– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

Bayesian confirmation theory is our best formal framework for describing inductive reasoning. The problem of old evidence is a particularly difficult one for confirmation theory, because it suggests that this framework fails to account for central and important cases of inductive reasoning and scientific inference. I show that we can appeal to the fragmentation of doxastic states to solve this problem for confirmation theory. This fragmentation solution is independently well-motivated because of the success of fragmentation in solving other problems. I (...) also argue that the fragmentation solution is preferable to other solutions to the problem of old evidence. These other solutions are already committed to something like fragmentation, but suffer from difficulties due to their additional commitments. If these arguments are successful, Bayesian confirmation theory is saved from the problem of old evidence, and the argument for fragmentation is bolstered by its ability to solve yet another problem. (shrink)

Various theories try to give accounts of how measures of this confidence do or ought to behave, both as far as the internal mental consistency of the agent as ...

I develop a strategy for representing epistemic states and epistemic changes that seeks to be sensitive to the difference between voluntary and involuntary aspects of our epistemic life, as well as to the role of pragmatic factors in epistemology. The model relies on a particular understanding of the distinction between full belief and acceptance , which makes room for the idea that our reasoning on both practical and theoretical matters typically proceeds in a contextual way. Within this framework, I discuss (...) how agents can rationally shift their credal probability functions so as to consciously modify some of their contextual acceptances; the present account also allows us to represent how the very set of contexts evolves. Voluntary credal shifts, in turn, might provoke changes in the agent’s beliefs, but I show that this is actually a side effect of performing multiple adjustments in the total lot of the agent’s acceptance sets. In this way we obtain a model that preserves many pre-theoretical intuitions about what counts as adequate rationality constraints on our actual practices—and hence about what counts as an adequate, normative epistemological perspective. (shrink)

It is valuable for inquiry to have researchers who are committed advocates of their own theories. However, in light of pervasive disagreement, such a commitment is not well explained by the idea that researchers believe their theories. Instead, this commitment, the rational attitude to take toward one’s favored theory during the course of inquiry, is what I call endorsement. Endorsement is a doxastic attitude, but one which is governed by a different type of epistemic rationality. This inclusive epistemic rationality is (...) sensitive to reasons beyond those to think the particular proposition in question is true. Instead, it includes extrinsic epistemic reasons, which concern the health of inquiry more generally. Such extrinsic reasons include the distribution of cognitive labor that a researcher will contribute to by endorsing a particular theory. Recognizing endorsement and inclusive epistemic rationality thus allows us to smooth a tension between individual rationality and collective rationality. It does so by showing how it can be epistemically rational to endorse a theory on the basis of the way this endorsement will benefit collective inquiry. I provide a decision theoretic treatment for inclusive epistemic rationality and endorsement which illustrates how this can be accomplished. (shrink)

This paper compares the epistemological conception of Isaac Levi with mine. We are joined in both giving a constructive answer to the relation of belief and probability, without reducing one to the other. However, our constructions differ in at least nine more or less important ways, all discussed in the paper. In particular, the paper explains the similarities and differences of Shackle's functions of potential surprise, as used by Levi, and my ranking functions in formal as well as in philosophical (...) respects. The appendix explains how ranking and probability theory can be combined in the notion of a ranked probability measure (or probabilified ranking function). (shrink)

I argue that believing that p implies having a credence of 1 in p. This is true because the belief that p involves representing p as being the case, representing p as being the case involves not allowing for the possibility of not-p, while having a credence that’s greater than 0 in not-p involves regarding not-p as a possibility.

It is argued that indicative conditionals are best viewed as having truth conditions (and so they are in part factual) but that these truth conditions are ‘gappy’ which leaves an explanatory gap that can only be filled by epistemic considerations (and so indicative conditionals are in part epistemic). This dual nature of indicative conditionals gives reason to rethink the relationship between logic viewed as a descriptive discipline (focusing on semantics) and logic viewed as a discipline with a normative import (focusing (...) on epistemic notions such as ‘reasoning’, ‘beliefs’ and ‘assumptions’). In particular, it is argued that the development of formal models for epistemic states can serve as a starting point for exploring logic when viewed as a normative discipline. (shrink)

