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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]
|