon (Dham)]
29. Religion / C. Spiritual Disciplines / 3. Buddhism
7900 Speak the truth, yield not to anger, give what you can to him who asks [Anon (Dham)]