This paper considers two novel Bayesian responses to a well-known skeptical paradox. The paradox consists of three intuitions: first, given appropriate sense experience, we have justification for accepting the relevant proposition about the external world; second, we have justification for expanding the body of accepted propositions through known entailment; third, we do not have justification for accepting that we are not disembodied souls in an immaterial world deceived by an evil demon. The first response we consider rejects the third intuition (...) and proposes an explanation of why we have a faulty intuition. The second response, which we favor, accommodates all three intuitions; it reconciles the first and the third intuition by the dual component model of justification, and defends the second intuition by distinguishing two principles of epistemic closure. (shrink)

Unspecific evidence calls for imprecise credence. My aim is to vindicate this thought. First, I will pin down what it is that makes one's imprecise credences more or less epistemically valuable. Then I will use this account of epistemic value to delineate a class of reasonable epistemic scoring rules for imprecise credences. Finally, I will show that if we plump for one of these scoring rules as our measure of epistemic value or utility, then a popular family of decision rules (...) recommends imprecise credences. In particular, a range of Hurwicz criteria, which generalise the Maximin decision rule, recommend imprecise credences. If correct, the moral is this: an agent who adopts precise credences, rather than imprecise ones, in the face of unspecific and incomplete evidence, goes wrong by gambling with the epistemic utility of her doxastic state in too risky a fashion. Precise credences represent an overly risky epistemic bet, according to the Hurwicz criteria. (shrink)

It is tempting to posit an intimate relationship between belief and assertion. The speech act of assertion seems like a way of transferring the speaker’s belief to his or her audience. If this is right, then you might think that the evidential warrant required for asserting a proposition is just the same as the warrant for believing it. We call this thesis entitlement equality. We argue here that entitlement equality is false, because our everyday notion of belief is unambiguously a (...) weak one. Believing something is true, we argue, is compatible with having relatively little confidence in it. Asserting something requires something closer to complete confidence. Specifically, we argue that believing a proposition merely requires thinking it likely, but that thinking that a proposition is likely does not entitle one to assert it. This conclusion conflict with a standard view that ‘full belief’ is the central commonsense non-factive attitude. (shrink)

This book is a sustained defense of the compatibility of the presence of idealizations in the sciences and scientific realism. So, the book is essentially a detailed response to the infamous arguments raised by Nancy Cartwright to the effect that idealization and scientific realism are incompatible.

The paper deals mainly with two problems in the epistemology of Frank Plumpton Ramsey. One concerns his account of knowledge, the other his fallibilism. I argue that Ramsey failed to make room for the social aspect of knowledge and, furthermore, that he did not separate the fallibility of our view from its corrigibility. My positive proposal is to combine social reliabilism and corrigibilism with a rejection of fallibilism.

Starting from the sixties of the past century theory change has become a main concern of philosophy of science. Two of the best known formal accounts of theory change are the post-Popperian theories of verisimilitude (PPV for short) and the AGM theory of belief change (AGM for short). In this paper, we will investigate the conceptual relations between PPV and AGM and, in particular, we will ask whether the AGM rules for theory change are effective means for approaching the truth, (...) i.e., for achieving the cognitive aim of science pointed out by PPV. First, the key ideas of PPV and AGM and their application to a particular kind of propositional theories - the so called "conjunctive propositions" - will be illustrated. Afterwards, we will prove that, as far as conjunctive propositions are concerned, AGM belief change is an effective tool for approaching the truth. (shrink)

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. (shrink)

We present a decision-theoretically motivated notion of contraction which, we claim, encodes the principles of minimal change and entrenchment. Contraction is seen as an operation whose goal is to minimize loses of informational value. The operation is also compatible with the principle that in contracting A one should preserve the sentences better entrenched than A (when the belief set contains A). Even when the principle of minimal change and the latter motivation for entrenchment figure prominently among the basic intuitions in (...) the works of, among others, Quine and Ullian (1978), Levi (1980, 1991), Harman (1988) and Gärdenfors (1988), formal accounts of belief change (AGM, KM – see Gärdenfors (1988); Katsuno and Mendelzon (1991)) have abandoned both principles (see Rott (2000)). We argue for the principles and we show how to construct a contraction operation, which obeys both. An axiom system is proposed. We also prove that the decision-theoretic notion of contraction can be completely characterized in terms of the given axioms. Proving this type of completeness result is a well-known open problem in the field, whose solution requires employing both decision-theoretical techniques and logical methods recently used in belief change. (shrink)

