Hans Rott

The development of science does not proceed as a monotonous addition of information. A superior successor theory often contradicts its predecessor. The question as to what the logical relationship is between such theories, insofar as the transition from one to the other embodies continuity and progress, is the subject of this book. Proceeding from a discussion of intertheory reductions, the author proves that theories revision models from philosophical logic are fruitful for questions of scientific theory. Formal analyses of conditionals, autoepistemic inferences, intertheoretical explanations and idealizations are carried out, as well as applications to the Kepler-Newton case and the case of the ideal gas law and van der Waals's law.

We distinguish the set of explicit beliefs of a reasoner, his "belief base", from the beliefs that are merely implicit. Syntax-based belief change governed by the structure of the belief base and the ranking ("prioritization") of its elements is reconstructed with the help of an epistemic entrenchment relation in the style of Gärdenfors and Makinson. Though priorities are essentially different from entrenchments, distinguished relations of epistemic entrenchment may be obtained from prioritized belief bases by a number of different constructions. An approximate reconstruction of syntax-based belief change is possible, which can be strengthened to a strict identity in some important special cases. A competitive interpretation and a minimal change interpretation of the basic idea of entrenchment are discussed. It is argued that entrenchment essentially involves multiple belief changes, i.e., changes by sets of sentences.

This paper combines various structures representing degrees of belief, degrees of disbelief, and degrees of non-belief (degrees of expectations) into a unified whole. The representation uses relations of comparative necessity and possibility, as well as non-probabilistic functions assigning numerical values of necessity and possibility. We define all-encompassing necessity structures which have weak expectations (mere hypotheses, guesses, conjectures, etc.) occupying the lowest ranks and very strong, ineradicable ('a priori') beliefs occupying the highest ranks. Structurally, there are no differences from the top to the bottom. I argue that belief is a vague notion, and that thresholds for belief, if there are any, are context-dependent.

This is a survey paper. Contents: 1 Introduction -- 2 The representation of belief -- 3 Kinds of belief change -- 4 Coherence constraints for belief revision -- 5 Different modes of belief change -- 6 Two strategies for characterizing rational changes of belief - 6.1 The postulates strategy - 6.2 The constructive strategy -- 7 An abstract view of the elements of belief change -- 8 Iterated changes of belief -- 9 Further developments - 9.1 Variants and extensions of belief revision - 9.2 Updates - 9.3 Default inferences as expectation revision - 9.4 Belief merging -- 10 Concluding remarks

The paper aims at a perspicuous representation of Isaac Levi's pragmatist epistemology, spanning from the 1967 classic "Gambling with Truth" to his 2004 book on "Mild Contraction". Based on a formal framework for Levi's notion of inquiry, I analyse his decision-theoretic approach with truth and information as basic cognitive values, and with Shackle measures as emerging structures. Both cognitive values figure prominently in Levi's model of inductive belief expansion, but only the value of information is employed in his model of belief contraction. I argue that the former model is more successful than the latter.

This collection includes twenty original philosophical essays in honour of Wolfgang Spohn. The contributions mirror the scope of Wolfgang Spohn’s work. They address topics from epistemology (e.g., the theory of ranking functions, belief revision, and the nature of knowledge and belief), philosophy of science (e.g., causation, induction, and laws of nature), the philosophy of language (e.g., the theory of meaning and the semantics of counterfactuals), and the philosophy of mind (e.g., intentionality and free will), as well as problems of ontology, logic, the theory of practical rationality, and meta-philosophy. ― Contributors: Ansgar Beckermann, Wolfgang Benkewitz, Bernd Buldt, Ralf Busse, Christoph Fehige, Wolfgang Freitag, Gordian Haas, Volker Halbach, Franz Huber, Andreas Kemmerling, Manfred Kupffer, Hannes Leitgeb, Godehard Link, Arthur Merin, Thomas Müller, Julian Nida-Rümelin, Martine Nida-Rümelin, Hans Rott, Holger Sturm, Thomas Ede Zimmermann, Alexandra Zinke.

