Alhassanain(p) Network for Heritage and Islamic Thought

3. Indicative conditionals

Debates about whether indicative conditional statements express propositions predate the recent flurry of discussion about epistemic modals, but the parallels are clear. I will argue that we can reconcile the propositional and non-propositional approaches, and my attempt to do this will replay the same themes seen in our discussion of deontic and epistemic modals. On the one side of the old debate about conditionals is the hypothesis that a conditional statement, whether indicative or subjunctive, expresses a proposition that is a function of the propositions expressed by its constituents, the antecedent and the consequent. The function may, and is usually assumed to be, context-dependent. On the other side is the hypothesis that the indicative conditional is used to make a distinctive kind of speech act involving just two propositions – those expressed by antecedent and consequent.  A conditional assertion is not the unqualified assertion of a conditional proposition, but a qualified assertion of the consequent, with the antecedent expressing the qualification. On this hypothesis, the conditional sentence does not purport to state a fact, but expresses an epistemic attitude, or makes a qualified commitment. Dorothy Edgington has been the most prominent proponent of the conditional assertion account. Building on earlier work by Ernest Adams, she has given both challenging arguments against the proposition analysis, and a constructive development of the view. Allan Gibbard has also argued for what Jonathan Bennett labeled the NTV (no truth-value) analysis of indicative conditionals, which Bennett also endorses. Gibbard and Bennett accept a propositional analysis ofsubjunctive conditionals, arguing that the two kinds of conditionals should receive separate analyses, while Edgington opts for a unified account according to which even counterfactuals should be understood as sentences that express certain probabilistic relations but do not express propositions. On the propositionalist side, some philosophers and linguists have defended the material conditional analysis, for indicative conditionals, attempting to explain away apparent counterexamples as cases that are true, but conversationally inappropriate. Grice adopted this strategy in his William James lectures. David Lewis, Frank Jackson, and Barbara Abbott have also argued for this analysis. Others have argued for a unified truth-conditional analysis for both kinds of conditionals. I have been on both sides of the debate between the propositionalists and the proponents of a conditional assertion account, first arguing, in a paper published in 1975[17], that the same abstract possible-worlds semantics developed for the interpretation of counterfactuals should also be used for the interpretation of indicative conditionals, with the semantic differences between the two kinds of conditionals explained by different constraints on the contextually determined parameter of the interpretation. I still think this is the right approach, though I later acknowledged, in response to arguments by Allan Gibbard, that if indicative conditionals are to play the roles that they seem to play, they “must be too closely tied to the epistemic states of the agents who utter them to express propositions which could be separated from the contexts in which they are accepted.”[18]In a recent paper, I argued that one could reconcile the conditional assertion analyses with a propositional account, seeing the former as equivalent to a special case of the latter. The general strategy parallels the one we have seen in the language game of commands and permissions, and in the semantic/pragmatic account of epistemic modals. In all of these cases, the aim is to combine the advantages of the compositional semantics that comes with a propositional approach with an acknowledgement that the expression in question is being used to do something other than to communicate an item of information.

To spell out how this idea applies to indicative conditionals, I will first review the semantic/pragmatic analysis of indicative conditionals that I have defended, and the spell out the sense in which one version of this account coincides with a conditional assertion analysis. The proposal will be that indicative conditional statements areprospective in exactly the way that permissions, commands, and epistemic ‘might’ and ‘must’ are prospective. After sketching the idea as it applies to simple conditional statements, I will look at indicative conditionals within the scope of quantifiers. As with the other modal expressions, quantified cases illustrate the advantages of the propositional form of analysis, but they also bring out problems raised by the interaction of the semantics with the pragmatic constraints. The discussion of conditionals will continue in the next chapter, where I will consider the relation between the fact-stating role of conditionals and their role in expressing epistemic attitudes.

On the propositional account of conditionals that I have defended,[19]the semantics interprets the conditional in terms of a context-dependent selection function taking a possible worldw and a propositionfto a possible world, f(w ,f) – intuitively, a world in whichfis true, but which otherwise differs minimally fromw . Nothing substantive is said in the abstract theory about the criteria for minimal difference, but formal constraints are put  on the selection function to ensure that it orders the possible worlds, with the base world,w first in the order (since any world is minimally different from itself). The semantic rule is a follows:

       (f>y) is true in possible worldw if and only ifyis true in f(f,w ). 

