In this paper it is argued that, in order to solve the problem of iterated belief change, both the belief state and its input should be represented as epistemic entrenchment (EE) relations. A belief revision operation is constructed that updates a given EE relation to a new one in light of an evidential EE relation. It is shown that the operation in question satisfies generalized versions of the Gärdenfors revision postulates. The account offered is motivated by Spohn's ordinal conditionalization functions, (...) and can be seen as the Jeffrization of a proposal considered by Rott. (shrink)

We propose a formal theory built upon an abstract argumentation framework for handling argumentation dynamics. To that end, we analyze the acceptability dynamics of arguments through the proposal of two different kinds of sets of arguments which are somehow responsible for the acceptability/rejection of a given argument. We develop a study of the consequences of breaking the construction of such sets towards the acceptance of an analyzed argument. This brings about the proposal of a novel change operation which allows to (...) determine which arguments should be removed from the framework so that another particular argument becomes accepted. Finally, the proposed model is formalized in the light of the theory of belief revision by characterizing the corresponding operations through constructive definition and an axiomatic characterization, connecting them through the corresponding representation theorem. The theoretical proposal constitutes the fundamentals for a system implementation in many dynamic domains of application. In particular, we show its application for handling the dynamics of legal interpretation. In that sense, this proposal constitutes a fundamental approach and theoretical justification to handle the dynamics of legal arguments through changes of interpretative canons. We show a possible concretisation of our abstract theory for the legal domain by analysing a real legal case from the Argentinean jurisprudence. Such a system would be capable of suggesting alternative critical points in the current state of affairs of a legal case towards pursuing a specific goal for which the case is being investigated. (shrink)

Epistemic entrenchment, as presented by Gärdenfors and Makinson (1988) and Gärdenfors (1988), is a formalisation of the intuition that, when forced to choose between two beliefs, an agent will giveup the less entrenched one. While their formalisation satisfactorilycaptures the intuitive notion of the entrenchment of beliefs in a number ofaspects, the requirement that all wffs be comparable has drawn criticismfrom various quarters. We define a set of refined versions of theirentrenchment orderings that are not subject to the same criticism, andinvestigate (...) the relationship between the refined entrenched orderings,the entrenchment orderings of Gärdenfors and Makinson, and AGM theorycontraction (Alchourrón et al., 1985). To conclude, we compare refinedentrenchment with two related approaches to epistemic entrenchment. (shrink)

Generalisations of theory change involving operations on arbitrary sets ofwffs instead of on belief sets (i.e., sets closed under a consequencerelation), have become known as base change. In one view, a base should bethought of as providing more structure to its generated belief set, whichmeans that it can be employed to determine the theory contraction operationassociated with a base contraction operation. In this paper we follow suchan approach as the first step in defining infobase change. We think of an infobase (...) as a finite set of wffs consisting of independently obtainedbits of information. Taking AGM theory change (Alchourrón et al. 1985) as the general framework, we present a method that uses the structure of aninfobase B to obtain an AGM theory contraction operation for contractingthe belief set Cn(B). Both the infobase and the obtained theory contraction operation then play a role in constructing a unique infobasecontraction operation. Infobase revision is defined in terms of an analogueof the Levi Identity, and it is shown that the associated theory revisionoperation satisfies the AGM postulates for revision. Because every infobaseis associated with a unique infobase contraction and revision operation, the method also allows for iterated base change. (shrink)

We show in this paper that some expressions indicating source of evidence are part of propositional content and are best analyzed as special kind of epistemic modal. Our evidence comes from the Japanese evidential system. We consider six evidentials in Japanese, showing that they can be embedded in conditionals and under modals and that their properties with respect to modal subordination are similar to those of ordinary modals. We show that these facts are difficult for existing theories of evidentials, which (...) assign evidentials necessarily widest scope, to explain. We then provide an analysis using a logical system designed to account for evidential reasoning; this logic is the first developed system of probabilistic dynamic predicate logic. This analysis is shown to account for the data we provide that is problematic for other theories. (shrink)