In this paper I discuss the relation between various properties that have been regarded as important for determining whether or not a belief constitutes a piece of knowledge: its stability, strength and sensitivity to truth, as well as the strength of the epistemic position in which the subject is with respect to this belief. Attempts to explicate the relevant concepts more formally with the help of systems of spheres of possible worlds (à la Lewis and Grove) must take care to keep apart the very different roles that systems of spheres can play. Nozicks sensitivity account turns out to be closer to the stability analysis of knowledge (versions of which I identify in Plato, Descartes, Klein and Lehrer) than one might have suspected.

Communication problems between members of different cultures may be due to "genuine" disagreement or "mere" misunderstanding. I argue that there is anthropological evidence that efficient communication across different cultures and languages is feasible, since (i) the degrees of sophistication in thinking or talking are not fundamentally different (the case of "Chinese counterfactuals") and (ii) the basic logics used are not fundamentally different (the case of "Zande logic"). Disagreements and misunderstandings are not clearly separable, however, because (iii) it is only relative to a given translational scheme that one can talk of a member of one culture denying what a member of another culture affirms. The latter claim is illustrated by a logical analysis of a made-up example.

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.

Drawing inspiration from Lakatos’s philosophy of science, the paper presents a notion of intertheory explanation that is suitable to explain, from the point of view of a successor theory, its predecessor theory’s success (where it is successful) as well as the latter’s failure (where it fails) at the same time. A variation of the Ramsey-test is used, together with a standard AGM belief revision model, to give a semantics for open and counterfactual conditionals and ’because’-sentences featuring in such intertheory explanations. Pre-theoretically described idealizing assumptions play a crucial role in this model, especially when the predecessor theory and the successor theory contradict each other.

This paper dwells upon formal models of changes of beliefs, or theories, which are expressed in languages containing a binary conditional connective. After defining the basic concept of a (non-trivial) belief revision model. I present a simple proof of Gärdenfors''s (1986) triviality theorem. I claim that on a proper understanding of this theorem we must give up the thesis that consistent revisions (additions) are to be equated with logical expansions. If negated or might conditionals are interpreted on the basis of autoepistemic omniscience, or if autoepistemic modalities (Moore) are admitted, even more severe triviality results ensue. It is argued that additions cannot be philosophically construed as parasitic (Levi) on expansions. In conclusion I outline somed logical consequences of the fact that we must not expect monotonic revisions in languages including conditionals.

The paper suggests a way of viewing the two Fregean principles of compositionality and contextuality as working together in the enterprise of interpretation. A third Fregean theme, that of elucidation (more precisely, the elucidation of primitive, undefinable terms of logic, mathematics and metamathematics) secures a place for some version of the context principle in Frege's later writings. When thinking about the functioning of elucidations, Frege acknowledges a principle of charitable interpretation. I argue that there is a deep connection between the three themes, and that not only compositionality and contextuality, but also charity is a genuinely Fregean theme. Context. Interpretation. Linguistics. Logic. Meaning. Word.

This paper addresses the question whether the past couple of decades of formal research in belief revision offers evidence of a new psychologism in logic. In the first part I examine five potential arguments in favour of this thesis and find them all wanting. In the second part of the paper I argue that belief revision research has climbed up a hierarchy of models for the change of doxastic states that appear to be clearly normative at the bottom, but are more amenable to an empirical-descriptive interpretation on higher levels. I conclude that this observation might offer a foothold for the thesis that there is a new psychologism in logic.

In their unifying theory to model uncertainty, Friedman and Halpern (1995–2003) applied plausibility measures to default reasoning satisfying certain sets of axioms. They proposed a distinctive condition for plausibility measures that characterizes “qualitative” reasoning (as contrasted with probabilistic reasoning). A similar and similarly fundamental, but more general and thus stronger condition was independently suggested in the context of “basic” entrenchment-based belief revision by Rott (1996–2003). The present paper analyzes the relation between the two approaches to formalizing basic notions of plausibility as used in qualitative default reasoning. While neither approach is a special case of the other, translations can be found that elucidate their relationship. I argue that Rott’s notion of plausibility allows for a more modular set-up and has a better philosophical motivation than that of Friedman and Halpern.

