31 ideas
23250 | Desired responsible actions result either from rational or from irrational desire [Aristotle] |
5847 | It is the role of dialectic to survey syllogisms [Aristotle] |
8623 | Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege] |
13907 | If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon] |
6297 | Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik] |
9603 | An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR] |
9894 | A unit is that according to which each existing thing is said to be one [Euclid] |
8738 | Postulate 2 says a line can be extended continuously [Euclid, by Shapiro] |
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] |
1600 | Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik] |
5862 | A single counterexample is enough to prove that a truth is not necessary [Aristotle] |
5854 | Nobody fears a disease which nobody has yet caught [Aristotle] |
5849 | Rhetoric is a political offshoot of dialectic and ethics [Aristotle] |
5851 | Pentathletes look the most beautiful, because they combine speed and strength [Aristotle] |
5858 | Men are physically prime at thirty-five, and mentally prime at forty-nine [Aristotle] |
5855 | We all feel universal right and wrong, independent of any community or contracts [Aristotle] |
5850 | Happiness is composed of a catalogue of internal and external benefits [Aristotle] |
5856 | Self-interest is a relative good, but nobility an absolute good [Aristotle] |
5853 | The best virtues are the most useful to others [Aristotle] |
5848 | All good things can be misused, except virtue [Aristotle] |
5857 | The young feel pity from philanthropy, but the old from self-concern [Aristotle] |
5859 | Rich people are mindlessly happy [Aristotle] |
5852 | The four constitutions are democracy (freedom), oligarchy (wealth), aristocracy (custom), tyranny (security) [Aristotle] |
1660 | It is noble to avenge oneself on one's enemies, and not come to terms with them [Aristotle] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
5861 | People assume events cause what follows them [Aristotle] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |