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.

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.

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 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.

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.

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.

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.

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).

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.

The paper attacks the almost universally held view that belief revison theories, as they have been studied in the literature of the past two decades, are founded on a Principle of Minimal Change, or Principle of Informational Economy. The principle comes in two versions. According to the first, an agent should, when accepting new information, aim at a posterior belief set that minimizes the items on which it disagrees with the prior belief set. If there are different ways to effect the belief change, then according to the second version, the agent should give up the beliefs that are least entrenched. Although widely endorsed and advertised by belief revision theorists, the paper argues that both versions of the principle are dogmas that are not in fact (and perhaps should not be) adhered to. Two simple mathematical observations substantiate this claim, and it is defended against four possible objections that involve contractions, reconstructions, dispositions, and truths.