Rational Belief Change Research Articles

Isaac Levi’s belief change methodology as a way to settle conflicting views: Case study of Palestinian teachers in Jewish schools

Tensions between conflicting values and views characterize multicultural democracies. This study deals with conflicting opinions within unequal power relations through the prism of rational belief change. We analyzed ten interviews with Palestinian teachers in Jewish schools in Israel, emphasizing conflicting values and ideas, and ways of settling discrepancies. Levi’s (2004) framework helped delineate the areas of contraction, expansion, and core beliefs. We identified negotiations on values and views in which participants oscillated between Israeliness and Palestinianess, and between traditionalism and modernism. We suggest that the fundamental sensitivity in Jewish-Palestinian encounters is the fear of attacks on core beliefs. Teachers refrain from dealing with other value contradictions for fear that they will unwittingly cross over to threatening core beliefs. Teachers prefer to discuss consensual topics such as professional and educational issues, and topics related to their personal life such as parenting. We suggest rational belief change as an important tool to maximize the possibility of settling conflicting values and views.

Credence, Conditionals, Knowledge and Truth

Epistemology, strictly speaking, is the theory of knowledge: what it is, when we have it, why it is valuable, what we can do with it. But the term has come to be used more widely, to include the theory of reasonable belief, rational belief change, non-conclusive inference, etc., in cases where knowledge may not be obtainable. Especially under the heading ‘formal epistemology’, probability theory typically plays a prominent role here, while it typically does not play much of a role in traditional, knowledge-centred epistemology, because, it is natural to think, probability theory typically governs something weaker than knowledge. It is about the management of uncertainty. Sarah Moss’s book Probabilistic Knowledge is revolutionary. It shares with traditional epistemology the claim that knowledge is the central concept. On the other hand, it is probabilistic through and through. In short, our ordinary probability judgements can be knowledge. There are different kinds of probability. Maybe we can know objective chances, but that is not Moss’s target. Maybe we can know that a certain body of evidence renders probable a conclusion, but that is not the target either. Our ordinary probability judgements are not statements about their relation to a body of evidence. The subject may not be capable of such second-order judgements. ‘Fido can believe that you are probably about to take him outside without being capable of any second-order belief about what is consistent with his evidence’ (23).1 The target is our ordinary credences – degrees of closeness to certainty, expressed by ‘probably’, ‘more likely than not’, etc. Recurrent examples are ‘Jones probably smokes’ and ‘it is 0.6 likely that Jones smokes’.

Changes of Mind: An Essay on Rational Belief Revision, by Neil Tennant

In his recent book Changes of Mind, Neil Tennant develops a finitistic theory on rational belief revision. The book is divided into three parts. In the first part, Tennant introduces and motivates his theory and shows that it can be implemented on a computer. In the second part, Tennant argues that core logic is the minimal logic enabling an agent to revise her beliefs in accordance with this theory. Furthermore, he argues that the restriction to a finitistic theory constitutes no loss in generality. In the third part, Tennant compares his account to other views on rational belief change, both in formal as well as in mainstream epistemology. Theories on belief revision try to answer the following question. If an agent believes the sentences in a set B and then comes to believe a sentence S, what should she end up believing? If S is consistent with B, the answer seems easy enough. The agent should believe the closure of B and S, that is the sentences in B, as well as S and everything that follows from B and S. This procedure is called expansion of B by S. If S is not consistent with B, matters are more difficult. Before expanding B by S, everything needs to be erased from B which is inconsistent with S. This erasing process is known as contraction of B by ¬S. According to the Levi identity, a revision of B by S is the process of first contracting B by ¬S and then expanding the result by S (Isaac Levi, ‘Subjunctives, Dispositions and Chances’, Synthese, 34, 1977, pp. 423–55). The most uncontroversial requirements imposed on expansion and contraction are success and minimal mutilation. Success demands that after expanding B by S, S needs to be believed and after contracting B by ¬S, ¬S should no longer follow from the sentences believed. Minimal mutilation demands that a contraction should not erase more beliefs than necessary.

Updating as Communication*

On many traditional theories of belief, your belief state is represented by an assignment of credences to propositions, or sets of possible worlds. If you are rational, your credence distribution will be a probability measure. Traditional theories of belief fit with a standard Bayesian theory of rational belief change: on learning a proposition, you must update your belief state by conditionalizing your credence distribution on the proposition you learn. That is, you must update by assigning 0 credence to those worlds incompatible with what you learn, and re-normalizing your credence distribution over the remaining worlds. Following Quine 1969, Lewis 1979 argues that we should instead represent your belief state by an assignment of credences to sets of centered worlds: world-timeindividual triples. For instance, if you have .5 credence that it is 3:00pm, your belief state should be represented by a measure that assigns .5 to the set of centered worlds with that time coordinate. Unlike traditional theories of belief, Lewis’s theory does not fit with a standard Bayesian theory of rational belief change. For instance, Bayesian conditionalization preserves certainties. If you update by conditionalizing on the set of centered worlds you learn, it follows that if you are ever certain that it is 3:00pm, you must always remain certain that it is 3:00pm. But clearly this is not what rationality requires. If we agree with Lewis about how to represent belief states, we must develop another set of principles governing rational belief change.