This semantic rule gives the truth-conditions for any conditional in a given possible world, and it also determines thesubordinate context for the conditional supposition. If C is the context set (the set of possibilities compatible with the common ground), then the subordinate context for the suppositionfis {f(w ,f):w ÎC}.

For indicative conditionals, the pragmatics adds a contextual constraint on the selection function. Where C is the context set, say that a selection function isadmissible if it meets the following condition:

       Ifw ÎC, then f(w ,f)ÎC.[20]

The effect of the constraint is to ensure that all of the presuppositions of the basic context are preserved in the subordinate context.

That is the truth-conditional semantics. We can also formulate, very simply, a conditional assertion analysis in our pragmatic framework, as follows: There is a speech act ofsupposition , which like the speech act of assertion, adds the content of the speech act to the common ground, but in this case it is added temporarily, and will no commitment to the truth of the supposition. The consequent of the conditional is then asserted in this temporary subordinate context. At the end, the possibilities that were temporarily removed are added back.[21]

Though one of these stories is propositional and the other is not, they have much in common. Each can explain why an indicative conditional assertion is very similar, in its effect, to the assertion of amaterial conditional, but each can also avoid some of the problems with a simple material conditional analysis. For example, each can explain why the rejection or denial of a conditional is very different from the rejection or denial of a material conditional. The similarity between the two analyses can be made precise by defining a version of the propositional analysis that is essentially a terminological variant of the conditional assertion view.[22]First, we note that any contextual parameter relative to which truth-conditions are specified (a modal base, a domain of discourse, a selection function, the referent of a demonstrative) may be underdetermined by the actual context. In such cases, a proposition may be partial – a truth-value determined for some, but not all possible worlds. Suppose we adopt a version of our propositional semantics for indicative conditionals that is maximally cautious, determining a truth-value for a conditional only when the rules we have specified suffice to determine one, as a function of the antecedent, the consequent, and the common ground. This is accomplished by saying that alladmissible selection functions are on a par. A conditional is true (relative to a given CG-context) if true for all admissible selection functions, false if false for all, and neither true nor false otherwise.[23]The upshot will be that a conditional sentence will be false in possible worlds compatible with the context if and only if that possibility would be excluded by the conditional assertion, according to the conditional assertion analysis. So one can see this version of the propositional theory as an implementation of the conditional assertion account. But this will work only if we assume that the interpretation of the conditional sentence isprospective . Here is the argument that this assumption is necessary: suppose Ibelieve that learningfwould be sufficient reason (given my other beliefs) for acceptingy, but that this is not common ground, since (f&~y) is compatible with the prior context. A conditional assertion would clearly be appropriate in this situation, since in a context in whichfis supposed, I am in a position to asserty. But on the maximally cautious version of our truth-conditional semantics, if we interpret the conditional (iff, theny), relative to theprior context, the conditional will be neither true nor false in the possible worlds in whichfis false. Since I am not in a position to rule out these possibilities, the conditional, interpreted this way, would not be assertible.  But if we interpret the conditional relative to theposterior context, where that context is the result of the minimal adjustment necessary to make the conditional true, relative to the adjusted context, then the conditional statement will be appropriate, and we get the equivalence between our two accounts.  Just as with the epistemic ‘may’ and ‘must’ statements, the effect is to adjust at once a parameter of the interpretation and the set of possibilities compatible with the common ground. In the epistemic modal case, the changing common groundis the parameter of the interpretation; in the case of conditionals, the parameter is closely constrained by the changing common ground. The general account explains both how the expressive speech acts are like assertions, and how they are different. In all cases, the end result of a successful speech act will be a context in which the proposition expressed is true in all of the possible worlds compatible with what is then the common ground. In the non-assertion cases, this success is achieved, in part, by changing the determinants of the truth-conditions for the proposition.

