Editing Zeno's paradoxes (section)

==== Hermann Weyl ====
Another proposed solution is to question one of the assumptions Zeno used in his paradoxes (particularly the Dichotomy), which is that between any two different points in space (or time), there is always another point. Without this assumption there are only a finite number of distances between two points, hence there is no infinite sequence of movements, and the paradox is resolved. According to [[Hermann Weyl]], the assumption that space is made of finite and discrete units is subject to a further problem, given by the "[[Weyl's tile argument|tile argument]]" or "distance function problem".<ref>{{cite encyclopedia| last=Van Bendegem| first=Jean Paul| title=Finitism in Geometry| url=http://plato.stanford.edu/entries/geometry-finitism/#SomParSolProDea| encyclopedia=Stanford Encyclopedia of Philosophy| access-date=2012-01-03| date=17 March 2010| archive-date=2008-05-12| archive-url=https://web.archive.org/web/20080512012132/http://plato.stanford.edu/entries/geometry-finitism/#SomParSolProDea| url-status=live}}</ref><ref name="atomism uni of washington">{{cite web| last=Cohen| first=Marc| title=ATOMISM| url=https://www.aarweb.org/syllabus/syllabi/c/cohen/phil320/atomism.htm|work=History of Ancient Philosophy, University of Washington| access-date=2012-01-03|date=11 December 2000  |url-status=dead |archive-url=https://web.archive.org/web/20100712095732/https://www.aarweb.org/syllabus/syllabi/c/cohen/phil320/atomism.htm |archive-date=July 12, 2010}}</ref> According to this, the length of the hypotenuse of a right angled triangle in discretized space is always equal to the length of one of the two sides, in contradiction to geometry. [[Jean Paul Van Bendegem]] has argued that the Tile Argument can be resolved, and that discretization can therefore remove the paradox.<ref name=boyer/><ref>{{cite journal |jstor=187807 |title=Discussion:Zeno's Paradoxes and the Tile Argument |first=Jean Paul |last=van Bendegem |location= Belgium |year=1987 |journal=Philosophy of Science |volume=54 |issue=2 |pages=295–302|doi=10.1086/289379|s2cid=224840314 }}</ref>