CONDITIONAL-ASSERTION THEORIES OF CONDITIONALS

William G. Lycan

Some clever ass has said that ‘if’ is the biggest word in the language, but I say it’s the most useless.
--Sir Harry Flashman[1]
Now under what circumstances is a conditional true?Even to raise this question is to depart from everyday attitudes.An affirmation of the form ‘if p then q’ is commonly felt less as an affirmation of a conditional than as a conditional affirmation of the consequent…. If, after we have made such an affirmation, the antecedent turns out true, then we consider ourselves committed to the consequent, and are ready to acknowledge error if it proves false.If on the other hand the antecedent turns out to have been false, our conditional affirmation is as if it had never been made.
            Departing from this usual attitude, however, let us think of conditionals simply as compound statements which, like conjunctions and alternations, admit as wholes of truth and falsity.
--W.V. Quine

Quine attributes the view here called the “usual attitude” to Dr. Philip Rhinelander.[2]His casual departure from it is now (half a century on) a bit controversial.While many theories have been offered according to which conditionals, subjunctive and indicative alike, are compound statements that have truth-values as wholes,[3] descendants of the conditional-assertion theory that he calls the “usual attitude” have recently made a strong comeback as competitors of the standard truth-conditional theories of indicative conditional sentences.My purpose in this paper is to assess their prospects in that role.

ithe quine-rhinelander theory

What Quine and Rhinelander termed “affirmation” is now more commonly called “assertion,” and affirming and asserting are illocutionary acts.The parallel is with common conditional speech acts such as conditional requests (“If you’re going out anyway, could you please pick up some Dos Equis?”) or conditional bets (“If Kerry gets the nomination, I bet you $100 he’ll win”); should the antecedents prove false, no request has been issued and the bet is off. (Or so it is widely supposed; the latter claims are not obvious.)Call the conditional-assertion view thus interpreted the “Simple Illocutionary theory.”

But to understand the conditional-assertion view in that light is to diminish its force as a competitor of the standard theories of conditionals, for those are semantic theories applying to sentences, or to sentences in contexts of utterance, not to acts of asserting or their social products.I suppose that is one reason why Quine did his departing; as is well known, there is no simple relation between speech acts of asserting and the semantic properties of the sentences uttered.[4](No doubt a more fundamental reason is that he was bent on what he called the “regimentation” of factual discourse, not on either commonsensical views of asserting or, for that matter, on the ordinary meanings of conditional sentences in natural language, whatever those might be if they existed at all.[5])

It is curious, though, that Quine took the Simple Illocutionary (SI) theory to be the “usual attitude” orcommon sense, or the ordinary person’s interpretation of conditional speech.For that is a very strange imputation.[6]I strongly doubt that any ordinary person, hearing a speaker utter an ordinary conditional sentence, would suspend judgment on whether any assertion had been made until it had been established whether the antecedent was actually true.My neighbor says to her daughter, “If you don’t finish mowing the yard this afternoon, you can’t go to the mall after dinner.”I think the daughter, at least, would perceive that something fairly substantial had been asserted, right then.And it is odd to suppose that by mowing the rest of the yard, she could see to it that her mother had asserted nothing at all.

Setting aside the question of common sense or ordinary usage, the SI theory is implausible in its own right.Some other examples to show that: “The element will burn out if you throw that switch while the red light is on”; “That figurine will break if dropped”; “She won’t pass unless she scores at least 75 on the final exam”; “If they get measles they’ll break out in spots.”In none of these cases do we feel that nothing at all has been asserted unless the antecedent happens to be true.(Call this the “Initial Implausibility” objection.)The late Richard Jeffrey (1963) objected that if Quine and Rhinelander are right, “The hearer of a conditional whose antecedent will turn out to have been false loses nothing if he fails to hear the consequent” (p. 42).Jeffrey offered a useful analogy.According to SI, to utter a conditional is as if to hand one’s hearer a sealed envelope.In our example, the mother would hand the daughter an envelope marked, “To be opened in case you do not finish mowing the yard this afternoon, but otherwise to be destroyed unopened.”[7]Only if the daughter does not finish mowing the yard would she then open the envelope and find within it a piece of paper on which is written, “You can’t go to the mall after dinner.” And similarly for the further examples.

(The analogy is not perfect, because the SI theory at least allows that the hearer knows what will have been asserted should the antecedent prove true; she gets a peek at the paper inside the envelope. But the fact remains that SI allows for no more definite actual illocutionary or cognitive event; what would have been asserted is irrelevant if the antecedent is false.)

