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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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16102
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Aether moves in circles and is imperishable; the four elements perish, and move in straight lines [Aristotle, by Gill,ML]
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Full Idea:
For Aristotle, aether and the four sublunary elements obey different physical laws. Aether moves naturally in a circle and, unlike its lower counterparts, is not a source of perishability. The four sublunary elements move naturally in straight lines.
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From:
report of Aristotle (On the Heavens [c.336 BCE]) by Mary Louise Gill - Aristotle on Substance Ch.2
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A reaction:
I think it is anachronistic for Gill to talk of 'obeying' and 'laws'. She should have said that they have different 'natures'. We can be amused by Greek errors, until we stare hard at the problems they were trying to solve.
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17463
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An element is what bodies are analysed into, and won't itself divide into something else [Aristotle]
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Full Idea:
An element is a body into which other bodies may be analyzed, present in them potentially or in actuality (which of these is still disputable), and not itself divisible into bodies different in form. That is what all men mean by element.
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From:
Aristotle (On the Heavens [c.336 BCE], 302a05), quoted by Weisberg/Needham/Hendry - Philosophy of Chemistry 1.1
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A reaction:
This is the classic definition of an element, which endured for a long time, and has been replaced by an 'actual components' view. Obviously analysis nowadays goes well beyond the atoms.
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