Ockham’s razor is the principle that, all other things being equal, scientists ought to prefer simpler theories. In recent years, philosophers have argued that simpler theories make better predictions, possess theoretical virtues like explanatory power, and have other pragmatic virtues like computational tractability. However, such arguments fail to explain how and why a preference for simplicity can help one find true theories in scientific inquiry, unless one already assumes that the truth is simple. One new solution to that problem is (...) the Ockham efficiency theorem, which states that scientists who heed Ockham’s razor retract their opinions less often and sooner than do their non-Ockham competitors. The theorem neglects, however, to consider competitors following random strategies and in many applications random strategies are known to achieve better worst-case loss than deterministic strategies. In this paper, we describe two ways to extend the result to a very general class of random, empirical strategies. The first extension concerns expected retractions, retraction times, and errors and the second extension concerns retractions in chance, times of retractions in chance, and chances of errors. (shrink)

We introduce a new operator – belief fusion– which aggregates the beliefs of two agents, each informed by a subset of sources ranked by reliability. In the process we definepedigreed belief states, which enrich standard belief states with the source of each piece of information. We note that the fusion operator satisfies the invariants of idempotence, associativity, and commutativity. As a result, it can be iterated without difficulty. We also define belief diffusion; whereas fusion generally produces a belief state with (...) more information than is possessed by either of its two arguments, diffusion produces a state with less information. Fusion and diffusion are symmetric operators, and together define a distributive lattice. Finally, we show that AGM revision can be viewed as fusion between a novice and an expert. (shrink)

The extent to which belief revision is affected by systematic variability and direct experience of a conditional (if A then B) relation was examined in two studies. The first used a computer generated apparatus. This presented two rows of 5 objects. Pressing one of the top objects resulted in one of the bottom objects being lit up. The 139 adult participants were given one of two levels of experience (5 or 15 trials) and one of two types of apparatus. One (...) of these was completely uniform, while the other had an element that randomly alternated in its result. Following the testing of the apparatus, participants were asked to rate their certainty of the action of the middle element, which was always uniform (the AB belief). Then they were told of an observation inconsistent with this belief. Participants were then asked whether they considered the AB belief or the anecdotal observation to be more believable. Results showed that increased experience decreased the tendency to reject the AB belief, when the apparatus did not have any randomness. However, the presence of a single element showing random variation in the system strongly increased rejection of this belief. A second study looked at the effect of a single random element on a mechanical system as well as an electronic system using graphical representations. This confirmed the generality of the effect of randomness on belief revision, and provided support for the effects of embedding a belief into a system of relations. These results provide some insight into the complex factors that determine belief revision. (shrink)

A model of inductive inquiry is defined within a first-order context. Intuitively, the model pictures inquiry as a game between Nature and a scientist. To begin the game, a nonlogical vocabulary is agreed upon by the two players along with a partition of a class of structures for that vocabulary. Next, Nature secretly chooses one structure ("the real world") from some cell of the partition. She then presents the scientist with a sequence of atomic facts about the chosen structure. With (...) each new datum the scientist announces a guess about the cell to which the chosen structure belongs. To succeed in his inquiry, the scientist's successive conjectures must be correct all but finitely often, that is, the conjectures must converge in the limit to the correct cell. A special kind of scientist selects his hypotheses on the basis of a belief revision operator. We show that reliance on belief revision allows scientists to solve a wide class of problems. (shrink)

Scientific inquiry is represented as a process of rational hypothesis revision in the face of data. For the concept of rationality, we rely on the theory of belief dynamics as developed in [5, 9]. Among other things, it is shown that if belief states are left unclosed under deductive logic then scientific theories can be expanded in a uniform, consistent fashion that allows inquiry to proceed by any method of hypothesis revision based on “kernel” contraction. In contrast, if belief states (...) are closed under logic, then no such expansion is possible. (shrink)

We explore ways in which purely qualitative belief change in the AGM tradition throws light on options in the treatment of conditional probability. First, by helping see why it can be useful to go beyond the ratio rule defining conditional from one-place probability. Second, by clarifying what is at stake in different ways of doing that. Third, by suggesting novel forms of conditional probability corresponding to familiar variants of qualitative belief change, and conversely. Likewise, we explain how recent work on (...) the qualitative part of probabilistic inference leads to a very broad class of 'proto-probability' functions. (shrink)