If the upshot is the equivalence of the conditional assertion analysis and (one version of) the propositional account, why is it important to go with the truth-conditional semantics? Part of the answer is the familiar one – that it provides a semantics for sentences in which conditionals are embedded in other constructions – but of course this is an advantage only if the compositional semantics gets the right result. Lewis appealed to compositionality in defending the presumption that indicative conditionals express propositions “We think we know how the truth conditions for compound sentences of various kinds are determined by the truth conditions of constituent subsentences, but this knowledge would be useless if any of those subsentences lacked truth conditions.”[24]But the particular analysis of indicative conditionals that Lewis defended was the material conditional analysis, and it is precisely with the embedded conditionals that this analysis gets things wrong. As we have seen, simple assertions of indicative conditionals have essentially the same effect as the assertion of the corresponding material conditional, on both the conditional assertion analysis, and on our minimal truth-conditional hypothesis, but the most dramatic divergence between ordinary indicative conditionals and material conditionals occur with denials, rather than assertions, or with conditionals embedded under negation. The truth-conditional account I am defending does better with embedding under negation, and I will argue that it also does better with conditionals in quantified sentences.

A second advantage of a truth-conditional semantics for indicative conditionals is that it allows for continuity between cases where conditionals seem to express an epistemic attitude and cases where their aim seems to be to communicate information about the world, information that is independent of the epistemic situation of the participants in a conversation in which the information is exchanged.  It may be a matter of debate and negotiation, not only what the facts are, but what there is a fact of the matter about, and it is good to have a framework that does not require that such questions be settled in advance. I have more about this issue in another context, but for now let’s look at the compositional considerations – particularly at the interaction of indicative conditionals with quantifiers.

  Jim Higginbotham argued that quantified conditionals present a prima facie case of non-compositionality.[25]He begins by comparing two examples, with different quantifers, each with the a conditional open clause in the scope of the quantifier:

       (1) Everyone will succeed if he works hard

       (2) No one will succeed if he goofs off

He claims that the first can be interpreted as a conditional in the scope of a quantifier, but that the second cannot. Higginbotham is not explicit about how he is interpreting the conditional at this point in the discussion, but what he says about (2) suggests that his noncompositionality claim is based on a strict conditional interpretation. Suppose we interpret (2) as saying that for no x (in the relevant domain) is it true that if x goofs off, x succeeds. His claim is that it would then say that goofing off is in no case a sufficient condition for success, while the actual meaning is that in no case is goofing off compatible with success. The point is all the more obvious if we interpret the conditional as a material conditional, for then (2) would assert that everyone will goof off, and that no one will succeed, which is obviously not what it says.  Higginbotham then suggests that compositionality can be restored if we give the semantic analysis that I proposed, and that I have sketched here, though he does not consider the pragmatic constraint.  On this analysis, one could paraphrase (2) this way:

(2’) The following is true of no x (in the relevant domain): in the world minimally different from ours (in relevant respects) in which x goofs off, x succeeds.

This seems to get things right.

Higginbotham considers an alternative analysis that takes ‘if’ clauses to be restrictors on the quantifier, rather than sentential connectives. On this analysis, (1) and (2) could be paraphrased this way:

       (1r) Everyone who works hard will succeed

       (2r) No one who goofs off will succeed.

This also seems to get things right for these cases, but Higginbotham argues that the analysis does not generalize. The clearest counterexamples are with the quantifiers ‘most’ and ‘few’, though there are also problem cases with all, some and none. Compare

       (3) Most (of these) students will get A’s if they work hard.

       (3r) Most (of these) students who work hard will get A’s.

(3r) will be true if a majority of the hard-working students will get A’s, while (3) will be true if a majority ofall the students meet the condition that they will get an A if they work hard. Neither statement entails the other. It might be that only a few students will work hard, and most of them will get A’s, but that the majority of students would get B or lower, however hard they worked. On the other hand, it could be that hard work would be sufficient for an A for most of the students, but unfortunately, only a minority of those who will actually work hard are among those capable of achieving an A.

Higginbotham argues that even with universal quantifiers, there is a difference between the quantifier restrictor analysis and the quantified conditional analysis, though in this case the latter entails the former. He uses the following minimal pair to illustrate the difference:

       (4)   Every professor will retire early if offered a generous pension.

       (4r) Every professor offered a generous pension will retire early.

“There might be,” Higginnbotham says, “many professors (but even one will do) who we can be sure will not retire early, quite independently of any pension they may be offered.” In this case, (4) will be false, while (4r) will be true, if all the professors who areactually offered a generous pension choose to retire early.

