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Belief Revision

Graham Priest

in Doubt Truth to be a Liar

This chapter discusses an account of belief-revision that is compatible with the rational belief of contradictions. In the process, a formal account of the model of rationality of the preceding ... More

This chapter discusses an account of belief-revision that is compatible with the rational belief of contradictions. In the process, a formal account of the model of rationality of the preceding chapter is provided. The account of belief-revision is contrasted with the familiar AGM account.Less

 The Representation of Belief: Some Standard Moves

Wolfgang Spohn

in The Laws of Belief: Ranking Theory and Its Philosophical Applications

This chapter introduces and discusses the standard static laws of belief, consistency and deductive closure, as well as the first steps towards a dynamics of belief. The latter amounts to an ... More

This chapter introduces and discusses the standard static laws of belief, consistency and deductive closure, as well as the first steps towards a dynamics of belief. The latter amounts to an introduction into AGM belief revision theory and some variant formulations. The chapter thus explains the three kinds of belief change commonly taken as basic: expansions, revisions, and contractions.Less

 Comparisons

Wolfgang Spohn

in The Laws of Belief: Ranking Theory and Its Philosophical Applications

There is a large spectrum of representations of belief states besides probabilities and ranks. The chapter cannot give a complete survey, but it presents comparisons with a number of important ... More

There is a large spectrum of representations of belief states besides probabilities and ranks. The chapter cannot give a complete survey, but it presents comparisons with a number of important accounts. It first discusses the predecessors of ranking theory: Shackle’s functions of potential surprise, Rescher’s hypothetical reasoning, and Cohen’s account of inductive support. It saves AGM belief revision theory from various critical examples. It carefully discusses Levi’s epistemology and finds discrepancies everywhere. It is critical of Lehrer’s account of knowledge and undefeated justification. Pollock’s theory of defeasible reasoning looks similar, but is quite different. This leads to a discussion of the nature of normative epistemology. The chapter closes with brief comparative remarks on formal learning theory, possibility theory, Dempster-Shafer belief functions, and non-monotonic reasoning.Less

Connections with Various Epistemological Accounts

Neil Tennant

in Changes of Mind: An Essay on Rational Belief Revision

The chapter surveys the relevant recent literature in epistemology with two aims in minds. First, the chapter wishes to show that the account of belief revision is orthogonal to, or invariant across, ... More

The chapter surveys the relevant recent literature in epistemology with two aims in minds. First, the chapter wishes to show that the account of belief revision is orthogonal to, or invariant across, the different ways in which ongoing epistemological debates might be resolved, concerning such matters as the role of experience in founding justifications, and the permissible global patterns of justificatory support (foundationalist, coherentist, or foundherentist?). Secondly, the chapter wishes to show how compatible the new account of belief revision is with various important epistemological accounts that touch on the topic of belief revision, albeit not in any great logical or computational detail. To this end, the chapter examines the writings of Sosa, BonJour, Cornman, Haack, Levi, Quine and Ullian, Harman, Klein and Gupta. This discussion should serve to situate the work for the epistemological readerLess

The Finitary Predicament

Neil Tennant

in Changes of Mind: An Essay on Rational Belief Revision

This chapter provides further argument justifying the claim that our use of finite dependency networks entails no loss at all of theoretical generality, as far as belief revision on the part of ... More

This chapter provides further argument justifying the claim that our use of finite dependency networks entails no loss at all of theoretical generality, as far as belief revision on the part of rational creatures is concerned. Some basic concepts in mathematical logic are defined, to lay the groundwork for the metatheorem, due to Harvey Friedman, that is proved in the next chapter.Less

Judgement Aggregation

Jon Williamson

in In Defence of Objective Bayesianism

Section. 8.1 introduces the problem of judgement aggregation and some of the difficulties encountered in trying to solve this problem. Section. 8.2 introduces the theory of belief revision and ... More

Section. 8.1 introduces the problem of judgement aggregation and some of the difficulties encountered in trying to solve this problem. Section. 8.2 introduces the theory of belief revision and merging and Pigozzi's application of this theory to judgement aggregation. Section. 8.3 argues that judgements should not be merged directly; rather, one should merge the evidence on which the judgements are based. Given this merged evidence, objective Bayesianism and decision theory can be used to derive an appropriate set of judgements—the resulting judgements should be viewed as the aggregate of the judgements of the original individuals (§8.4).Less

Conditional Belief and Belief Dynamics

Hannes Leitgeb and Hannes Leitgeb

in The Stability of Belief: How Rational Belief Coheres with Probability

This chapter turns to the notion of conditional belief: rationally believing a proposition given another proposition. Among other things, conditional belief plays a role for belief revision by ... More

