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Whether-conditionals

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Abstract

In this paper I look at indicative nested whether-conditionals, sentences like:

If I pass the exam, I will pass whether I pray or not.

The behavior of ‘if’ in these examples is to be contrasted with the behavior of ‘if’ in or-to-if conditionals:

If Mary is at home or at work, then if she is not at home, she is at work.

I argue that no currently available semantics for indicative conditionals can explain both the behavior of ‘if’ in nested whether-conditionals and the behavior of ‘if’ in or-to-ifs. We need a theory that predicts both. While no currently available theory makes the right predictions, one theory comes close—Heim’s rendition of Stalnaker’s semantics (Heim in J Semant 9(3):183–221, 1992). I show how to fix Heim’s view to get the right results for all cases. In sum, the paper argues for a particular development of Stalnaker’s semantics, and shows that whether-conditionals cannot be dealt with on other approaches.

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Notes

  1. Although important and interesting, I leave out of account non-truth-conditional theories of the indicative conditional in this paper.

  2. According to the view I will defend, ‘if’ does indeed always shift context, but this shift is sometimes cancelled through presupposition accommodation—hence the appearance, in certain special cases, that the context had not been shifted.

  3. This is a necessary feature of the example. If we knew that a Republican will win, the conclusion would plausibly be true, and not false, as intended.

  4. McGee’s counter-examples have met with some objections. For discussion see, e.g., Lowe (1987), Piller (1996), Katz (1999). I think McGee’s argument is successful, but whether it is will not matter for the argument to follow.

  5. The logical truth of the or-to-if conditional is to be distinguished from the validity of what is often called the or-to-if inference: \(\phi\) or \(\psi\) \(\models\) if not \(\phi\), then \(\psi\). The or-to-if inference may well be invalid even if the or-to-if conditionals are logically true.

  6. One can think of the epistemic context as a set of propositions, or as a set of worlds. It will be crucial to the proposal I develop in Sect. 7 that we think of the epistemic context in the first way.

  7. Since c\(\cup \phi\) is not a proposition, but a set of propositions, strictly speaking, sim(w, c + \(\phi\)) returns the closest world w\(\prime\) in which all the propositions in c + \(\phi\) are true.

  8. This is a helpful way of thinking about indicative even if one does not adapt Heim’s dynamic view of meaning. The proposal I articulate in this paper is truth-conditional. The choice between dynamic and truth-conditional versions of the view would have to be decided on other grounds. I wll not discuss this issue.

  9. This is a static version based on Heim’s dynamic formulation: c+ if \(\phi\), then \(\psi\) = w\(\in\)c: sim(w, c + \(\phi\)) + \(\psi\) = sim(w, c + \(\phi\))) (Heim 1992, p. 196).

  10. Here are the predictions for a generic right-nested conditional ‘if \(\phi\), then if \(\psi\), \(\theta\)’:

    Stalnaker:

    An indicative ‘if \(\phi\), then if \(\psi\), \(\theta\)’ is true in w, c, iff ‘if \(\psi\), \(\theta\)’ is true in sim(w, c + \(\phi\)), c, iff ‘\(\theta\)’ is true in sim(sim(w, c + \(\phi\)), c + \(\psi\)), c

    Heim:

    An indicative ‘if \(\phi\), then if \(\psi\), \(\theta\)’ is true in w, c, iff ‘if \(\psi\), \(\theta\)’ is true in sim(w, c + \(\phi\)), c + \(\phi\) iff ‘\(\theta\)’ is true in sim(sim(w, c + \(\phi\)), c + \(\phi\) + \(\psi\)), c + \(\phi\) + \(\psi\)

  11. The argument has a long history. Cf. Cicero, On Fate:

    ‘Nor will we be blocked by the so called ’Lazy Argument’ (the argos logos, as the philosophers entitle it). If we gave in to it, we would do nothing whatever in life. They pose it as follows: ‘if it is your fate to recover from this illness, you will recover, regardless of whether or not you call the doctor. Likewise, if it is your fate not to recover from this illness, you will not recover, regardless of whether or not you call the doctor. And one or the other is your fate. Therefore it is pointless to call the doctor...’ (Long & Sedley, The Hellenistic Philosophers, 55S, p. 339).

    Of course, there is a major difference: the Lazy Argument is fallacious, while Ivan’s argument is not.

  12. Pass/Fail appeals to our dynamic intuitions, intuitions about informativeness. But things are the same if we ask instead about our static intuitions—intuitions about what is and is not true in a given context. So consider also Pass/Fail*: Pass/Fail with the stipulation that in fact there is a god who rewards prayers and punishes lack of prayer. Then the initial observation is: (6) and (7) are false in Pass/Fail*.