We get the same contrast in the negative universal case, again using Higginbotham’s examples:

       (5) No professor will retire early if not offered a generous pension.

       (5r) No professor not offered a generous pension will retire early.

“If Professor X is going to retire early, period, then he is a counterexample to [(5)], but if he is amongst those offered a generous pension, then he is no counterexample to [(5r)].”

As Higginbotham notes, to get the right result for (5), by straightforward application of compositional rules, we need to assume the principle of conditional excluded middle (CEM), which is validated by the semantics sketched above.[26]Assuming that  “no x” means “for all x, not”, (5) has the structure: for all x, it is not the case that [if x is not offered a generous pension, x will retire early].  CEM gets us from this to: for all x, [if x is not offered a generous pension, then x will not retire early], which seems to be the right result.

Higginbotham’s discussion ignores the distinctive features ofindicative conditionals: both the contextual constraint on the selection function used to interpret conditionals, and the prospective character of the interpretation. As he notes, his treatment of the examples “very much depends on the sensitivity of the conditional to counterfactual situations,” but one cannot assume, in general, that the correctness or adequacy of an indicative conditional claim (if Professor X is offered a generous pension, he will retire early”) will correspond to the truth or acceptability of the corresponding counterfactual (if Professor X, who will not in fact be offered a generous pension,were offered a generous pension, he would retire early.) Suppose we know that our administration will offer pensions only to those they predict will accept, and while we have no idea who will be offered a pension in exchange for early retirement, or who is disposed to accept the offer, we believe the crafty administrators are very good at such predictions. Then we might believe, of each professor, that he or she will retire early if offered a pension, while not being prepared to accept that every professorwould accept the deal, if offered. But this hypothesis is contrived. Higginbotham’s examples still work if we assume, as is plausible for this example in the normal case, that there is no epistemic or causal correlation between those who will be offered pensions in exchange for early retirement and those who are disposed to accept them.  For some other examples, however, including one discussed by Higginbotham, the distinctive features of indicative conditionals matter, and ignoring them raises new problems.

Suppose (to use another of Higginbotham’s examples) I have been told by someone I trust, and who shares my standards for boringness, that

(6*) every book on that shelf with a red cover is boring.

At least if we assume that we don’t know anything in advance about what books are on the shelf, this seems to be enough to justify my statement

(6) every book on the shelf is boring if it has a red cover.

But, Higginbotham observes,

we know in advance that giving a book a red cover does not alter its contents, so does not affect whether it is boring. Letb be a book on that shelf with a blue cover. In the closest possible world, whatever it is, in whichb has a red cover, it is boring or not, just as it is boring or not as things are. But then it seems that [(6)] should be false if there are non-boring books on the shelf whose covers are not red, although they might have been!

This is, as Higginbotham observes, the wrong result. I don’t understand his response to the problem, but it seems to be an ad hoc fix. Instead, I think we should recognize what we have independent reason to recognize: that the contextual and epistemic relations that are relevant to the interpretation of indicative conditionals can come apart from the causal relations that are relevant to counterfactual conditionals.

Suppose I learn that one of the books on the shelf isInfinite Jest by David Foster Wallace. I know nothing about the book, let us suppose. I plan to check the cover before deciding whether to read it, since I believe (based on the information from my trustworthy informant) that if it has a red cover, it will be a boring read.  The same could be said for any of the books on the shelf, assuming that I don’t have an independent opinion about any of them. On the other hand, suppose I do know aboutInfinite Jest – I’ve read it, and it is definitely not boring. I conclude (again, based on the information from my informant) that it must not have a red cover. I don’t, however, have any independent reason to have an opinion about the color of this book’s cover, so if I were to learn that it has a red cover, I would conclude that the informant was mistaken. In this case (after I have learned thatInfinite Jest is on the shelf, but before learning what color its cover is), I still believe that every book on the shelf with a red cover is boring, but I am not longer prepared to say, of every book on the shelf, that it is boring if it has a red cover.

