Systematic Withdrawal

Although AGM theory contraction (Alchourrón et al., 1985; Alchourrón and Makinson, 1985) occupies a central position in the literature on belief change, there is one aspect about it that has created a fair amount of controversy. It involves the inclusion of the postulate known as Recovery. As a result, a number of alternatives to AGM theory contraction have been proposed that do not always satisfy the Recovery postulate (Levi, 1991, 1998; Hansson and Olsson, 1995; Fermé, 1998; Fermé and Rodriguez, 1998; Rott and Pagnucco, 1999). In this paper we present a new addition, systematic withdrawal, to the family of withdrawal operations, as they have become known. We define systematic withdrawal semantically, in terms of a set of preorders, and show that it can be characterised by a set of postulates. In a comparison of withdrawal operations we show that AGM contraction, systematic withdrawal and the severe withdrawal of Rott and Pagnucco (1999) are intimately connected by virtue of their definition in terms of sets of preorders. In a future paper it will be shown that this connection can be extended to include the epistemic entrenchment orderings of Gärdenfors (1988) and Gärdenfors and Makinson (1988) and the refined entrenchment orderings of Meyer et al. (2000).     

Models and lawlikeness

Do analogical models ever play an essential role in scientific explanation and confirmation, or is their role (at most) heuristic? For many years scientists and philosophers have debated this question. I argue that such models may sometimes play an essential role. My argument is based on a proposal to augment Goodman's theory of projection in order to make it easier for novel predicates (extensions) to acquire entrenchment. The heart of this proposal is the claim that analogical models may, under certain conditions, be the medium whereby entrenchment is passed from well established predicates to new and unfamiliar ones.     

Comparative Possibility in Set Contraction

In a recent article, Zhang and Foo generalized the AGM postulates for contraction to include infinite epistemic input. The new type of belief change is called set contraction. Zhang and Foo also introduced a constructive model for set contraction, called nicely ordered partition, as a generalization of epistemic entrenchment. It was shown however that the functions induced from nicely ordered partitions do not quite match the postulates for set contraction. The mismatch was fixed with the introduction of an extra condition called the limit postulate. The limit postulate establishes a connection between contraction by infinite epistemic input and contraction by finite epistemic input (reducing the former to the latter) and it is appealing both on mathematical and on conceptual grounds. It is debatable however whether the limit postulate can be adopted as a general feature of rationality in set contraction. Instead we propose that the limit postulate is viewed as a condition characterizing an important special case of set contraction functions. With this reading in mind, in this article we introduce an alternative generalization of epistemic entrenchment, based on the notion of comparative possibility. We prove that the functions induced from comparative possibility preorders precisely match those satisfying the postulates for set contraction (without the limit postulate). The relationship between comparative possibility and epistemic entrenchment is also investigated. Finally, we formulate necessary and sufficient conditions under which the functions induced from comparative possibility preorders coincide with the special class of contraction functions characterized by the limit postulate.     

Basic Entrenchment

In contrast to other prominent models of belief change, models based on epistemic entrenchment have up to now been applicable only in the context of very strong packages of requirements for belief revision. This paper decomposes the axiomatization of entrenchment into independent modules. Among other things it is shown how belief revision satisfying only the ‘basic’ postulates of Alchourrón, Gärdenfors and Makinson can be represented in terms of entrenchment.     

Reversing the Levi identity

The AGM (Alchourrón-GÄrdenfors-Makinson) model of belief change is extended to cover changes on sets of beliefs that arenot closed under logical consequence (belief bases). Three major types of change operations, namely contraction, internal revision, and external revision are axiomatically characterized, and their interrelations are studied. In external revision, the Levi identity is reversed in the sense that onefirst adds the new belief to the belief base, and afterwards contracts its negation. It is argued that external revision represents an intuitively plausible way of revising one's beliefs. Since it typically involves the temporary acceptance of an inconsistent set of beliefs, it can only be used in belief representations that distinguish between different inconsistent sets of belief.     