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. (shrink)

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. (shrink)

This chapter presents a new semantics for inductive empirical knowledge. The epistemic agent is represented concretely as a learner who processes new inputs through time and who forms new beliefs from those inputs by means of a concrete, computable learning program. The agent’s belief state is represented hyper-intensionally as a set of time-indexed sentences. Knowledge is interpreted as avoidance of error in the limit and as having converged to true belief from the present time onward. Familiar topics are re-examined within (...) the semantics, such as inductive skepticism, the logic of discovery, Duhem’s problem, the articulation of theories by auxiliary hypotheses, the role of serendipity in scientific knowledge, Fitch’s paradox, deductive closure of knowability, whether one can know inductively that one knows inductively, whether one can know inductively that one does not know inductively, and whether expert instruction can spread common inductive knowledge—as opposed to mere, true belief—through a community of gullible pupils. (shrink)

Sven-Ove Hansson and Erik Olsson studied in Hansson and Olsson, 103–119 1995) the logical properties of an operation of contraction first proposed by Isaac Levi in Levi. They provided a completeness result for the simplest version of contraction that they call Levi-contraction but left open the problem of characterizing axiomatically the more complex operation of value-based contraction or saturatable contraction. In this paper we propose an axiomatization for this operation and prove a completeness result for it. We argue that the (...) resulting operation is better behaved than various rival operations of contraction defined in recent years. (shrink)

Given the role consensus is supposed to play in the social aspects of inquiry and deliberation, it is important that we may always identify a consensus as the basis of joint inquiry and deliberation. However, it turns out that if we think of an agent revising her beliefs to reach a consensus, then, on the received view of belief revision, AGM belief revision theory, certain simple and compelling consensus positions are not always available.

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. (shrink)

I. Levi has advocated a decision-theoretic account of belief revision. We argue that the game-theoretic framework of Interrogative Inquiry Games, proposed by J. Hintikka, can extend and clarify this account. We show that some strategic use of the game rules generate Expansions, Contractions and Revisions, and we give representation results. We then extend the framework to represent explicitly sources of answers, and apply it to discuss the Recovery Postulate. We conclude with some remarks about the potential extensions of interrogative games, (...) with respect to some issues in the theory of belief change. (shrink)

In this paper I critically examine the notion of explanation used in Artificial Intelligence in general, and in the theory of belief revision in particular. I focus on two of the best known accounts in the literature: Pagnucco’s abductive expansion functions and Gärdenfors’ counterfactual analysis. I argue that both accounts are at odds with the way in which this notion has historically been understood in philosophy. They are also at odds with the explanatory strategies used in actual scientific practice. At (...) the end of the paper I outline the desiderata for an epistemologically motivated, scientifically informed belief revision model for explanation. (shrink)

This paper is concerned with the role of rational belief change theory in the philosophical understanding of experimental error. Today, philosophers seek insight about error in the investigation of specific experiments, rather than in general theories. Nevertheless, rational belief change theory adds to our understanding of just such cases: R. A. Fisher’s criticism of Mendel’s experiments being a case in point. After an historical introduction, the main part of this paper investigates Fisher’s paper from the point of view of rational (...) belief change theory: what changes of belief about Mendel’s experiment does Fisher go through and with what justification. It leads to surprising insights about what Fisher had done right and wrong, and, more generally, about the limits of statistical methods in detecting error. (shrink)

One goal of normative multi-agent system theory is to formulate principles for normative system change that maintain the rule-like structure of norms and preserve links between norms and individual agent obligations. A central question raised by this problem is whether there is a framework for norm change that is at once specific enough to capture this rule-like behavior of norms, yet general enough to support a full battery of norm and obligation change operators. In this paper we propose an answer (...) to this question by developing a bimodal logic for norms and obligations called NO. A key to our approach is that norms are treated as propositional formulas, and we provide some independent reasons for adopting this stance. Then we define norm change operations for a wide class of modal systems, including the class of NO systems, by constructing a class of modal revision operators that satisfy all the AGM postulates for revision, and constructing a class of modal contraction operators that satisfy all the AGM postulates for contraction. More generally, our approach yields an easily extendable framework within which to work out principles for a theory of normative system change. (shrink)

Belief revision from the point of view of doxastic logic. Logic Journal of the IGPL, 3(4), 535–553. Segerberg, K. (1995). Conditional action. In G. Crocco, L. Fariñas, & A. Herzig (Eds.), Conditionals: From philosophy to computer science, Studies ...

