21 ideas
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] |
10302 | Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays] |
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] |
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] |
9264 | Persons are distinguished by a capacity for second-order desires [Frankfurt] |
9266 | A person essentially has second-order volitions, and not just second-order desires [Frankfurt] |
9267 | Free will is the capacity to choose what sort of will you have [Frankfurt] |
9265 | The will is the effective desire which actually leads to an action [Frankfurt] |
20015 | Freedom of action needs the agent to identify with their reason for acting [Frankfurt, by Wilson/Schpall] |
9270 | A 'wanton' is not a person, because they lack second-order volitions [Frankfurt] |
9269 | A person may be morally responsible without free will [Frankfurt] |
16713 | Philosophers are the forefathers of heretics [Tertullian] |
6610 | I believe because it is absurd [Tertullian] |