This chapter turns to the notion of conditional belief: rationally believing a proposition given another proposition. Among other things, conditional belief plays a role for belief revision by entailing a disposition for how to revise one’s belief given new evidence. The numerical version of conditional belief is subjective conditional probability, and first the chapter calls to mind how the concept of conditional probability figures in the standard diachronic norm on degree-of-belief change. Afterwards the same is done for conditional all-or-nothing belief and the standard diachronic norm on all-or-nothing belief change, which rely on the so-called AGM postulates for belief revision. Finally, a stability account of rational conditional belief is developed according to which subjective conditional probability and rational conditional all-or-nothing belief cohere with each other just as their unconditional versions did in Chapters 2 and 3. From this, together with the standard diachronic norms on belief change, it follows that also rational degree-of-belief change and categorical belief change must cohere with each other once the stability theory is in place. Other than extending the stability account to conditional belief, the chapter also serves the purpose of supplying some of the mathematical machinery on which the theory in this book is based.Less

Belief Revision

Franz Huber

in Belief and Counterfactuals: A Study in Means-End Philosophy

This chapter first introduces the AGM theory of belief revision. Then it focuses on the problem of iterated belief revisions.

The Twilight of Empiricism

Charles Travis

in Objectivity and the Parochial

What we experience of the world—for example, that pig on the lawn—does not bear logical relations to thoughts, or propositions. That pig on the lawn is not of the form of a proposition. Logical ... More

What we experience of the world—for example, that pig on the lawn—does not bear logical relations to thoughts, or propositions. That pig on the lawn is not of the form of a proposition. Logical relations relate thoughts, or propositions, to one another. Quine thus correctly notes that one could, on no pain of contradiction, respond to any experience with any constellation of beliefs. He incorrectly takes this to mean that any constellation of beliefs could be consistent with one's having experienced what he did. Revision can come anywhere; if it does not, this merely reflects the ways of our people. This is a mistake, and in fact destroys the very possibility of judgement. Quine has given us no reason (even if, in fact, there is one) to think that any proposition may (not incorrectly) be held to have been falsified by experience. So goes the present argument.Less

Iterated Belief Revision

Robert C. Stalnaker

in Knowledge and Conditionals: Essays on the Structure of Inquiry

A discussion of the problem of extending the basic AGM belief revision theory to iterated belief revision: the problem of formulating rules, not only for revising a basic belief state in response to ... More

A discussion of the problem of extending the basic AGM belief revision theory to iterated belief revision: the problem of formulating rules, not only for revising a basic belief state in response to potential new evidence, but also for revising one’s revision rules in response to potential new evidence. The emphasis in the chapter is on foundational questions about the nature of and motivation for various constraints, and about the methodology of the evaluation of putative counterexamples to proposed constraints. Some specific constraints that have been proposed are criticized. The chapter emphasizes the importance of meta-information—information about one’s sources of information—and argues that little of substance can be said about constraints on iterated belief revision at a level of abstraction that lacks the resources for explicit representation of meta-information.Less

Further reflections

Graham Priest

in Beyond the Limits of Thought

This chapter provides replies to criticisms on the concept of dialetheism or the existence of true contradictions. It clarifies that dialetheism is not incompatible with predication because the ... More

This chapter provides replies to criticisms on the concept of dialetheism or the existence of true contradictions. It clarifies that dialetheism is not incompatible with predication because the former is concerned with the simultaneous truth of statements while the latter is an independent issue. In reply to a criticism on account of negation, it explains that dialetheism only rejects paraconsistent logic, and that there is no logical bar to dialetheism. On the issue of belief-revision, the chapter clarifies that dialetheism does not require abandonment of theories, only the relocation of beliefs to either low or high probabilities.Less

Testimony

Alvin I. Goldman

in Knowledge in a Social World

Whether a simple reporting practice produces positive changes in knowledge, or V‐value, depends on what reports a message sender sends, who actually receives them, what the receivers’ antecedent ... More

Whether a simple reporting practice produces positive changes in knowledge, or V‐value, depends on what reports a message sender sends, who actually receives them, what the receivers’ antecedent degrees of belief are, and how they revise their degrees of belief as a function of the reports. Does any belief‐revision practice have a general propensity to improve a hearer's degrees of knowledge? Assuming objective conditional probabilities, revising degrees of belief by Bayesian conditionalization yields (objectively) expected increases in degrees of knowledge (V‐value), as long as subjective likelihoods match objective likelihoods. This general theorem applies to the special case of reasoning from social communications. As a separate subtopic, theories of justification for testimonial belief are briefly reviewed.Less

Thinking and Belief

Soteriou Matthew

in The Mind's Construction: The Ontology of Mind and Mental Action

This chapter considers how the proposed account of the epistemology of mental action, and the proposed account of the self-knowledge involved in conscious thinking, bear on an account of one's ... More

This chapter considers how the proposed account of the epistemology of mental action, and the proposed account of the self-knowledge involved in conscious thinking, bear on an account of one's knowledge of what one believes. The chapter also explores some of the ways in which the ethics of belief, and accounts of the suspension of judgement and belief revision, may be affected by the fact that we are, as self-conscious subjects, capable of engaging in agential epistemic conscious mental activity, including self-critical reflection.Less

Conditional Belief

Franz Huber

in Belief and Counterfactuals: A Study in Means-End Philosophy

This chapter first presents the static and dynamic rules of ranking theory. Then it shows how ranking theory solves the problem of iterated belief revisions.

