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Single Idea 8660

[filed under theme 26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature ]

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.

Gist of Idea

There are potential infinities (never running out), but actual infinity is incoherent

Source

report of Aristotle (works [c.330 BCE]) by Michèle Friend - Introducing the Philosophy of Mathematics 1.3

Book Ref

Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.7

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.

The 14 ideas with the same theme [time or space or matter could be infinite]:

8659 The gods alone live forever with Shamash. The days of humans are numbered. [Anon (Gilg)]
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
5093 Continuity depends on infinity, because the continuous is infinitely divisible [Aristotle]
5095 The heavens seem to be infinite, because we cannot imagine their end [Aristotle]
8660 There are potential infinities (never running out), but actual infinity is incoherent [Aristotle, by Friend]
14032 Totality has no edge; an edge implies a contrast beyond the edge, and there can't be one [Epicurus]
14033 Bodies are unlimited as well as void, since the two necessarily go together [Epicurus]
22743 Unlike Epicurus, Stoics distinguish the Whole from the All, with the latter including the void [Stoic school, by Sext.Empiricus]
5704 There can be no centre in infinity [Lucretius]
5703 The universe must be limitless, since there could be nothing outside to limit it [Lucretius]
4821 An infinite line can be marked in feet or inches, so one infinity is twelve times the other [Spinoza]
18519 If there were infinite electrons, they could vanish without affecting total mass-energy [Heil]
9635 Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR]
20469 There are probably no infinities, and 'infinite' names what we do not yet know [Rovelli]