De se belief and rational choice

The Sleeping Beauty puzzle has dramatized the divisive question of how de se beliefs should be integrated into formal theories of rational belief change. In this paper, I look ahead to a related question: how should de se beliefs be integrated into formal theories of rational choice? I argue that standard decision theoretic frameworks fail in special cases of de se uncertainty, like Sleeping Beauty. The nature of the failure reveals that sometimes rational choices are determined independently of one’s credences in the kinds of ‘narrow’ de se propositions that Sleepy Beauty has set in relief. Consequently, in addition to pinpointing a failure of standard decision theoretic frameworks, this result casts doubt on a large class of strategies for determining principles for the rationally updating de se beliefs in cases like Sleeping Beauty, and also calls into question the importance of making such a determination at all.

In search of the best explanation about the nature of the gene: Avery on pneumococcal transformation

In this paper I present a model of rational belief change, and I show how to use it to obtain a better insight into the debate about the nature of pneumococcal transformation, genes and DNA that took place in the forties, as a result of Oswald T. Avery’s work. The model offers a particular elaboration of the concept of inference to the best explanation, along decision theoretic lines. Within this framework, I distinguish different senses in which Avery’s team can be said to have proceeded with caution, thus throwing some light upon a persistent source of disagreement among researchers in the history of genetics. In addition, I explain why we are entitled to say that rival parties such as physicist Maclyn McCarty and biochemist Alfred Mirsky were epistemically rational, in spite of the fact that they reached different conclusions on the basis of the same evidence.

Statistics is not enough: revisiting Ronald A. Fisher’s critique (1936) of Mendel’s experimental results (1866)

This paper is concerned with the role of rational belief change theory in the philosophical understanding of experimental error. Today, philosophers seek insight about error in the investigation of specific experiments, rather than in general theories. Nevertheless, rational belief change theory adds to our understanding of just such cases: R. A. Fisher’s criticism of Mendel’s experiments being a case in point. After an historical introduction, the main part of this paper investigates Fisher’s paper from the point of view of rational belief change theory: what changes of belief about Mendel’s experiment does Fisher go through and with what justification. It leads to surprising insights about what Fisher had done right and wrong, and, more generally, about the limits of statistical methods in detecting error.

Capacity Updating Rules and Rational Belief Change

Choquet expected utility substitutes capacities for subjective probabilities to explain uncertainty aversion and related phenomena. This paper studies capacities as models of belief. The notions of inner and outer acceptance context are defined. These are shown to be the natural acceptance contexts when belief expansion is described by naive Bayesian and Dempster–Shafer updating of capacities respectively. We also show that Eichberger and Kelsey's (1999b) use of Dempster–Shafer updating as a model of belief revision may lead to violations of the AGM axioms for rational belief change.

Severe Withdrawal (and Recovery)

The problem of how to remove information from an agent's stock of beliefs is of paramount concern in the belief change literature. An inquiring agent may remove beliefs for a variety of reasons: a belief may be called into doubt or the agent may simply wish to entertain other possibilities. In the prominent AGM framework for belief change, upon which the work here is based, one of the three central operations, contraction, addresses this concern (the other two deal with the incorporation of new information). Makinson has generalised this work by introducing the notion of a withdrawal operation. Underlying the account proffered by AGM is the idea of rational belief change. A belief change operation should be guided by certain principles or integrity constraints in order to characterise change by a rational agent. One of the most noted principles within the context of AGM is the Principle of Informational Economy. However, adoption of this principle in its purest form has been rejected by AGM leading to a more relaxed interpretation. In this paper, we argue that this weakening of the Principle of Informational Economy suggests that it is only one of a number of principles which should be taken into account. Furthermore, this weakening points toward a Principle of Indifference. This motivates the introduction of a belief removal operation that we call severe withdrawal. We provide rationality postulates for severe withdrawal and explore its relationship with AGM contraction. Moreover, we furnish possible worlds and epistemic entrenchment semantics for severe withdrawals.

Why Bayesian Psychology Is Incomplete

Bayesian psychology, in what is perhaps its most familiar version, is incomplete: Jeffrey conditionalization is not a complete account of rational belief change. Jeffrey conditionalization is sensitive to the order in which the evidence arrives. This order effect can be so pronounced as to call for a belief adjustment that cannot be understood as an assimilation of incoming evidence by Jeffrey's rule. Hartry Field's reparameterization of Jeffrey's rule avoids the order effect but fails as an account of how new evidence should be assimilated.

Preferential belief change using generalized epistemic entrenchment

A sentence A is epistemically less entrenched in a belief state K than a sentence B if and only if a person in belief state K who is forced to give up either A or B will give up A and hold on to B. This is the fundamental idea of epistemic entrenchment as introduced by Gärdenfors (1988) and elaborated by Gärdenfors and Makinson (1988). Another distinguishing feature of relations of epistemic entrenchment is that they permit particularly simple and elegant construction recipes for minimal changes of belief states. These relations, however, are required to satisfy rather demanding conditions. In the present paper we liberalize the concept of epistemic entrenchment by removing connectivity, minimality and maximality conditions. Correspondingly, we achieve a liberalization of the concept of rational belief change that does no longer presuppose the postulates of success and rational monotony. We show that the central results of Gärdenfors and Makinson are preserved in our more flexible setting. Moreover, the generalized concept of epistemic entrenchment turns out to be applicable also to relational and iterated belief changes.