28 ideas
12456 | I aim to establish certainty for mathematical methods [Hilbert] |
12461 | We believe all mathematical problems are solvable [Hilbert] |
1553 | No perceptible object is truly straight or curved [Protagoras] |
9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
12462 | Only the finite can bring certainty to the infinite [Hilbert] |
12455 | The idea of an infinite totality is an illusion [Hilbert] |
12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
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] |
3317 | You can only state the problem of the relative warmth of an object by agreeing on the underlying object [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] |
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] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
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] |
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] |
1551 | He said he didn't know whether there are gods - but this is the same as atheism [Diogenes of Oen. on Protagoras] |