Sven Ove Hansson

Ever since the beginnings of modern engineering education at the end of the eighteenth century, mathematics has had a prominent place in its curricula. In the 1890s, a zealous “anti-mathematical” movement emerged among teachers in technological disciplines at German university colleges. The aim of this movement was to reduce the mathematical syllabus and reorient it towards more applied topics. Its members believed that this would improve engineering education, but many of them also had more ideological motives. They distrusted modern, rigorous mathematics, and demanded a more intuitive approach. For instance, they preferred to base calculus on infinitesimals rather than the modern (“epsilon delta”) definitions in terms of limits. Some of them even demanded that practically oriented engineers should replace mathematicians as teachers of the (reduced) mathematics courses for engineers. The anti-mathematical movement was short-lived, and hardly survived into the next century. However calls for more intuitive and less formal mathematics reappeared in another, more sinister context, namely the Nazi campaign for an intuitive “German” form of mathematics that would replace the more abstract and rigorous “Jewish” mathematics.

The use of technology to support mathematics goes back to ancient tally sticks, khipus, counting boards, and abacuses. The reciprocal relationship, the use of mathematics to support technology, also has a long history. Preliterate weavers, most of them women, combined geometrical and arithmetical thinking to construct number series that give rise to intricate symmetrical patterns on the cloth. Egyptian scribes performed the technical calculations needed for large building projects. Islamic master builders covered walls and ceilings with complex geometric patterns, constructed with advanced ruler-and-compass methods. In Europe, medieval masons used the same tools to construct intricate geometrical patterns for instance in rose windows. These masters lacked formal mathematical schooling, but they developed advanced skills in constructive geometry. Even today, the practical mathematics of the crafts is often based on traditions that differ from school mathematics.

In almost any decision situation, there are so many uncertainties that we need to evaluate their importance and prioritize among them. This chapter begins with a series of warnings against improper ways to do this. Most of the fallacies described consist in programmatically disregarding certain types of decision-relevant information. The types of information that can be disregarded differ between different decisions, and therefore decision rules that exclude certain types of information should not be used. The chapter proceeds by introducing a collection of useful and legitimate rules for the evaluation and prioritization of uncertainties. These rules are divided into three major groups: rules extending the scope of what we consider, rules for evaluating each uncertainty, and rules for the comparative evaluation of uncertainties (in both moral and instrumental terms). These rules should be applied in an adaptable process that allows the introduction of new and unforeseen types of arguments.

Due to its high demands on information input, traditional decision theory is inadequate to deal with many real-life situations. If, for instance, probabilities or values are undetermined, the standard method of maximizing expected values cannot be used. The difficulties are aggravated if further information is lacking or uncertain, for instance information about what options are available and what their potential consequences may be. However, under such conditions, methods from philosophical analysis and in particular argumentation analysis can be used to systematize our deliberations. Such methods are also helpful if the framing of the decision problem is contested. The argumentative turn in policy analysis is a widened rationality approach that scrutinises inferences from what is known and what is unknown in order to substantiate decision-supporting deliberations. It includes and recognises the normative components of decisions and makes them explicit to help finding reasonable decisions with democratic legitimacy.

​This book describes argumentative tools and strategies that can be used to guide policy decisions under conditions of great uncertainty. Contributing authors explore methods from philosophical analysis and in particular argumentation analysis, showing how it can be used to systematize discussions about policy issues involving great uncertainty. The first part of the work explores how to deal in a systematic way with decision-making when there may be plural perspectives on the decision problem, along with unknown consequences of what we do. Readers will see how argumentation tools can be used for prioritizing among uncertain dangers, for determining how decisions should be framed, for choosing a suitable time frame for a decision, and for systematically choosing among different decision options. Case studies are presented in the second part of the book, showing argumentation in practice in the areas of climate geoengineering, water governance, synthetic biology, nuclear waste, and financial markets. In one example, argumentation analysis is applied to proposals to solve the climate problem with various technological manipulations of the natural climate system, such as massive dispersion of reflective aerosols into the stratosphere. Even after a thorough investigation of such a proposal, doubt remains as to whether all the potential risks have been identified. In such discussions, conventional risk analysis does not have much to contribute since it presupposes that the risks have been identified, whereas the argumentative approach to uncertainty management can be used to systematize discussions.

