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Single Idea 4821
[filed under theme 26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
]
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.
Gist of Idea
An infinite line can be marked in feet or inches, so one infinity is twelve times the other
Source
Baruch de Spinoza (The Ethics [1675], I Pr 15)
Book Ref
Spinoza,Benedict de: 'Ethics, Improvement of Understanding, Letters', ed/tr. Elwes,R [Dover 1955], p.56
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.
The
14 ideas
with the same theme
[time or space or matter could be infinite]:
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8659
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The gods alone live forever with Shamash. The days of humans are numbered.
[Anon (Gilg)]
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1748
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Archelaus was the first person to say that the universe is boundless
[Archelaus, by Diog. Laertius]
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5093
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Continuity depends on infinity, because the continuous is infinitely divisible
[Aristotle]
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5095
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The heavens seem to be infinite, because we cannot imagine their end
[Aristotle]
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8660
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There are potential infinities (never running out), but actual infinity is incoherent
[Aristotle, by Friend]
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14032
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Totality has no edge; an edge implies a contrast beyond the edge, and there can't be one
[Epicurus]
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14033
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Bodies are unlimited as well as void, since the two necessarily go together
[Epicurus]
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22743
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Unlike Epicurus, Stoics distinguish the Whole from the All, with the latter including the void
[Stoic school, by Sext.Empiricus]
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5704
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There can be no centre in infinity
[Lucretius]
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5703
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The universe must be limitless, since there could be nothing outside to limit it
[Lucretius]
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4821
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An infinite line can be marked in feet or inches, so one infinity is twelve times the other
[Spinoza]
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18519
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If there were infinite electrons, they could vanish without affecting total mass-energy
[Heil]
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9635
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Given atomism at one end, and a finite universe at the other, there are no physical infinities
[Brown,JR]
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20469
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There are probably no infinities, and 'infinite' names what we do not yet know
[Rovelli]
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