Notice, incidentally, that the opening argument from analogy to other conditional speech acts is flawed.There is a special reason why the conditional request and conditional bet examples work as they do:In each case, the locutionary content in question itself presupposes the truth of the antecedent.It is a logical truth that you cannot do anything for me while you are out if you are not going to be out; it is at least a constitutive institutional fact that to win the election one must first have been nominated.Absent the truth of their respective antecedents, the request and bet would be so grievously defective as speech acts that they could hardly count as request or bet at all.But ordinary conditional declaratives exhibit no such presuppositional phenomenon.To assert to someone that she cannot go to the mall after dinner presupposes nothing whatever about mowing yards.Notice that there are declarative conditionals whose consequents presuppose their antecedents: “If Richard Nixon stole money, someone somewhere knows he did”; “If Sheila owns a heavy overcoat, it’s green.”These are plausibly taken to be conditional assertions, precisely because of the presuppositional feature but only because of it.

By the same token, there are interrogative and imperative conditionals that are not plausibly taken as vehicles of merely conditional speech acts.In our mother-daughter situation, “Is it true that if she doesn’t finish mowing the yard, she can’t go to the mall?” would unequivocally be used to ask a question (attempting to confirm the mother’s threat), whether or not the daughter will later finish the mowing.“Make it so that the mine will explode if anyone touches it even lightly” is an unmistakable command whether or not anyone is ever going to touch the mine; if the mine is not already so rigged and the subordinate does nothing, s/he has disobeyed the command.

iifurther criticism of quine-rhinelander

The SI theory faces further problems.One is that contraposition is utterly ruled out from the beginning.If a conditional is used to assert something true, that is because its antecedent is true and so is its consequent.But then its contrapositive has a false antecedent, and so cannot be used to assert anything whatever.[8]Of course, given the frequent dislocation between semantic properties and (illocutionary) assertion properties, this is not in itself surprising, but if a speaker utters a conditional with assertive intent, we should expect that speaker to be ready, willing and able to use its contrapositive to make an assertion as well.

Yet another problem is that of nested conditionals.Conditionals with conditional consequents are perhaps manageable.On the SI theory, to utter “If we have a tomato, then if I can get some bacon I’ll make a BLT” cannot be to assert that if I can get some bacon I will make a BLT on the condition that we have a tomato, because one cannot assert a distinctively conditional content.The SI theorist must say that the uttering is a conditional conditional assertion:If we do have a tomato, then I have issued the (merely) conditional assertion, “If I can get some bacon I’ll make a BLT,” and if also I can get some bacon, I will have succeeded in asserting that I will make a BLT.[9]But conditionals with conditional antecedents are harder to handle.According to SI, one who utters “If this vase will break if I drop it on the driveway, then I will be careful not to drop it on the driveway” asserts, on the condition that the vase will break if s/he drops it on the driveway, that s/he will be careful not to drop the vase on the driveway.But also according to SI, the “condition” specified is not a matter of fact, and so the antecedent cannot be true, and so nothing can have been asserted at all.(It would not help to let the condition be, rather, that the speaker does drop the vase and it does break, because that would make the original consequent, hence the assertion, automatically false.)“If you will fail unless you study hard, I suggest you hit the books.”Another nice example (from Edgington (1995), p. 284) is “If John should be punished if he took the money, then Mary should be punished if she took the money.”

And what about disjunctions with conditional disjuncts?: “Either Geoff will go to the dance, or if Laura allows him in, he will go to her party.”Are we to suppose that if Laura does not allow Geoff in, the speaker will have asserted nothing?No, because if Geoff does go to the dance, the speaker will have asserted something true.I suppose the best position for the SI theorist to take is that if either Geoff goes to the dance or Laura allows him in, the speaker will have succeeded in asserting that either Geoff will go to the dance or he will go to Laura’s party, but if Geoff does not go to the dance and Laura does not allow him in, nothing has been asserted; this seems ad hoc at best.[10]

Finally, it is hard to see how to extend the SI theory to the propositional attitudes, because it is a purely illocutionary theory, about the performing of public, convention-governed speech acts.(By the same token exactly, one may call this criticism unfair, since the SI theorist is a philosopher of language, not a philosopher of mind, SI being a thesis in linguistic pragmatics.But remember that we are considering conditional-assertion theories in their recent role as competitors of truth-conditional semantic theories of conditional sentences; and truth-conditional theories of conditional sentences extend very naturally to the corresponding propositional attitudes.)

It is easy enough to carry over the SI model to belief or judgment:As E.W. Adams and others do,[11] we can let belief having conditional form be belief of the conditional’s consequent conditionally upon supposition of the antecedent, modeling this as the subject’s subjective conditional probability of the consequent given the antecedent.But this will run into trouble over complex belief sentences.How would the Adams adaptation of SI handle something like, “Angie believes that Bob believes that Cindy will attend if she does, and Dave dislikes Cindy so much that he thinks if it’s true that she will attend if Angie does, he will try to persuade Angie that if Cindy does attend, Angie should try to convince her that if she gets anywhere near him she’ll catch something”?