Preference-based belief revision for rule-based agents

Agents which perform inferences on the basis of unreliable information need an ability to revise their beliefs if they discover an inconsistency. Such a belief revision algorithm ideally should be rational, should respect any preference ordering over the agent’s beliefs (removing less preferred beliefs where possible) and should be fast. However, while standard approaches to rational belief revision for classical reasoners allow preferences to be taken into account, they typically have quite high complexity. In this paper, we consider belief revision for agents which reason in a simpler logic than full first-order logic, namely rule-based reasoners. We show that it is possible to define a contraction operation for rule-based reasoners, which we call McAllester contraction, which satisfies all the basic Alchourrón, Gärdenfors and Makinson (AGM) postulates for contraction (apart from the recovery postulate) and at the same time can be computed in polynomial time. We prove a representation theorem for McAllester contraction with respect to the basic AGM postulates (minus recovery), and two additional postulates. We then show that our contraction operation removes a set of beliefs which is least preferred, with respect to a natural interpretation of preference. Finally, we show how McAllester contraction can be used to define a revision operation which is also polynomial time, and prove a representation theorem for the revision operation.     

New Foundations for a Relational Theory of Theory-revision

AGM-theory, named after its founders Carlos Alchourrón, Peter Gärdenfors and David Makinson, is the leading contemporary paradigm in the theory of belief-revision. The theory is reformulated here so as to deal with the central relational notions ‘J is a contraction of K with respect to A’ and ‘J is a revision of K with respect to A’. The new theory is based on a principal-case analysis of the domains of definition of the three main kinds of theory-change (expansion, contraction and revision). The new theory is stated by means of introduction and elimination rules for the relational notions. In this new setting one can re-examine the relationship between contraction and revision, using the appropriate versions of the so-called Levi and Harper identities. Among the positive results are the following. One can derive the extensionality of contraction and revision, rather than merely postulating it. Moreover, one can demonstrate the existence of revision-functions satisfying a principle of monotonicity. The full set of AGM-postulates for revision-functions allow for completely bizarre revisions. This motivates a Principle of Minimal Bloating, which needs to be stated as a separate postulate for revision. Moreover, contractions obtained in the usual way from the bizarre revisions, by using the Harper identity, satisfy Recovery. This provides a new reason (in addition to several others already adduced in the literature) for thinking that the contraction postulate of Recovery fails to capture the Principle of Minimal Mutilation. So the search is still on for a proper explication of the notion of minimal mutilation, to do service in both the theory of contraction and the theory of revision. The new relational formulation of AGM-theory, based on principal-case analysis, shares with the original, functional form of AGM-theory the idealizing assumption that the belief-sets of rational agents are to be modelled as consistent, logically closed sets of sentences. The upshot of the results presented here is that the new relational theory does a better job of making important matters clear than does the original functional theory. A new setting has been provided within which one can profitably address two pressing questions for AGM-theory: (1) how is the notion of minimal mutilation (by both contractions and revisions) best analyzed? and (2) how is one to rule out unnecessary bloating by revisions?     

Common Law Approaches to the Relationship Between Law and Morality

How are general relations of law and morality typically conceived in an environment of Anglo-saxon common law? This paper considers some classical common law methods and traditions as these have confronted and been overlaid with modern ideas of legal positivism. While classical common law treated a community and its morality as the cultural foundation of law, legal positivism's analytical separation of law and morals, allied with liberal approaches to legal regulation, have made the relationship of legal and moral principles more complex and contested. Using ideas from Durkheim's and Weber's sociology, I argue that the traditional common law emphasis on an inductive, empirical treatment of moral practices has continuing merit, but in contemporary conditions the vague idea of community embedded in classical common law thought must be replaced with a much more precise conceptualisation of coexisting communities, whose moral bonds are diverse and require a corresponding diversity of forms of legal recognition or protection.     

Against Teleological Essentialism

In two recent papers, Rose and Nichols present evidence in favor of the view that humans represent category essences in terms of a telos, such as honey-making, and not in terms of scientific essences, such as bee DNA. Here, I challenge their interpretation of the evidence and show that it is directly predicted by the main theory they seek to undermine. I argue that their results can be explained as instances of diagnostic reasoning about scientific essences.     

Briggs on antirealist accounts of scientific law

Rachel Briggs’ critique of “antirealist” accounts of scientific law— including my own perspectivalist best-system account—is part of a project meant to show that Humean conceptions of scientific law are more problematic than has been commonly realized. Indeed, her argument provides a new challenge to the Humean, a thoroughly epistemic version of David Lewis’ “big, bad bug” for Humeanism. Still, I will argue, the antirealist (perspectivalist and expressivist) accounts she criticizes have the resources to withstand the challenge and come out stronger for it. Attention to epistemic possibilities, I argue, shows a number of advantages to a perspectivalist account of scientific law.     

