Variable-sharing is a syntactic criterion that fails to track genuine relevance, as logically equivalent formulations of the same proposition may share or lack variables arbitrarily.
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Does not mean 'random' or that all qualities are equally adequate as differentia; refers instead to the availability of multiple similarly good and natural grounds for classification.
logically equivalent(used to describe when different phrasings express the identical logical claim)
Two statements are logically equivalent when they mean exactly the same thing and must always have the same truth value (both true or both false).
proposition(Used in the context of a semantic theory sensitive to differences in subject matter.)
The content expressed by a sentence, individuated at least in part by the subject matter of the sentence and the contents of its subsentential expressions.