In order to make sense of this paper, to readers who are not familiar with Conversation Theory and its proto-lanquage or proto-logic, this introduction contains a terse account of their essentials, insofar as they are relevant to the main topic of complementarity. Henceforward, the abbreviation C.T. will be used for "conversation theory" and Lp for its attendant "proto-languages or proto-logics", so called because they are not usually metalanguages, (although they might be employed with some augmentation for that purpose). Taken as they stand, they are primitive or underlying languages, (underlying, for example, the delicacies of natural languages, or symbolism in the form of art, of ballet, of mime, of music, or even of general behaviour). Lp does, of course, have rules and constraints, without which it would be pretty useless, but these are derived from the foundations of C.T., imaging them crudely and imcompletely for all that.