Underdetermination,realism and empirical equivalence

Are theories ‘underdetermined by the evidence’ in any way that should worry the scientific realist? I argue that no convincing reason has been given for thinking so. A crucial distinction is drawn between data equivalence and empirical equivalence. Duhem showed that it is always possible to produce a data equivalent rival to any accepted scientific theory. But there is no reason to regard such a rival as equally well empirically supported and hence no threat to realism. Two theories are empirically equivalent if they share all consequences expressed in purely observational vocabulary. This is a much stronger requirement than has hitherto been recognised—two such ‘rival’ theories must in fact agree on many claims that are clearly theoretical in nature. Given this, it is unclear how much of an impact on realism a demonstration that there is always an empirically equivalent ‘rival’ to any accepted theory would have—even if such a demonstration could be produced. Certainly in the case of the version of realism that I defend—structural realism—such a demonstration would have precisely no impact: two empirically equivalent theories are, according to structural realism, cognitively indistinguishable.     

Contraction: On the Decision-Theoretical Origins of Minimal Change and Entrenchment

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.     

On relevance and justification of legal decisions

The author discusses a question related to a certain aspect of justification of legal decisions, often so-called internal justification-a legal decision is internally justified if and only if it can be deduced from the norm(s) applicable to the case, and from the statement(s) describing the facts of the case. According to this notion, infinite irrelevant logical consequences are justified. To avoid this counterintuitive conclusion, the author analyzes three notions of relevance: Sperber-Wilson's notion, Anderson-Belnap's notion, and Schurz's notion. The author presents a reconstruction of the notion of relevance very close to Schurz's notion, extended to make it suitable to the particular characteristics of deontic logic. Finally, this notion of relevance is used to discuss some aspects of the concept of normative system, conceived as a deductive system, that is, a system containing all its logical consequences.I am indebted to C. Alchourrón, E. Bulygin, R. Caracciolo, R. Hernández Marín, P. Navarro, J. Raz, C. Redondo and two referees of this journal for helpful comments and suggestions.     

The inconceivability of zombies

I argue for the claim that if Lewis’s regularity theory of laws were true, we could not know any positive law statement to be true. Premise 1: According to that theory, for any law statement true of the actual world, there is always a nearby world where the law statement is false (a world that differs with respect to one matter of particular fact). Premise 2: One cannot know a proposition to be true if it is false in a nearby world (the epistemological safety principle). The conclusion that no law statement can be known to be true follows immediately from the two premises.     

Basic desert,conceptual revision,and moral justification

I examine Manuel Vargas's revisionist justification for continuing with our responsibility-characteristic practices in the absence of basic desert. I query his claim that this justification need not depend on how we settle questions about the content of morality, arguing that it requires us to reject the Kantian principle that prohibits treating anyone merely as a means. I maintain that any convincing argument against this principle would have to be driven by concerns that arise within the sphere of moral theory itself, whereas Vargas's argument draws solely on concerns about the expensive metaphysics involved in a libertarian conception of freedom. I argue that this amounts not just to changing the concept of free will by stipulation, but also (more problematically) to changing our moral principles by stipulation.     

The Kantian Moral Hazard Argument for religious fictionalism

In this paper I do three things. Firstly, I defend the view that in his most familiar arguments about morality and the theological postulates, the arguments which appeal to the epistemological doctrines of the first Critique, Kant is as much of a fictionalist as anybody not working explicitly with that conceptual apparatus could be: his notion of faith as subjectively and not objectively grounded is precisely what fictionalists are concerned with in their talk of nondoxastic attitudes. Secondly, I reconstruct a logically distinct argument to a fictionalist conclusion which I argue Kant also gives us, this time an argument to the conclusion that it is a good thing if our commitment to the existence of God is nondoxastic. And finally, I argue that this argument is of continuing interest, to Kantians and non-Kantians alike, not only because it raises interesting questions about the relation of morality to belief in God (which go in the opposite direction to most discussions, which focus on whether and to what extent belief in God can be an aid to morality), but also because this ‘Moral Hazard Argument’ seems to be available to religious realists and non-realists alike, thus suggesting that religious fictionalism is not by any means just an interesting version of religious non-realism.     

