# What resolves Zeno's argument for the non-existence of place?

Aristotle discusses six dialectical arguments for the non-existence of place in Physics bk. Δ On Place, ch. 1 (209a); Zeno's argument is #5:

if everything that exists has a place, place too will have a place, and so on ad infinitum

Does what I call "idempotence of place" resolve the paradox?:

Place is an idempotent relation because the the place of the place of something is still its place. Thus place(place)=place. Therefore place(place(place(…)))=place.

• (1) You should be more formal. Your use of symbol is a bit ambiguous. (2) Mathematically speaking it's not transitivity but rather looks like idempotence (3) You should think about what it means to "resolve the paradox" Mar 1, 2017 at 19:21
• Agreed it is idempotence. Mar 1, 2017 at 19:23
• Aristotle considers the idea that a place is not a part of that whose place it is to be one of our basic intuitions about "place". So this proposal would be a non-starter for him, see Aristotle on Space, Time, and Motion Mar 1, 2017 at 21:04
• Why do you think that there is a paradox at all ? A., Phy, IV 4, 212a20-21 "the place of a thing is the innermost motionless boundary of what contains it." Boundary does not mean that it is a thing itself. Thus, if place is not a thing, there is no need of "the place" of place. Mar 2, 2017 at 14:04
• If you agree that this is about idempotence and not transitivity, please edit your post to clarify that. Also, I believe your last expression 'place(place(place(...)))=place' should actually read something like 'place(place(...(place)...))=place', to avoid plugging in something else than a place.
– user2953
Mar 5, 2017 at 12:29