Confirmation is commonly identified with positive relevance, E being said to confirm H if and only if E increases the probability of H. Today, analyses of this general kind are usually Bayesian ones that take the relevant probabilities to be subjective. I argue that these subjective Bayesian analyses are irremediably flawed. In their place I propose a relevance analysis that makes confirmation objective and which, I show, avoids the flaws of the subjective analyses. What I am proposing is in some (...) ways a return to Carnap's conception of confirmation, though there are also important differences between my analysis and his. My analysis includes new accounts of what evidence is and of the indexicality of confirmation claims. Finally, I defend my analysis against Achinstein's criticisms of the relevance concept of confirmation. (shrink)

ABSTRACT We consider evolution of knowledge bases caused by a sequence of basic steps of acquisition of a new information, either consistent or inconsistent with the original system. To make this process comply with the Principe of Minimal Change, a special evidence metric is introduced for measuring distance between states of knowledge. Then a novel semantics of knowledge bases is developed suggested by the heuristics of weighted maximally consistent subsets. The latter is efficiently applied to the processes of consistent and (...) inconsistent acquisition of knowledge, belief revision and contraction. (shrink)

Science depends on judgments of the bearing of evidence on theory. Scientists must judge whether an observation or the result of an experiment supports, disconfirms, or is simply irrelevant to a given hypothesis. Similarly, scientists may judge that, given all the available evidence, a hypothesis ought to be accepted as correct or nearly so, rejected as false, or neither. Occasionally, these evidential judgments can be made on deductive grounds. If an experimental result strictly contradicts a hypothesis, then the truth of (...) the data deductively entails the falsity of the hypothesis. In the great majority of cases, however, the connection between evidence and hypothesis is non-demonstrative, or inductive. In particular, this is so whenever a general hypothesis is inferred to be correct on the basis of the available data, since the truth of the data will not deductively entail the truth of the hypothesis. It always remains possible that the hypothesis is false even though the data are correct. (shrink)

The theories of belief change developed within the AGM-tradition are not logics in the proper sense, but rather informal axiomatic theories of belief change. Instead of characterizing the models of belief and belief change in a formalized object language, the AGM-approach uses a natural language — ordinary mathematical English — to characterize the mathematical structures that are under study. Recently, however, various authors such as Johan van Benthem and Maarten de Rijke have suggested representing doxastic change within a formal logical (...) language: a dynamic modal logic. Inspired by these suggestions Krister Segerberg has developed a very general logical framework for reasoning about doxastic change: dynamic doxastic logic (DDL). This framework may be seen as an extension of standard Hintikka-style doxastic logic with dynamic operators representing various kinds of transformations of the agent's doxastic state. Basic DDL describes an agent that has opinions about the external world and an ability to change these opinions in the light of new information. Such an agent is non-introspective in the sense that he lacks opinions about his own belief states. Here we are going to discuss various possibilities for developing a dynamic doxastic logic for introspective agents: full DDL or DDL unlimited. The project of constructing such a logic is faced with difficulties due to the fact that the agent’s own doxastic state now becomes a part of the reality that he is trying to explore: when an introspective agent learns more about the world, then the reality he holds beliefs about undergoes a change. But then his introspective (higher-order) beliefs have to be adjusted accordingly. In the paper we shall consider various ways of solving this problem. (shrink)

Theoria, Volume 88, Issue 3, Page 494-528, June 2022.

This essay develops a joint theory of rational (all-or-nothing) belief and degrees of belief. The theory is based on three assumptions: the logical closure of rational belief; the axioms of probability for rational degrees of belief; and the so-called Lockean thesis, in which the concepts of rational belief and rational degree of belief figure simultaneously. In spite of what is commonly believed, this essay will show that this combination of principles is satisfiable (and indeed nontrivially so) and that the principles (...) are jointly satisfied if and only if rational belief is equivalent to the assignment of a stably high rational degree of belief. Although the logical closure of belief and the Lockean thesis are attractive postulates in themselves, initially this may seem like a formal “curiosity”; however, as will be argued in the rest of the essay, a very reasonable theory of rational belief can be built around these principles that is not ad hoc and that has various philosophical features that are plausible independently. In particular, this essay shows that the theory allows for a solution to the Lottery Paradox, and it has nice applications to formal epistemology. The price that is to be paid for this theory is a strong dependency of belief on the context, where a context involves both the agent's degree of belief function and the partitioning or individuation of the underlying possibilities. But as this essay argues, that price seems to be affordable. (shrink)

We investigate the research programme of dynamic doxastic logic (DDL) and analyze its underlying methodology. The Ramsey test for conditionals is used to characterize the logical and philosophical differences between two paradigmatic systems, AGM and KGM, which we develop and compare axiomatically and semantically. The importance of Gärdenfors’s impossibility result on the Ramsey test is highlighted by a comparison with Arrow’s impossibility result on social choice. We end with an outlook on the prospects and the future of DDL.

