
120Every Proposition is a CounterfactualActa Analytica 31 (2): 117137. 2016.I present and discuss two logical results. The first shows that a nontrivial counterfactual analysis exists for any contingent proposition that is false in at least two possible worlds. The second result identifies a set of conditions that are individually necessary and jointly sufficient for the success of a counterfactual analysis. I use these results to shed light on the question whether disposition ascribing propositions can be analyzed as StalnakerLewis conditional propositions. The answe…Read more

48Conditionals: from philosophy to computer science, edited by G. Crocco, L. Fariñas del Cerro, and A. Herzig, Studies in logic and computation, no. 5, Clarendon Press, Oxford University Press, Oxford and New York1995, viii + 368 pp (review)Journal of Symbolic Logic 62 (4): 14871490. 1997.This is a review of CONDITIONALS: FROM PHILOSOPHY TO COMPUTER SCIENCE, edited by Crocco G., del Cerro L. Fariñas, and Herzig A., Studies in logic and computation, no. 5, Clarendon Press, Oxford University Press, Oxford and New York 1995.

67Victor Dudman's Grammar and Semantics by Jean Curthoys and Victor H. Dudman: Basingstoke, UK: Palgrave Macmillan, 2012, pp. xi + 158, £58 (review)Australasian Journal of Philosophy 92 (4): 789791. 2014.This is a review of Jean Curthoys and Victor H. Dudman, VICTOR DUDMAN'S GRAMMAR AND SEMANTICS (Hampshire, UK: Palgrave Macmillan, 2012).

70Review: Counterfactuals and Probability by Moritz Schulz (review)Australasian Journal of Philosophy 97 (2): 414417. 2019.This is a review of Moritz Schulz, COUNTERFACTUALS AND PROBABIITY (Oxford: Oxford University Press, 2017).

40Time and the Russell Definition of NumberSouthwestern Journal of Philosophy 10 (2): 177180. 1979.

Studies in the Semantics of ModalityDissertation, University of Pittsburgh. 1985.Possible worlds talk is, in my view, a metaphor, and what makes it a good metaphor is its capacity to be extended and elaborated in fruitful ways. The essays in this dissertation all concern ways of adding structure to the basic apparatus of possible worlds semanticsthe Kripke frameso as to make it bear more fruit. ;One way of adding structure is to think of possible worlds as histories. In "A Theory of Conditionals in the Context of Branching Time" Richmond Thomason and Anil Gupta use this …Read more

41The modal logic of discrepancyJournal of Philosophical Logic 26 (2): 143168. 1997.Discrepancies between an agent's goals and beliefs play an important, if implicit, role in determining what a rational agent is motivated to do. This is most obvious in cases where an agent achieves a complex goal incrementally and must deliberate anew as each milestone is reached. In such cases the concept of goal/belief discrepancy defines an appropriate space to which a degreeofachievement yardstick can be applied. This paper presents soundness and completeness results concerning a logic fo…Read more

259Max Black on the identity of indiscerniblesPhilosophical Quarterly 45 (180): 350360. 1995.I give a critique of the argument against the Identity of Indiscernibles found in Max Black's dialogue "The Identity of Indiscernibles". I begin by postulating and giving existence and individuation conditions for actually existent thought experiment characters on analogy with fictional characters as postulated in Peter van Inwagen's "Creatures of Fiction". I then show that Black's twospheres thought experiment raises not one but two discernibility questions: 1) Is it true in the twospheres th…Read more

283Causal Independence, the Identity of Indiscernibles, and the Essentiality of OriginsJournal of Philosophy 106 (5): 277291. 2009.In his wellknown 1952 dialogue Max Black describes a counterexample to the Principle of the Identity of Indiscernibles (PII). The counterexample is a world containing nothing but two purportedly indiscernible iron spheres. Reflecting on Black's example, Robert Adams uses the possibility of a world containing two almost indiscernible spheres to argue for the possibility of the indiscernible spheres world. One of Adams's almost indiscernible spheres has a small impurity, and, Adams writes, "Surel…Read more

66A theorem concerning syntactical treatments of nonidealized beliefSynthese 129 (3). 2001.[IMPORTANT CORRECTION  See end of abstract.] In Syntactical Treatments of Modality, with Corollaries on Reflexion Principles and Finite Axiomatizability, Acta Philosophica Fennica 16 (1963), 153–167, Richard Montague shows that the use of a single syntactic predicate (with a contextindependent semantic value) to represent modalities of alethic necessity and idealized knowledge leads to inconsistency. In A Note on Syntactical Treatments of Modality, Synthese 44 (1980), 391–395, Richmond Thomaso…Read more

