8660
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There are potential infinities (never running out), but actual infinity is incoherent [Aristotle, by Friend]
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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.
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From:
report of Aristotle (works [c.330 BCE]) by Michèle Friend - Introducing the Philosophy of Mathematics 1.3
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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.
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6731
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No one can explain how matter affects mind, so matter is redundant in philosophy [Berkeley]
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Full Idea:
How matter should operate on a spirit, or produce any idea in it, is what no philosopher will pretend to explain; it is therefore evident there can be no use of matter in natural philosophy.
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From:
George Berkeley (The Principles of Human Knowledge [1710], §50)
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A reaction:
An intriguing argument for idealism, which starts in Cartesian dualism, but then discards the physical world because of the notorious interaction problem. Of course, if he had thought that matter and spirit were one (Spinoza) the problem vanishes.
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6730
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We discover natural behaviour by observing settled laws of nature, not necessary connections [Berkeley]
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Full Idea:
That food nourishes, sleep refreshes, and fire warms us; all this we know, not by discovering any necessary connexion between our ideas, but only by the observation of the settled laws of nature.
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From:
George Berkeley (The Principles of Human Knowledge [1710], §31)
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A reaction:
Hume is famous for this idea, but it is found in Hobbes too (Idea 2364), and is the standard empiricist view of causation. The word 'settled' I take to imply that the laws are contingent, because they could become unsettled at any time.
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