Although Kripke’s œuvre has had a major impact on analytic philosophy and nearly every aspect of his studies has been thoroughly examined, this does not hold for his schmidentity argument, which, so far, has been widely neglected. To the extent to which it has been treated at all, it has been for the most part radically misunderstood. I hold that this argument, in its correctly reconstructed form, has general relevance for a treatment of Frege’s Puzzle and points towards a fundamental (...) methodological restriction for philosophy of language and especially for semantics, as far as informativity and the general topic of cognitive significance are concerned. To show this, I will briefly set out the context of the schmidentity argument and, in Sects. 2 and 4, sketch a reconstruction thereof, including some criticisms of the argument, and an excursion about Kit Fine’s semantic relationism, which stands in stark contrast to this paper’s central claim. Moreover, I will draw a genuinely new and probably quite unexpected conclusion from all the above, to finally give a glimpse at a bigger picture of where this conclusion should lead our thinking about a theoretical treatment of informativity and a linguistic expression’s cognitive value. (shrink)