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Full Idea
Aristotle says that a length does not already contain, waiting to be discovered, an infinite number of parts; such parts only come into existence once they are defined by an act of division.
Gist of Idea
Lengths do not contain infinite parts; parts are created by acts of division
Source
report of Aristotle (Physics [c.337 BCE]) by Robin Le Poidevin - Travels in Four Dimensions 07 'Two'
Book Ref
Le Poidevin,Robin: 'Travels in Four Dimensions' [OUP 2003], p.106
A Reaction
If that is true of infinite parts then it must also be true of finite parts. So a cake has no parts at all until it is cut. That could play merry hell with discussions of mereology. Wholes are ontologically prior to parts.
Related Idea
Idea 6128 Objects decompose (it seems) into non-overlapping parts that fill its whole region [Merricks]