Combining Texts

All the ideas for 'fragments/reports', 'Of the original contract' and 'Elements of Geometry'

expand these ideas     |    start again     |     specify just one area for these texts

21 ideas

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 / 5. Action Dilemmas / a. Dilemmas
21103 Moral questions can only be decided by common opinion [Hume]
24. Political Theory / A. Basis of a State / 3. Natural Values / b. Natural equality
21099 People must have agreed to authority, because they are naturally equal, prior to education [Hume]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
21100 The idea that society rests on consent or promises undermines obedience [Hume]
20495 We no more give 'tacit assent' to the state than a passenger carried on board a ship while asleep [Hume]
21101 The people would be amazed to learn that government arises from their consent [Hume]
25. Social Practice / A. Freedoms / 7. Freedom to leave
6703 Poor people lack the knowledge or wealth to move to a different state [Hume]
25. Social Practice / C. Rights / 4. Property rights
21102 We all know that the history of property is founded on injustices [Hume]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]