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Full Idea
For Aristotle infinity is not so much a property of some set of objects - the numbers - as of the process of counting, namely of its not having a natural limit. This is 'potential' infinite
Gist of Idea
Aristotle's infinity is a property of the counting process, that it has no natural limit
Source
report of Aristotle (Physics [c.337 BCE]) by Robin Le Poidevin - Travels in Four Dimensions 06 'Illusion'
Book Ref
Le Poidevin,Robin: 'Travels in Four Dimensions' [OUP 2003], p.96
A Reaction
I increasingly favour this view. Mathematicians have foisted fictional objects on us, such as real infinities, limits and zero, because it makes their job easier, but it makes discussion of the natural world very obscure.
13212 | Infinity is only potential, never actual [Aristotle] |
22929 | Aristotle's infinity is a property of the counting process, that it has no natural limit [Aristotle, by Le Poidevin] |
9632 | Kant only accepts potential infinity, not actual infinity [Kant, by Brown,JR] |
15938 | Platonists ruin infinity, which is precisely a growing structure which is never completed [Dummett] |
15940 | The intuitionist endorses only the potential infinite [Lavine] |