Hans Rott

According to the Lockean thesis, a proposition is believed just in case it is highly probable. While this thesis enjoys strong intuitive support, it is known to conflict with seemingly plausible logical constraints on our beliefs. One way out of this conflict is to make probability 1 a requirement for belief, but most have rejected this option for entailing what they see as an untenable skepticism. Recently, two new solutions to the conflict have been proposed that are alleged to be non-skeptical. We compare these proposals with each other and with the Lockean thesis, in particular with regard to the question of how much we gain by adopting any one of them instead of the probability 1 requirement, that is, of how likely it is that one believes more than the things one is fully certain of.

This paper reorganizes and further develops the theory of partial meet contraction which was introduced in a classic paper by Alchourron, Gardenfors, and Makinson. Our purpose is threefold. First, we put the theory in a broader perspective by decomposing it into two layers which can respectively be treated by the general theory of choice and preference and elementary model theory. Second, we reprove the two main representation theorems of AGM and present two more representation results for the finite case that "lie between" the former, thereby partially answering an open question of AGM. Our method of proof is uniform insofar as it uses only one form of "revealed preference", and it explains where and why the finiteness assumption is needed. Third, as an application, we explore the logic characterizing theory contractions in the finite case which are governed by the structure of simple and prioritized belief bases.

In this paper I discuss the foundations of a formal theory of coherent and conservative belief change that is (a) suitable to be used as a method for constructing iterated changes of belief, (b) sensitive to the history of earlier belief changes, and (c) independent of any form of dispositional coherence. I review various ways to conceive the relationship between the beliefs actually held by an agent and her belief change strategies (that also deal with potential belief sets), show the problems they suffer from, and suggest that belief states should be represented by unary revision functions that take sequences of inputs. Three concepts of coherence implicit in current theories of belief change are distinguished: synchronic, diachronic and dispositional coherence. Diachronic coherence is essentially identified with what is known as conservatism in epistemology. The present paper elaborates on the philosophical motivation of the general framework; formal details and results are provided in a companion paper.

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.

Using Gärdenfors's notion of epistemic entrenchment, we develop the semantics of a logic which accounts for the following points. It explains why we may generally infer `If ~A then B´ if all we know is AvB while must not generally infer `If ~A then B´ if all we know is {AvB, A}. More generally, it explains the nonmonotonic nature of the consequence relation governing languages which contain conditionals, and it explains how we can deduce conditionals from premise sets without conditionals. Depending on the language at hand, our logic provides different ways of keeping the Ramsey test and getting round the Gärdenfors triviality theorem. I argue that consistent additions of new items of belief are not to be performed by transitions to logical expansions.

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 is a survey paper. Contents: 1 Introduction ― 2 Preliminary remarks on information, truth and mind - 2.1 Remarks on information and truth - 2.2 Some clues from the philosophy of mind - 2.3 Functionalism as applied to belief revision - 2.4 Filling in the parameters ― 3 Belief change = revision + reflection - 3.1 Foundationalism - 3.2 Coherentism ― 4 Inference operations for simple change operations: three examples - 4.1 Example 1: flat data bases - 4.2 Example 2: up-sets in prioritized data bases - 4.3 Example 3: maximal-consistent sets in prioritized data bases ― 5 Representing coherentist belief change by operations on prioritized data bases - 5.1 Moderate revision - 5.2 Revision by comparison ― 6 A very brief history of belief revision - 6.1 The 1980s: AGM's classical model - 6.2 The 1990s: iteration - 6.3 The 2000s: merging ― 7 Conclusion

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 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 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 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.

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.

According to Otto Neurath, the practice of science consists in a large undertaking of setting up and maintaining systems of statements: In unified science we try ... to create a consistent system of protocol statements and nonprotocol statements . When a new statement is presented to us we compare it with the system at our disposal and check whether the new statement is in contradiction with the system or not. If the new statement is in contradiction with the system, we can discard this statement as unusable , for example, the statement: ‘In Africa lions sing only in major chords’ ; however, one can also ‘accept’ the statement and change the system accordingly so that it remains consistent if this statement is added. The statement may then be called ‘true’

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.

Richard Bradley has initiated a new debate, with Brian Hill and Jake Chandler as further participants, about the implications of a number of so-called triviality results surrounding the Ramsey test for conditionals. I comment on this debate and argue that ‘Inclusion’ and ‘Preservation’, which were originally introduced as postulates for the rational revision of factual beliefs, have little to recommend them in the first place when extended to languages containing conditionals. I question the philosophical method of postulation that was applied in the new debate, and instead base my arguments on explicit representations of belief states and canonical constructions of belief state revisions.

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.

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.

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.

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.