Sven Ove Hansson

It was understood from the beginning that the use of logically closed sets of sentences to represent belief states is not cognitively realistic. In an article published in 1985 Makinson pointed out that “in real life, when we perform a contraction or derogation, we never do it to the theory itself (in the sense of a set of propositions closed under consequence) but rather on some finite or recursive or at least recursively enumerable base for the theory” [238, p. 357]. The use of belief bases rather than (logically closed) belief sets has turned out to increase the expressive power of the belief change framework in important ways.

This chapter introduces a new approach to belief revision that was recently presented in [182] and has been further developed in [190, 183, 185, 189, 187, 184, 341]. It provides us with a mechanism for belief change that is in important respects more general than previous approaches. Descriptor revision is based on two new formal constructions: A generalized notation for success conditions and the application of choice mechanisms directly to the set of potential outcomes of the belief change operation.

This chapter offers a brief presentation of major models of belief change that have been developed in previous research. It begins by introducing the basic features shared by most such models: Belief states are represented by logically closed sets of sentences, commonly called belief sets. Changes take the form of either introducing a new sentence into the belief set while retaining consistency (revision) or removing a sentence from it without adding anything else (contraction). The standard model for performing such changes, the so-called AGM model, is introduced along with the axioms used to characterize it. Two of the most important equivalent formulations of the AGM model, possible world models and epistemic entrenchment, are introduced. A couple of other important approaches are also briefly mentioned.

This is the first of three chapters in which the major traditional belief change operations, namely (sentential) revision and contraction, are constructed as special cases of descriptor revision. In both its local and global forms, sentential revision $$(*)$$ ( ∗ ) can be constructed with the simple formula $$K*p= K\circ \mathfrak {B}p$$ K ∗ p = K ∘ B p. Two axiomatic characterizations show how the properties of the derived operation $$*$$ ∗ depend on those of the underlying descriptor revision $$\circ $$ ∘. The most important results in this chapter are two theorems showing that the major revision operations of AGM, namely partial meet revision and its transitively relational variant, are both reconstructible as subcases of sentential revision in the descriptor framework. In other words, both these classes of sentential revision $$(*)$$ ( ∗ ) coincide with operations obtained with the defining formula $$K*p= K\circ \mathfrak {B}p$$ K ∗ p = K ∘ B p from certain classes of descriptor revision $$(\circ )$$ ( ∘ ) that are identified here. These results provide important connections between AGM revision and the more general category of descriptor revision. Furthermore, they provide useful insights into the properties of the AGM operations. The chapter also investigates relations of believability, i.e. the relations on sentences that are obtainable from relations of epistemic proximity on descriptors (see Chapter 5 ) according to the simple principle that p is more believable than q if and only if $$\mathfrak {B}p$$ B p is epistemically more proximate than $$\mathfrak {B}q$$ B q. Finally, some results are presented on multiple sentential revision, i.e. simultaneous revision by several sentences, and on the operation of making up one’s mind.

The standard operation of contraction ( $$\div $$ ÷ ) is assumed to satisfy the inclusion postulate ( $$K\div p\subseteq K$$ K ÷ p ⊆ K ), according to which nothing new is added to the belief set (K) when a sentence (p) is contracted. However, inclusion is not a particularly credible postulate. Although many belief changes have the purpose to give up a certain belief, such changes tend to be generated by some new information that is then also added to the belief set. This is a good reason to investigate the wider category of operations of revocation, i.e. operations in which a specified sentence is removed in a process that may possibly also involve the addition of some new information to the belief set. In descriptor revision, revocation can be obtained with the defining formula. Some classes of such operations are constructed, and it is shown how the properties of the derived operation of revocation depend on those of the underlying descriptor revision ( $$\circ $$ ∘ ). Another major topic in this chapter is relations of entrenchment. Such relations are usually associated with AGM contraction, but they are also applicable to revocation. They can be constructed from proximity relations on descriptors (Chapter 5 ). Entrenchment relations can be applied not only to sentences, but also to sets of sentences. These extended entrenchment relations are studied in connection with operations of multiple revocation, in which a set of sentences rather than a single sentence is removed. Finally, the alternative approach of “revisionary revocation” is introduced. Its basic idea is that the revocation of a sentence p takes the form of revision by some sentence that can be interpreted as saying that there are sufficient reasons not to believe in p.

