Talk:Aristotle's wheel paradox
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[edit] Bijections, really?
I'm glad that this article exists, but its statement of the problem is troublesome. Surely "sets of points" and "bijections" are anachronisms when recounting a problem posed by Aristotle? There is a paradox if one naively assumes that equal cardinalities have equal measures, but I fear that our modern eagerness to dispel that notion has caused us to project it backwards in time. Wolfram[1] does the same, but it's a well-known hotbed of original research and shouldn't be trusted.
From this book and the included external link[2], it appears that the original paradox is a matter of geometry and mechanics, arising from the erroneous assumption that the small wheel traces out its own circumference. And this assumption is not necessarily made by corresponding points between the path and the circumference. It seems to be made without any explanation at all, which shouldn't be too surprising; paradoxes arise by sleight of hand and gaps in reasoning at least as often as explicit falsehoods. Melchoir (talk) 09:30, 2 March 2008 (UTC)
The above comment is in reference to this version. I've since replaced the material in question, with a citation to Bunch, whose treatment is very similar although obviously more extended. Melchoir (talk) 10:01, 2 March 2008 (UTC)
