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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]
|