Recovery Recovered

The most controversial condition that the AGM theory of rational belief change places on belief contraction is the recovery condition. The condition is controversial because of a series of putative counterexamples due (separately) to I. Levi and S. O. Hansson. In this paper we show that the conflicts that Levi and Hansson arrange between AGM contraction and our intuitions about how to give up beliefs are merely apparent. We argue that these conflicts disappear once we attend more closely to the identification of the beliefs contracted away in each counterexample case. Since, on our view, speakers" belief contraction intentions are often more complicated than they may first appear, we are led to develop apparatus for thinking about the communication and identification of those intentions. Our argument refocuses attention on the difficult question of how to apply the AGM theory to particular cases.     

Logic Without Contraction as Based on Inclusion and Unrestricted Abstraction

On the one hand, the absence of contraction is a safeguard against the logical (property theoretic) paradoxes; but on the other hand, it also disables inductive and recursive definitions, in its most basic form the definition of the series of natural numbers, for instance. The reason for this is simply that the effectiveness of a recursion clause depends on its being available after application, something that is usually assured by contraction. This paper presents a way of overcoming this problem within the framework of a logic based on inclusion and unrestricted abstraction, without any form of extensionality. This revised version was published online in June 2006 with corrections to the Cover Date.     

FOIL Axiomatized

In an earlier paper, [5], I gave semantics and tableau rules for a simple firstorder intensional logic called FOIL, in which both objects and intensions are explicitly present and can be quantified over. Intensions, being non-rigid, are represented in FOIL as (partial) functions from states to objects. Scoping machinery, predicate abstraction, is present to disambiguate sentences like that asserting the necessary identity of the morning and the evening star, which is true in one sense and not true in another.In this paper I address the problem of axiomatizing FOIL. I begin with an interesting sublogic with predicate abstraction and equality but no quantifiers. In [2] this sublogic was shown to be undecidable if the underlying modal logic was at least K4, though it is decidable in other cases. The axiomatization given is shown to be complete for standard logics without a symmetry condition. The general situation is not known. After this an axiomatization for the full FOIL is given, which is straightforward after one makes a change in the point of view.This paper is a version of the invited talk given by the author at the conference Trends in Logic III, dedicated to the memory of A. MOSTOWSKI, H. RASIOWA and C. RAUSZER, and held in Warsaw and Ruciane-Nida from 23rd to 25th September 2005.     

Expansion and Contraction of Finite States

We present a theory that copes with the dynamics of inconsistent information. A method is set forth to represent possibly inconsistent information by a finite state. Next, finite operations for expansion and contraction of finite states are given. No extra-logical element — a choice function or an ordering over (sets of) sentences — is presupposed in the definition of contraction. Moreover, expansion and contraction are each other's duals. AGM-style characterizations of these operations follow.     

Naïve Comprehension and Contracting Implications

In his paper [6], Greg Restall conjectured that a logic supports a naïve comprehension scheme if and only if it is robustly contraction free, that is, if and only if no contracting connective is definable in terms of the primitive connectives of the logic. In this paper, we present infinitely many counterexamples to Restall's conjecture, in the form of purely implicational logics which are robustly contraction free, but which trivialize naïve comprehension.     

Non-Prioritized Ranked Belief Change

Traditional accounts of belief change have been criticized for placing undue emphasis on the new belief provided as input. A recent proposal to address such issues is a framework for non-prioritized belief change based on default theories (Ghose and Goebel, 1998). A novel feature of this approach is the introduction of disbeliefs alongside beliefs which allows for a view of belief contraction as independently useful, instead of just being seen as an intermediate step in the process of belief revision. This approach is, however, restrictive in assuming a linear ordering of reliability on the received inputs. In this paper, we replace the linear ordering with a preference ranking on inputs from which a total preorder on inputs can be induced. This extension brings along with it the problem of dealing with inputs of equal rank. We provide a semantic solution to this problem which contains, as a special case, AGM belief change on closed theories.     

