Kyburg on Random Designators

Extract

To ground judgments of credal probability on knowledge of chance via direct inference, one should appeal to the information about chances available relative to the most specific description known to be true of the trial event.

Thus, to obtain a judgment of credal probability concerning the hypothesis that coin a landed heads at t given that it is known that at t it is known that a was tossed by Levi in 728 Philosophy Hall, the pertinent knowledge of chances concerns the chances of coin a landing heads on a toss of coin a which is (i) a toss at t, (ii) a toss in 728 Philosophy Hall and (iii) a toss by Levi. In many contexts, appeal is made to knowledge of the chance of coin a landing heads on a toss. This appeal, when legitimate, takes for granted that the additional information about the specific tossing listed in (i), (ii) and (iii) is stochastically irrelevant to landing heads and, hence, may be ignored. Such an assumption is a substantive presupposition about chances and not an a priori, self evident or pragmatic principle of methodology.