Sven Ove Hansson

In standard Bayesian probability revision, the adoption of full beliefs (propositions with probability 1) is irreversible. Once an agent has full belief in a proposition, no subsequent revision can remove that belief. This is an unrealistic feature, and it also makes probability revision incompatible with belief change theory, which focuses on how the set of full beliefs is modified through both additions and retractions. This problem in probability theory can be solved in a model that (i) lets the codomain of the probability function be a hyperreal-valued rather than the real-valued closed interval [0, 1], and (ii) identifies the full beliefs as the propositions whose probability is either 1 or infinitesimally smaller than 1. In this model, changes in the probability function will result in changes in the set of full beliefs (belief set), which constitutes a submodel that can be conceived as the “tip of the iceberg” within the larger model that also contains beliefs on lower levels of probability. The patterns of change in the set of full beliefs in this modified Bayesian model coincides with the corresponding pattern in a slightly modified version of AGM revision, which is commonly conceived as the gold standard of (dichotomous) belief change. The modification only concerns the marginal case of revision by an inconsistent input sentence. These results show that probability revision and dichotomous belief change can be unified in one and the same framework, or – if we so wish – that belief change theory can be subsumed under a modified version of probability revision that allows for iterated change and for the removal of full beliefs.

Close connections between probability theory and the theory of belief change emerge if the codomain of probability functions is extended from the real-valued interval [0, 1] to a hyperreal interval with the same limits. Full beliefs are identified as propositions with a probability at most infinitesimally smaller than 1. Full beliefs can then be given up, and changes in the set of full beliefs follow a pattern very close to that of AGM revision. In this contribution, iterated revision is investigated. The iterated changes in the set of full beliefs generated by repeated revisions of a hyperreal probability function can, semantically, be modelled with the same basic structure as the sphere models of belief change theory. The changes on the set of full beliefs induced by probability revision satisfy the Darwiche–Pearl postulates for iterated belief change.

In their recently published book Nudge (2008) Richard H. Thaler and Cass R. Sunstein (T&S) defend a position labelled as ‘libertarian paternalism’. Their thinking appeals to both the right and the left of the political spectrum, as evidenced by the bedfellows they keep on either side of the Atlantic. In the US, they have advised Barack Obama, while, in the UK, they were welcomed with open arms by the David Cameron's camp (Chakrabortty 2008). I will consider the following questions. What is Nudge? How is it different from social advertisement? Does Nudge induce genuine preference change? Does Nudge build moral character? Is there a moral difference between the use of Nudge as opposed to subliminal images to reach policy objectives? And what are the moral constraints on Nudge?

This introduction to formal philosophy has its focus on the basic methodology of formalization: the selection of concepts for formalization, appropriate splittings and merges of concepts to be formalized, the idealization that is necessary prior to formalization, the identification of variables and their domains, and the construction of a formal language. Other topics covered in this chapter are the advantages and pitfalls of formal philosophy, the relationships between formal models and that which they represent, and the use of non-logical models in philosophy.

All formal models of belief change involve choices between different ways to accommodate new information. However, the models differ in their loci of choice, i.e. in what formal entities the choice mechanism is applied to. Four models of belief change with different loci of choice are investigated in terms of how they satisfy a set of important properties of belief contraction and revision. It is concluded that the locus of epistemic choice has a large impact on the properties of the resulting belief change operation.

Our uncertainty about matters of fact can often be adequately represented by probabilities, but there are also cases in which we, intuitively speaking, know too little even to assign meaningful probabilities. In many of these cases, other formal representations can be used to capture some of the prominent features of our uncertainty. This is a non-technical overview of some of these representations, including probability intervals, belief functions, fuzzy sets, credal sets, weighted credal sets, and second order probabilities.

We encounter the notion of coherence in many branches of philosophy. This overview introduces some basic distinctions that can be used to characterize concepts of coherence. After that, two formal frameworks for the analysis of coherence are introduced. The first of these is based on the logic of support relations. It is used to show that coherentism and foundationalism may be combinable rather than antithetical. The second framework assumes that coherence comes in degrees and that it can be measured in probability-based units. The properties of such measures is discussed, and so are the difficulties in constructing a measure of coherence that satisfies intuitively reasonable constraints.