Modern belief revision theory is based to a large extent on partial meet contraction that was introduced in the seminal article by Carlos Alchourrón, Peter Gärdenfors, and David Makinson that appeared in 1985. In the same year, Alchourrón and Makinson published a significantly different approach to the same problem, called safe contraction. Since then, safe contraction has received much less attention than partial meet contraction. The present paper summarizes the current state of knowledge on safe contraction, provides some new results and offers a list of unsolved problems that are in need of investigation.

There are two prominent ways of formally modelling human belief. One is in terms of plain beliefs, i.e., sets of propositions. The second one is in terms of degrees of beliefs, which are commonly taken to be representable by subjective probability functions. In relating these two ways of modelling human belief, the most natural idea is a thesis frequently attributed to John Locke: a proposition is or ought to be believed just in case its subjective probability exceeds a contextually fixed probability threshold \. This idea is known to have two serious drawbacks: first, it denies that beliefs are closed under conjunction, and second, it may easily lead to sets of beliefs that are logically inconsistent. In this paper I present two recent accounts of aligning plain belief with subjective probability: the Stability Theory of Leitgeb (2013, 2014, 2015, 2017) and the Probalogical Theory of Lin and Kelly (2012a, 2012b). I argue that Leitgeb’s theory may be too sceptical for the purposes of real life.

The book addresses the questions how literature can convey knowledge and how literary meaning can arise in the face of the fact that fictional texts waive the usual claim to truth. Based on the interdisciplinary cooperation of literary scholars and analytic philosophers, the present anthology attempts a) to analyze the possibility and conditions of gaining knowledge through literature, and b) to apply, in a fruitful way, philosophical theories of meaning and interpretation to the constitution of meaning within the language of literature. The project is guided by the hypothesis that the cognitive function of literature cannot be understood without such fundamental modelings of the complex interaction of meaning, truth and knowledge.

Pragmatists have argued that doxastic or epistemic norms do not apply to beliefs, but to changes of beliefs; thus not to the holding or not-holding, but to the acquisition or removal of beliefs. Doxastic voluntarism generally claims that humans acquire beliefs in a deliberate and controlled way. This paper introduces Negative Doxastic Voluntarism according to which there is a fundamental asymmetry in belief change: humans tend to acquire beliefs more or less automatically and unreflectively, but they tend to withdraw beliefs in a controlled and deliberate way. I first present a variety of philosophical, empirical and logical arguments for Negative Doxastic Voluntarism. Then I raise two objections against it. First, the apparent asymmetry may result from a confusion of belief with other doxastic attitudes like assumption, supposition, hypothesis or opinion. Second, the apparent asymmetry seems to vanish if we focus on doxastic states rather than just beliefs. Some rejoinders and their consequences for the vague concept of belief are sketched

Descartes' Meditations do not end up sceptical at all. In fact, the sixth meditation displays an intriguing epistemological optimism. Descartes affirms without reservation that knowledge of the external world is possible. The antisceptical argument at the end of the Meditations is often interpreted as a refutation of dream scepticism, with the conclusion that a person in the waking state can also determine that he or she is awake. We examine the logic of the argument in detail and find that this is not the point. Our reconstruction shows that the question of waking or dreaming which seems to be so crucial for Descartes can even be dropped from his argument.