72Nonmonotonic InconsistencyArtificial Intelligence 149 (2): 161178. 2003.Nonmonotonic consequence is the subject of a vast literature, but the idea of a nonmonotonic counterpart of logical inconsistency—the idea of a defeasible property representing internal conflict of an inductive or evidential nature—has been entirely neglected. After considering and dismissing two possible analyses relating nonmonotonic consequence and a nonmonotonic counterpart of logical inconsistency, this paper offers a set of postulates for nonmonotonic inconsistency, an analysis of nonmonot…Read more

93Embedded counterfactuals and possible worlds semanticsPhilosophical Studies 173 (3): 665673. 2016.Stephen Barker argues that a possible worlds semantics for the counterfactual conditional of the sort proposed by Stalnaker and Lewis cannot accommodate certain examples in which determinism is true and a counterfactual Q > R is false, but where, for some P, the compound counterfactual P > (Q > R) is true. I argue that the completeness theorem for Lewis’s system VC of counterfactual logic shows that Stalnaker–Lewis semantics does accommodate Barker’s example, and I argue that its doing so should…Read more

134'Can' and the logic of abilityPhilosophical Studies 50 (1): 5364. 1986.A selection function based semantics is offered for the 'can' of ability based on the idea that 'John can run a four minute mile' is true iff John would do so under the right conditions, meaning that he would do so under at least one appropriately chosen test condition. Completeness is proved for an axiom system and semantics based on this idea, and the logic turns out to be interestingly different from any standard system of modal logic.

95A characterization of imaging in terms of Popper functionsPhilosophy of Science 67 (2): 316338. 2000.Despite the results of David Lewis, Peter Gärdenfors, and others, showing that imaging and classical conditionalization coincide only in the most trivial probabilistic models of belief revision, it turns out that imaging on a proposition A can always be described via Popper function conditionalization on a proposition that entails A. This result generalizes to any method of belief revision meeting certain minimal requirements. The proof is illustrated by an application of imaging in the context …Read more

79Temporal necessity and the conditionalStudia Logica 49 (3): 345363. 1990.Temporal necessity and the subjunctive conditional appear to be related by the principle of Past Predominance, according to which past similarities and differences take priority over future similarities and differences in determining the comparative similarity of alternative possible histories with respect to the present moment. R. H. Thomason and Anil Gupta have formalized Past Predominance in a semantics that combines selection functions with branching time; in this paper I show that Past Pred…Read more

114More on the paradox of the knower without epistemic closureMind 113 (449): 109114. 2004.In “The Paradox of the Knower without Epistemic Closure”, MIND 110:31933, 2001, I develop a version of the Knower Paradox which does not assume epistemic closure, and I use it to argue that the original Knower Paradox does not support an argument against epistemic closure. In “The Paradox of the Knower without Epistemic Closure?”, MIND 113:95107, 2004, Gabriel Uzquiano, using his own result, argues that my rebuttal to the anticlosure argument is not successful. I respond here by arguing that…Read more

105Conditional logic and the significance of Tooleys exampleAnalysis 66 (4). 2006.In "Backward causation and the StalnakerLewis approach to counterfactuals," Analysis 62 (2002): 191–97, Michael Tooley argues that if a certain kind of backward causation is possible, then a StalnakerLewis style comparative world similarity account of the truth conditions of counterfactuals cannot be sound. Tooley’s target is one particular type of semantics, but, as I show, the significance of Tooley’s example goes well beyond its consequences for any one semantics for the conditional.

268Brute facts, the necessity of identity, and the identity of indiscerniblesPacific Philosophical Quarterly 92 (1): 110. 2011.In ‘Two Spheres, Twenty Spheres, and the Identity of Indiscernibles,’ Della Rocca argues that any counterexample to the PII would involve ‘a brute fact of nonidentity [. . .] not grounded in any qualitative difference.’ I respond that Adams's socalled Continuity Argument against the PII does not postulate qualitatively inexplicable brute facts of identity or nonidentity if understood in the context of Kripkean modality. One upshot is that if the PII is understood to quantify over modal as wel…Read more

89Review: Against Coherence: Truth, Probability, and Justification (review)Mind 115 (459): 790793. 2006.This is a review of Erik J. Olsson, AGAINST COHERENCE: TRUTH, PROBABILITY AND JUSTIFICATION (Oxford: Clarendon Press, 2005).

