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191Freedom and the Fixity of the PastPhilosophical Review 121 (2): 179-207. 2012.According to the Principle of the Fixity of the Past (FP), no one can now do anything that would require the past to have unfolded differently than it actually did, for the past is fixed, over and done with. Why might doing something in the future require the past to be different? Because if determinism is true—if the laws of nature and the initial conditions of the Big Bang determined a unique future for our universe—then doing anything other than what you are determined to do would require one…Read more
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145Moorean Phenomena in Epistemic LogicIn Lev Dmitrievich Beklemishev, Valentin Goranko & Valentin Shehtman (eds.), Advances in Modal Logic 8, College Publications. pp. 178-199. 2010.A well-known open problem in epistemic logic is to give a syntactic characterization of the successful formulas. Semantically, a formula is successful if and only if for any pointed model where it is true, it remains true after deleting all points where the formula was false. The classic example of a formula that is not successful in this sense is the “Moore sentence” p ∧ ¬BOXp, read as “p is true but you do not know p.” Not only is the Moore sentence unsuccessful, it is self-refuting, for it ne…Read more
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29Locales, Nuclei, and Dragalin FramesIn Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11, Csli Publications. pp. 177-196. 2016.It is a classic result in lattice theory that a poset is a complete lattice iff it can be realized as fixpoints of a closure operator on a powerset. Dragalin [9,10] observed that a poset is a locale (complete Heyting algebra) iff it can be realized as fixpoints of a nucleus on the locale of upsets of a poset. He also showed how to generate a nucleus on upsets by adding a structure of “paths” to a poset, forming what we call a Dragalin frame. This allowed Dragalin to introduce a semantics for int…Read more
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79Response to Egré and XuIn Johan van Benthem Fenrong Liu (ed.), Logic Across the University: Foundations and Applications, College Publications. pp. 39-46. 2013.In this note, I respond to comments by Paul Egré and Xu Zhaoqing on my “Epistemic Closure and Epistemic Logic I: Relevant Alternatives and Subjunctivism” (Journal of Philosophical Logic).
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48A bimodal perspective on possibility semanticsJournal of Logic and Computation 27 (5). 2017.In this article, we develop a bimodal perspective on possibility semantics, a framework allowing partiality of states that provides an alternative modelling for classical propositional and modal logics. In particular, we define a full and faithful translation of the basic modal logic K over possibility models into a bimodal logic of partial functions over partial orders, and we show how to modulate this analysis by varying across logics and model classes that have independent topological motivat…Read more
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200Fallibilism and Multiple Paths to KnowledgeOxford Studies in Epistemology 5 97-144. 2015.This chapter argues that epistemologists should replace a “standard alternatives” picture of knowledge, assumed by many fallibilist theories of knowledge, with a new “multipath” picture of knowledge. The chapter first identifies a problem for the standard picture: fallibilists working with this picture cannot maintain even the most uncontroversial epistemic closure principles without making extreme assumptions about the ability of humans to know empirical truths without empirical investigation. …Read more
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182Information dynamics and uniform substitutionSynthese 190 (1): 31-55. 2013.The picture of information acquisition as the elimination of possibilities has proven fruitful in many domains, serving as a foundation for formal models in philosophy, linguistics, computer science, and economics. While the picture appears simple, its formalization in dynamic epistemic logic reveals subtleties: given a valid principle of information dynamics in the language of dynamic epistemic logic, substituting complex epistemic sentences for its atomic sentences may result in an invalid pri…Read more
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227Measure Semantics and Qualitative Semantics for Epistemic ModalsProceedings of SALT 23 514-534. 2013.In this paper, we explore semantics for comparative epistemic modals that avoid the entailment problems shown to result from Kratzer’s (1991) semantics by Yalcin (2006, 2009, 2010). In contrast to the alternative semantics presented by Yalcin and Lassiter (2010, 2011), based on finitely additive probability measures, we introduce semantics based on qualitatively additive measures, as well as semantics based on purely qualitative orderings, including orderings on propositions derived from orderin…Read more
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185A note on cancellation axioms for comparative probabilityTheory and Decision 80 (1): 159-166. 2016.We prove that the generalized cancellation axiom for incomplete comparative probability relations introduced by Rios Insua and Alon and Lehrer is stronger than the standard cancellation axiom for complete comparative probability relations introduced by Scott, relative to their other axioms for comparative probability in both the finite and infinite cases. This result has been suggested but not proved in the previous literature
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University of California, BerkeleyDepartment of Philosophy
Group in Logic and the Methodology of ScienceProfessor
Berkeley, California, United States of America