Isaac Levi

Columbia University | CU · Department of Philosophy

Inquirers ought to change beliefs for good reason. What those good reasons are depend on the proximate goals of their inquiries. William James urged us to seek Truth and avoid Error in forming beliefs. He ought to have said: Seek Information and avoid Error. The common features of the proximate goals of scientific inquiries ought to be to answer qu...

SOME men disclaim certainty about anything. I am certain that they deceive themselves. Be that as it may, only the arrogant and foolish maintain that they are certain about everything. It is appropriate, therefore, to consider how judgments of uncertainty discriminate between hypotheses with respect to grades of uncertainty, probability, belief, or...

Foundationalism in epistemology imposes two demands on the beliefs of intelligent inquirers: (1) that current beliefs be justified, and (2) that there be foundational premisses and principles of reasoning that are self-certifying on the basis of which the merits of other current beliefs and principles may be derived. Many anti-foundationalists give...

This is a brief review of issues over which Henry Kyburg and I differed concerning the requirement that full beliefs should be closed under deductive consequence.

cording to Henry Kyburg, all extralogical and extramathematical propositions accepted as evidence and all propositions accepted inductively on the basis of such evidence are uncertain. There is a possibility of error. Consequently, neither the corpus of inductively accepted statements nor the corpus of statements accepted as evidence can serve as a...

This volume presents a series of chapters which investigate the nature of intellectual inquiry: what its aims are and how it operates. The starting-point is the work of the American Pragmatists C. S. Peirce and John Dewey. Inquiry according to Peirce is a struggle to replace doubt by true belief. Dewey insisted that the transformation was from an i...

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 momen...

In Chapter 6 of A Treatise on Probability (1973 [1921], hereafter TP), John Maynard Keynes raised a question he described as “somewhat novel.” This concerned the problem he labeled “The weight of arguments.”

“Knowledge” is an honorific intended to distinguish sources of information that are approved from those that are not and also to distinguish full beliefs that are prized from full beliefs that are despised. These are two distinct functions. The function of sources of information is quite different from the function of states of full belief. We shou...

Dewey and Peirce shared a common focus on the elaboration of a model of inquiry that seeks to remove doubt concerning the answer to some question by identifying potential answers to the question, ascertaining the evidence available for evaluating the candidacy of such answers as solutions to the problem posed, conducting experiments to acquire more...

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 confirm...

This essay has two objectives: (1) To offer a general motivation for the use of sets of probabilities to represent states of credal probability judgment. Doubt as to which of rival answers to a given question is true is representable by the set of potential answers that have not ruled out as impossible. Doubt concerning probability is representable...

This chapter discusses some issues concerning the representation of the valuation of options when decision makers have different probability judgments, different value commitments or both, and must engage in a joint deliberation based on some kind of consensus. The representation of consensus in such a setting is assumed to exhibit a structure simi...

This article surveys various accounts of degrees of belief and the relation between degrees of belief and full belief or absolute certainty. Corresponding to each notion of degree of belief is a conception of evidential support. Three different kinds of degrees of belief and the corresponding notions of evidential support are considered: probabilit...

Etude du mecanisme evidentiaire (evidentiary) developpe par S. Hallden et M. Edman qui consiste a evaluer un systeme operationel, place dans une situation donnee, en fonction de la reponse e' qu'il apporte a l'hypothese h' et de l'importance du programme d'expansion routiniere qui lui est imparti

Etude de l'explication evolutionniste de la matrice biologique (Dewey) de la connaissance humaine proposee par S. Hallden. Il s'agit de rendre compte de l'emergence des attitudes propositionnelles de l'agent intelligent et de la possibilite de l'enquete intelligente par la production d'un processus de selection artificielle deliberee

Deductive Rules and Fulfilling CommitmentsRules as Programs for Routine ExpansionRules in Deliberate or Inferential ExpansionWhat Recommends Scientific Method over Other Methods of Fixing Belief?Deliberation and Inconsistency

1. Thanks are due to Akeel Bilgrami for discussions that helped clarify my thoughts about the topics discussed here. 2. The material on value commitments is based on Levi (1986, chap. 2). 3. This does not entail utilitarianism or any variety of consequentialism except the most trivial. Implementing one of the options in a given choice situation may...

Authors like Keynes, H. Jeffreys and Carnap advocated using a concept of "logical probability". Logical probability had the following properties: (a) it was representable as a function from potential states of full belief (or "evidence") to states of subjective or credal probability judgment. (b) Such functions were alleged to be constrained by pri...

An argument is advanced to show why E-admissibility should be preferred over maximality as a principle of rational choice where rationality is understood as minimal rationality. Consideration is given to the distinction between second best and second worst options in three way choice that is ignored according to maximality. It is shown why the beha...

