30 ideas
| 14240 | The empty set is something, not nothing! [Oliver/Smiley] |
| 14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
| 14241 | We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley] |
| 14242 | Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley] |
| 14243 | The unit set may be needed to express intersections that leave a single member [Oliver/Smiley] |
| 14234 | If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley] |
| 14237 | We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley] |
| 14245 | Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley] |
| 1553 | No perceptible object is truly straight or curved [Protagoras] |
| 14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
| 14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
| 1549 | Everything that exists consists in being perceived [Protagoras] |
| 1545 | Protagoras was the first to claim that there are two contradictory arguments about everything [Protagoras, by Diog. Laertius] |
| 1547 | Man is the measure of all things - of things that are, and of things that are not [Protagoras] |
| 3305 | There is no more purely metaphysical doctrine than Protagorean relativism [Benardete,JA on Protagoras] |
| 3313 | If my hot wind is your cold wind, then wind is neither hot nor cold, and so not as cold as itself [Benardete,JA on Protagoras] |
| 3317 | You can only state the problem of the relative warmth of an object by agreeing on the underlying object [Benardete,JA on Protagoras] |
| 247 | God is "the measure of all things", more than any man [Plato on Protagoras] |
| 606 | Protagoras absurdly thought that the knowing or perceiving man is 'the measure of all things' [Aristotle on Protagoras] |
| 612 | Relativists think if you poke your eye and see double, there must be two things [Aristotle on Protagoras] |
| 6016 | Early sophists thought convention improved nature; later they said nature was diminished by it [Protagoras, by Miller,FD] |
| 1580 | For Protagoras the only bad behaviour is that which interferes with social harmony [Protagoras, by Roochnik] |
| 205 | Protagoras contradicts himself by saying virtue is teachable, but then that it is not knowledge [Plato on Protagoras] |
| 7346 | Jeremiah implied a link between weakness and goodness, and the evil of the state [Jeremiah, by Johnson,P] |
| 1659 | Protagoras seems to have made the huge move of separating punishment from revenge [Protagoras, by Vlastos] |
| 532 | Successful education must go deep into the soul [Protagoras] |
| 1552 | He spent public money on education, as it benefits the individual and the state [Protagoras, by Diodorus of Sicily] |
| 22920 | Do I not fill heaven and earth? saith the Lord [Jeremiah] |
| 22089 | Am I a God afar off, and not a God close at hand? [Jeremiah] |
| 1551 | He said he didn't know whether there are gods - but this is the same as atheism [Diogenes of Oen. on Protagoras] |