For simple indicative conditionals, on our account, it is a constraint that the antecedent must be compatible with the CG-context. I can say “iff” (indicative) only in a context that allows that it might be thatf. When the constraint is not met by what the addressee takes the common ground to be, he must accommodate.[27]The same constraint should be met with quantified conditionals: if I say that all or most or some of the Fs are H if they are G, then it should be true of each of the F’s that it might be G. But it is not always straightforward how to apply this constraint, since even when it seems, in a sense, true of each of the Fs that it might be G, there may be ways of describing one of the Fs such that it isnot compatible with the common ground that an F fitting that description be a G. Suppose we know that not all of the books on the shelf have red covers. It is common ground that there are some blue ones. It is compatible with this assumption that each of the books on the shelf (the first one, the second one, etc.) might have a red cover. But it is of course not true that the firstblue one might have a red cover.  It may be unclear, in some cases, whether it is right to say that each of the Fs might be a G, but these will be just the cases where it is unclear whether the quantified conditional is acceptable. Higginbotham mentions this example,

       ??(7) Every coin is silver if it is in my pocket

which is distinctly odd, in contrast with

       (7*) Every coin in my pocket is silver

which is fine.  It would be equally odd to say that every coin is such that it might be in my pocket.

My original discussion of the account of indicative conditionals that I am defending here began with what I called the direct argument:

       Either the butler or the gardener did it, so if the butler didn’t, the gardener did.

The puzzle was that if this argument, which seems compelling, issemantically valid , then the material conditional analysis of the indicative conditional must be right. But it seems that we have other reasons to reject that analysis.[28]The solution to the puzzle was to use the dynamic interaction of the semantic analysis with the pragmatic constraint to explain how the argument could be a compelling inference, even though not semantically valid. The acceptance of the premise changed the context in a way that ensured that the proposition expressed by the conclusion, relative to that revised context, would be true.  So the semantic/pragmatic analysis accepts, and explains, the data that motivate the material conditional analysis without being saddled with the problems faced by that analysis. The possible-worlds semantics for the conditional is a part of the theory that accommodates and explains these data, but the contextual constraint, distinctive to the indicative, is also an essential part of the explanation. Barbara Abbott, in her Gricean defense of the material conditional analysis, presents counterexamples to the possible-worlds semantic analysis, but she ignores the pragmatic side of the analysis, which shows why the examples she gives are not counterexamples. Nevertheless, her main example is interesting, involving quantifiers, so let’s look at it, and see how our semantic/pragmatic account explains her, and our, judgments about it.

Here is Abbott’s Snodgrass example:

We have received a number of letters about the water shortage. Almost all of them were 5 pages or less, and all of those received an answer. One letter (from Byram Snodgrass) was 5 pages plus a few words, and the last letter was 8 pages. We did not reply to the last two letters. The 8-page one was just too long to consider, and Byram Snodgrass is a crank who has been writing incoherent letters to us about everything under the sun ever since we took on the post of Water Commissioner. We never answer his

letters.

Byram called our office to find out whether his letter had been sent a reply. Based on the truth in (12),

(12)            Every letter no longer than 5 pages was answered.

we said (13):

(13)            If your letter was no longer than 5 pages, it was answered.

Our reply was truthful.

There is a sharp contrast between the true indicative conditional in (13) and the corresponding subjunctive conditional in (14), which is not true:

(14)            If your letter had been no longer than 5 pages, it would have

been answered.

As noted, we never answer letters from Byram Snodgrass.

All of this seems right, and it is exactly as predicted by our analysis of the indicative conditional. The reply to Byram’s inquiry wasmisleading , as I am sure Abbott would agree, since it implicated that the speaker was not in a position to give a complete answer to his question (“was my letter answered?”). But our account agrees that it is truthful, since even though both the speaker and the addressee know that the letter was longer than five pages, and so that the antecedent of the conditional is false, this is not common ground. (the indicative antecedent indicates that it is not.)  On our analysis, the conditional is true in all possible worlds compatible with the prospective common ground, and we may presume that this includes the actual world, since none of the relevant presuppositions are false. The indicative conditional claim (on our modal analysis) does exactly what the assertion of the material conditional does: it excludes possible worlds in which the antecedent is true and the consequent false.

The Water Commissioner’s office might have replied to Snodgrass’s inquiry (equally truthfully, and equally misleadingly) with a universal generalization:

       (15) Every letter was answered if it was no more than five pages long.