A comparison is made between the criterion of choice of E-admissibility I proposed in Levi, 1974 and elaborated in Levi, 1980 and 1986, and the ideas about norms elaborated by Alchourrón and Bulygin (1971 and 1981) with an emphasis on the fact that choice cannot always be evaluated in terms of binary comparisons as the distinction between second wo...

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...

In “Truth and Probability” Ramsey claimed that the logic of consistency for probability is not a logic of truth. After supporting this claim, he proceeded to explore the possibilities for a logic of truth for probability. An examination of Ramsey's intent reveals that Ramsey was far from being an orthodox Bayesian when it comes to statistical reaso...

Inductive Inference is reasoning that justifies change from one state of full belief or absolute certainty to another by adding new information to the initial state that is consistent with it but does not entail it. Inductive inference is, therefore, But the deviations from monotonicity differ from those characterized by belief revision according t...

This book is a continuation of Isaac Levi's work on formal epistemology, focusing on the problem of contraction. It argues that the problem of how to contract is essential both to an account of justified or legitimate belief change, and to modal judgment conditional on a supposition. It presents a formal characterization of mild contraction, which...

This document gathers the panelists' contribution. @InProceedings{levi_et_al:DSP:2005:358, author = {Isaac Levi and Giacomo Bonanno and Bernard Walliser and Didier Dubois and Hans Rott and James Delgrande and J{'e}r{^o}me Lang}, title = {05321 -- Panel on belief change}, booktitle = {Belief Change in Rational Agents: Perspectives from Artificial In...

We contrast three decision rules that extend Expected Utility to contexts where a convex set of probabilities is used to depict uncertainty: #-Maximin, Maximality, and E-admissibility. The rules extend Expected Utility theory as they require that an option is inadmissible if there is another that carries greater expected utility for each probabilit...

PROBABLE DEDUCTION Peirce wrote extensively on deduction, induction, and hypothesis beginning with the Harvard Lectures of 1865 and Lowell Lectures of 1866. The ideas that he examined in those early discussions were reworked over nearly two decades until the comprehensive statement of his view contained in “A Theory of Probable Inference” of 1883 t...

I respond to Erik Olsson's critique of my account of contraction frominconsistent belief states, by admitting that such contraction cannot be rationalized as adeliberate decision problem. It can, however, be rationalized as a routine designed prior toinadvertent expansion into inconsistency when the deliberating agent embraces a consistent point of...

David Makinson has argued that the compelling character of counterexamples to the Recovery Condition on contraction is due to an appeal to justificational structure. In “naked theories” where such structure is ignored or is not present, Recovery does apply. This note attempts to show that Makinson is mistaken on both counts. Recovery fails when no...

We contrast three decision rules that extend Expected Utility to contexts where a convex set of probabilities is used to depict uncertainty: Γ-Maximin, Maximality, and E-admissibility. The rules extend Expected Utility theory as they require that an option is inadmissible if there is another that carries greater expected utility for each probabilit...

The idea that rational agents should have acyclic preferences and should obey conditionalization has been defended on the grounds that otherwise an agent is threatened with becoming a "money pump." This essay argues that such arguments fail to prove their claims.

This paper argues that if changes in confirmational commitment (or changes in prior probabilities) are to be defended without begging the question, indeterminacy in probability judgment is required. But no other modification of strict Bayesian doctrine is needed. The resulting qualified version of the Bayesian approach is compared with the way inde...

In his early writings (e.g. Harvard Lectures of 1865, Peirce [1982]), Peirce followed Aristotle in defining inductive argument formally as the apogogic inversion of valid syllogistic argument where the major premise of the syllogism becomes the conclusion of the induction and the erstwhile conclusion becomes a premise of the induction. Peirce contr...

Bayesian advocates of expected utility maximization use sets of probability distributions to represent very different ideas. Strict Bayesians insist that probability judgment is numerically determinate even though the agent can represent such judgments only in imprecise terms. According to Quasi-Bayesians rational agents may make indeterminate subj...

Leeds (1990) levels an objection against the criterion of rational choice I have proposed (Levi 1997, Ch. 6; 1980; 1986), pointing out that the criterion is sensitive to the way possible consequences are partitioned. Seidenfeld, Kadane and Schervish (1989) call into question the defense of the cross product rule by appeal to Pareto Unanimity Princi...

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 standa...

Isaac Levi is one of the preeminent philosophers in the areas of pragmatic rationality and epistemology. This collection of essays constitutes an important presentation of his original and influential ideas about rational choice and belief. A wide range of topics is covered, including consequentialism and sequential choice, consensus, voluntarism o...

Isaac Levi is one of the preeminent philosophers in the areas of pragmatic rationality and epistemology. This collection of essays constitutes an important presentation of his original and influential ideas about rational choice and belief. A wide range of topics is covered, including consequentialism and sequential choice, consensus, voluntarism o...