Also, what of nondoxastic attitudes?[12]“Dave is afraid that if Cindy looks at him his left cheek will tic visibly”; “Angie is embarrassed that if Dave sees her he will send her what he thinks are subtle secret signals”; “Bob hopes that if Cindy and Dave both attend, no one will sing ‘You Must Have Been a Beautiful Baby’”; “Cindy is sad that Bob will leave the room if she sings anything at all”; “Bob is ashamed that he will run crying from the room if someone does sing ‘You Must Have Been a Beautiful Baby’.” I do not see how such attitudes can be explicated in terms of conditional probability, unless possibly by some convolute analysis of embarrassment, hope et al. in terms of belief.

I believe, then, that the trick for the conditional-assertion theorist is to move beyond the SI theory, avoiding the four objections raised in these two sections.[13]

Notice, incidentally, that there is a close affinity between the conditional-assertion view even in its SI form and the thesis defended by Adams (1965) and others[14] that indicative conditionals lack truth-conditions and truth-values.(Call that thesis “NTV”; we shall return to it.)Suppose a conditional has a truth-condition, hence a truth-value given totality of fact.Then if a speaker utters that sentence in assertive mode, presumably s/he would (unconditionally) assert of its truth-condition that that condition obtains; if the conditional sentence is true constitutivelyiff P, then the speaker has asserted that P.But for the SI theorist, no conditional sentence can be used to assert a conditional content.Therefore, the SI theorist would find it hard to explain how a conditional sentence could have a truth-condition or a truth-value.

iiisemanticizing quine-rhinelander

Rhinelander’s immediate followers in the matter of conditional assertion happily abandoned strictly illocutionary notions and gave the issue a purely semantic turn.

Jeffrey (1963) explored an extensional, truth-functional treatment of conditionals in three-valued logic, adding a value “indeterminate” to “true” and “false.”He argued that if certain disputable assumptions are made, we get a logic for the three-valued conditional that preserves the core conditional inferences such as modus ponens, modus tollens, contraposition and conditional proof.However, he also pointed out that if we dispute the disputable assumptions, we start to lose the core inferences.For example, if we hold that the negation of an indeterminate sentence is itself indeterminate rather than false, we cannot preserve contraposition.And if we give up the strong thesis that all indeterminate sentences are “assertable” (meaning roughly that for any one of them, there could always be some point in asserting it), undesirable indeterminacies would result.

Jeffrey further points out a damaging feature of his truth-functional version of the conditional-assertion theory, one that does not depend on any of the disputable assumptions.Obviously, according to the SI theory, whenever someone assertively utters a conditional whose antecedent and consequent are both true, that person has made a true assertion, and that feature carries over into Jeffrey’s truth table.But suppose a conditional consequent is true only by fluke.His example (p. 41):The dentist says, “If you don’t undergo this treatment, you’ll lose all your teeth.”I turn down the treatment.Then I am in an auto accident that knocks out all my teeth, but the dental surgeons who treat me report that in fact all my teeth had been perfectly sound.The dentist’s conditional seems to have been false; it would be no defense for her/him to point out that I did, after all, lose all my teeth.

Better yet, suppose antecedent and consequent are mutually irrelevant, and the consequent is true only by fluke: “If you do not finish mowing the yard this afternoon, then in 2017 there will be violent solar flares”; “If I fail to learn Swedish within five years, then there will have been a mouse in the cellar this afternoon”; “If you cough sharply twice, then the winning lottery number will be 275489.”That these would be severely defective assertions does not prove that they would not be true ones, but it is hard to hear them as true ones.I join Jeffrey in rejecting such sentences, indeed holding them to be false.[15](Call this the “TT” objection.)

NuelBelnap (1970) offered an intensional treatment, saying that he “believe[d Jeffrey’s analysis] does not yield a structure rich enough to do justice to the underlying idea of conditional…[assertion]” (p. 4).He stipulates (pp. 4-6):Every atomic sentence “asserts” a proposition (conceived as a set of worlds), but not every compound sentence does.A negation asserts a proposition at a world iff its negand does there, and the proposition it asserts is the negation of the proposition asserted by the negand.A conjunction asserts a proposition at a world iff at least one of its conjuncts does there, and the proposition it asserts is the conjunction of the proposition(s) asserted by its conjuncts; similarly for disjunction. But the rule for the conditional is more complicated, and follows Quine:A > B asserts a proposition at a world iff A is true at that world; if A is true there, the proposition A > B asserts is the proposition B asserts there. 

