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pragmatist comments on Natural Laws Are Descriptions, not Rules - Less Wrong
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Regularities of the kind you describe would very plausibly not be the axioms of the best system for any vocabulary we care about. Adding the jeans regularity to the list of axioms in a system would give up simplicity for a trivial gain in information content.
So it comes down to laws being separated from other regularities because of some ratio of parsimony to information? Without some reason to declare a particular boundary on that, that seems like a rather arbitrary distinction.