We can express values in three major ways: in terms of classification, comparison, and quantity. The interrelations among these three types of value expressions are surveyed, with a particular emphasis on relations of interdefinability. Furthermore, interrelations between value terms and terms expressing norms or choices are explored. Several of these connections have been surprisingly little studied, and further investigations may possibly lead to the discovery of additional connections among the different formal representations of value and value-related concepts.

A money-pump is a thought experiment involving a person whose preferences form a circle. Repeatedly, she pays some money to go from one alternative to another that she likes better. When she has paid her way around the full circle she is back at the starting-point, but with less money. Money-pumps have been used to show that certain preference patterns are irrational since they make a person exploitable. Formal tools can be used to analyze money-pumps in a precise manner, distinguish between different types of money-pumps, and investigate decision strategies to avoid their pernicious effects. Although money-pumps are rather contrived constructions, these investigations have practical relevance since there seem to be decision situations in the real world with the same structure.

Preferences and choices have central roles in moral philosophy, economics, and the decision sciences in general. In a formal language we can express and explore the properties of preferences, choices, and their interrelations in a precise way, and uncover connections that are inaccessible without formal tools. In this chapter, the plausibility of different such properties is discussed, and it is shown how close attention to the logical details can help dissolve some apparent paradoxes in informal and semi-formal treatments.

Deontic logic is the logic of normative concepts such as obligation, permission, and prohibition. This non-technical overview of the area has a strong emphasis on the connections between deontic logic and problems discussed in moral philosophy. Major issues treated are the distinction between ought-to-be and ought-to-do, the various meanings of permissive expressions, the logical relations among norms, the paradoxes of deontic logic, and the nature of moral conflicts and moral dilemmas. It is concluded that deontic logic has resources for precise treatment of important issues in moral philosophy, but in order to make full use of these resources, more co-operation between logicians and moral philosophers is needed.

Despite Vision Zero’s moral appeal and its expansion throughout the world, it has been criticized on different grounds. This chapter is based on an extensive literature search for criticism of Vision Zero, using the bibliographic databases Philosopher’s Index, Web of Science, Science Direct, Scopus, Google Scholar, PubMed, and Phil Papers, and by following the references in the collected documents. Even if the primary emphasis was on Vision Zero in road traffic, our search also included documents criticizing Vision Zero policies in other safety areas, such as public health, the construction and mining industries, and workplaces in general. Based on the findings, we identify and systematically characterize and classify the major arguments that have been put forward against Vision Zero. The most important arguments against Vision Zero can be divided into three major categories: moral arguments, arguments concerning the rationality of Vision Zero, and arguments aimed at the practical implementation of the goals. We also assess the arguments. Of the 13 identified main arguments, 6 were found to be useful for a constructive discussion on safety improvements.

Climate science denial has a perhaps surprisingly strong standing in anthroposophy. Anthroposophical deniers of climate science usually do not contest the existence of global warming, but they ascribe it to “cosmic” processes that are largely described in astrological terms. Thoroughly refuted claims that ongoing global warming depends on variations in solar activity have been adopted by anthroposophists. This article proposes three major explanations for the persistence of climate science denial in the anthroposophical movement: Anthroposophists constantly look for guidance on scientific issues in the writings of their founder Rudolf Steiner, who made claims far off from the mainstream science of his time. They consider the material world to be constantly influenced by “spiritual” factors, including astrological constellations and a host of supernatural beings. Finally, they cherish ideas on a predetermined, largely cyclic, cosmic plan, of which humanity is a part.

Practical methods are introduced for the construction of definitions, both for philosophical purposes and for uses in other disciplines. The structural and contentual requirements on definitions are clarified. It is emphasized that the development of a definition should begin with careful choice of a primary definiendum, followed by the selection of appropriate variables for the definition. Two methods are proposed for the construction of the definiens, the case list method and the method of successive improvements. Four classes of concepts are discussed that are particularly difficult to define: vague concepts, value-laden concepts, controversial concepts, and inconsistent concepts