On the basis of impossibility results on probability, belief revision, and conditionals, it is argued that conditional beliefs differ from beliefs in conditionals qua mental states. Once this is established, it will be pointed out in what sense conditional beliefs are still conditional, even though they may lack conditional contents, and why it is permissible to still regard them as beliefs, although they are not beliefs in conditionals. Along the way, the main logical, dispositional, representational, and normative properties of conditional (...) beliefs are studied, and it is explained how the failure of not distinguishing conditional beliefs from beliefs in conditionals can lead philosophical and empirical theories astray. (shrink)

This is part A of a paper in which we defend a semantics for counterfactuals which is probabilistic in the sense that the truth condition for counterfactuals refers to a probability measure. Because of its probabilistic nature, it allows a counterfactual ‘ifAthenB’ to be true even in the presence of relevant ‘Aand notB’-worlds, as long such exceptions are not too widely spread. The semantics is made precise and studied in different versions which are related to each other by representation theorems. (...) Despite its probabilistic nature, we show that the semantics and the resulting system of logic may be regarded as a naturalistically vindicated variant of David Lewis’ truth-conditional semantics and logic of counterfactuals. At the same time, the semantics overlaps in various ways with the non-truth-conditional suppositional theory for conditionals that derives from Ernest Adams’ work. We argue that counterfactuals have two kinds of pragmatic meanings and come attached with two types of degrees of acceptability or belief, one being suppositional, the other one being truth based as determined by our probabilistic semantics; these degrees could not always coincide due to a new triviality result for counterfactuals, and they should not be identified in the light of their different interpretation and pragmatic purpose. However, for plain assertability the difference between them does not matter. Hence, if the suppositional theory of counterfactuals is formulated with sufficient care, our truth-conditional theory of counterfactuals is consistent with it. The results of our investigation are used to assess a claim considered by Hawthorne and Hájek, that is, the thesis that most ordinary counterfactuals are false. (shrink)

We will present a new lottery-style paradox on counterfactuals and chance. The upshot will be: combining natural assumptions on the truth values of ordinary counterfactuals, the conditional chances of possible but non-actual events, the manner in which and relate to each other, and a fragment of the logic of counterfactuals leads to disaster. In contrast with the usual lottery-style paradoxes, logical closure under conjunction—that is, in this case, the rule of Agglomeration of counterfactuals—will not play a role in the derivation (...) and will not be entailed by our premises either. We will sketch four obvious but problematic ways out of the dilemma, and we will end up with a new resolution strategy that is non-obvious but less problematic: contextualism about what counts as a proposition. This proposal will not just save us from the paradox, it will also save each premise in at least some context, and it will be motivated by independent considerations from measure theory and probability theory. (shrink)

An article is an introductory analysis of concept of religious belief in the language of logic. In its first part, there is a comparison of the concept of religious belief with the concept of scientific belief, next part is a presentation and analysis of Bocheński’s conception of rationality of religious beliefs, and the third part of article is an attempt of analysis of Aquinas conception of faith in the light of contemporary logic.

This paper primarily deals with theconceptual prospects for generalizing the aim ofabduction from the standard one of explainingsurprising or anomalous observations to that ofempirical progress or even truth approximation. Itturns out that the main abduction task then becomesthe instrumentalist task of theory revision aiming atan empirically more successful theory, relative to theavailable data, but not necessarily compatible withthem. The rest, that is, genuine empirical progress aswell as observational, referential and theoreticaltruth approximation, is a matter of evaluation andselection, and possibly new (...) generation tasks forfurther improvement. The paper concludes with a surveyof possible points of departure, in AI and logic, forcomputational treatment of the instrumentalist taskguided by the `comparative evaluation matrix''. (shrink)

