Epistemic Logic, Monotonicity, and the Halbach–Welch Rapprochement Strategy
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Predicate approaches to modality have been a topic of increased interest in recent intensional logic. Halbach and Welch (Mind 118(469):71–100, 2009) have proposed a new formal technique to reduce the necessity predicate to an operator, demonstrating that predicate and operator methods are ultimately compatible. This article concerns the question of whether Halbach and Welch’s approach can provide a uniform formal treatment for intensionality. I show that the monotonicity constraint in Halbach and Welch’s proof for necessity fails for almost all possible-worlds theories of knowledge. The nonmonotonicity results demonstrate that the most obvious way of emulating Halbach and Welch’s rapprochement of the predicate and operator fails in the epistemic setting.
KeywordsEpistemic logic Intensional logic Modal logic
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I would like to thank Sean Walsh, David Woodruff Smith, Kai Wehmeier, and Brian Skyrms. Early versions of this work were presented at the following events: The Predicate Approaches to Modality Conference at the Munich Center for Mathematical Philosophy, LMU Munich, in September 2014; the C-ALPHA Logic Seminar, UC Irvine, in Winter 2016. I am grateful to the audiences for their responses. Thanks is owed in particular to the following people who gave me invaluable feedback and comments on these and other occasions: Tim Button, Volker Halbach, Greg Lauro, Richard Mendelsohn, Jeff Schaz, Johannes Stern, and Philip Welch.
- 2.Belnap, N., and A. Gupta, The Revision Theory of Truth, MIT Press, Cambridge, 1993.Google Scholar
- 3.Birkhoff, G., Lattice Theory, 3rd edn., American Mathematical Society, Providence, 1967.Google Scholar
- 12.Hawke, P., Relevant alternatives in epistemology and logic, in J. Redmond, O. Pombo Martins, and A. Nepomuceno Fernández, (eds.), Epistemology, Knowledge and the Impact of Interaction, Springer, 2016, pp. 207–235.Google Scholar
- 18.Kripke, S., Is there a problem about substitutional quantification?, in The Ways of Paradox and Other Essays, Oxford University Press, 1976, pp. 324–419.Google Scholar
- 21.Montague, R., Syntactical treatments of modality, with corollaries on reflexion principles and finite axiomatizability, in R. H. Thomason, (ed.), Formal Philosophy: Selected Papers of Richard Montague, chap. 10, Yale University Press, 1963, pp. 286–302.Google Scholar
- 22.Montague, R., Formal Philosophy: Selected Papers of Richard Montague, Yale University Press, New Haven, 1974.Google Scholar
- 23.Nozick, R., Philosophical Explanations, Harvard University Press, Cambridge, 1981.Google Scholar
- 24.Priest, G., An Introduction to Non-Classical Logic, Cambridge, 2008.Google Scholar
- 25.Pritchard, D., Sensitivity, safety, and anti-luck epistemology, in J. Greco, (ed.), The Oxford Handbook of Skepticism, Oxford University Press, Oxford, 2008, pp. 437–455.Google Scholar
- 26.Quine, W. V., Three grades of modal involvement, in The Ways of Paradox and Other Essays, Random House, 1966, pp. 156–174.Google Scholar
- 28.Steup, M., and E. Sosa, Contemporary Debates in Epistemology, Blackwell Publishers Inc., Malden, 2005.Google Scholar
- 32.Xu, Z., and B. Chen, Epistemic logic with evidence and relevant alternatives, in Jaakko Hintikka on Knowledge and Game-Theoretical Semantics, Springer, 2018, pp. 535–555.Google Scholar