display all the ideas for this combination of texts
8 ideas
8660 | There are potential infinities (never running out), but actual infinity is incoherent [Aristotle, by Friend] |
Full Idea: Aristotle developed his own distinction between potential infinity (never running out) and actual infinity (there being a collection of an actual infinite number of things, such as places, times, objects). He decided that actual infinity was incoherent. | |
From: report of Aristotle (works [c.330 BCE]) by Michèle Friend - Introducing the Philosophy of Mathematics 1.3 | |
A reaction: Friend argues, plausibly, that this won't do, since potential infinity doesn't make much sense if there is not an actual infinity of things to supply the demand. It seems to just illustrate how boggling and uncongenial infinity was to Aristotle. |
14032 | Totality has no edge; an edge implies a contrast beyond the edge, and there can't be one [Epicurus] |
Full Idea: The totality is unlimited. For what is limited has an extreme; but an extreme is seen in contrast to something else, so that since it has no extreme it has no limit. | |
From: Epicurus (Letter to Herodotus [c.293 BCE], 41) | |
A reaction: I presume that the 'limit' is the edge, and the 'extreme' is what is beyond the edge. Why could not the extreme be nothingness, which then contrast dramatically with what exists? |
14033 | Bodies are unlimited as well as void, since the two necessarily go together [Epicurus] |
Full Idea: The number of bodies and the magnitude of the void are unlimited. If void were unlimited, and bodies limited, bodies move in scattered fashion with no support of checking collisions; in limited void, unlimited bodies would not have a place to be in. | |
From: Epicurus (Letter to Herodotus [c.293 BCE], 42) | |
A reaction: Seems good. The point is that without collisions, bodies would not stop relative to one another, and combine to form the objects we perceive. Of course if the started off (anathema!) stuck together, they may not have dispersed yet. |
12058 | Aristotle's matter can become any other kind of matter [Aristotle, by Wiggins] |
Full Idea: Aristotle's conception of matter permits any kind of matter to become any other kind of matter. | |
From: report of Aristotle (works [c.330 BCE]) by David Wiggins - Substance 4.11.2 | |
A reaction: This is obviously crucial background information when we read Aristotle on matter. Our 92+ elements, and fixed fundamental particles, gives a quite different picture. Aristotle would discuss form and matter quite differently now. |
14034 | There exists an infinity of each shape of atom, but the number of shapes is beyond our knowledge [Epicurus] |
Full Idea: For each type of shape there is an unlimited number of similar atoms, but with respect to the differences they are not simply unlimited but ungraspable. | |
From: Epicurus (Letter to Herodotus [c.293 BCE], 42) | |
A reaction: Epicurus's view of the nature of atoms rests on his empiricism, so while he can reason from experience to how they must be, he admits (impressively) his ignorance of the full facts. He has arguments for the unlimited number. |
14035 | Atoms just have shape, size and weight; colour results from their arrangement [Epicurus] |
Full Idea: There are not even any qualities in atoms, except shape and size and weight; their colour changes according to the arrangement of the atoms. | |
From: Epicurus (Letter to Herodotus [c.293 BCE], 44 schol) | |
A reaction: [This is quoted by a 'scholiast' - an early writer quoting from Epicurus's '12 Basic Principles'] He appears to have got this one wrong, as it is evidently the type of atom, as well as the arrangement, which contributes to the colour. |
14038 | There cannot be unlimited division, because it would reduce things to non-existence [Epicurus] |
Full Idea: One must eliminate unlimited division into smaller pieces (to avoid making everything weak and being forced in our comprehensive grasps of compound things to exhaust the things which exist by reducing them to non-existence). | |
From: Epicurus (Letter to Herodotus [c.293 BCE], 56) | |
A reaction: A basic argument for atoms, but it seems to rest on Zenonian paradoxes about infinite subdivision. An infinite subdivision of a unit doesn't seem to turn it into zero. |
14049 | We aim to know the natures which are observed in natural phenomena [Epicurus] |
Full Idea: Blessedness lies in knowing the natures which are observed in meteorological phenomena. | |
From: Epicurus (Letter to Herodotus [c.293 BCE], 78) | |
A reaction: This pursuit of 'natures' seems to be at the heart of scientific essentialism. Epicurus demonstrates his proposal, by offering speculations about the natures of all sorts of phenomena (esp. in 'Letter to Pythocles'). |