Belief revision theories standardly endorse a principle of intensionality to the effect that ideal doxastic agents do not discriminate between pieces of information that are equivalent within classical logic. I argue that this principle should be rejected. Its failure, on my view, does not require failures of logical omniscience on the part of the agent, but results from a view of the update as _mighty_: as encoding what the agent learns might be the case, as well as what must be. (...) The view is motivated by consideration of a puzzle case, obtained by transposing into the context of belief revision a kind of scenario that Kit Fine has used to argue against intensionalism about counterfactuals. Employing the framework of truthmaker semantics, I go on to develop a novel account of belief revision, based on a conception of the update as mighty, which validates natural hyperintensional counterparts of the usual AGM postulates. (shrink)

Formal models of theory contraction entered the philosophicalliterature with the prototype model by Alchourrón, Gärdenfors,and Makinson (Alchourrón et al. 1985). One influential modelinvolves theory contraction with respect to a relation calledepistemic entrenchment which orders the propositions of a theoryaccording to their relative degrees of theoretical importance.Various postulates have been suggested for characterizingepistemic entrenchment formally. I argue here that threesuggested postulates produce inappropriately bizarre results whenapplied to scientific theories. I argue that the postulates callednoncovering, continuing up, and continuing down, implyrespectively that, (...) (i) no scientific law is more epistemicallyentrenched than any of its instances, (ii) two distinct instances ofthe same scientific law must have different degrees of epistemicentrenchment, and (iii) any two scientific laws must have differentdegrees of epistemic entrenchment. I also argue that continuingup and continuing down each lead to incoherency. (shrink)

The preface paradox can be motivated by appealing to a plausible inference from an author’s reasonable assertion that her book is bound to contain errors to the author’s rational belief that her book contains errors. By evaluating and undermining the validity of this inference, I offer a resolution of the paradox. Discussions of the preface paradox have surprisingly failed to note that expressions of fallibility made in prefaces typically employ terms such as surely, undoubtedly, and bound to be. After considering (...) what these terms mean, I show that the motivating inference is invalid. Moreover, I argue that a closer consideration of our expressions of fallibility suggest that epistemically responsible authors would not be rational to believe that their books contain errors. I conclude by considering alternative expressions of fallibility that employ terms such as possible and probable, and discuss the role that expressions of fallibility play in conversation. (shrink)

The Ramseyan thesis that the probability of an indicative conditional is equal to the corresponding conditional probability of its consequent given its antecedent is both widely confirmed and subject to attested counterexamples (e.g., McGee 2000, Kaufmann 2004). This raises several puzzling questions. For instance, why are there interpretations of conditionals that violate this Ramseyan thesis in certain contexts, and why are they otherwise very rare? In this paper, I raise some challenges to Stefan Kaufmann's account of why the Ramseyan thesis (...) sometimes fails, and motivate my own theory. On my theory, the proposition expressed by an indicative conditional is partially determined by a background partition, and hence its probability depends on the choice of such a partition. I hold that this background partition is contextually determined, and in certain conditions is set by a salient question under discussion in the context. I show how the resulting theory offers compelling answers to the puzzling questions raised by failures of the Ramseyan thesis. (shrink)

This paper places formal learning theory in a broader philosophical context and provides a glimpse of what the philosophy of induction looks like from a learning-theoretic point of view. Formal learning theory is compared with other standard approaches to the philosophy of induction. Thereafter, we present some results and examples indicating its unique character and philosophical interest, with special attention to its unified perspective on inductive uncertainty and uncomputability.

I propose that empirical procedures, like computational procedures, are justified in terms of truth-finding efficiency. I contrast the idea with more standard philosophies of science and illustrate it by deriving Ockham's razor from the aim of minimizing dramatic changes of opinion en route to the truth.