This paper presents the model of ‘bounded revision’ that is based on two-dimensional revision functions taking as arguments pairs consisting of an input sentence and a reference sentence. The key idea is that the input sentence is accepted as far as (and just a little further than) the reference sentence is ‘cotenable’ with it. Bounded revision satisfies the AGM axioms as well as the Same Beliefs Condition (SBC) saying that the set of beliefs accepted after the revision does not depend on the reference sentence (although the posterior belief state does depend on it). Bounded revision satisfies the Darwiche–Pearl (DP) axioms for iterated belief change. If the reference sentence is fixed to be a tautology or a contradiction, two well-known one-dimensional revision operations result. Bounded revision thus naturally fills the space between conservative revision (also known as natural revision) and moderate revision (also known as lexicographic revision). I compare this approach to the two-dimensional model of ‘revision by comparison’ investigated by Fermé and Rott (Artif Intell 157:5–47, 2004 ) that satisfies neither the SBC nor the DP axioms. I conclude that two-dimensional revision operations add substantially to the expressive power of qualitative approaches that do not make use of numbers as measures of degrees of belief.

Ein theoretischer Begriff erhält seine Bedeutung aus einer Reihe von bedeutungskonstitutiven oder "analytischen" Sätzen der betreffenden Theorie. Die Bedeutungen der theoretischen Begriffe können sich ändern, wenn sich die Theorien ändern. Nach einer Diskussion von Kant und Frege schlage ich eine weitgehend quineanische Interpretation von Analytizität vor, ohne jedoch die Quine'sche Bedeutungsskepsis zu übernehmen. Ein Satz einer bestimmten Theorie in einer bestimmten Sprache wird analytisch genannt, wenn die Revision der Theorie, so dass dieser Satz verloren geht, die Aufgabe des gegebenen sprachlichen (oder alternativ: des gegebenen theoretischen) Rahmens mit sich bringt. Diese Lösung des Problems der Definition von Analytizität gründet auf den intuitiven Urteilen der Mitglieder einer Sprachgemeinschaft über die Identität von Sprachen oder Theorien.

Theories of belief and meaning have long occupied philosophers. Typically, there is a correlation between the meaning of a sentence that is uttered and the content of the attitude that the speaker thereby conveys. This is also why a sentence can be used to specify content in an attribution of the attitude to the speaker. From the perspective of a theory of semantic content, there is a level of description where mental states and sentences can be said to share a content or meaning. But there is a contrary view gaining currency, claiming that belief and meaning have to be kept apart conceptually, theoretically, and methodologically. Thus it could be that meaning is an internal or private notion that can be accounted for purely linguistically (or even non-intentionally altogether), while the same may not be true of belief. The volume brings together researchers from various areas in philosophy, psychology, and linguistics to address these questions. The tradition of logical positivism, sometimes thought of as having been a passing phase in twentieth-century philosophy, has as a matter of record remained a vibrant force. But it has shifted from broadside critiques of other systems of thought into a deeper study of how the structure of logic and language impact human behavior and psychological conditioning. Among the contributors to this international symposium are Michael Esfeld, Wolfram Hisses, Max Kolbel, Isaac Levi, Diego Marconi, James McGilvary, Olaf Muller, Paul Peitroski and Norbert Hornstein, Sebastian Rodl, and Alberto Voltolini.

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

This paper compares three accounts of what can be inferred from a knowledge base that contains conditionals: Lehmann and Magidor’s Rational Entailment; Pearl’s System Z, later extended and refined in collaboration with Goldszmidt; and the present author’s Nonmonotonic conditional logic for belief revision. We show that although the ideas motivating these systems are strikingly different, they are formally equivalent. An explanation of the surprising parallel is offered in terms of the interpretation of conditionals in the context of nonmonotonic reasoning and belief revision. Finally, some common problems with the equivalent systems are outlined, as well as some problems in assessing these problems which indicate that a general definition of dependence between the items in a knowledge base is needed.

