In engagement with Frege, Wittgenstein, and Chomsky, the thesis is developed that the attempt to delineate the realm of linguistically meaningful expressions in a formal and thus technical manner, and to thereby master it calculatively, is doomed to fail for precisely identifiable reasons. It is philosophically enlightening and of utmost importance for the humanities to study these reasons in detail. The competence to distinguish sense from nonsense cannot be reconstructed as a purely calculative, formal, or schematic competence. Natural language is not a calculus, although it has important aspects that can be appropriately represented in that way. Rather, the non-technical ability for spontaneous, rule-free action, which is hinted at in the title with the word imagination, permeates it in such a way that it also encompasses the formal.