Now, how does this intensional treatment improve on Jeffrey’s truth-functional one?Once Belnap has gone on to develop similar semantic rules for quantifiers, he applies the resulting apparatus to the analysis of Aristotelian A-, I-, E- and O-forms; it also affords a partial solution to the Raven Paradox.But if we assess it according to the concerns raised against Jeffre/y, there is no visible improvement.Contraposition fails for Belnap’s conditional.And Belnap is subject to the TT objection as well; on his semantics, a conditional whose antecedent and consequent are both true is automatically true.That may not be obvious, precisely because Belnap’s system is intensional rather than truth-functional; but recall that if the conditional’s antecedent is true, the proposition then asserted by the whole conditional is exactly the proposition asserted by its consequent, and by hypothesis that proposition is true.

Belnap’s account faces still a further problem, distinctive to it.He makes it very clear that his term “asserts,” applying to sentences, is only the thin semantic shadow of the SI theory’s core illocutionary notion of asserting.But then, what is the relation between a sentence’s “asserting” a proposition and the sentence’s expressing one?A dilemma arises:Suppose that for a sentence to “assert” a proposition is just for it to express that proposition.(Belnap says nothing to discourage this reading.)Then a conditional with a false antecedent expresses no proposition at all.That result would in itself be fine with the proponents of NTV (mentioned in the previous section), because they hold that indicative conditionals are not in the business of expressing propositions in the first place.But the failure here is selective, for on the present interpretation of Belnap, conditionals with true antecedents do express propositions, while conditionals with false antecedents do not.That seems too radical a difference to be made in a sentence’s semantic status by the (possibly chance) obtaining or not of a contingent fact.

Suppose then, that asserting is a stronger notion than that of expressing (I pass over the strange possibility that asserting is weaker than expressing).But, once “asserting” has been drained of its action-theoretic and illocutionary character, what could the difference be?On this second horn of the dilemma, a sentence’s failing to assert a proposition is compatible with its expressing one.If it expresses a proposition and the proposition is true, then the sentence is true; but on Belnap’s view, a sentence that fails to assert a proposition lacks truth-value.Here we have an apparent contradiction and no help in resolving it.

ivfurther objections to the semanticized accounts

Let us revisit our other objections to the SI theory and see if they cause trouble for the semanticized views.Contraposition has already been seen to carry over.

What about Initial Implausibility?Recall my neighbor’s sentence, “If you don’t finish mowing the yard this afternoon, you can’t go to the mall after dinner,” and her daughter’s likely reception of it.Belnap holds that if the daughter does mow the yard, the sentence has asserted no proposition.[16]As before, that would be all right with and for NTVists, but Belnap’s claim is selective and would not apply if the daughter had not mowed the yard.From the daughter’s point of view, at least, the selective claim is implausible. The same can be said in regard to our other sample sentences from section i.

Jeffrey’s truth-table account[17] perhaps does better against the implausibility charge, for it says, not that the mother’s sentence asserts no proposition, but only that it lacks truth-value.Some will see that as a distinction without a difference; others, having a more generous notion of a proposition, will grant the improvement, however small the improvement may be.

Nesting:I believe that for either semanticized account, the problem of nesting is only technical.If Jeffrey’s three-valued tables work at all, they should work for nested conditionals, though I have not tried to verify that.And I would never doubt that someone of Belnap’s ingenuity and technical skill could accommodate nested constructions.What made nesting a grave difficulty for the SI theory was that SI deals not just with formal semantics of sentences but with speech acts that are individuated according to their actual illocutionary force.

Propositional attitudes:Here too, the semanticizing turns out to help, because what made the SI theory unattractive for nondoxastic attitudes was primarily its official focus on the speech act of asserting.The semanticized views are merely about the semantics of sentences, and all propositional attitudes—not just the doxastic ones—have sentence-like properties.In particular, being embarrassed that P, hoping that P, being sorry that P, etc., have representational and other semantical properties, even if those properties are not the most important things about those attitudes.Nonetheless, an analogue of Initial Implausibility remains: Are the respective fears, embarrassments, hopes and sadnesses of Angie et al. from section 2 contentless if their antecedent conditions do not obtain?E.g., the extension of Belnap’s view to propositional attitudes entails that if in fact Dave will not see Angie, then either she is not after all embarrassed that if Dave sees her he will send her secret signals, or she is embarrassed but (contrary to its description) her embarrassment lacks propositional content.

