Editing Zeno's paradoxes (section)

=== Other paradoxes ===
Aristotle gives three other paradoxes.
==== Paradox of place ====
From Aristotle:
{{quote
|If everything that exists has a place, place too will have a place, and so on ''[[ad infinitum]]''.<ref>Aristotle [http://classics.mit.edu/Aristotle/physics.4.iv.html ''Physics'' IV:1, 209a25] {{Webarchive|url=https://web.archive.org/web/20080509083946/http://classics.mit.edu//Aristotle/physics.4.iv.html |date=2008-05-09 }}</ref>}}

==== Paradox of the grain of millet ====
{{see also|Sorites paradox}}
Description of the paradox from the ''Routledge Dictionary of Philosophy'':
{{quote
|The argument is that a single grain of [[millet]] makes no sound upon falling, but a thousand grains make a sound. Hence a thousand nothings become something, an absurd conclusion.<ref>The Michael Proudfoot, A.R. Lace. Routledge Dictionary of Philosophy. Routledge 2009, p. 445</ref>}}

Aristotle's response:
{{quote
|Zeno's reasoning is false when he argues that there is no part of the millet that does not make a sound: for there is no reason why any such part should not in any length of time fail to move the air that the whole bushel moves in falling. In fact it does not of itself move even such a quantity of the air as it would move if this part were by itself: for no part even exists otherwise than potentially.<ref>Aristotle [http://classics.mit.edu/Aristotle/physics.7.vii.html ''Physics'' VII:5, 250a20] {{Webarchive|url=https://web.archive.org/web/20080511153804/http://classics.mit.edu//Aristotle/physics.7.vii.html |date=2008-05-11 }}</ref>}}

Description from Nick Huggett:
{{quote
|This is a [[Parmenides|Parmenidean]] argument that one cannot trust one's sense of hearing. Aristotle's response seems to be that even inaudible sounds can add to an audible sound.<ref>Huggett, Nick, "Zeno's Paradoxes", The Stanford Encyclopedia of Philosophy (Winter 2010 Edition), Edward N. Zalta (ed.), http://plato.stanford.edu/entries/paradox-zeno/#GraMil {{Webarchive|url=https://web.archive.org/web/20220301174333/https://plato.stanford.edu/entries/paradox-zeno/#GraMil |date=2022-03-01 }}</ref>}}

==== The moving rows (or stadium) ====
[[File:Zeno Moving Rows Paradox.png|thumb|The moving rows]]

From Aristotle:
{{quote
|... concerning the two rows of bodies, each row being composed of an equal number of bodies of equal size, passing each other on a race-course as they proceed with equal velocity in opposite directions, the one row originally occupying the space between the goal and the middle point of the course and the other that between the middle point and the starting-post. This...involves the conclusion that half a given time is equal to double that time.<ref>Aristotle [http://classics.mit.edu/Aristotle/physics.6.vi.html ''Physics'' VI:9, 239b33] {{Webarchive|url=https://web.archive.org/web/20080515224131/http://classics.mit.edu//Aristotle/physics.6.vi.html |date=2008-05-15 }}</ref>}}

An expanded account of Zeno's arguments, as presented by Aristotle, is given in [[Simplicius of Cilicia|Simplicius's]] commentary ''On Aristotle's Physics''.<ref name=":2">{{Cite book |last1=Simplikios |title=Simplicius on Aristotle's Physics 6 |last2=Konstan |first2=David |last3=Simplikios |date=1989 |publisher=Cornell Univ. Pr |isbn=978-0-8014-2238-6 |series=Ancient commentators on Aristotle |location=Ithaca N.Y}}</ref><ref name=":1">{{Citation |last=Huggett |first=Nick |title=Zeno's Paradoxes |date=2024 |encyclopedia=The Stanford Encyclopedia of Philosophy |editor-last=Zalta |editor-first=Edward N. |url=https://plato.stanford.edu/archives/spr2024/entries/paradox-zeno/ |access-date=2024-03-25 |edition=Spring 2024 |publisher=Metaphysics Research Lab, Stanford University |editor2-last=Nodelman |editor2-first=Uri}}</ref><ref name=":0">{{Cite web |title=Zeno's Paradoxes {{!}} Internet Encyclopedia of Philosophy |url=https://iep.utm.edu/zenos-paradoxes/ |access-date=2024-03-25 |language=en-US}}</ref>

According to Angie Hobbs of The University of Sheffield, this paradox is intended to be considered together with the paradox of Achilles and the Tortoise, problematizing the concept of discrete space & time where the other problematizes the concept of infinitely divisible space & time.<ref>{{Cite web |title=Zeno's Paradoxes: The Moving Rows |url=https://digitalmedia.sheffield.ac.uk/media/Zeno%27s+ParadoxesA+The+Moving+Rows/1_e2yi73na |access-date=2024-06-28 |website=The University of Sheffield Kaltura Digital Media Hub |language=en}}</ref>