Isaac Levi

(1930 - 2018)

We present a decision-theoretically motivated notion of contraction which, we claim, encodes the principles of minimal change and entrenchment. Contraction is seen as an operation whose goal is to minimize loses of informational value. The operation is also compatible with the principle that in contracting A one should preserve the sentences better entrenched than A (when the belief set contains A). Even when the principle of minimal change and the latter motivation for entrenchment figure prominently among the basic intuitions in the works of, among others, Quine and Ullian (1978), Levi (1980, 1991), Harman (1988) and Gärdenfors (1988), formal accounts of belief change (AGM, KM – see Gärdenfors (1988); Katsuno and Mendelzon (1991)) have abandoned both principles (see Rott (2000)). We argue for the principles and we show how to construct a contraction operation, which obeys both. An axiom system is proposed. We also prove that the decision-theoretic notion of contraction can be completely characterized in terms of the given axioms. Proving this type of completeness result is a well-known open problem in the field, whose solution requires employing both decision-theoretical techniques and logical methods recently used in belief change.

Newcomb's paradox rests on two arguments one appealing to the principle of maximizing expected utility and one appealing to dominance in order to generate conflicting recommendations in certain kinds of choice situations. In my essay, I argue that the applications of the principle of maximizing expected utility and of the dominance principle are both fallacious and that the specification of the decision problem is too indeterminate to render a verdict between the two options considered. I also show that if Nozick's case for invoking the dominance principle is taken seriously, it leads to contradictions.

Richard Rorty sings in the antifoundationalist chorus. His song equates the rise of foundationalist epistemology with the professionalization of philosophy. The discordant notes he finds in the foundationalist score become, as a consequence, subversive of philosophy as an autonomous discipline.Nonetheless, the most salient feature of Rorty's recent book, Philosophy and the Mirror of Nature, is that it is by a professional philosopher, for professional philosophers and about the future of philosophy as a profession. The early chapters of the book are polished pieces of professional philosophical prose addressed to issues which have provoked interest in recent years among members of academic philosophy departments. They represent efforts to undermine foundationalist epistemology even in some of its currently fashionable guises as philosophy of language.

Hans Herzberger's 1973 essay 'Ordinal Preference and Rational Choice' is a classic milestone in the erosion of the idea that rational agents are maximizers of utility. By the time Herzberger wrote, many authors had replaced this claim with the thesis that rational agents are maximizers of preference. That is to say, it was assumed that at the moment of choice a rational agent has a weak ordering representing his or her preferences among the options available to the agent for choice and that the rational agent restricts choice to one of the optimal options. Such an option is an available option judged at least as good as any other.Herzberger explored the prospects of weakening this ordinalist view of maximizing ..

In a pair of controversy provoking papers1, Kadane and Larkey argued that the normative or prescriptive understanding of expected utility theory recommended that participants in a game maximize expected utility given their assessments of the probabilities of the moves that other players would make. They observed that no prescription, norm or standard of Bayesian rationality recommends how they should come to make probability judgments about the choices of other players. For any given player, it is an empirical question as to whether other players are Bayes rational, judge him to be Bayes rational, etc., just as it is an empirical question as to what the other players’ goals and beliefs are. Participants in the game should, of course, use all empirical information available to them about how other players have behaved and how they are likely to behave in the given context of choice. Kadane and Larkey pointed out that rational players could participate in a game meeting these requirements without the game’s terminating with a Nash equilibrium or a result satisfying any other particular solution concept

It is a commonplace that in making decisions agents often have to juggle competing values, and that no choice will maximise satisfaction of them all. However, the prevailing account of these cases assumes that there is always a single ranking of the agent's values, and therefore no unresolvable conflict between them. Isaac Levi denies this assumption, arguing that agents often must choose without having balanced their different values and that to be rational, an act does not have to be optimal, only what Levi terms 'admissible'. This book explores the consequences of denying the assumption and develops a general approach to decision-making under unresolved conflict. Professor Levi discusses conflicts of value in several domains - those arising in moral dilemmas, the drawing of scientific inferences, decisions taken under uncertainty, and in social choice. In each of these he adapts his theoretical framework, showing how conflict may often be reduced though not always altogether eliminated.