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komponisto2 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.)
Mathematics is largely already excepted from the above discussion - this post is talking about empirical clusters only ("When you draw a boundary around a group of extensional points empirically clustered in thingspace"), and mathematics largely operates in a priori truths derived from axioms. For example, no one needs to do a study of triangles to see whether their angle all do, indeed, add up to 180 degrees - when that's not part of the definition of triangles, it follows from the other definitions and axioms.
"Definition" has a different definition in math.