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15987
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Physics only needs geometry or abstract mathematics, which can explain and demonstrate everything [Descartes]
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Full Idea:
I do not accept or desire any other principle in physics than in geometry or abstract mathematics, because all the phenomena of nature may be explained by their means, and sure demonstrations can be given of them.
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From:
René Descartes (Principles of Philosophy [1646], 2.64), quoted by Peter Alexander - Ideas, Qualities and Corpuscles 7
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A reaction:
This is his famous and rather extreme view, which might be described as hyper-pythagoreanism (by adding geometry to numbers). It seems to leave out matter, forces and activity.
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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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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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16601
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Matter is not hard, heavy or coloured, but merely extended in space [Descartes]
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Full Idea:
The nature of matter, or body viewed as a whole, consists not in its being something which is hard, heavy, or colored, or which in any other way affects the senses, but only in its being a thing extended in length, breadth and depth.
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From:
René Descartes (Principles of Philosophy [1646], 2.4), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 04.5
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