  13. The past-tense analogues of (6) and (7) are similarly informative. So, if the exam has already taken place, but the results have not yet come in, Ivan can informatively say ‘If you passed, you passed whether or not you prayed’. But I have found that some informants’ intuitions are that the past-tense analogues of (6) and (7) are trivially true. Perhaps some context-setting might help regain the informativeness intuition. Suppose the exam had already taken place, but Grandma and Grandpa have not yet heard how Joe fared. Grandpa: ‘I am worried about Joe’s exam. I sure hope he studied for it.’ Grandma: ‘Oh, don’t you worry, you know how our Joe is: a bright boy, no problem too hard for him, but always gets so nervous on tests. I am sure that if he passed, he passed whether or not he studied.’—here it seems clear that Grandma is communicating that studying had no influence on passing, though nervousness during the exam might have.

  14. There are at least two ways of thinking about rewards: one may imagine that the relevant god just makes you pass, or one may imagine that the relevant god gives you some extra points—whether the extra points are or are not sufficient to make the passing grade. I will be assuming the first way of thinking about rewards and punishments.

  15. Note that Stalnaker’s semantics gets (6) [and so (9)] right. So the situation is curiously symmetrical: Stalnaker gets the deviant readings right, and the normal readings wrong; all the other theories of conditionals get the normal readings right, and the deviant readings wrong.

  16. Why is epistemic context-shifting normal, and not shifting deviant, rather than the other way around? First, the normal behavior is indeed wide-spread (hence the intuitive appeal of import-export). Second, as we shall see (Sect. 6), the deviant behavior arises only in very special circumstances.

  17. Note that I am not here attempting to arrive at the meaning of whether-conditionals compositionally, and so derive Face Value. For an analysis that does derive such an equivalence, as well as for further details on the syntax and semantics of whether-conditionals and other related constructions, see Rawlins (2013).

  18. Note that the argument against Heim’s view does not in fact need Face Value to go through. All one needs is the very weak assumption that ‘\(\phi\), whether or not \(\psi\)’ is trivially true in a context that takes \(\phi\) for granted. Then Heim would still predict (6) to be trivially true in Pass/Fail.

  19. Thanks to my anonymous reviewer for urging these concerns on my attention.

  20. The standard view on even if conditionals is something like this:

    1. 1.

      \(\psi\), even if \(\phi\)’ is true in w, c, just in case ‘if \(\phi\), then \(\psi\)’ is true in w, c.

    2. 2.

      \(\psi\), even if \(\phi\)’, uttered at w, c, carries the presupposition that

      1. (a)

        1. the context c is partitioned by some salient partition \(\hbox {R}=\hbox {R}_1, \hbox { R}_2,\ldots \hbox {R}_n\), that is ordered by some salient relation \(>\) (let’s say \(\hbox {R}_1>\hbox {R}_2>\cdots >\hbox {R}_n\)).

      2. (b)

        2. \(\phi =\hbox {R}_n\). (alternatively, perhaps \(\phi =\hbox {R}_j\), for some \(\hbox {j}\le \hbox {n}\))

      3. (c)

        3. ‘if \(\hbox {R}_i\), then \(\psi\)’ is true in w, c, for all \(\hbox {R}_i<\phi\).

    For a review of the semantics of ‘even’, see Giannakidou (2007). For more on ‘even if’, see Lycan (2001), Barker (1994), Bennett (1982). Note that the precise semantics of ‘even if’ does not matter much for the point I wish to make here: (12) would still come out trivially true in Pass/Fail.

  21. I am focusing on nested whether-conditionals here. But the generalization extends immediately to nested even-ifs and plain nested indicatives: these are singular when the nested consequent is identical to the antecedent.

  22. Note that it is very natural to think that singularity extends also to those nested whether-conditionals ‘if \(\phi\), then \(\psi\), whether or not \(\theta\)’ in which \(\phi\) entails \(\psi\)). I do not have the data to test this generalization. However, the arguments below would not be affected if it turned out deviance is more wide-spread.

  23. Although there is not much evidence for the open consequent presupposition, it has one strong argument in its favor: as von Fintel (1998, pp. 8–9) shows, it allows us to solve the problem of non-counterfactual subjunctives (aka the Anderson sentences like ‘Had the patient taken arsenic, he would be showing just the symptoms he does in fact show’). von Fintel calls it ‘consequent variety’, but suggests that it is weaker than a presupposition—merely a ‘presumption’. I am not sure what presumptions are, and so stick with the status of presupposition.

  24. An anonymous reviewer proposed the following counter-example to the open consequent presupposition: ‘If Ramsey’s theorem holds for two colors, it holds for any finite number of colors’. The conditional is felicitous, and yet there are no possible worlds in which the consequent is false. I think such examples show little. Examples involving necessarily true antecedents could, in the same fashion, be considered counter-examples to the open antecedent presupposition for indicatives, and yet this presupposition is firmly established: in our present state of knowledge, no indicative beginning with ‘if Kennedy is alive,...’ is felicitous. Perhaps such examples are to be treated by postulating epistemically possible yet metaphysically impossible worlds. That said, I do not claim to have an outright argument for the open consequent presupposition. In the present context, I am putting it forward as part of a package that best explains the data (viz. the deviant behavior of ‘if’).

  25. For more on presupposition accommodation, see von Fintel (2008).

  26. Do we have examples of accommodation by expansion? Perhaps we do. When one believes that P, and someone else asserts that Q, such that Q presupposes \(\lnot\)P, one can only accommodate by expansion, if one accommodates at all.

