Quotes about Plato
290 Sourced Quotes
Coleridge observes that all men are born Aristotelians or Platonists. The latter feel that classes, orders, and genres are realities; the former, that they are generalizations. For the latter, language is nothing but an approximative set of symbols; for the former, it is the map of the universe. The Platonist knows that the universe is somehow a cosmos, an order; that order, for the Aristotelian, can be an error or a fiction of our partial knowledge. Across the latitudes and the epochs, the two immortal antagonists change their name and language: one is Parmenides, Plato, Spinoza, Kant, Francis Bradley; the other, Heraclitus, Aristotle, Locke, Hume, William James. What is philosophy? This is a notoriously difficult question. One of the easiest ways of answering it is to say that philosophy is what philosophers do, and then point to the writings of Plato, Aristotle, Descartes, Hume, Kant, Russell, Wittgenstein, Sartre, and other famous philosophers. However, this answer is unlikely to be of much use to you if you are just beginning the subject, as you probably won't have read anything by these writers. Menæchmus, a pupil of Eudoxus, and a contemporary of Plato, found the two mean proportionals by means of conic sections, in two ways, (α) by the intersection of two parabolas, the equations of which in Cartesian co-ordinates would be x2=ay, y2=bx, and (β) by the intersection of a parabola and a rectangular hyperbola, the corresponding equations being x2=ay, and xy=ab respectively. It would appear that it was in the effort to solve this problem that Menæchmus discovered the conic sections, which are called, in an epigram by Eratosthenes, "the triads of Menæchmus".