Abstract
This paper defends a counterexample to Modus Tollens, and uses it to draw some conclusions about the logic and semantics of indicative conditionals and probability operators in natural language. Along the way we investigate some of the interactions of these expressions with knows, and we call into question the thesis that all knowledge ascriptions have truth-conditions. A probabilistic dynamic semantics for probability operators, conditionals, and acceptance attitudes is developed around the idea of representing the common ground of a conversation as a set of probability spaces.
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Anand, P., & Hacquard, V. (2008). Attitudes and epistemics. In T. Friedman, & S. Ito (Eds.), Proceedings of SALT XVIII (pp. 37–54). Eau Claire: Cornell.
Beaver, D. (2001). Presupposition and assertion in dynamic semantics. Studies in logic, language and information. Stanford: CSLI Publications.
Bennett, J. (2003). A philosophical guide to conditionals. Oxford: Oxford University Press.
Cantwell, J. (2008). Changing the modal context. Theoria, 74(4), 331–351.
Carroll, L. (1894). A logical paradox. Mind, 3(11), 436–440.
Edgington, D. (1995). On conditionals. Mind, 104(414), 235–329.
Forrester, J. W. (1984). Gentle murder, or the adverbial samaritan. The Journal of Philosophy, 81(4), 193–197.
Gibbard, A. (1981). Two recent theories of conditionals. In W. Harper, R. Stalnaker, & G. Pearce (Eds.), Ifs (pp. 211–47). Dordrecht: D. Reidel.
Gillies, A. (2004). Epistemic conditionals and conditional epistemics. Nous, 38, 585–616.
Gillies, A. (2010). Iffiness. Semantics and Pragmatics, 3, 1–42.
Groenendijk, J., & Stokhof, M. (1991). Dynamic predicate logic. Linguistics and Philosophy, 14, 39–100.
Heim, I. (1982). The semantics of definite and indefinite noun phrases. PhD thesis, University of Massachusetts.
Heim, I. (1983). On the projection problem for presuppositions. In M. Barlow, D. Flickinger, & M. Wescoat (Eds.), WCCFL 2: Second annual west coat conference on formal linguistics (pp. 114–125). Stanford: Stanford University.
Jeffrey, R. (1983). Bayesianism with a human face. In J. Earman (Ed.), Testing scientific theories. Minnesota studies in the philosophy of science (Vol. 10, pp. 133–156).
Kolodny, N., & MacFarlane, J. (2010). Ifs and oughts. Journal of Philosophy, CVII(3), 115–143.
Kratzer, A. (1981). The notional category of modality. In H.-J. Eikmeyer, & H. Rieser (Eds.), Words, worlds, and contexts, new approaches to word semantics (pp. 38-74). Berlin: Walter de Gruyter.
Kratzer, A. (1983). Conditionals. In A. Farley, P. Farley, & K.-E. McCullough (Eds.), Papers from the parasession on pragmatics and grammatical theory. Chicago: Chicago Linguistics Society.
Kratzer, A. (1991). Modality. In A. von Stechow, & D. Wunderlich (Eds.), Semantics: An international handbook of contemporary research (pp. 639–650). Berlin: Walter de Gruyter.
Lewis, D. K. (1973). Counterfactuals. Malden: Blackwell.
Lewis, D. K. (1975). Adverbs of quantification. In E. L. Keenan (Ed.), Formal semantics of natural language (pp. 3–15). Cambridge: Cambridge University Press.
Lewis, D. K. (1976). Probabilities of conditionals and conditional probabilities. Philosophical Review, 85, 297–315.
MacFarlane, J. (2011). Epistemic modals are assessment-sensitive. In A. Egan, & B. Weatherson (Eds.), Epistemic modality (pp. 144–178). Oxford: Oxford University Press.
McGee, V. (1985). A counterexample to Modus Ponens. Journal of Philosophy, 82(9), 462–471.
Moss, S. (2012). Epistemology formalized. Philosophical Review (forthcoming).
Rothschild, D. (2011). Do indicative conditionals express propositions? Nous. doi:10.1111/j.1468-0068.2010.00825.x
Rothschild, D. (2012). Expressing credences. In Proceedings of the Aristotelian Society (forthcoming).
Stalnaker, R. (1968). A theory of conditionals. In N. Rescher (Ed.), Studies in logical theory (pp. 98–112). Oxford: Basil Blackwell.
Stalnaker, R. (1973). Indicative conditionals. Philosophia, 3, 269–286.
Van Fraassen, B. (1976). Probabilities of conditionals. Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, 1, 261–308.
Veltman, F. (1985). Logics for conditionals. PhD thesis, University of Amsterdam.
Veltman, F. (1996). Defaults in update semantics. Journal of Philosophical Logic, 25(3), 221–261.
von Fintel, K., & Iatridou, S. (2003). Epistemic containment. Linguistic Inquiry, 34(2), 173–198.
Willer, M. (2010). Modality in flux. PhD thesis, University of Texas, Austin.
Yalcin, S. (2005). Epistemic modals. In J. Gajewski, V. Haquard, B. Nickel, & S. Yalcin (Eds.), New work on modality (pp. 231–272). MIT Working Papers in Linguistics (Vol. 51).
Yalcin, S. (2007). Epistemic modals. Mind, 116(464), 983–1026.
Yalcin, S. (2009). More on epistemic modals. Mind, 118(471), 785.
Yalcin, S. (2010). Probability operators. Philosophy Compass, 5(11), 916–937.
Yalcin, S. (2011). Nonfactualism about epistemic modality. In A. Egan, & B. Weatherson (Eds.), Epistemic modality (pp. 295–332). Oxford: Oxford University Press.
Yalcin, S. (2012a). Bayesian Expressivism. In Proceedings of the Aristotelian Society (forthcoming).
Yalcin, S. (2012b). Context probabilism. In M. Aloni, V. Kimmelman, F. Roelofsen, G. W. Sassoon, K. Schulz, & M. Westera (Eds.), Proceedings of the 18th Amsterdam Colloquium, FoLLI, lecture notes in computer science. Springer. (forthcoming).
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Yalcin, S. A Counterexample to Modus Tollens. J Philos Logic 41, 1001–1024 (2012). https://doi.org/10.1007/s10992-012-9228-4
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DOI: https://doi.org/10.1007/s10992-012-9228-4