  27. Note that here it is crucial that c is a set of propositions, rather than a set of worlds. If we removed all the Q-worlds from c, we would be left with the empty set, in cases where up-accommodation is triggered by the failure of the open consequent presupposition. The issue here is related to the problem of making counterfactual assumptions discussed by Veltman (2005). In fact, the two issues might just be one.

  28. Note also that if we wanted up-accommodation to guarantee that the resulting context satisfies the open consequent presupposition, there would of course be, in principle, many ways to do it: if a set of propositions \(\Gamma\) entails \(\phi\), there can, in principle, be many ways of subtracting some propositions from \(\Gamma\) in such a way that \(\Gamma \backslash \{\psi 1,\psi 2,\ldots \}\) no longer entails \(\phi\). Clearly there is more work to be done on exactly how up-accommodation works.

  29. Thanks to an anonymous reviewer for pressing this point, and suggesting an example.

  30. Here is how McGee explains it: ‘It is not hard to modify the Stalnaker semantics so that it has the right logical features. instead of a simple notion of truth in a world, we develop a notion of truth in a world under a set of hypotheses. To be simply true in a world is to be true in that world under the empty set of hypotheses. If there is no world accessible from w in which all the member of \(\Gamma\) are true, then every sentence is true in w under the set of hypotheses \(\Gamma\). Otherwise we have the following: An atomic sentence is is true in w under the set of hypotheses \(\Gamma\) iff it is true in the possible world most similar to w in which all the members of \(\Gamma\) are true. A conjunction is true in a world under a given set of hypotheses iff each of its conjuncts is. A disjunction is true in a world under a set of hypotheses iff one or both disjuncts are. \(\lnot \phi\) is true in w under the set of hypotheses \(\Gamma\) iff \(\phi\) is not true in w under that set of hypotheses. Finally, ‘\(\phi \rightarrow \psi\)’ is true in w under the set of hypotheses \(\Gamma\) iff \(\psi\) is true in w under the set of hypotheses \(\Gamma \cup \{\phi \}\). Thus to evaluate whether ‘\(\phi \rightarrow (\psi \rightarrow \theta )\)’ is true under the set of hypotheses \(\Gamma\), we add first \(\phi\) and then \(\psi\) to our set of hypotheses, and we see whether \(\theta\) is true under the augmented set of hypotheses \(\Gamma \cup \{\phi , \psi \}\).’ (McGee 1985, p. 469).

References

  • Barker, S. J. (1994). The consequent-entailment problem for even if. Linguistics and Philosophy, 17(3), 249–260.

    Article  Google Scholar 

  • Bennett, J. (1982). Even if. Linguistics and Philosophy, 5(3), 403–418.

    Article  Google Scholar 

  • Giannakidou, A. (2007). The landscape of EVEN. Natural Laguage and Linguistic Theory, 25(1), 39–81.

    Article  Google Scholar 

  • Heim, I. (1992). Presupposition projection and the semantics of attitude verbs. Journal of Semantics, 9(3), 183–221.

    Article  Google Scholar 

  • Katz, B. D. (1999). On a supposed counterexample to modus ponens. Journal of Philosophy, 96(8), 404–415.

    Article  Google Scholar 

  • Kratzer, A. (1986). Conditionals. CLS, 22.

  • Lowe, E. J. (1987). Not a counterexample to modus ponens. Analysis, 47(1), 44–47.

    Article  Google Scholar 

  • Lycan, W. G. (2001). Real conditionals. Oxford: Oxford University Press.

    Google Scholar 

  • McGee, V. (1985). A counterexample to modus ponens. Journal of Philosophy, 82(9), 462–471.

    Article  Google Scholar 

  • Piller, C. (1996). Vann McGee’s counterexample to modus ponens. Philosophical Studies, 82(1), 27–54.

    Article  Google Scholar 

  • Rawlins, K. (2013). (Un)conditionals. Natural Language Semantics, 21(2), 111–178.

    Article  Google Scholar 

  • Stalnaker, R. (1975). Indicative conditionals. Philosophia, 5(3).

  • Veltman, F. (2005). Making counterfactual assumptions. Journal of Semantics, 22, 159–180.

    Article  Google Scholar 

  • von Fintel, K. (1998). The presupposition of subjunctive conditionals. In U. Sauerland, & O. Percus (Eds.), The interpretive tract, MIT Working Papers in Linguistics (vol. 25, pp. 29–44). Cambridge, MA: MITWPL.

  • von Fintel, K. (2008). What is presupposition accommodation, again? Philosophical Perspectives, 22(1), 137–170.

    Article  Google Scholar 

Download references

Acknowledgments

I would like to thank Matti Eklund, Harold Hodes, Nico Silins, Will Starr, and Fabrizio Cariani for extensive comments on earlier drafts of this paper.

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Korzukhin, T. Whether-conditionals. Philos Stud 173, 609–628 (2016). https://doi.org/10.1007/s11098-015-0510-5

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