This book provides a critical examination of how the choice of what to believe is represented in the standard model of belief change. In particular the use of possible worlds and infinite remainders as objects of choice is critically examined. Descriptors are introduced as a versatile tool for expressing the success conditions of belief change, addressing both local and global descriptor revision. The book presents dynamic descriptors such as Ramsey descriptors that convey how an agent’s beliefs tend to be changed in response to different inputs. It also explores sentential revision and demonstrates how local and global operations of revision by a sentence can be derived as a special case of descriptor revision. Lastly, the book examines revocation, a generalization of contraction 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.

This volume is the first extensive study of the historical and philosophical connections between technology and mathematics. Coverage includes the use of mathematics in ancient as well as modern technology, devices and machines for computation, cryptology, mathematics in technological education, the epistemology of computer-mediated proofs, and the relationship between technological and mathematical computability. The book also examines the work of such historical figures as Gottfried Wilhelm Leibniz, Charles Babbage, Ada Lovelace, and Alan Turing.

This is the first of two chapters devoted to problems in the currently dominant model of belief change (the AGM model) that justify the development of alternative frameworks for belief change. In this chapter the focus is on the selection mechanisms that are used to determine which previous beliefs are retained and which are given up in operations of change. In the AGM model, such epistemic choices are assumed to be performed in two steps (the select-and-intersect method). First, a selection is made among a set of logically infinite objects of choice (remainders or possible worlds) that are not themselves representations of plausible belief states. This is followed by a second step in which the outcome is obtained by intersecting the objects that were chosen in the first step. The plausibility of this sequence of operations is critically examined, and the formal limits to its applicability are also pointed out. One of its problems is that epistemic choiceworthiness is not in general preserved under intersection. It is argued that epistemic choices should instead be represented as choices directly among the potential outcomes of the operation of change, i.e., choices among potential belief states.

Contraction differs from revocation (Chapter 9 ) in satisfying the inclusion postulate $$(K\div p\subseteq K)$$ ( K ÷ p ⊆ K ). In spite of the problems connected with that postulate, contraction represents an interesting idealization, namely that in which losses of beliefs are described with an exclusive focus on the beliefs that are lost and a corresponding disregard for the additions to the belief set that push them out. In this chapter, some major ways to construct operations of contraction in the descriptor revision framework are introduced, and the properties of these constructions are investigated. Two impossibility theorems make it clear that contrary to AGM revision, AGM contraction cannot be reconstructed as descriptor revision. Furthermore, three extensions of the descriptor revision framework are introduced in which operations of contraction can deal with ties in ways that are more consonant with how this is done in the AGM framework. Unsurprisingly, these contraction methods all deviate from the simple one-step choice mechanism that is one of the major advantages of the descriptor revision framework.

In this chapter the properties of descriptor revision, as defined in Chapter 4, are further explored. Several alternative selection mechanisms are presented, and the properties of the resulting operations are investigated. In one of these variants, the choice function is based on a relation on belief sets that can be interpreted as representing distances from the current belief set. In another, descriptor revision is constructed from a blockage relation on the outcome set (set of potential outcomes). A belief set blocks another belief set if the latter is ineligible as a revision outcome whenever the first is available. The different variants of descriptor revision are axiomatically characterized with plausible postulates. The controversial axioms discussed in Chapter 3 do not hold in the new framework. Finally, a binary relation on descriptors, the relation of epistemic proximity, is introduced. A descriptor is more epistemically proximate than another descriptor if some belief set satisfying it is closer at hand for the agent, or it can be satisfied with a less far-reaching change. For instance, $$\mathfrak {B}_p \succeq \lnot \mathfrak {B}_q$$ denotes that it is closer at hand for the epistemic agent to believe in p than not to believe in q. Relations of epistemic proximity (between descriptors) generalize the relations of epistemic entrenchment (between sentences) that have been developed in the AGM framework. The translation is straight-forward: p is less entrenched than q if and only if $$\lnot \mathfrak {B}_p$$ is more proximate than $$\lnot \mathfrak {B}_q$$. The chapter also contains a section about indeterministic descriptor revision, in which the operation does not specify a single outcome for each input, but only a set of possible outcomes.

