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

Question

Aristotle discusses six dialectical arguments for the non-existence of place in Physics bk. Δ On Place, ch. 1 (209^a); 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.

Answer 1

Aristotle resolves the argument in Physics bk. Δ On Place, ch. 3 (210^b):

Zeno's problem—that if Place is something it must be in something—is not difficult to solve. There is nothing to prevent the first place from being 'in' something else—not indeed in that as 'in' place, but as health is 'in' the hot as a positive determination of it or as the hot is 'in' body as an affection. So we escape the infinite regress.

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^{For an in-depth treatment of the "problem" of place, see "Part II: Place" of:}

• ^{Duhem, Pierre Maurice Marie. Medieval Cosmology: Theories of Infinity, Place, Time, Void, and the Plurality of Worlds. Edited and translated by Roger Ariew. Chicago: University of Chicago Press, 1985.}