Extracting fictional truth from unreliable sources

Emar Maier and Merel Semeijn

in The Language of Fiction

A fictional text is commonly viewed as constituting an invitation to play a certain game of make-believe, with the individual sentences written by the author providing the propositions we are to ... More

A fictional text is commonly viewed as constituting an invitation to play a certain game of make-believe, with the individual sentences written by the author providing the propositions we are to imagine and/or accept as true within the fiction. However, we can’t always take the text at face value. What narratologists call ‘unreliable narrators’ may present a confused or misleading picture of the fictional world. Meanwhile, there has been a debate in philosophy about ‘imaginative resistance’ in which we resist imagining (or even accepting as true in the fiction) what’s explicitly stated in the text. But if we can’t take the text’s word for it, how do we determine what’s true in a fiction? The chapter proposes an account of fiction interpretation in a dynamic setting (a version of Discourse Representation Theory (DRT) with a mechanism for opening, updating, and closing temporary ‘workspaces’) and combines this framework with belief revision logic.Less

From the Value of Knowledge to Skills and Stereotypes: The Individual Ideal of Known Freedom

Boudewijn de Bruin

in The Business of Liberty: Freedom and Information in Ethics, Politics, and Law

This chapter develops the normative ideal of known freedom. You possess known freedom to the extent that you possess knowledge about your opportunity set—that is, about available actions, their ... More

This chapter develops the normative ideal of known freedom. You possess known freedom to the extent that you possess knowledge about your opportunity set—that is, about available actions, their consequences, and the likelihood with which they arise. I first discuss an objection to such an ideal based on Isaiah Berlin’s notion of the ‘retreat to the inner citadel’. I critically examine recent work on the value of knowledge (the ‘Meno problem’) undertaken by Timothy Williamson and John Hawthorne, as well Duncan Pritchard’s case of the ‘ravine jumper’ purportedly illustrating the value of false beliefs. Using insights on belief revision, I argue that this body of research does not affect the value of known freedom. On the basis of theoretical and empirical work on skills, I then argue for a view of skills as known freedom and show how stereotype threats as studied by psychologists negatively affect the ideal of known freedom.Less

The Psychology of (Pseudo)Science: Cognitive, Social, and Cultural Factors

Emilio J. C. Lobato and Corinne Zimmerman

in Pseudoscience: The Conspiracy Against Science

We review findings from the psychology of science that are relevant to understanding or explaining peoples’ tendencies to believe both scientific and pseudoscientific claims. We discuss relevant ... More

We review findings from the psychology of science that are relevant to understanding or explaining peoples’ tendencies to believe both scientific and pseudoscientific claims. We discuss relevant theoretical frameworks and empirical findings to support the proposal that pseudoscientific beliefs arise in much the same way as other scientific and non-scientific beliefs do. In particular, we focus on (a) cognitive and metacognitive factors at the individual level; (b) trust in testimony and judgments of expertise at the social level; and (c) personal identity and the public’s relationship with the scientific community at a cultural level.Less

What Must and Can Must and Can Mean *

Angelika Kratzer

in Modals and Conditionals: New and Revised Perspectives

The chapter presents an account of the meaning of “must” and “can” that relies on general principles for reasoning from premise sets. Premise sets can be inconsistent, so the account has to allow for ... More

The chapter presents an account of the meaning of “must” and “can” that relies on general principles for reasoning from premise sets. Premise sets can be inconsistent, so the account has to allow for conflict resolution. There are many areas in human cognition where inconsistencies arise. Inconsistent beliefs are the topic of theories of belief revision; conflicting grammatical constraints are investigated in Optimality Theory; and clashes between presuppositions, conversational implicatures, and at issue meanings have been explored in formal pragmatics since the late 1970s. With potentially inconsistent premise sets, the presentation of premises matters. Deductively equivalent premise sets like {p&q} and {p, q} can show different behavior when a conflicting premise is added. The chapter takes this fact as an invitation for a promising research program that seeks evidence for the way the premises from which we reason are split up and lumped together. The semantics of counterfactuals is a rich source for such evidence, as shown in subsequent chapters.Less