This chapter explores some of the problematic properties of the standard (AGM) operations of change. Both contraction and revision violate the highly plausible postulate of finite-based outcome. Contraction has further problems relating to the postulates of success, recovery, and inclusion, and revision has implausible monotonicity-related properties. Additional problems arise when the framework is extended to include conditional sentences and iterated change. The chapter concludes with a list of ten desiderata for an alternative approach to belief change that eschews the major problems exhibited in this and the previous chapter.

A dynamic descriptor carries information on how an agent’s beliefs are disposed to be changed in response to potential input(s). A particularly important class of dynamic descriptors are the Ramsey descriptors that have the form $$\Psi \Rightarrow \Xi $$ Ψ ⇒ Ξ where $$\Psi $$ Ψ and $$\Xi $$ Ξ are (static) descriptors of the types introduced in Chapter 4. For example, $$\mathfrak {B}(p \vee q) \Rightarrow \lnot \mathfrak {B}r$$ B ( p ∨ q ) ⇒ ¬ B r denotes that if the agent changes her beliefs to believe that $$p \vee q$$ p ∨ q, then she will not believe in r. Ramsey descriptors are axiomatically characterized with a set of plausible postulates that are generalizations of postulates commonly used in the logic of conditional sentences. It is also shown that Ramsey descriptors can unproblematically be inserted into belief sets. Revision by Ramsey descriptors does not give rise to the problems that arise when Ramsey test conditionals are inserted into the AGM framework or related models of belief change. The special case represented by the Ramsey descriptor $$\mathfrak {B}p \Rightarrow \mathfrak {B}q$$ B p ⇒ B q corresponds to standard Ramsey test conditionals, and we can define the epistemic conditional $$p \rightarrowtail q$$ p ↣ q (“if p then q”) to hold if and only if $$\mathfrak {B}p \Rightarrow \mathfrak {B}q$$ B p ⇒ B q. However, this is not the only way to derive a sentential conditional from a Ramsey descriptor. Two alternatives to the standard approach are introduced. Furthermore, a formula for deriving non-monotonic inference from a Ramsey descriptor is presented. This proposal is offered as an improvement over the common view that the logic of non-monotonic inference is a fragment of the logic of conditional sentences. The chapter also explores various methods to introduce modalities and autoepistemic beliefs into the belief change framework. The introduction of modalities serves to connect descriptor revision with Dynamic Doxastic Logic (DDL) and related systems.

Clear-cut cases of decision-making under risk (known probabilities) are unusual in real life. The gambler’s decisions at the roulette table are as close as we can get to this type of decision-making. In contrast, decision-making under uncertainty (unknown probabilities) can be exemplified by a decision whether to enter a jungle that may contain unknown dangers. Life is usually more like an expedition into an unknown jungle than a visit to the casino. Nevertheless, it is common in decision-supporting disciplines to proceed as if reasonably reliable probability estimates were available for all possible outcomes, i.e. as if the prevailing epistemic conditions were analogous to those of gambling at the roulette table. This mistake can be called the tuxedo fallacy. It is argued that traditional engineering practices such as safety factors and multiple safety barriers avoid this fallacy and that they therefore manage uncertainty better than probabilistic risk analysis (PRA). PRA is a useful tool, but it must be supplemented with other methods in order not to limit the analysis to dangers that can be assigned meaningful probability estimates.

