Throughout his career, Isaac Levi has advocated a unity of reason thesis according to which practical deliberation and theoretical inquiry, while differing as regards values and goals, are nonetheless similar from a structural point of view. In support of this thesis he has argued, first and foremost, that problems of induction can be seen as decision problems analogous to practical ones; both kinds of reasoning can be represented within the framework of Bayesian decision theory. In the practical case, the decision maker's options are practical actions. In the theoretical setting, they are, Levi thinks, acts of accepting potential answers to the inquirer's question. In this chapter I argue that his latter view exposes him to criticism unnecessarily.

LEVI'S COGNITIVE DECISION THEORY

Suppose that the agent is in an initial state of full belief K. There is a question that the agent wants to answer, and so he has identified a set of relevant propositions exclusive and exhaustive relative to K in the manner proposed by Levi in his first book from 1967 and defended in later works. This set is his ultimate partition U. Given U, a set of potential expansions relevant to the inquirer's demands for information can be identified. These potential expansions or, as Levi also calls them, cognitive options are formed by adding to K an element of U or a disjunction of such elements. The result is then closed under logical consequence. Levi assumes that adding some belief contravening proposition is also a potential expansion.

Isaac Levi's philosophical thinking has shown remarkable stability over the years. Basically, it all started with his first book, Gambling with Truth, which outlines a research program whose key element is the decision-theoretic reconstruction of epistemology. Much of the rest of his work in epistemology has been devoted to extending and implementing this original program. With one important exception, there is little in his philosophical picture that has changed radically over the years. There have been changes, to be sure, but they have taken place at the level of detail rather than at the level of fundamental principle. The main exception is the issue of fallibilism. Starting out as a fallibilist, Levi became an infallibilist in the 1970s. The problem is that the corrigibility of our view suggests its fallibility: If we agree, as we must, that our view may change in the future, then it seems that we are never entitled to accept as true any claims of empirical substance now. But we do accept things as true now. Levi writes, in retrospect, that in the 1960s he unwittingly solved this problem for himself “by remaining in a fog of confusion” (Levi 1984, p. xiv), adding that by 1971 he had reached the conclusion that corrigibility and fallibility are best kept separate and, in particular, that endorsing corrigibilism is compatible with rejecting fallibilism. The paper “Truth, Fallibility and the Growth of Knowledge” was the first expression of this important revision.

INTRODUCTION

Consider a lottery of 1,000,000 tickets where there is one and only one winner and where one ticket is as likely as any other to be the winner. In this sort of scenario it is extremely improbable that any given ticket will win. The probability that a given ticket will lose is as high as that of any statistical hypothesis one can think of. If we are ever allowed to accept a hypothesis as true, then surely we are allowed to accept, of any given ticket, that it will lose. But to accept, for each ticket, that it will lose is to commit oneself to there being no winning ticket. This contradicts our background knowledge that there is a winning ticket. It seems, then, that common sense gives us a license for holding contradictory beliefs.

The lottery paradox, first formulated by Henry Kyburg, is still a hotly disputed subject that is thought to have all sorts of radical consequences for human inquiry. Kyburg saw it as an argument for cultivating a tolerance for inconsistency and against demanding logical closure of a rational agent's beliefs.

Isaac Levi has retired from his academic position as prestigious John Dewey Professor of Philosophy at Columbia University, and yet there is no sign that he has retired from philosophy. On the contrary, he just published a new book entitled Mild Contraction with Oxford University Press, and he continues to write papers and participate in conferences and workshops. This collection is dedicated to Isaac on the occasion of his retirement, in celebration of his exceptional contribution to philosophy in general and to the great tradition of American pragmatism in particular. It is far more than a Festschrift in the usual sense; all the papers included are substantial contributions to the understanding and appraisal of Isaac's pragmatist philosophy by leading experts on his work. They were all written specifically for this volume and appear here for the first time. I am greatly indebted to all authors for their dedication and commitment to this project, and especially to Isaac for his extensive replies to all the papers.

My own intellectual debt to Isaac is great. My first internationally published paper, written jointly with Sven Ove Hansson, who was my thesis adviser back then, addressed Isaac's theory of belief contraction. In this connection, reading his book The Fixation of Belief and Its Undoing was especially rewarding, although some of his more intricate arguments were beyond my grasp at the time.