According to the Ramsey Test, conditionals reflect changes of beliefs: α > β is accepted in a belief state iff β is accepted in the minimal revision of it that is necessary to accommodate α. Since Gärdenfors’s seminal paper of 1986, a series of impossibility theorems (“triviality theorems”) has seemed to show that the Ramsey test is not a viable analysis of conditionals if it is combined with AGM-type belief revision models. I argue that it is possible to endorse that Ramsey test for conditionals while staying true to the spirit of AGM. A main focus lies on AGM’s condition of Preservation according to which the original belief set should be fully retained after a revision by information that is consistent with it. I use concrete representations of belief states and (iterated) revisions of belief states as semantic models for (nested) conditionals. Among the four most natural qualitative models for iterated belief change, two are identified that indeed allow us to combine the Ramsey test with Preservation in the language containing only flat conditionals of the form α > β. It is shown, however, that Preservation for this simple language enforces a violation of Preservation for nested conditionals of the form α > (β > γ). In such languages, no two belief sets are ordered by strict subset inclusion. I argue that it has been wrong right from the start to expect that Preservation holds in languages containing nested conditionals.

The paper proposes a unified analysis of the natural language connectives 'if', 'if … might', 'even if' (all of them with indicative and subjunctive mood), 'because' and 'though'. They are all interpreted as instances of universal (pro)conditionals, unconditionals, or counterconditionals. The paper imports the notion of relevance into the meaning of conditionals, viewing conditionals as close in meaning to explanations and statements about causal relations. The antecedent of a conditional is interpreted as being relevant for its consequent, thus avoiding the general inference from A and B to 'If A, B'. The analysis is based on different variants of the Ramsey test (among them the 'Strong Ramsey Test') together with a fragment of the belief revision theory of Alchourrón, Gärdenfors and Makinson.

Change, Choice and Inference develops logical theories that are necessary both for the understanding of adaptable human reasoning and for the design of intelligent systems. The book shows that reasoning processes - the drawing on inferences and changing one's beliefs - can be viewed as belonging to the realm of practical reason by embedding logical theories into the broader context of the theory of rational choice. The book unifies lively and significant strands of research in logic, philosophy, economics and artificial intelligence. It elaborates on the relevant theories and provides a mathematically precise foundation for the thesis that large parts of theoretical reason can be subsumed under practical reason.

Dogmatic, naive and sophisticated falsificationism are construed as being distinguished by different views on the revisability of scientific theories. Then Lakatos's methodology of scientific research programs (SRP) is reinterpreted: The structure of an SRP is a target theory equipped with a priority structure for hypothetical revisions that accommodate idealizing assumptions. Idealizations pointing "backwards" capture predecessor theories, thus showing both their virtues and limitations. The core of an SRP is assigned top priority; its positive heuristics consists in a strategy of how to work off the idealizing assumptions. In the dynamics of SRP's, progressive intertheoretic relations within an SRP are characterized as generating continuity through revisions, while those that hold across SRP's only have excess empirical content. Finally, we contrast our account with a reconstruction of Lakatos's in the structuralist philosophy of science (W. Stegmüller).

The paper addresses the situation of a dispute in which one speaker says ϕ and a second speaker says not-ϕ. Proceeding on an idealising distinction between "basic" and "interesting" claims that may be formulated in a given idiolectal language, I investigate how it might be sorted out whether the dispute reflects a genuine disagreement, or whether the speakers are only having a merely verbal dispute, due to their using different interesting concepts. I show that four individually plausible principles for the determination of the nature of a dispute are incompatible. As an example, I discuss the question whether Sarai lied in the story told in Genesis 12.

The paper attacks the widely held view that belief revision theories, as they have been studied in the past two decades, are founded on the Principle of Informational Economy. The principle comes in two versions. According to the first, an agent should, when accepting a new piece of information, aim at a minimal change of his previously held beliefs. If there are different ways to effect the belief change, then the agent should, according to he second version, give up those beliefs that are least entrenched. Although widely proclaimed by belief revision theorists, I argue that both versions of the principle are dogmas that are not (and perhaps should not be) adhered to. I substantiate this claim with two simple mathematical observations, and I defend it against four possible objections that involve contractions, reconstructions, dispositions, and truths.