23 ideas
2666 | Carneades' pinnacles of philosophy are the basis of knowledge (the criterion of truth) and the end of appetite (good) [Carneades, by Cicero] |
8623 | Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege] |
21390 | Future events are true if one day we will say 'this event is happening now' [Carneades] |
21672 | We say future things are true that will possess actuality at some following time [Carneades, by Cicero] |
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] |
15825 | Carneades denied the transitivity of identity [Carneades, by Chisholm] |
21389 | Carneades distinguished logical from causal necessity, when talking of future events [Long on Carneades] |
604 | Knowledge is mind and knowing 'cohabiting' [Lycophron, by Aristotle] |
21671 | Voluntary motion is intrinsically within our power, and this power is its cause [Carneades, by Cicero] |
21391 | Some actions are within our power; determinism needs prior causes for everything - so it is false [Carneades, by Cicero] |
21674 | Even Apollo can only foretell the future when it is naturally necessary [Carneades, by Cicero] |
7398 | Carneades said that after a shipwreck a wise man would seize the only plank by force [Carneades, by Tuck] |
21392 | People change laws for advantage; either there is no justice, or it is a form of self-injury [Carneades, by Lactantius] |