Hempel's Paradox, Law-likeness and Causal Relations

It is widely thought that Bayesian confirmation theory has provided a solution to Hempel's Paradox (the Ravens Paradox). I discuss one well-known example of this approach, by John Mackie, and argue that it is unconvincing. I then suggest an alternative solution, which shows that the Bayesian approach is altogether mistaken. Nicod's Condition should be rejected because a generalisation is not confirmed by any of its instances if it is not law-like. And even law-like non-basic empirical generalisations, which are expressions of assumed underlying causal regularities, are not so confirmed if they are absurd in the light of our causal background knowledge or if their instances are not also possible instances of the relevant causal claim.     

On empirical interpretation

The view that scientific theories are partially interpreted deductive systems (theoretical deductivism) is defended against recent criticisms by Hempel. Hempel argues that the reliance of theoretical inferences (both from observation to theory and also from theory to theory) uponceteris paribus conditions orprovisos must prevent theories from establishing deductive connections among observations. In reply I argue, first, that theoretical deductivism does not in fact require the establishing of such deductive connections: I offer alternative H-D analyses of these inferences. Second, I argue that when the refined character of scientific observation is taken into account, we find that a theorymay after all establish such deductive connections among scientific observations, without reliance on provisos.These conclusions are based on the multi-level Popperian contextualist account of empirical interpretation sketched in a previous paper. As before, I claim that the supposed objections to theoretical deductivism depend upon questionable empiricist theses unnecessarily conjoined with theoretical deductivism by the Logical Positivists. Theoretical deductivism itself is unaffected by these arguments, and remains (when empirical interpretation is properly analyzed) the best account of scientific theories.This paper develops points first made very briefly in my forthcoming review (c). I would like to thank Professor Hempel for correspondence regarding an earlier version of that review, and Professor Demopoulos for commissioning the review.     

Representation and the First-Person Perspective

The orthodox view in the study of representation is that a strictly third-person objective methodology must be employed. The acceptance of this methodology is shown to be a fundamental and debilitating error. Toward this end I defend what I call “the particularity requirement, ”discuss an important distinction between representers and information bearers, and identify what I call “the fundamental fact of representation” I argue that any theory of representation must accommodate these, but that any theory that also is based upon a strictly third-person methodology lacks the resources to provide for any of them. It is shown that this failure extends to teleological accounts of representation, despite appearances to the contrary. In the course of this, I argue for the acceptance of a methodological principle, methodological chauvinism, and I show how it implicates a restricted use of the first-person perspective in the study of representation. I explain a nonphenomenal first-person concept, minimal content, which I have introduced and defended more fully elsewhere, the features of which lead to the recognition of a unique intentional state that I call the fundamental intentional state. It is so called since “normal” intentional states presuppose it. Importantly, the logical structure of this state is different from all other intentional states. Lastly, I argue that the expanded methodology I adopt is neither unscientific nor anthropomorphic, despite its employment of a first-person perspective. Ironically, it is the exclusive use of third-person methodologies that leads to anthropomorphism in the study of representation.     

Iterated Belief Change and the Recovery Axiom

The axiom of recovery, while capturing a central intuition regarding belief change, has been the source of much controversy. We argue briefly against putative counterexamples to the axiom—while agreeing that some of their insight deserves to be preserved—and present additional recovery-like axioms in a framework that uses epistemic states, which encode preferences, as the object of revisions. This makes iterated revision possible and renders explicit the connection between iterated belief change and the axiom of recovery. We provide a representation theorem that connects the semantic conditions we impose on iterated revision and our additional syntactical properties. We show interesting similarities between our framework and that of Darwiche–Pearl (Artificial Intelligence 89:1–29 1997). In particular, we show that intuitions underlying the controversial (C2) postulate are captured by the recovery axiom and our recovery-like postulates (the latter can be seen as weakenings of (C2)). We present postulates for contraction, in the same spirit as the Darwiche–Pearl postulates for revision, and provide a theorem that connects our syntactic postulates with a set of semantic conditions. Lastly, we show a connection between the contraction postulates and a generalisation of the recovery axiom. Portions of this paper were originally presented at ECAI 2002.