Now, here are three further objections to the semanticized accounts.First, it is widely agreed that many if not all conditionals are equivalent to the corresponding disjunctions.(Since like most conditional-assertion theorists I reject the material or horseshoe theory of indicatives, I deny that conditionals are equivalent to truth-functional disjunctions[18]; I believe the relevant disjunctions are intensional.)IfA > Bfails to assert any proposition, or at least lacks truth-value, whenA is false, is the same true of~A-or-B?(The Disjunction objection.)

Second, what if a conditional is entailed by a law of logic, a law of nature, or just a true universal generalization, or some other categorical fact?Every piece of iron heated to 200°C glows red; it follows that if this piece of iron is heated to 200°C, it will glow red.What, then, do we say if this piece of iron is not going to be heated?That the true generalization logically entails an untrue sentence, or that the generalization is itself not true after all?Chapel Hill is in North Carolina; it follows that you do not live in Chapel Hill unless you live in North Carolina.And so on.(The Entailment objection.)

Third, Stalnaker (1984, pp. 111-12) has emphasized the many linguistic parallels between indicative and subjunctive conditionals.On the assumption that subjunctive conditionals have truth-conditions and express propositions, our semanticized views imply that when an indicative’s antecedent fails, the sentence differs from its corresponding subjunctive in a very fundamental semantical way—for example, “If your piece of iron is now at 200°C, it is glowing red” would get a Belnap conditional-assertion semantics and asserts a proposition at all only if the iron is in fact at 200°C, asserting only its consequent even if its antecedent is true, but “If your piece of iron were now at 200°C, it would be glowing red” would be assigned a straightforward truth-condition of quite a different kind, say in terms of closeness of possible worlds.[19]But that consequence makes nonsense of the glaring parallels and analogies between indicatives and subjunctives.Indicatives and subjunctives are expressed by the same lexemes, not only in English but in most other languages.Indicatives and subjunctives have the same syntax but for their distinctive tense and aspect differences, including their modification by “only” and “even.”More importantly, they have virtually the same logic.And they admit almost all the same paraphrases.All this would be surprising, to say the least, if the two kinds of sentences differ so greatly in their semantics.(The Subjunctive Parallel objection.)

vntv and conditional assertion

Dorothy Edgington (1986, 1995), Stephen Barker (1995) and Michael Woods (1997) defend versions of NTV, but they also describe their theories as conditional-assertion views.The relation is not immediately clear.Indeed, one reason it is positively unclear is that according to either of the semanticized conditional-assertion views we have seen, an indicative with a true antecedent and a true consequent is true, which is incompatible with NTV; more obviously, an indicative with true antecedent and false consequent is false. (Of course, Edgington’s, Barker’s and Woods’ theories are competitors of standard truth-conditional theories, if only because they deny that indicative conditionals have truth-conditions at all.)I shall discuss primarily Edgington’s version, because it is the one I think I understand the best, but I shall note any significant points on which Barker’s or Woods’ views differ.

Edgington holds that a conditional belief is (roughly) the believer’s corresponding subjective conditional probability.It is not belief of a proposition, not a belief that anything.If this seems odd—a belief that is not a belief that P despite being described using the usual sort of ‘that’-complement—so be it; call it “acceptance” or “endorsement” or some such.And of course it has no truth-value. 

There are several objections to this in its own right (before we get to the conditional-assertion theory of indicative sentences).First, there is the problem of nondoxastic attitudes.Edgington offers an account of conditional desire ((1995), p. 288):One desires that if A then B iff one prefers A & BtoA & ~B.But what about fear, embarrassment, sadness, and shame?

Second, there is the probability version of the TT objection:If I firmly believeA & B, my conditional probability of B given A will be high; but sometimes I will not and should not believe that if A then B.(Edgington is well aware of this objection and stiffarms it; she thinks the intuition can be explained away (pp. 268-69).)

The Disjunction and Entailment objections carry over to belief as well.

Moreover, though I do not expect to convert many souls here, I reject in the first place Adams’ widely accepted contention (which Edgington (p. 263) calls “the Thesis”) that one’s degree of belief in a conditional matches the relevant conditional probability.I have what I maintain are counterexamples.Here is one:I believe each of two propositions that are not only probabilistically independent of each other but mutually irrelevant in topic.I believe the first only tentatively.Right now I am inclined to think that my copy of Stalnaker’s Inquiry is lying on a shelf in my office near my desk, though I may well be wrong because I am always absent-mindedly picking up things and putting them somewhere else without realizing I have done so.I also believe, but pretty firmly, that the Australians will win their next test against Sri Lanka.I am confident to degree .9 that Australia will win.Since the two propositions are probabilistically independent, my subjective conditional probability for the second given the first is equal to its own subjective probability, .9.According to Adams’ generalization, then, I should believe to degree .9 that if my copy of Stalnaker’s Inquiry is lying on a shelf in my office near my desk, then the Australians will win their next test against Sri Lanka.But I do not have the latter belief at all; I think it is false.[20]