In local change, the operation $$\circ $$ ∘ is specific for the original belief set K. Formally it is a function that takes us from a descriptor $$\Psi $$ Ψ to an element $$K\circ \Psi $$ K ∘ Ψ of the outcome set $$\mathbb {X}$$ X (the set of belief sets that are potential outcomes of belief change). It only represents changes that have K as their starting-point. In this chapter the framework of descriptor revision is widened to global (iterated) belief change. This means that the operation $$\circ $$ ∘ can be applied to any potential belief set. Formally, it is a function that takes us from a pair consisting of a belief set K and a descriptor $$\Psi $$ Ψ to a new belief set $$K\circ \Psi $$ K ∘ Ψ. This makes it possible to cover successive changes, such as $$K\circ \mathfrak {B}p\circ \lnot \mathfrak {B} p$$ K ∘ B p ∘ ¬ B p. Several constructions of global descriptor revision are presented and axiomatically characterized. The most orderly of these constructions is based on pseudodistances (distance measures that allow the distance from X to Y to differ from the distance from Y to X). For any elements X and Y of the outcome set, i.e. the set of belief sets that are eligible as outcomes, there is a number $$\delta (X, Y)$$ δ ( X, Y ) denoting how far away Y is from X. When revising a belief set K by some descriptor $$\Psi $$ Ψ, the outcome $$K\circ \Psi $$ K ∘ Ψ is the belief set satisfying $$\Psi $$ Ψ that is closest to K, as measured with $$\delta $$ δ. If we revise $$K\circ \Psi $$ K ∘ Ψ by $$\Xi $$ Ξ, then the outcome $$K\circ \Psi \circ \Xi $$ K ∘ Ψ ∘ Ξ is the belief set $$\delta $$ δ -closest to $$K\circ \Psi $$ K ∘ Ψ that satisfies $$\Xi $$ Ξ, etc. The chapter also provides a generalization of blockage revision to global operations.

This is the first of four chapters that form the central part of the book, introducing and developing a new approach to belief change, descriptor revision. In this chapter, the new model is constructed from its basic components. We begin with a skeletal input-output model that contains no sentences but only primitive (i.e., unstructured) belief states and inputs, together with a revision function $$\circledcirc $$ that takes us from any belief state $$\mathcal {K}$$ and input $$\text {\i }$$ to a new belief state $$\mathcal {K} \circledcirc \text {\i }$$. This model has the advantage of making few controversial assumptions but also the disadvantage of low expressive power. It is used as a starting-point to which more structure is added successively, allowing us to see what assumptions are needed to obtain the resulting increase in expressive power. Sentences are added to the framework with the help of a support function that takes us from any belief state $$\mathcal {K}$$ to the set of sentences representing the beliefs that it supports. After that, the two major components of the new framework are introduced. The first is belief descriptors, a versatile construct for describing belief states. The metalinguistic expression $$\mathfrak {B}p$$ denotes that p is believed in the belief state under consideration. Truth-functional combinations are interpreted in the usual way, thus $$\lnot \mathfrak {B}p$$ denotes that p is not believed and $$\mathfrak {B}p \vee \mathfrak {B}\lnot p$$ that either p or $$\lnot p$$ is believed. Sets of such expressions are used to denote combined properties, hence $$\{\lnot \mathfrak {B}p, \lnot \mathfrak {B}q\}$$ denotes that neither p nor q is believed. Belief descriptors (either single sentences or sets of such sentences) are used as inputs for belief change (replacing primitive inputs such as $$\text {\i }$$ ). Due to their versatility, all changes can be performed with a single, uniform change operation $$\circ $$. In order to revise the belief set K by a sentence p we use the input (success condition) $$\mathfrak {B}p$$, and the outcome is $$K \circ \mathfrak {B}p$$. In order to remove the sentence q we perform the operation $$K \circ \lnot \mathfrak {B}q$$, etc. In order to perform these operations, the second major component of the new framework is introduced, namely a selection mechanism (a monoselective choice function) that directly selects the output from those among a given set of potential outcomes (the “outcome set”) that satisfy the success condition.

The notion of practical arts goes back to antiquity. It covers what we today call technology but also many other types of activities, such as farming, manual crafts, cooking, housekeeping, sport activities, artistic work, and medicine. Interesting discussions on the practical arts can be found in medieval texts on knowledge classification for instance by Hugh of Saint Victor and Robert Kilwardby, and also in Renaissance and Enlightenment literature. In this chapter it is argued that the philosophy of practical arts should be revitalized and that the philosophy of technology should have a major role when this is done. Many of the topics studied in the latter discipline have interesting extensions to practical arts in general. Some examples are the relationship between action knowledge and factual knowledge, the epistemological roles of actions, explanations in practical knowledge, and the role of functional terms and descriptions. The Empirical Turn in the Philosophy of Technology provides an excellent starting-point for widening the philosophy of technology to a general philosophy of the practical arts.

