Isaac Levi

(1930 - 2018)

There are two uses of randomization in efforts to control systematic bias in experimental design: (a) Alchemical uses seek to convert unavoidable systematic errors into random errors. (b) Hygienic uses seek to reduce the prospect of the experimenter's involvement with the implementation of the experiment contributing to bias. A few remarks are made at the end of the paper about the hygienic use of randomization as a preventative against sticky fingers. The bulk of the discussion addresses the alchemical applications. The thesis is that attitudes towards the cogency of Fisher's alchemical use of randomization ought to depend on views concerning statistical deduction or direct inference.

This paper seeks to defend the following conclusions: The program advanced by Carnap and other necessarians for probability logic has little to recommend it except for one important point. Credal probability judgments ought to be adapted to changes in evidence or states of full belief in a principled manner in conformity with the inquirer’s confirmational commitments—except when the inquirer has good reason to modify his or her confirmational commitment. Probability logic ought to spell out the constraints on rationally coherent confirmational commitments. In the case where credal judgments are numerically determinate confirmational commitments correspond to Carnap’s credibility functions mathematically represented by so—called confirmation functions. Serious investigation of the conditions under which confirmational commitments should be changed ought to be a prime target for critical reflection. The necessarians were mistaken in thinking that confirmational commitments are immune to legitimate modification altogether. But their personalist or subjectivist critics went too far in suggesting that we might dispense with confirmational commitments. There is room for serious reflection on conditions under which changes in confirmational commitments may be brought under critical control. Undertaking such reflection need not become embroiled in the anti inductivism that has characterized the work of Popper, Carnap and Jeffrey and narrowed the focus of students of logical and methodological issues pertaining to inquiry.

Several authors have recently contended that modern statistical theory provides a powerful argument in favor of the view that if scientists accept or reject hypotheses at all they do so only in a behavioral sense--i.e., in a sense which reduces "accepting P" to "acting on the basis of P relative to an objective O". In this paper, the argument from statistics in favor of a behavioral view is outlined; an interpretation of two statistical procedures (Bayes method and signifigance testing) is offered which does not entail a behavioral analysis of "accepting a hypothesis"; and the conclusion that non-behavioral analyses of belief are compatible with the application of current statistical theory in the sciences is tentatively advanced

For three centuries, philosophers have mounted defenses against the melan genie with an obsessive intensity comparable to the Reaganite determination to squander American wealth on defenses against a Communist threat. And for three centuries, skeptics have argued for the futility of the expenditure of conceptual effort with no more success than critics of the Pentagon have had in stemming the flow of funds to the military and its industrial minions. My own sympathies are with the skeptics. However, their own intense involvement with the obsessions of the epistemological fear mongers and their failure to address the analogue of the problem of conversion from military to civilian industry in an acceptable manner often deprive the skeptical position of the subversive force it ought to have.

Two views of the role of truth as an aim of inquiry are contrasted: The Peirce-Popper or messianic view of approach to the truth as an ultimate aim of inquiry and the myopic view according to which a concern to avoid error is a proximate aim common to many otherwise diverse inquiries. The messianic conception is held to be responsible for the tendency to conflate fallibilism with corrigibilism and for the consequent problems faced by Peirceans and Popperians alike in squaring the alleged relevance of the fruits of scientific inquiry for practice while insisting on the corrigibility of knowledge. Myopic realism is advocated as promising escape from these difficulties

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