Prioritized bases, i.e., weakly ordered sets of sentences, have been used for specifying an agent’s ‘basic’ or ‘explicit’ beliefs, or alternatively for compactly encoding an agent’s belief state without the claim that the elements of a base are in any sense basic. This paper focuses on the second interpretation and shows how a shifting of priorities in prioritized bases can be used for a simple, constructive and intuitive way of representing a large variety of methods for the change of belief (...) states—methods that have usually been characterized semantically by a system-of-spheres modeling. Among the methods represented are ‘radical’, ‘conservative’ and ‘moderate’ revision, ‘revision by comparison’ in its raising and lowering variants, as well as various constructions for belief expansion and contraction. Importantly, none of these methods makes any use of numbers. (shrink)

By replacement is meant an operation that replaces one sentence by another in a belief set. Replacement can be used as a kind of Sheffer stroke for belief change, since contraction, revision, and expansion can all be defined in terms of it. Replacement can also be defined either in terms of contraction or in terms of revision. Close connections are shown to hold between axioms for replacement and axioms for contraction and revision. Partial meet replacement is axiomatically characterized. It is (...) shown that this operation can have outcomes that are not obtainable through either partial meet contraction or partial meet revision. (shrink)

In the paper "On the role of the research agenda in epistemic change", Olsson and Westlund have suggested that the notion of epistemic state employed in the standard framework of belief revision (Alchourrón et al. 1985; Gärdenfors 1988) should be extended to include a representation of the agent's research agenda (Olsson and Westlund 2006). The resulting framework will here be referred to as interrogative belief revision. In this paper, I attempt to deal with the problem of how research agendas should (...) change in contraction, a problem largely left open by Olsson and Westlund. Two desiderata of an appropriate solution are suggested: one is a principle of continuity, stating that changes in the research agenda should somehow reflect that certain long term research interests are kept fixed. The other desideratum, which is based on part of Olsson and Westlund's motivation for adding research agendas to the epistemic states, is that we should be able to account for how contraction may serve to open up new, fruitful hypotheses for investigation. In order to achieve these desiderata, I base my solution on a revised version of Olsson and Westlund's notion of epistemic state. (shrink)

This paper seeks to defend the following conclusions: The program advanced by Carnap and other necessarians for probability logic has little to recommend it except for one important point. Credal probability judgments ought to be adapted to changes in evidence or states of full belief in a principled manner in conformity with the inquirer’s confirmational commitments—except when the inquirer has good reason to modify his or her confirmational commitment. Probability logic ought to spell out the constraints on rationally coherent confirmational (...) commitments. In the case where credal judgments are numerically determinate confirmational commitments correspond to Carnap’s credibility functions mathematically represented by so—called confirmation functions. Serious investigation of the conditions under which confirmational commitments should be changed ought to be a prime target for critical reflection. The necessarians were mistaken in thinking that confirmational commitments are immune to legitimate modification altogether. But their personalist or subjectivist critics went too far in suggesting that we might dispense with confirmational commitments. There is room for serious reflection on conditions under which changes in confirmational commitments may be brought under critical control. Undertaking such reflection need not become embroiled in the anti inductivism that has characterized the work of Popper, Carnap and Jeffrey and narrowed the focus of students of logical and methodological issues pertaining to inquiry. (shrink)

This is a brief review of issues over which Henry Kyburg and I differed concerning the requirement that full beliefs should be closed under deductive consequence.

