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Single Idea 5093

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

Full Idea

In defining continuity one is almost bound to rely on the notion of infinity; it is because the continuous is what is infinitely divisible.

Gist of Idea

Continuity depends on infinity, because the continuous is infinitely divisible

Source

Aristotle (Physics [c.337 BCE], 200b18)

Book Ref

Aristotle: 'Physics', ed/tr. Waterfield,Robin [OUP 1996], p.56

A Reaction

Parmenides and the Achilles Paradox lie behind this view, and the fact that Aristotle was opposed to the view that some things are indivisible ('atomism'). Nice point, though - that space and time immediately imply the infinite.

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]