Edgington’s account of conditional belief is not itself analogous to a conditional-assertion theory of conditional sentences, for it does not say that if the antecedent is false, nothing is believed.(As before, she holds that no proposition is believed, but that holds regardless of the antecedent’s truth-value, so she does not join in the conditional-assertion-analogue view that whether a proposition is expressed depends on the truth of the antecedent.)Indeed, she explicitly acknowledges that when one assigns a high subjective conditional probability to B given A, and one learns that A is true, one does not necessarily affirm B; one might be obliged to withdraw the conditional ((1995), p. 270).But when she turns to the topic of speech acts, she does defend a conditional-assertion theory. It has two distinctive features.

First (p. 289), she rejects Jeffrey’s envelope model: Of course it is not true that, should the antecedent prove false, nothing whatever has been said and no speech act has occurred.Nothing has been asserted, but something has been said and something has been conditionally-asserted.(She seems to regard conditional assertion as a speech act type of its own.[21])

Second, of course conditional assertions—unlike conditional beliefs and conditional sentences—have truth-value when their antecedents are true, because they then constitute assertions of their consequents. So one can make a true or false assertion by uttering a truth-valueless sentence. (This distinguishes Edgington’s view from the semanticized accounts, according to which a conditional sentence is itself a true or a false one when its antecedent is true.) 

Each of those two points is correct.That a speech act is not one of assertion does not entail that there is no related illocutionary category such as that of conditional-assertion.And we have already noted the common mismatch between truth-value of assertion made and that of sentence uttered.The conditional-assertion theory gives us yet another example of such a mismatch:One may utter a truth-valueless sentence and thereby make a true or false assertion, because when the sentence is a conditional with a true antecedent, one has asserted the consequent alone.[22]

But on the first point, I would reply as before that in our mother-daughter example from section i, an assertion flatly has been made.It is not just that the mother has said something which may or may not turn out to have been an assertion.I contend that in this case, conditional-assertion vs. assertion is a distinction without a difference, and the objection applies as before.(I do not expect Edgington to concede this, since she obviously does see a difference between conditional-assertion and assertion.She makes a related claim about conditional commands (pp. 289-90).

A child is told ‘If you go out, wear your coat’.If he cannot find his coat, he stays in, in order to comply with the command.On my interpretation, if the child can’t find his coat, he has a choice between disobeying the command, and behaving in such a way that no categorical command has been made (not: behaving as though nothing had been said).If he wishes not to disobey, he must stay in [in which case no categorical command has been issued, though a conditional command has been].

I join Dummett (1973) in denying the alleged distinction between not disobeying the command and obeying it.Edgington says that “other examples make this implausible” (p. 290), but the one example she gives is tendentious.[23])

Let us see how Edgington’s account fares against our remaining objections to previous theories.TT, Disjunction and Entailment continue to apply.Subjunctive Parallel does not; Edgington doughtily favors an NTV, subjective conditional probability theory of subjunctives themselves (pp. 311ff.).(I am not sure whether she accepts a conditional-assertion view of subjunctive conditional utterances.) 

That leaves Nesting, especially the problem of conditionals with conditional antecedents.Here Edgington makes what has become a standard NTVist move: to insist that the antecedents are anomalous and at best must be reinterpreted ad hoc as expressing propositions that are not (of course) conditional propositions (Gibbard (1981), pp. 234-38; Appiah (1985), pp. 205-10; Woods (1997), pp. 65-66).Edgington (pp. 283-84) suggests that we reinterpret the speaker as asserting the “obvious [categorical] basis” of the conditional belief being expressed, such as the categorical fact that serves as the speaker’s immediate evidence for the conditional, or perhaps the existence of a disposition that grounds the conditional.

I have to say that this has always struck me as desperate.The examples I and others have given of conditionals with conditional antecedents are perfectly clear and in need of no reinterpretation at all.True, there are further examples which are odd; but that is due to the absence of any natural context for them.[24]The Nesting objection remains severe.

To his credit, Barker (1995) does not take the standard line on conditional antecedents, but insists that they are (often) fine as they stand.His position on them (p. 206) is that while the “if” in a simple conditional signals that the antecedent is a supposition which initiates a pretense, the “if” in a conditional with a conditional antecedent signals that that antecedent is “stipulated [merely] to be assertible” (as opposed to the usual case of being stipulated to be true).

I am fairly sure Barker does not mean that the speaker institutes a metalinguistic supposition, about the assertibility of a sentence; that would be to no purpose.But what, then, is supposed?This departure from Barker’s existing theory is both hard to parse and ad hoc.

