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26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature

[time or space or matter could be infinite]

14 ideas
The gods alone live forever with Shamash. The days of humans are numbered. [Anon (Gilg)]
     Full Idea: The gods alone are the ones who live forever with Shamash. / As for humans, their days are numbered.
     From: Anon (Gilg) (The Epic of Gilgamesh [c.2300 BCE], 3.2.34), quoted by Michèle Friend - Introducing the Philosophy of Mathematics 1.2
     A reaction: Friend quotes this to show the antiquity of the concept of infinity. It also, of course, shows that Sumerians at that time did not believe in human immortality.
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
     Full Idea: Archelaus was the first person to say that the universe is boundless.
     From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3
Continuity depends on infinity, because the continuous is infinitely divisible [Aristotle]
     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.
     From: Aristotle (Physics [c.337 BCE], 200b18)
     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 heavens seem to be infinite, because we cannot imagine their end [Aristotle]
     Full Idea: The region beyond the heavens seems to be infinite because it does not give out in our thoughts.
     From: Aristotle (Physics [c.337 BCE], 203b25)
     A reaction: An interesting case of inconceivability (of a limit) implying impossibility. But it is undeniable that the outer limit of the cosmos is unimaginable for us. Is there a 'Road Closed' sign?
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.
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?
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.
Unlike Epicurus, Stoics distinguish the Whole from the All, with the latter including the void [Stoic school, by Sext.Empiricus]
     Full Idea: The Stoic school say that the Whole is the Cosmos, whereas the All is the external void together with the Cosmos, so the Whole is limited but the All is unlimited. (Epicurus gives the two names indifferently to both).
     From: report of Stoic school (fragments/reports [c.200 BCE]) by Sextus Empiricus - Against the Physicists (two books) I.332
     A reaction: Epicurus needed the void as part of the Cosmos, into which the atoms can move. Presumably the Stoic void is infinite, but how far does the Stoic Cosmos extend?
There can be no centre in infinity [Lucretius]
     Full Idea: There can be no centre in infinity.
     From: Lucretius (On the Nature of the Universe [c.60 BCE], I.1069)
     A reaction: This is highly significant, because if we can establish that the universe is infinite (as Epicurus believes), it follows that the human race cannot be at the centre of it, as the Ptolemaic/medieval view proposed.
The universe must be limitless, since there could be nothing outside to limit it [Lucretius]
     Full Idea: The universe is not bounded in any direction. If it were, it would necessarily have a limit somewhere, but a thing cannot have a limit unless there is something outside to limit it.
     From: Lucretius (On the Nature of the Universe [c.60 BCE], I.959)
     A reaction: This is a subtler argument than the mere enquiry about why you would have to stop at the end of the universe. It still seems a nice argument, though Einstein's curvature of space seems to have thwarted it.
An infinite line can be marked in feet or inches, so one infinity is twelve times the other [Spinoza]
     Full Idea: If an infinite line be measured out in feet, it will consist of an infinite number of such parts; it would equally consist of an infinite number of parts, if each part was only an inch; therefore, one infinity would be twelve times as great as the other.
     From: Baruch de Spinoza (The Ethics [1675], I Pr 15)
     A reaction: This seems to anticipate Cantor. Spinoza's point seemed bewildering then, but is now accepted as a standard feature of the concept of infinity.
If there were infinite electrons, they could vanish without affecting total mass-energy [Heil]
     Full Idea: In a universe containing an infinite number of electrons would mass-energy be conserved? ...Electrons could come and go without affecting the total mass-energy.
     From: John Heil (The Universe as We Find It [2012], 03.6)
     A reaction: This seems to be a very persuasive reason for doubting that the universe contains an infinite number of electrons. In fact I suspect that infinite numbers have no bearing on nature at all. (Actually, I suspect them of being fictions).
Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR]
     Full Idea: There seem to be no actual infinites in the physical realm. Given the correctness of atomism, there are no infinitely small things, no infinite divisibility. And General Relativity says that the universe is only finitely large.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 5)
     A reaction: If time was infinite, you could travel round in a circle forever. An atom has size, so it has a left, middle and right to it. Etc. They seem to be physical, so we will count those too.
There are probably no infinities, and 'infinite' names what we do not yet know [Rovelli]
     Full Idea: 'Infinite', ultimately, is the name that we give to what we do not yet know. Nature appears to be telling us that there is nothing truly infinite.
     From: Carlo Rovelli (Reality is Not What it Seems [2014], 11)