On Being Responsible and Holding Responsible

A number of philosophers have recently argued that we should interpret the debate over moral responsibility as a debate over the conditions under which it would be “fair” to blame a person for her attitudes or conduct. What is distinctive about these accounts is that they begin with the stance of the moral judge, rather than that of the agent who is judged, and make attributions of responsibility dependent upon whether it would be fair or appropriate for a moral judge to react to the agent in various (negative) ways. This is problematic, I argue, because our intuitions about whether and when it would be fair to react negatively to another are sensitive to a host of considerations that appear to have little or nothing to do with an agent’s responsibility or culpability for her attitudes or behavior. If this is correct, then theories which make attributions of responsibility dependent upon the appropriateness of our reactions as moral judges will turn out to be fundamentally misguided. I am grateful to Barbara Herman, T. M. Scanlon, and two anonymous reviewers for The Journal of Ethics for their helpful comments on earlier drafts of this paper. I am also grateful to Pamela Hieronymi and the members of her Fall 2201 graduate seminar on moral responsibility at UCLA, and to the audience members at Simon Fraser University, for their valuable feedback on earlier versions of this material. My biggest debt of gratitude goes to Jean Roberts, for stimulating discussion and insightful commentary on multiple drafts of this paper.     

Action sentences

I would like to thank Eddy Zemach, Jonathan Stavi, Julius Moravcsik and Dov Gabbay for some very good discussions on the logical form of action sentences. Also, I am indebted to an anonymous referee of Erkenntnis for some very helpful comments on an earlier draft of this paper.     

An atheological argument from evil natural laws

I should like to thank Keith Chrzan, P.G. McGrath, Susan Ament Smith and an anonymous referee for this journal for helpful comments on an earlier version of this paper. I should also like to thank two anonymous referees for Philosophy and Phenomenological Research for extensive and brilliant criticisms of an earlier and very different version of this paper; many of the improvements in the present version were motivated by their criticisms.     

Vague objects for those who want them

The authors would like to express their thanks to an anonymous reader for Philosophical Studies, who supplied extremely thorough and helpful comments on an earlier draft of this paper. We also would like to thank our colleague Thomas Blackson for helpful criticism of the penultimate draft of the paper.     

Many Concepts and Two Logics of Algorithmic Reduction

Within the program of finding axiomatizations for various parts of computability logic, it was proven earlier that the logic of interactive Turing reduction is exactly the implicative fragment of Heyting’s intuitionistic calculus. That sort of reduction permits unlimited reusage of the computational resource represented by the antecedent. An at least equally basic and natural sort of algorithmic reduction, however, is the one that does not allow such reusage. The present article shows that turning the logic of the first sort of reduction into the logic of the second sort of reduction takes nothing more than just deleting the contraction rule from its Gentzen-style axiomatization. The first (Turing) sort of interactive reduction is also shown to come in three natural versions. While those three versions are very different from each other, their logical behaviors (in isolation) turn out to be indistinguishable, with that common behavior being precisely captured by implicative intuitionistic logic. Among the other contributions of the present article is an informal introduction of a series of new — finite and bounded — versions of recurrence operations and the associated reduction operations. Presented by Robert Goldblatt     

Society Against Societies: The Possibility of Transcultural Criticism

This paper argues against particularism about social criticism of the form presented by Walzer. I contend that while limitation of the scope of criticism depends on the existence of our shared meanings, which are not shared by them, shared meaning itself depends on society. So, an account of society showing that societies are not discrete and mutually inaccessible refutes particularism. I argue for such an account. I deal with the objection that the focus of particularism is culture, not society, and conclude that the conditions of possibility of shared meaning have anti-particularist consequences. This paper draws on Samuel Clark, Living Without Domination: The Possibility of an Anarchist Utopia (Aldershot: Ashgate, forthcoming 2007), chapter 2. I would like to thank Gideon Calder, and two anonymous referees for Res Publica, for their helpful comments on an earlier draft.     

Transcendental empiricism: Deleuze''s response to Hegel

Funding for the research leading to this article was generously provided by a Social Sciences and Humanities Research Council of Canada Post-Doctoral Fellowship. I would like to thank Andrew Irvine and Steve Savitt for criticisms of an earlier version of this paper, as well as the anonymousMan and World referee.     