Explaining the connection, if any, between simplicity and truth is among the deepest problems facing the philosophy of science, statistics, and machine learning. Say that an efficient truth finding method minimizes worst case costs en route to converging to the true answer to a theory choice problem. Let the costs considered include the number of times a false answer is selected, the number of times opinion is reversed, and the times at which the reversals occur. It is demonstrated that (1) (...) always choosing the simplest theory compatible with experience, and (2) hanging onto it while it remains simplest, is both necessary and sufficient for efficiency. †To contact the author, please write to: Department of Philosophy, Carnegie Mellon University, Baker Hall 135, Pittsburgh, PA 15213-3890; e-mail: [email protected]. (shrink)

The connection between the probabilities of conditionals and the corresponding conditional probabilities has long been explored in the philosophical literature, but its implementation faces both technical obstacles and objections on empirical grounds. In this paper I ?rst outline the motivation for the probabilistic turn and Lewis’ triviality results, which stand in the way of what would seem to be its most straightforward implementation. I then focus on Richard Jeffrey’s ’random-variable’ approach, which circumvents these problems by giving up the notion that (...) conditionals denote propositions in the usual sense. Even so, however, the random-variable approach makes counterintuitive predictions in simple cases of embedded conditionals. I propose to address this problem by enriching the model with an explicit representation of causal dependencies. The addition of such causal information not only remedies the shortcomings of Jeffrey’s conditional, but also opens up the possibility of a uni?ed probabilistic account of indicative and counterfactual conditionals. (shrink)

The rise of causality and the attendant graph-theoretic modeling tools in the study of counterfactual reasoning has had resounding effects in many areas of cognitive science, but it has thus far not permeated the mainstream in linguistic theory to a comparable degree. In this study I show that a version of the predominant framework for the formal semantic analysis of conditionals, Kratzer-style premise semantics, allows for a straightforward implementation of the crucial ideas and insights of Pearl-style causal networks. I spell (...) out the details of such an implementation, focusing especially on the notions of intervention on a network and backtracking interpretations of counterfactuals. (shrink)

This paper addresses the ongoing debate over the relation between belief and credence. A proposal is made to reverse the currently predominant order of analysis, by taking belief as conceptually basic and credence as the phenomenon to be clarified. In brief, the proposal is to explicate an agent’s credence in a proposition P as the agent’s tendency toward believing P. Platitudinous as this reduction may seem, it runs counter to all of the major positions in the debate, including the Threshold (...) View, the Certainty View as conventionally understood, Dualism, Eliminativism, as well as Credence Primitivism. Section 1 gives an overview on the current state of the debate. Section 2 considers unsuccessful predecessors of the proposed belief-first approach to credence. Section 3 motivates and lays out the basics of a conceptual framework for thinking about doxastic states that characterizes such states in terms of two formally independent dimensions, one pertaining to the agent’s tendency toward believing P, the other to the level of resilience with which the agent manifests that tendency. Against this backdrop, it is argued in Sect. 4 that the present reduction satisfies a set of standard, theoretically neutral criteria of adequacy for theories of credence, at least once they are purged of a quite common conflation of tendency and resilience. Section 5 argues against all of the above competing accounts. (shrink)

You buy a lottery ticket and you lose. You are sorry, but you wouldn't dream of complaining. Why then do you feel entitled to complain in the following sorts of cases?

If the logic of belief changes is extended to cover belief states which contain both factual and normative beliefs, it is easily shown that a change of a factual belief (an 'Is') in a mixed belief state can imply a change of a normative belief (an 'Ought') in the same state. With regard to Hume's so-called 'Is-Ought problem', this means that one has to distinguish its statics from its dynamics. When this is done, it becomes clear that changes of factual (...) beliefs can, for rational reasons, have far-reaching normative consequences. Similarly, a change of a factual belief can imply a change of a value belief. (shrink)

The Bayesian model is used in psychology as the reference for the study of dynamic probability judgment. The main limit induced by this model is that it confines the study of revision of degrees of belief to the sole situations of revision in which the universe is static (revising situations). However, it may happen that individuals have to revise their degrees of belief when the message they learn specifies a change of direction in the universe, which is considered as changing (...) with time (updating situations). We analyze the main results of the experimental literature with regard to elementary qualitative properties of these two situations of revision. First, the order effect phenomenon is confronted with the commutative property. Second, an apparent new phenomenon is presented: the redundancy effect that is confronted with the idempotence property. Finally, results obtained in this kind of experimental situations are reinterpreted in the light of pragmatic analysis. (shrink)