This volume is a collation of original contributions from the key actors of a new trend in the contemporary theory of knowledge and belief, that we call “dynamic epistemology”. It brings the works of these researchers under a single umbrella by highlighting the coherence of their current themes, and by establishing connections between topics that, up until now, have been investigated independently. It also illustrates how the new analytical toolbox unveils questions about the theory of knowledge, belief, preference, action, and (...) rationality, in a number of central axes in dynamic epistemology: temporal, social, probabilistic and even deontic dynamics. (shrink)

This book illustrates the program of Logical-Informational Dynamics. Rational agents exploit the information available in the world in delicate ways, adopt a wide range of epistemic attitudes, and in that process, constantly change the world itself. Logical-Informational Dynamics is about logical systems putting such activities at center stage, focusing on the events by which we acquire information and change attitudes. Its contributions show many current logics of information and change at work, often in multi-agent settings where social behavior is essential, (...) and often stressing Johan van Benthem's pioneering work in establishing this program. However, this is not a Festschrift, but a rich tapestry for a field with a wealth of strands of its own. The reader will see the state of the art in such topics as information update, belief change, preference, learning over time, and strategic interaction in games. Moreover, no tight boundary has been enforced, and some chapters add more general mathematical or philosophical foundations or links to current trends in computer science. The theme of this book lies at the interface of many disciplines. Logic is the main methodology, but the various chapters cross easily between mathematics, computer science, philosophy, linguistics, cognitive and social sciences, while also ranging from pure theory to empirical work. Accordingly, the authors of this book represent a wide variety of original thinkers from different research communities. And their interconnected themes challenge at the same time how we think of logic, philosophy and computation. Thus, very much in line with van Benthem's work over many decades, the volume shows how all these disciplines form a natural unity in the perspective of dynamic logicians (broadly conceived) exploring their new themes today. And at the same time, in doing so, it offers a broader conception of logic with a certain grandeur, moving its horizons beyond the traditional study of consequence relations. (shrink)

The paper suggests a way of modeling belief changes within the tradition of formal belief revision theories. The present model extends the scope of traditional proposals, such as AGM, so as to take care of “structural belief changes” – a type of radical shifts that is best illustrated with, but not limited to, instances of scientific discovery; we obtain AGM expansions and contractions as limiting cases. The representation strategy relies on a non-standard use of a semantic machinery. More precisely, the (...) model seeks to correlate knowledge states with interpretations of a given formal language L, in such a way that the epistemic state of an agent at a given time gives rise to a picture of how things could be, if there weren’t anything else to know. Interpretations of L proceed along supervaluational ideas; hence, the model as a whole can be seen as a particular application of supervaluational semantics to epistemic matters. (shrink)

An important trend in contemporary epistemology centers on elaborating an old idea of pragmatist pedigree: theory selection (and in general the process of changing view and fixing beliefs) presupposes epistemic values. This article focuses on analyzing the case where epistemic values are indeterminate or when the sources of valuation are multiple (epistemic values like coherence and simplicity need not order options in compatible ways). According to the theory that thus arises epistemic alternatives need not be fully ordered by an underlying (...) notion of information-value and therefore the usual economic techniques of optimization cannot be applied in order to compute optimal contractions. But in cases of this sort it is still rational to maximize, i.e. to deem an option as choosable when it is not known to be worse that any other. We present here basic results about a notion of liberal contraction based on maximizing quasi-orderings. This requires the previous solution of some open problems in the theory of rational choice functions, namely a full characterization of choice functions rationalizable in terms of maximization of quasi-transitive relations. We conclude by discussing the problem of what is the adequate feasible set for calculating maximizing solutions for contraction problems and by considering the epistemological roots of some counterexamples against the most fundamental axioms on choice functions (like α). While the first part of the paper shows how economic insights can be used to improve our understanding of the principles of belief formation and change, this final section reverses this strategy by showing the utility of epistemological insights and techniques for providing invariance conditions capable of regulating the applicability of the pure principles of choice. (shrink)

In an earlier paper [Rational choice and AGM belief revision, _Artificial Intelligence_, 2009] a correspondence was established between the set-theoretic structures of revealed-preference theory (developed in economics) and the syntactic belief revision functions of the AGM theory (developed in philosophy and computer science). In this paper we extend the re-interpretation of those structures in terms of one-shot belief revision by relating them to the trichotomous attitude towards information studied in Garapa (Rev Symb Logic, 1–21, 2020) where information may be either (...) (1) fully accepted or (2) rejected or (3) taken seriously but not fully accepted. We begin by introducing the syntactic notion of _filtered belief revision_ and providing a characterization of it in terms of a mixture of both AGM revision and contraction. We then establish a correspondence between the proposed notion of filtered belief revision and the above-mentioned set-theoretic structures, interpreted as semantic _partial_ belief revision structures. We also provide an interpretation of the trichotomous attitude towards information in terms of the degree of implausibility of the information. (shrink)