124Probability, evidence, and the coherence of the whole truthSynthese 103 (2). 1995.The coherence of the whole truth is a presupposition of any holistic coherence theory of justification that postulates a positive connection between justification and truth, for unless the whole truth is itself systemically coherent there is no reason to look for systemic coherence when deciding whether one is justified in accepting a given body of beliefs as true. This paper develops a formal model of holistic evidential coherence and uses this model to formalize and defend the claim that the w…Read more

86From worlds to probabilities: A probabilistic semantics for modal logicJournal of Philosophical Logic 22 (2). 1993.I give a probabilistic semantics for modal logic in which modal operators function as quantifiers over Popper functions in probabilistic model sets, thereby generalizing Kripke's semantics for modal logic.

48Coherence and truth conducive justificationAnalysis 59 (3): 186193. 1999.In a 1994 ANALYSIS article Peter Klein and Ted Warfield show that an epistemically more coherent set of beliefs often has a smaller unconditional probability of joint truth than some of its less coherent subsets. They conclude that epistemic justification, as understood in one version of a coherence theory of justification, is not truth conducive. After getting clear about what truth conduciveness requires, I show that their argument does not tell against BonJour's coherence theory.

38A correction to “Nonmonotonic inconsistency” [Artificial Intelligence 149 (2003) 161–178]Artificial Intelligence 160 (12): 191192. 2004.This note corrects an error in the statement and proof of Propositions 9 and 10 of [C. Cross, Nonmonotonic inconsistency, Artificial Intelligence 149 (2) (2003) 161–178]. Both results turn out to depend on the postulate of Consistency Preservation.

164The Paradox of the Knower without Epistemic Closure  CorrectedMind 121 (482): 457466. 2012.This essay corrects an error in the presentation of the Paradox of the KnowledgePlus Knower, which is the variant of Kaplan and Montague’s Knower Paradox presented in C. Cross 2001: ‘The Paradox of the Knower without Epistemic Closure,’ MIND, 110, pp. 319–33. The correction adds a universally quantified transitivity principle for derivability as an additional assumption leading to paradox. This correction does not affect the status of the KnowledgePlus paradox as a rebuttal to an argument agai…Read more

176Nonbelief and the desireasbelief thesisActa Analytica 23 (2): 115124. 2008.I show the incompatibility of two theses: (a) to desire the truth of p amounts to believing a certain proposition about the value of p’s truth; (b) one cannot be said to desire the truth of p if one believes that p is true. Thesis (a), the DesireAsBelief Thesis, has received much attention since the late 1980s. Thesis (b) is an epistemic variant of Socrates’ remark in the Symposium that one cannot desire what one already has. It turns out that (a) and (b) cannot both be true if it is possible …Read more

59Doesn'twill and didn'tdidAustralasian Journal of Philosophy 80 (1). 2002.In "Against the Indicative," AUSTRALASIAN JOURNAL OF PHILOSOPHY 72 (1994): 1726, and more recently in "Classifying `Conditionals': the Traditional Way is Wrong", ANALYSIS 60 (2000): 147, V.H. Dudman argues that (a) `If Oswald didn't shoot Kennedy then someone else did' and (b) `If Oswald doesn't shoot Kennedy then someone else will' should not be classified together as "indicative conditionals." Dudman relies on the assumption that (a) is entailed by (c) `Someone shot Kennedy', whereas (…Read more

57Belief Revision, NonMonotonic Reasoning, and the Ramsey TestIn Kyburg Henry E. , Loui Ronald P. & Carlson Greg N. (eds.), Knowledge Representation and Defeasible Reasoning, Kluwer Academic Publishers. pp. 223244. 1990.Peter Gärdenfors has proved (Philosophical Review, 1986) that the Ramsey rule and the methodologically conservative Preservation principle are incompatible given innocuouslooking background assumptions about belief revision. Gärdenfors gives up the Ramsey rule; I argue for preserving the Ramsey rule and interpret Gärdenfors's theorem as showing that no rational beliefreviser can avoid reasoning nonmonotonically. I argue against the Preservation principle and show that counterexamples to it alw…Read more

133Review: Conditionals in Context (review)Mind 116 (464): 11191122. 2007.This is a review of Christopher Gauker, CONDITIONALS IN CONTEXT (Cambridge, MA: The MIT Press, 2005).
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