Incidentally, I do not see that any conditional-assertion view of conditional utterances is required by NTV.Indeed, Bennett (2003) has persuasively argued that the NTVist would do well to embrace an expressivist view: that to utter a conditional is to express one’s subjective conditional probability rather than to make any statement of fact.[25]

Indeed, I think the expressivist account would fit a bit better with the NTV theory of conditional belief.Utterances generally express beliefs.Even if the “belief” in question is not belief of a proposition, and the corresponding sentence lacks truth-value, the more obvious account of the matter is that a conditional utterance (even when the antecedent is true) genuinely asserts nothing but only expresses the relevant cognitive state. 

viverdict

We have not found that conditional-assertion theories are very plausible in their own right.Nor are they required by NTV, by the Thesis, or by Edgington’s theory of conditional belief.At this stage, the conditional-assertion idea seems expendable.

References

Adams, E.W. (1965).‘The Logic of Conditionals’, Inquiry 8: 166-197.

Appiah, A. (1985).Assertion and Conditionals.CambridgeCambridgeUniversity Press.

Austin, J.L. (1961).‘Ifs and Cans’, in Philosophical Papers.OxfordOxfordUniversity Press.

Barker, S.J. (1995).‘Towards a Pragmatic Theory of “If”’, Philosophical Studies 79: 185-211.

Belnap, N. (1970).‘Conditional Assertion and Restricted Quantification’, Noûs 4: 1-12.

Bennett, J. (2003). A Philosophical Guide to Conditionals.OxfordOxfordUniversity Press.

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Footnotes



[1] George MacDonald Fraser, Flashman and the Tiger (New York: Alfred A. Knopf, 2000) p. 198.

[2]Quine (1950), p. 12.The conditional-affirmation view of conditionals may be Professor (later Dean) Rhinelander’s best-known contribution to philosophy, but his influence extends outside the field and into the military and political history of the United States; see J.B. Stockdale, “Master of My Fate—A Stoic Philosopher in a Hanoi Prison,” The World and I (May, 1995), reprinted at http://www.geocities.com/stoicvoice/journal/0600/js0600a1.htm.

[3] The recipient and honoree of this volume led the field, in Stalnaker (1968), closely followed by Lewis (1973); see also Stalnaker (1975).Others who have offered truth-conditional accounts of whole conditionals include:Davis (1979); Jackson (1979, 1987); Lycan (1984, 2001); and Kratzer (1986).

My own semantic ideas about conditionals have been most heavily influenced by Bob Stalnaker’s, and they remain very close to his.He does not entirely welcome my company in this area, but I wholeheartedly thank him for his kind and critical conversation over the years.

[4] Only some of a sentence’s entailments are asserted when the sentence is uttered; in particular, there is a contrast between assertion and presupposition (though it is vexed).Explicit performatives strongly motivate a distinction between the truth of such a sentence and the truth of the assertion made in uttering it (consider the sentence, “Mindful that I am under oath, I hereby state that I have never met or had any contact with the defendant”).According to some recent Relevance theorists, one can unequivocally and actionably assert propositions that are not entailed by the sentence one utters (e.g., Carston (2002)).And so far as speaker-meaning figures in the analysis of “what is asserted,” a mismatch between speaker-meaning and sentence meaning may result in a truth-value difference.

[5] On regimentation and the death of meaning, see respectively Chapters V and II of Quine (1960).

[6] His famous footnote to p. 12 does not say whether Professor Rhinelander himself offered the conditional-assertion view merely as representing common sense, or as correct.

[7] Notice that that instruction is itself the conjunction of two conditionals.So, strictly, there would have to be duplicate envelopes, each containing the piece of paper with “You can’t go to the mall…” and each inside a bigger envelope also containing a cover sheet.One of the bigger envelopes would say, “To be opened in case you do not finish mowing the yard this afternoon, but otherwise to be destroyed unopened,” and the cover sheet inside would say, “Open the accompanying envelope.”The other bigger envelope would say, “To be opened in case you do finish mowing the yard this afternoon, but otherwise to be destroyed unopened,” and the cover sheet inside it would say, “Destroy the accompanying envelope unopened.”But of course the instructions on the bigger envelopes would be conjunctions of conditionals…. 

[8] Stalnaker (1968) and others have questioned the validity of contraposition for English conditionals.But counterexamples to contraposition have been limited to what Goodman (1947) called “semifactuals” and Wayne Davis’ (1983) “weak” conditionals.Most conditionals still do contrapose.(See Lycan (2001), pp. 31-36.)

[9] Someone might appeal to the principle that a nested conditionalA > (B > C)is equivalent to (A & B) > C(Gibbard (1981)); but I think that principle is fairly easily refuted (Lycan (2001), p. 82).