Our daily lives are affected by new technologies at an ever increasing rate. It is becoming more and more important to assess future technologies from an ethical point of view, and to do this before they are introduced on a massive scale. Such assessments require systematic use of many different kinds of knowledge. In this important new book, an international team of leading experts in the field provides the first comprehensive treatment of the methods available for ethical assessments of technologies and their social introduction. The book explores how information from empirical research can be used in ethical analyses of technology and includes chapters showing how ethical analysis can shed light on topics such as privacy, risk, sustainability, dual use, gender issues, justice, international technology transfer, and the responsibility of engineers. It provides an invaluable resource for students in the philosophy and ethics of technology, science and technology studies, applied ethics, bioethics, business ethics and the ethics of computing.

Models employing hyperreal probabilities can be used to represent epistemic agents that have both credences (represented by propositions whose probability has a non-unit standard part) and full beliefs (represented by propositions with a probability at most infinitesimally smaller than 1). This article introduces operations of belief contraction in such models. Contraction is a process in which a proposition that was initially fully believed becomes a credence. We investigate two operations for such probability-based belief contraction. The first operation, which employs Jeffrey revision, gives rise to an operation that is close to the AGM operation of full meet contraction. The second, somewhat more complex, operation is of a more general type, and has AGM partial meet contraction as a special case. In both models, standard relations of epistemic entrenchment can be constructed from the probability function, which reveals a possibly somewhat surprising connection between probability and epistemic entrenchment.

We live in a world of rapidly growing gaps between rich and poor. In the rich parts of the world, new resource-consuming devices are launched every year. But at the same time, about a fourth of the world’s population does not have access to clean drinking water, and more than half lack safely managed sanitation. What role does technology have in these growing global inequalities? Is technological development the root cause of inequality? Or is the unequal distribution of technology just a mirror of social inequities that have other causes? And can new technologies be instrumental in making the world less unfair? In _Technology and Equality_, these issues are addressed from a wide range of perspectives by scholars in disciplines such as history, sociology, gender studies, anthropology, economics, law, ethics, and philosophy. Case studies highlight technology-related inequalities for instance in climate mitigation, public transport, access to water, waste management, sanitation, air pollution, healthcare, digital communication, and law enforcement. The more theoretical chapters provide tools and concepts that are helpful for analyzing and understanding the relationships between technology and inequality in other applications and in more general perspectives.

It has usually been assumed that monadic value notions can be defined in terms of dyadic value notions, whereas definitions in the opposite direction are not possible. In this paper, inspired by van Benthem’s work, it is shown that the latter direction is feasible with a method in which shifts in context have a crucial role. But although dyadic preference orderings can be defined from context-indexed monadic notions, the monadic notions cannot be regained from the preference relation that they gave rise to. Two formal languages are proposed in which reasoning about context can be represented in a fairly general way. One of these is a modal language much inspired by van Benthem’s work. Throughout the paper the focus is on relationships among the value notions “good”, “bad”, and “better”. Other interpretations like “tall” and “taller” are equally natural. It is hoped that the results of this paper can be relevant for the analysis of natural language comparatives and of vague predicates in general.

It could hardly be denied that healthcare should be patient-centred. However, some of the practices commonly described as patient-centred care may have ethically problematic consequences. This article identifies and discusses twelve ethical conflicts that may arise in the application of (some variants of) person-centred care. The conflicts concern e.g. privacy, autonomous decision-making, safeguarding medical quality, and maintaining professional egalitarianism as well as equality in care. Awareness of these potential conflicts can be helpful in finding the best way to ensure that healthcare has its focus on the needs and interests of the patients. Patient-centred care may have to take different forms, depending of the nature of the disease, the patient’s life situation, and the economic, organizational and technological resources available to the healthcare unit.

This Undergraduate Textbook introduces key methods and examines the major areas of philosophy in which formal methods play pivotal roles. Coverage begins with a thorough introduction to formalization and to the advantages and pitfalls of formal methods in philosophy. The ensuing chapters show how to use formal methods in a wide range of areas. Throughout, the contributors clarify the relationships and interdependencies between formal and informal notions and constructions. Their main focus is to show how formal treatments of philosophical problems may help us understand them better. Formal methods can be used to solve problems but also to express new philosophical problems that would never have seen the light of day without the expressive power of the formal apparatus. Formal philosophy merges work in different areas of philosophy as well as logic, mathematics, computer science, linguistics, physics, psychology, biology, economics, political theory, and sociology. This title offers an accessible introduction to this new interdisciplinary research area to a wide academic audience.