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DanielLC comments on The Cluster Structure of Thingspace - Less Wrong
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But if a definition works well enough in practice to point out the intended empirical cluster, objecting to it may justly be called "nitpicking".
You should probably put in a disclaimer excepting mathematics from this -- assuming that you agree it should be excepted. (That is, assuming you agree that "Aristotelian" precision -- what mathematicians call "rigor" -- is appropriate in mathematics.)
"Definition" has a different definition in math.