It is almost universally acknowledged that risks have to be weighed against benefits, but there are different ways to perform the weighing. In conventional risk analysis, collectivist risk-weighing is the standard. This means that an option is accepted if the sum of all individual benefits outweighs the sum of all individual risks. In practices originating in clinical medicine, such as ethical appraisals of clinical trials, individualist risk-weighing is the standard. This implies a much stricter criterion for risk acceptance, namely that the risk to which each individual is exposed should be outweighed by benefits for that same individual. The different choices of risk-weighing methods in different policy areas seem to have emerged from traditional thought patterns and social relations, rather than from explicit deliberations on possible justifications for the alternative ways to weigh risks against benefits. It is not obvious how the prevalent differences in risk-weighing practices can be reconstructed in terms of consistent underlying principles of preventive health or social priority-setting.

Workplace inspections are undertaken because they are believed to lead to better conditions In the workplace. It is therefore essential to know if inspections have the desired effects on working conditions. We introduce a theoretical framework for the evaluation of workplace inspections with respect to their effects on working conditions. Criteria of efficiency and priority-setting are discussed. Some empirical results concerning priority-setting in Swedish inspection agencies are presented. Further, we argue that in order to obtain reliable information about the effects of different inspection methods, it is necessary to perform controlled comparative studies in which different methods are used in different workplaces. Given the facility with which such studies can be performed, it is surprising how few such studies have been made. We conclude by surveying some empirical studies that concern the issue of efficient inspections.

The typical function of goals is to regulate action in a way that furthers goal achievement. Goals are typically set on the assumption that they will help bring the agent closer to the desired state of affairs. However, sometimes endorsement of a goal, or the processes by which the goal is set, can obstruct its achievement. When this happens, the goal is self-defeating. Self-defeating goals are common in both private and social decision-making but have not received much attention by decision theorists. In this paper, we investigate different variants of three major types of self-defeating mechanisms: The goal can be an obstacle to its own fulfilment, goal-setting activities can impede goal achievement, and disclosure of the goal can interfere with its attainment. Different strategies against self-defeasance are tentatively explored, and their efficiency against different types of self-defeasance is investigated.

As part of the conference commemorating Theoria's 75th anniversary, a round table discussion on philosophy publishing was held in Bergendal, Sollentuna, Sweden, on 1 October 2010. Bengt Hansson was the chair, and the other participants were eight editors-in-chief of philosophy journals: Hans van Ditmarsch (Journal of Philosophical Logic), Pascal Engel (Dialectica), Sven Ove Hansson (Theoria), Vincent Hendricks (Synthese), Søren Holm (Journal of Medical Ethics), Pauline Jacobson (Linguistics and Philosophy), Anthonie Meijers (Philosophical Explorations), Henry S. Richardson (Ethics) and Hans Rott (Erkenntnis)

As part of the conference commemorating Theoria's 75th anniversary, a round table discussion on philosophy publishing was held in Bergendal, Sollentuna, Sweden, on 1 October 2010. Bengt Hansson was the chair, and the other participants were eight editors‐in‐chief of philosophy journals: Hans van Ditmarsch (Journal of Philosophical Logic), Pascal Engel (Dialectica), Sven Ove Hansson (Theoria), Vincent Hendricks (Synthese), Søren Holm (Journal of Medical Ethics), Pauline Jacobson (Linguistics and Philosophy), Anthonie Meijers (Philosophical Explorations), Henry S. Richardson (Ethics) and Hans Rott (Erkenntnis).

The AGM theory of belief contraction is extended tomultiple contraction, i.e. to contraction by a set of sentences rather than by a single sentence. There are two major variants: Inpackage contraction all the sentences must be removed from the belief set, whereas inchoice contraction it is sufficient that at least one of them is removed. Constructions of both types of multiple contraction are offered and axiomatically characterized. Neither package nor choice contraction can in general be reduced to contractions by single sentences; in the finite case choice contraction allows for reduction.