This book is a continuation of Isaac Levi’s work on formal epistemology, focusing on the problem of contraction. It argues that the problem of how to contract is essential both to an account of justified or legitimate belief change, and to modal judgment conditional on a supposition. It presents a formal characterization of mild contraction, which...

How to accept a conditional? F. P. Ramsey proposed the following test in (Ramsey 1990). (RT) ‘If A, then B’ must be accepted with respect to the current epistemic state iff the minimal hypothetical change of it needed to accept A also requires accepting B. In this article we propose a formulation of (RT), which unlike some of its predecessors, is c...

Koehler's target article attempts a balanced view of the relevance of knowledge of base rates to judgments of subjective or credal probability, but he is not sensitive enough to the difference between requiring and permitting the equation of probability judgments with base rates, the interaction between precision of base rate and reference class in...

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 a...

There is an important class of conditionals whose assertibility conditions are not given by the Ramsey test but by an inductive extension of that test. Such inductive Ramsey conditionals fail to satisfy some of the core properties of plain conditionals. Associated principles of nonmonotonic inference should not be assumed to hold generally if inter...

: This paper is concerned with the construction of a base contraction (revision) operation such that the theory contraction (revision) operation generated by it will be fully AGM-rational. It is shown that the theory contraction operation generated by Fuhrmann's minimal base contraction operation, even under quite strong restrictions, fails to sati...

Charles Peirce insisted a long time ago that justifying beliefs currently held is unnecessary. Only changes in belief require justification. Epistemologists should turn away from the question of justifying what they already believe and focus instead on when and how rational inquirers should change their minds.

This paper discusses the function of principles of rationality in inquiry and deliberation rather than the content of such principles. Appealing to the belief-doubt model of inquiry pioneered by C. S. Peirce and J. Dewey, I shall argue that principles of rationality should impose weak constraints on the coherence of the beliefs, values and choices...

We sometimes add new information to our states of full belief by routine expansion and sometimes by deliberate expansion. (Levi, 1980a, ch.2; 1991b, ch.3.)

Principles of rationality are invoked for several purposes: they are often deployed in explanation and prediction; they are also used to set standards for rational health for deliberating agents or to furnish blueprints for rational automata; and they are intended as guides to perplexed decision makers seeking to regulate their own attitudes and co...

There has been a great deal of interaction among game theorists, philosophers and logicians in certain foundational problems concerning rationality, the formalization of knowledge and practical reasoning, and models of learning and deliberation. This volume brings together the work of some of the pre-eminent figures in their respective disciplines,...

Isaac Levi's new book is concerned with how one can justify changing one's beliefs. The discussion is deeply informed by the belief-doubt model advocated by C. S. Peirce and John Dewey, of which the book provides a substantial analysis. Professor Levi then addresses the conceptual framework of potential changes available to an inquirer. A structura...

Patrick Suppes contends that philosophers “are no longer Sunday’s preachers for Monday’s scientific workers”. Yet, precisely because of the diversity and complexity Suppes rightly recognized in scientific disciplines, there is a need for sermonizing about science which might be less urgent in times of greater simplicity. To say this is not to say t...

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 re...

Suppose an unbiased coin is tossed a million times. Suppose further that the coin lands heads exactly half a million times. The result of the million tosses may be described correctly (a) as a half million cases of landing heads among a million cases of landing heads or tails, (b) as approximately a half million cases of landing heads (or as betwee...

The chapter discusses the fact that probability exists—but just barely. It is incredible that all applications of the calculus of probability in the natural and social sciences are representations and evaluations of subjective attitudes. Quantum mechanics is not a description of opinion, nor are statistical mechanics and genetics. Both the probabil...

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 assumpti...

In The Enterprise of Knowledge (Levi, 1980a), I proposed a general theory of rational choice which I intended as a characterization of a prescriptive theory of ideal rationality. A cardinal tenet of this theory is that assessments of expected value or expected utility in the Bayesian sense may not be representable by a numerical indicator or indeed...

Bayesians often confuse insistence that probability judgment ought to be indeterminate (which is incompatible with Bayesian ideals) with recognition of the presence of imprecision in the determination or measurement of personal probabilities (which is compatible with these ideals). The confusion is discussed and illustrated by remarks in a recent e...

Ignorance is sometimes understood to be deprivation of information. By reviewing different types of ignorance, some understanding of different senses of information may be obtained. This paper surveys some possibilities along these lines. Reliance on entropy based measures of information is held to be inappropriate to several important senses of ig...

-

According to a familiar story, beliefs qualify as knowledge only if they can be justified on the basis of impeccable first premisses via equally immaculate first principles. The story has no truth to it. Centuries of criticism suggest that our interesting beliefs are born on the wrong side of the blanket.