Isaac Levi

(1930 - 2018)

This book by one of the world's foremost philosophers in the fields of epistemology and logic offers an account of suppositional reasoning relevant to practical deliberation, explanation, prediction and hypothesis testing. Suppositions made 'for the sake of argument' sometimes conflict with our beliefs, and when they do, some beliefs are rejected and others retained. Thanks to such belief contravention, adding content to a supposition can undermine conclusions reached without it. Subversion can also arise because suppositional reasoning is ampliative. These two types of nonmonotonic logic are the focus of this book. A detailed comparison of nonmonotonicity appropriate to both belief contravening and ampliative suppositional reasoning reveals important differences that have been overlooked.

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 a toss at t, a toss in 728 Philosophy Hall and 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, and 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.

De Finetti was a strong proponent of allowing 0 credal probabilities to be assigned to serious possibilities. I have sought to show that (pace Shimony) strict coherence can be obeyed provided that its scope of applicability is restricted to partitions into states generated by finitely many ultimate payoffs. When countable additivity is obeyed, a restricted version of ISC can be applied to partitions generated by countably many ultimate payoffs. Once this is appreciated, perhaps the compelling character of the Shimony argument will be less overwhelming and the attractiveness of de Finetti's more permissive attitude will become more apparent.I want to push the permissive tendency in de Finetti still further. It seems doubtful that RUIWC should be required as de Finetti apparently suggested. It is also excessively dogmatic and restrictive to require that the credal states of ideally situated rational agents be numerically definite (Levi 1974, 1980). And de Finetti's rejection of objectivism in statistics overreached itself when he dismissed objective probabilities as meaningless metaphysical artefacts (Levi 1986). In this respect, the philosophically most important lessons de Finetti has to teach us are to be found not in his celebrated representation theorem but in his discussions of the relations between 0-probability and possibility, conditional probability and countable additivity. Perhaps, the technical issues involved are remote and pedantic. But the attitude de Finetti sought to inculcate is of profound importance