Over the past thirty years or so a number of scholars, mostly but not entirely American, have sought to elucidate problems of genetic linguistics by employing, explicitly or not, some form of probability mathematics. As I reread these efforts, my own included, I wonder that no one has ever seriously questioned the pertinence or, indeed, the legitimacy of such employment in elucidating historical problems. Mathematics takes vaguely defined terms of ordinary speech like ‘probability’ and ‘chance’ and gives them precise meanings, but when we use such terms in linguistics, together with their associated mathematical procedures, do we always keep the precise meaning? Or do we fall back unwittingly into the popular use and thus vitiate our results? And even if we are careful to keep the precise meanings, are we justified in supposing that mathematical probability can furnish a theory to account for the phenomena of history in languages, or, if not a theory, then a model? Such questions as these deserve answers, and by now enough experience has accumulated to warrant an attempt to answer them. The present paper is offered as such an attempt with the hope that, if it does no more, it will at least ask the right questions. But first a word must be said about theories and models.