This introduction proposes to investigate mismatches and indeterminacies in languages much more than has hitherto been done. Such seemingly unruly aspects of language(s), it is argued, are interesting since they may help shed light on the internal make-up of grammatical systems. The question of the internal make-up of grammar(s), it is argued, cannot be addressed by the normal modus operandi of linguistic research, which is to find matches (rather than mismatches) between the observable (sound and meaning) interface systems, and to find how the interface representations map unto each other deterministically: It is only in the "lo-fi" aspects of mappings that the internal mechanisms of the overall grammatical architecture may reveal themselves.
The introduction also points out that our concern is independent of the various theoretical orientations linguists may choose for their work, since the problem presents itself in all approaches to language research currently available, it seems - if in slightly different ways.
We propose, in sum, that mismatches and indeterminacies are an extremely worthwhile field for future linguistic research, and one that should be on the agenda (or minimally, within the field of view) for linguists of all theoretical convictions.