Spacetime theory as physical geometry

Discussions of the metaphysical status of spacetime assume that a spacetime theory offers a causal explanation of phenomena of relative motion, and that the fundamental philosophical question is whether the inference to that explanation is warranted. I argue that those assumptions are mistaken, because they ignore the essential character of spacetime theory as a kind of physical geometry. As such, a spacetime theory does notcausally explain phenomena of motion, but uses them to construct physicaldefinitions of basic geometrical structures by coordinating them with dynamical laws. I suggest that this view of spacetime theories leads to a clearer view of the philosophical foundations of general relativity and its place in the historical evolution of spacetime theory. I also argue that this view provides a much clearer and more defensible account of what is entailed by realism concerning spacetime.I would like to thank William Demopoulos and Michael Friedman for their comments on earlier drafts. I also thank the anonymous referees forErkenntnis for their suggestions. Work on this paper was supported by the Social Sciences and Humanities Research Council of Canada.     

Is space-time discrete or continuous? — An empirical question

In this paper I present the Discrete Space-Time Thesis, in a way which enables me to defend it against various well-known objections, and which extends to the discrete versions of Special and General Relativity with only minor difficulties. The point of this presentation is not to convince readers that space-time really is discrete but rather to convince them that we do not yet know whether or not it is. Having argued that it is an open question whether or not space-time is discrete, I then turn to some possible empirical evidence, which we do not yet have. This evidence is based on some slight differences between commonly occurring differential equations and their discrete analogs.I would like to express my thanks to John McKie with whom I have had several inspiring conversations about discrete space. I would also like to thank the audience of a paper on this topic which I read in October 1991 at the College Park campus of the University of Maryland. Finally I would like to thank the referees ofSynthese for their comments. One of them, in particular, should be thanked especially for help in improving Appendix Two.     

Reply to Dews,and a plea for Schelling

The discussion is a response to Dews on the question of how Schelling's Freiheitsschrift should be interpreted. It falls into two halves, the first defending my interpretation, and the second expanding on the case that Dews makes for the unavoidability of metaphysics in the theory of human freedom, with which I am in full agreement. The main criticism that Dews makes of my reading is that the argument I attribute to Schelling concerning the metaphysical significance of evil rests on Kantian assumptions regarding the existence of pure practical reason, which Schelling rejects. I argue that, though certainly matters are more complicated than my earlier discussion made them seem, Schelling remains sufficiently close to Kant for the argument I attribute to avoid inconsistency. In the second half I raise what I claim to be a neglected but important question: Why is the legacy of classical German philosophy not regarded as significant for contemporary discussion of human freedom? My answer in brief is that the concept of freedom has undergone a profound contraction. In this context I also try to define more precisely what is distinctive of Schelling's view of human freedom.     

Whether any individual at all could have a guise structure

I am indebted to Hector-Neri Castañeda for commenting on an earlier version of this paper, which is not to say that he would endorse everything in the present version.     

Pure Extensions, Proof Rules, and Hybrid Axiomatics

In this paper we argue that hybrid logic is the deductive setting most natural for Kripke semantics. We do so by investigating hybrid axiomatics for a variety of systems, ranging from the basic hybrid language (a decidable system with the same complexity as orthodox propositional modal logic) to the strong Priorean language (which offers full first-order expressivity).We show that hybrid logic offers a genuinely first-order perspective on Kripke semantics: it is possible to define base logics which extend automatically to a wide variety of frame classes and to prove completeness using the Henkin method. In the weaker languages, this requires the use of non-orthodox rules. We discuss these rules in detail and prove non-eliminability and eliminability results. We also show how another type of rule, which reflects the structure of the strong Priorean language, can be employed to give an even wider coverage of frame classes. We show that this deductive apparatus gets progressively simpler as we work our way up the expressivity hierarchy, and conclude the paper by showing that the approach transfers to first-order hybrid logic.A preliminary version of this paper was presented at the fifth conference on Advances in Modal Logic (AiML 2004) in Manchester. We would like to thank Maarten Marx for his comments on an early draft and Agnieszka Kisielewska for help with the proof reading.Special Issue Ways of Worlds II. On Possible Worlds and Related Notions Edited by Vincent F. Hendricks and Stig Andur Pedersen