What role should statistical probability, based on a predictable distribution of outcomes in a hypothesized long run of trials, play in a decisionsituation involving an individual case? Does a statistical interpretation of probability require one, in rational decision-making, to decide in an isolated individual case just as one would in a rational decision-situation involving many repetitions of the individual case? Often one will do in an isolated individual case what one would do in a long run of repetitions of such a case. For example, given the option to bet (with the same odds) either that a toss of a die will not be a 6 or that it will be a 6, one ought to bet that it will not be a 6; for the probability of getting not-6 is five times the probability of getting 6. According to a statistical interpretation of probability, this means that in a suitable long run, not-6 would result (approximately) five times as often as 6. In such a long run, one ought to bet every time on not-6, as this would quintuple one's number of wins as compared to betting on 6.A statistical interpretation of probability judgments regarding an isolated individual case (a case that is not part of a statistically relevant long run) suggests the following: The rationally preferable strategy of one's betting only on not-6 in a long run is suficient for the rational preferability of one's betting on not-6 in an isolated individual case. Is this true universally? Is it, alternatively, ever rationally permissible to do in an isolated individual case what would not be rationally preferable in a suitable long run of cases (that is, the kind of long run constitutive of statistical probability judgments)? This paper examines these 109 Downloaded by [McMaster University] at

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Many theorists of explanation from Hempel onward have worked with the explicit or implicit assumption that considerations of the subjective sense of understanding should be kept out of the formulation of a proper theory of explanation. They claim that genuine understanding of an event comes only from being in an appropriate cognitive relation to the true explanation of that event. I argue that considerations of the subjective sense of understanding cannot be completely removed from the process of formulating and justifying an acceptable theory of explanation. Although understanding is neither a necessary nor sufficient condition for an explanation, understanding is necessary as an initial guide to the nature of explanation. The widespread method of providing counterexamples for criticizing theories of explanation presupposes that there is a neutral method of identifying at least some clear cases of explanation and some clear cases of non-explanations. I argue that the only plausible method to fill this role relies essentially on the subjective sense of understanding. Objective validation of judgments about explanatoriness comes only through a complex process of social correction of our initial intuitive judgments regarding explanation.