Abstract
Epistemic modals in consequent place of indicative conditionals give rise to apparent counterexamples to Modus Tollens. Familiar assumptions behind familiar truth conditional theories of embedded modality facilitate a prima facie explanation—viz., that the target cases harbor epistemic modal equivocations. However, this sort of explanation goes too far. It fosters other predictions of equivocation in places where in fact there are none. It is argued that the solution is to drop the credo that modal claims are inherently relational (i.e., that they express a logical relation between a prejacent and a contextually determined premise-set) in favor of a view that treats them as inherently quantificational. In particular it is suggested that epistemic modals express covert mass noun descriptions of information of the form “the actionable information stands in logical relation L to prejacent p”. We demonstrate how this approach unlocks the equivocation problem.
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Notes
Thanks to Josh Heter for the variation on the example.
Yalcin (2012) denies that there are even apparently invalid instances of modus ponens along these lines. However, that position is the result of his understanding of validity in terms of what one may conclude given the information in the premises, rather than more standardly in terms of what must be true given the truth of the premises. In these latter terms there is a modus ponens problem.
The bouletic and teleological versions do not carry invalid readings, most likely because the mere truth of the non-modal minor premise is sufficient to alter the default semantic content of the embedded modal. I have in mind here the default premise-set or modal base, of which much more will be said later. By contrast, with the epistemic reading, the mere truth of the minor premise is not sufficient to affect the content of the embedded epistemic modal. Knowledge (or some other epistemic state, but not mere truth) of the minor premise is minimally required to affect content. Admittedly there are “deontic” variations of the problem in the recent literature, for example in the miner’s puzzle in Kolodny and MacFarlane (2010). However even there we find that the epistemic states of the relevant subjects are contributing to our understanding of the modals.
A discussion and generalization of the theorem (as it pertains to deontic modality) is found in Anette Frank’s dissertation (1996: 53). For our purposes: ‘If \(\phi\) then \(M(\psi )\)’ is true, whenever \(\phi\) necessitates \(\psi\) and ‘M’ is epistemic ‘must’ or ‘might’. Endorsements of the epistemic version of principle appear in Zvolenszky (2006: 167–168) and Geurts (manuscript: 10–11).
Even if there are some notions of epistemic possibility that are not entailed by truth (e.g., “possible for all Jake falsely believes”), the argument is general enough to be a problem for substantial notions of epistemic possibility that are entailed by truth.
Kratzer (2012: 98–99) revises this position—claiming that explicit “must” but not bare “if” is an evidential marker, and so avows further information about how the information supports the prejacent (e.g., inferentially rather than directly). The evidentiality issues are orthogonal to present concerns.
Notice that a “relativist”, “non-indexical contextualist”, “expressivist”, or anyone else who denies that the premise-set contributes to content, will be unable to explain the obvious equivocation of content.
If we generalize content inheritance to cover the embeddings (of epistemic ‘must’ and ‘might’) in the right-hand-side of disjunctions and conjunctions [proposed in Klinedinst and Rothschild (2012); and adopted by Dorr and Hawthorne (2013)], then we can helpfully reply to Yalcin’s (2007) puzzle. The trouble with “p but it might be that not-p” is not the same as the trouble with “p but it is unknown that p”. The latter but not the former can be coherently embedded under “suppose”. Generalized content inheritance offers a solution. In the right conjunct ‘might’, but not ‘knows’, inherits content from the left conjunct. ‘Might not p’ expresses a claim that is true if and only if not-p is compatible with the information set comprised of p together with what is known. And since not-p is not compatible with that set, the embedded occurrence of ‘might not p’ literally contradicts the left conjunct.
Thanks to John Hawthorne and to Jim Stone for raising versions of this objection to an earlier formulation of (Coin).
Suppressing (Content Inheritance) in counterfactual contexts may seem tempting at this point, but only until we realize that it welcomes the paradoxes of implication, as demonstrated in the last section. If the epistemic modal embedded in consequent place is not enriched by the counterfactual antecedent, then it will be equivalent to the corresponding conditional regardless of its antecedent. It remains unclear how to block these problems on the current framework.
Dorr and Hawthorne (2013) do take that very conditional to be true, regardless of the truth value of the antecedent. So one may charitably read their conditional as the material conditional.
The actionability approach is developed in Heter and Salerno (manuscript), where information is said to be “actionable” just in case the salient practical deliberators can afford to access it for the purposes of the salient deliberation.
References
Dorr, C., & Hawthorne, J. (2013). Embedding epistemic modals. Mind, 122, 867–914.
Frank, A. (1996). Context dependence and modal constructions. Ph.D. dissertation. Institut für Maschinelle Sprachverarbeitung, Stuttgart.
Geurts, B. (manuscript). On an ambiguity in quantified conditionals. https://www.academia.edu/405239/On_An_Ambiguity_In_Quantified_Conditionals.
Gillies, A. (2009). On truth-conditions for if (but not quite only if). Philosophical Review, 118, 325–349.
Heter, J., & Salerno, J. (manuscript). Epistemic modals in action.
Klinedinst, N., & Rothschild, D. (2012). Connectives without truth tables. Natural Language Semantics, 20, 137–175.
Kolodny, N., & MacFarlane, J. (2010). Ifs and oughts. Journal of Philosophy, 107, 115–143.
Kratzer, A. (1977). What ‘must’ and ‘can’ must and can mean. Linguistics and Philosophy, 1, 337–355.
Kratzer, A. (1979). Conditional necessity and possibility. In R. Bäuerle, U. Egli, & A. von Stechow (Eds.), Semantics from different points of view (pp. 117–147). Berlin: Springer.
Kratzer, A. (1981). A notional category of modality. In H. J. Eikmeyer & H. Rieser (Eds.), Words, worlds, and contexts (pp. 38–74). Berlin: de Gruyter.
Kratzer, A. (1986). Conditionals. In A. M. Farley, P. Farley, & K. E. McCollough (Eds.), Papers from the parasession on pragmatics and grammatical theory (pp. 115–135). Chicago: Chicago Linguistics Society.
Kratzer, A. (2012). Modals and conditionals. Oxford: Oxford University Press.
Lewis, D. (1975). Adverbs of quantification. In E. Keenan (Ed.), Semantics of natural language (pp. 3–15). Cambridge: Cambridge University Press.
Nolan, D. (2003). Defending a possible-worlds account of indicative conditionals. Philosophical Studies, 116, 215–269.
Stalnaker, R. (1975). Indicative conditionals. Philosophia, 5, 269–286.
Yalcin, S. (2007). Epistemic modals. Mind, 116, 983–1026.
Yalcin, S. (2012). A counterexample to modus tollens. Journal of Philosophical Logic, 41, 1001–1024.
Zvolenszky, Z. (2006). A semantic constraint on the logic of modal conditionals. Proceedings of the Ninth Symposium on Logic and Language (LoLa 9). http://philpapers.org/archive/ZVOASC.pdf
Acknowledgments
This paper was supported by visiting research at the Institut Jean Nicod and by the Provost’s Facutly Research Grant as Saint Louis University. Material here has benefitted from conversations with Fabrizio Cariani, Paul Egré, André Fuhrmann, John Greco, Valentine Hacquard, John Hawthorne, Roy Sorensen, Ben Spector, Jim Stone, Seth Yalcin and audience members at the Goethe University of Frankfurt in the Spring of 2011.
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Salerno, J. Epistemic modals and modus tollens. Philos Stud 173, 2663–2680 (2016). https://doi.org/10.1007/s11098-016-0669-4
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DOI: https://doi.org/10.1007/s11098-016-0669-4