This paper aims to make explicit the methodological conditions that should be satisfied for the Bayesian model to be used as a normative model of human probability judgment. After noticing the lack of a clear definition of Bayesianism in the psychological literature and the lack of justification for using it, a classic definition of subjective Bayesianism is recalled, based on the following three criteria: an epistemic criterion, a static coherence criterion and a dynamic coherence criterion. Then it is shown that (...) the adoption of this framework has two kinds of implications. The first one regards the methodology of the experimental study of probability judgment. The Bayesian framework creates pragmatic constraints on the methodology that are linked to the interpretation of, and the belief in, the information presented, or referred to, by an experimenter in order for it to be the basis of a probability judgment by individual participants. It is shown that these constraints have not been satisfied in the past, and the question of whether they can be satisfied in principle is raised and answered negatively. The second kind of implications consists of two limitations in the scope of the Bayesian model. They regard (1) the background of revision (the Bayesian model considers only revising situations but not updating situations), and (2) the notorious case of the null priors. In both cases Lewis’ rule is an appropriate alternative to Bayes’ rule, but its use faces the same operational difficulties. (shrink)

For various domains in proportional reasoning cognitive development is characterized as a progression through a series of increasingly complex rules. A multiplicative relationship between two task features, such as weight and distance information of blocks placed at both sides of the fulcrum of a balance scale, appears difficult to discover. During development, children change their beliefs about the balance scale several times: from a focus on the weight dimension (Rule I) to occasionally considering the distance dimension (Rule II), guessing (Rule (...) III), and applying multiplication (Rule IV; Siegler, 1981). Because of the detailed empirical findings the balance scale task has become a benchmark task for computational models of proportional reasoning. In this article, we present a large empirical study (N = 420) of which the findings provide a challenge for computational models. The effect of feedback and the effect of individually adapted training items on rule transition were tested for children using Rule I or Rule II. Presenting adapted training items initiates belief revision for Rule I but not for Rule II. The experience of making mistakes (by providing feedback) induces a change for both Rule I and Rule II. However, a delayed posttest shows that these changes are preserved after 2 weeks only for children using Rule I. We conclude that the transition from Rule I to Rule II differs from the transition from Rule II to a more complex rule. Concerning these empirical findings, we will review performance of computational models and the implications for a future belief revision model. It is one Thing, to show a Man that he is in an Error, and another, to put him in possession of Truth. John Locke. (shrink)

Belief-credence dualism is the view that we have both beliefs and credences and neither attitude is reducible to the other. Pragmatic encroachment is the view that practical stakes can affect the epistemic rationality of states like knowledge or justified belief. In this paper, I argue that dualism offers a unique explanation of pragmatic encroachment cases. First, I explain pragmatic encroachment and what motivates it. Then, I explain dualism and outline a particular argument for dualism. Finally, I show how dualism can (...) explain the intuitions that underlie pragmatic encroachment. My basic proposal is that in high-stakes cases, it is not that one cannot rationally believe that p; instead, one ought not to rely on one's belief that p. One should rather rely on one's credence in p. I conclude that we need not commit ourselves to pragmatic encroachment in order to explain the intuitiveness of the cases that motivate it. (shrink)

A realist approach to learning is what I propose here. This is based on a non-epistemic dimension whose presence is a necessary assumption for a concept of learning of a life-world as complementary to learning within a life-world. I develop my approach in opposition to Jürgen Habermas' pragmatic approach, which seems to lack of something from a realist point of view.

– 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)

The Spohnian paradigm of ranking functions is in many respects like an order-of-magnitude reverse of subjective probability theory. Unlike probabilities, however, ranking functions are only indirectly—via a pointwise ranking function on the underlying set of possibilities W —defined on a field of propositions A over W. This research note shows under which conditions ranking functions on a field of propositions A over W and rankings on a language L are induced by pointwise ranking functions on W and the set of (...) models for L, ModL, respectively. (shrink)

This paper expounds a simple and non-trivial Ramsey Test. Drawing on the work of Peter Gärdenfors, it aims to help establish an epistemic alternative to the semantics of variably strict conditionals by Robert Stalnaker (in: Rescher (ed), Studies in logical theory, Blackwell, Oxford, 1968) and David Lewis (Counterfactuals, Blackwell, Oxford, 1973). The novelty of the present contribution lies in considering the framework of Preferred Subtheories as model of belief change upon which conditionals are defined. The resulting semantics avoids triviality in (...) the sense that a major premise of the proof of Gärdenfors’ triviality theorem is violated. (shrink)