Both our analysis and the material conditional analysis predict that this is true.  Or, the office might have replied (again, misleadingly but truthfully) with a negative universal generalization:

       (16) No letter was answered if it was more than five pages long.

In this case, the reply will inform Byram (assuming he remembers how long his letter was) that his letter was not answered, but will be misleading because it implicates that the answer explains why it was not answered, and this is false. But in this case, the material conditional analysis gets the truth conditions dramatically wrong, since the negative universal material conditional falsely implies that every letter was longer than five pages, and that none of them was answered. We can save the material conditional analysis, in the negative universal case, only by giving up compositionality. But our truth-conditional version of the conditional assertion account gives a compositional analysis that I think gets the facts right.

References

1-Abbott, B. 2008. “Presuppositions and common ground,”Linguistics and Philosophy 31: 523-538.

2-Abbott, B. 2010. “Conditionals in English and first order predicate logic,” in D. Shu & K. Turner, eds.,Contrasting meaning in languages of the east and west . Oxford: Peter Lang, 579-606.

3-Donnellan, K. 1966. “Reference and definite descriptions,”Philosophical Review 75: 281-304.

4-Edgington, D. 1986. “Do conditionals have truth-conditions?”Critica 18: 3-30.

5-von Fintel, K. and A. Gillies. 2011. “’Might’ made right,” in A. Egan and B. Weatherson, eds.,Epistemic modality . Oxford: Oxford University Press, 108-130.

6-van Fraassen, B. 1966. “Singular terms, truth value gaps, and free logic.Journal of Philosophy 63: 481-95.

7-Higginbotham, J. 2003. “Conditionals and compositionality,” in J. Hawthorne and D. Zimmerman,Philosophical Perspectives, 17,Language and Philosophical Linguisitcs . Oxford: Blackwell, 181-194.

8-Lewis, D. 1973.Counterfactuals . Cambridge, MA: Harvrd University Press.

9-Lewis, D. 1974.  “Semantic analysis for dyadic deontic logic,” in S. Stenlund,Logical theory and semantic analysis Essays dedicated to Stig Kanger on his fiftieth birthday . Dordrecht: Rediel. (Reprinted in Lewis, 2000, 5-19.

10-Lewis, D. 1975. “A problem about permission,” in E. Saarinen et al, eds.Essays in honour of Jaakko Hintikka , Reidel, Dordrecht, 163-75. (Reprinted in Lewis, 2000, pp. 20-33. Page references to the reprinted version.)

11-Lewis, D. 2000.Papers in Ethics and Social Philosophy . Cambridge: Cambridge University Press.

12-Ninan, Dilip. 2005. “Two puzzles about deontic necessity.”New work on modality, MIT working papers in linguistics 52. ed. by J. Gajewski, V. Hacquard, B. Nickel and S. Yalcin. Cambridge, Mass.: MIT Press.

13-Stalnaker, R. 1968. “A theory of conditionals,” in N Rescher, ed.,Studies in Logical Theory , Oxford, Blackwell, 98-112.

14-Stalnaker, R. 1975. “Indicative conditionals,”Philosophia 5: ??. (Reprinted in Stalnaker, 1999, 63-77.)

15-Stalnaker, R. 1984.Inquiry . Cambridge, MA: The MIT Press.

16-Stalnaker, R. 2008. “A response to Abbott on presupposition and common ground”Linguistics and Philosophy , 31: 539-44.

17-Stalnaker, R. 2011b. “Conditional propositions and conditional assertions,” in A. Egan and B. Weatherson, eds.,Epistemic modality . Oxford: Oxford University Press, 227-248.

18-Yablo, S. 2011. “A problem about permission and possibility,” in A. Egan and B. Weatherson, eds.,Epistemic modality . Oxford: Oxford University Press, 270-294.

19-Yalcin, S. 2007. “Epistemic modals,”Mind , 116: 983-1026.

20-Yalcin, S. 2011. “Nonfactualism about epistemic modality,” in A. Egan and B. Weatherson, eds.,Epistemic modality . Oxford: Oxford University Press, 295-332.

21-Yalcin, S. and J. Knobe. 2010. “Fat Tony might be dead. An experimental note on epistemic modals.” (http://www.semanticsarchive.net/Archive/TdiZjA3N/)

Notes