This article argues that the much-maligned ‘notational variants’ of a given formal linguistic theory play a role similar to alternative numerical measurement scales. Thus, they can be used to identify the invariant components of the grammar; i.e., those features that do not depend on the choice of empirically equivalent representation. Treating these elements as the ‘meaningful’ structure of language has numerous consequences for the philosophy of science and linguistics. I offer several such examples of how linguistic theorizing can profit from (...) adopting a measurement-theoretic viewpoint. The first concerns a measurement-theoretic response to a famous criticism of Quine's. Others follow from issues of simplicity in the current biolinguistics program. An unexpected similarity with behaviorist practices is also uncovered. I then argue that managable and useful steps can be taken in this area. (shrink)