[10] Barker (1995) offers an ingenious discussion of such disjunctions on the conditional-assertion theorist’s behalf (pp. 202-05).He considers the sentence “Either Fred will marry Jane, if she asks him, or we are just completely wrong about Fred and this marriage business”—very much a case in point??but I do not see how his remarks on it are responsive (though they are true).

[11] Adams (1965), and most prominently, Dorothy Edgington (1986).

[12] This point is made by Michael Kremer (1987).

[13] G.H. von Wright (1957) offers a type of conditional-assertion account, and he emphasizes that by “assertion” he too means the speech act of asserting, or rather a slightly idealized version of that act.But his view differs crucially from the SI theory.He does hold that one who utters an indicative conditional “If p, then q” “licenses others to take him as having asserted q, if the condition p is found to be, in fact, fulfilled” (p. 130), but he does not hold that if the antecedent p is false, nothing has been asserted.Whether the antecedent is true or false, von Wright maintains, the assertion pattern is as follows:The speaker asserts the material conditionalpÉ q(and any logical equivalent of it such as~(p~q), but neither asserts nor denies p and neither asserts nor denies q (p. 134).

Nonetheless von Wright insists that the conditional sentence does not express any proposition.(He gives a compressed and bilocated argument (pp. 131, 135):If a sentence expresses a proposition, then that proposition has a negation.But when one asserts a conditional sentence, the only proposition asserted is the corresponding material conditional, and that is only part of the assertive act—the rest of it being the four refrainings listed above—so there is no proposition that is the negation of what is asserted.He does not say why~(pÉ~q)does not qualify.)Notice that on this view, either a proposition that is centrally and literally asserted by utterance of a sentence may not be entailed by the sentence, or a sentence that does not express a proposition may entail a proposition.

[14]Gibbard (1981); Appiah (1985); Edgington (1986, 1995); Bennett (2003).

[15] If the “then” is removed from each of those sentences, they acquire readings on which they are arguably true: semifactual or “weak” readings in the sense of Davis (1983).Contrast, for example, “If you open the refrigerator, it won’t explode” with “If you open the refrigerator, then it won’t explode.”I was careful to put in the “then”’s precisely to block the weak readings. 

[16]N.b., Belnap would never say that the sentence is meaningless in the context; he is careful to detach his notion of asserting-a-proposition from that of meaningfulness.A nonassertive sentence “continues to have determinate semantic relations, etc.” (p. 2).

[17] Remember that he did not himself accept it, though I shall continue to call it that.

[18]Lycan (2001), p. 27.(In that discussion I offered two other examples of clearly nonconditional sentences that are allegedly equivalent to conditional ones, but David Sanford and Jonathan Bennett have persuaded me that the equivalences hold only for the material conditional and not even for my own; see especially Bennett (2003), pp. 354-55.I am duly ashamed.) 

[19] Most conditional-assertion theorists and NTVists do grant the assumption that subjunctives have normal truth-conditions.However, shining exceptions are Dorothy Edgington (1986, 1995) and Stephen Barker (1995); so the present objection does not apply to them.Von Wright (1957) is an intermediate case; he gives an initially conditional-assertion account of subjunctives, but he then argues that subjunctives have truth-conditions and truth-values (p. 162), for “[i]t is not part of what we do, when we assert q on the counterfactual condition p, that we leave certain propositions unasserted.” 

[20] Fairness compels me to record that Edgington’s view has a great advantage over my own theory (Lycan (2001)):My theory assigns a vanishingly low probability to conditionals that are epistemically uncertain, as in, “How likely is it that if I undergo this treatment I will be cured?,” when intuitively the probability of such a conditional is or is close to the conditional probability of its consequent given its antecedent.See Edgington (2003).

[21] As does Barker.But although Barker declares allegiance to Rhinelander (p. 186), his text does not make it clear whether he agrees that the utterer of a conditional has actually and flatly asserted its consequent when its antecedent is in fact true.

Barker thinks of the conditional assertion ofA > Bas part of a pretense: We are affecting to believe A, and while doing so we assert B.The usual sincerity condition on assertion is suspended, as it would be for a stage actor.“If” is a particle of conventional implicature, or what Lycan (1984) calls “lexical presumption”; it serves simply to signal that the conditional consequent B is asserted only conditionally upon A.I think this is a neat and well motivated view. 

[22] Moreover, Edgington offers a new argument in favor of the conditional-assertion view—roughly, that (a) the treatment of assertions of indicative conditionals should parallel that of conditional imperative and conditional interrogative speech acts, but (b) no standard truth-conditional account of the latter is adequate.Barker independently makes similar arguments, in considerable detail.

DeRose and Grandy (1999) offer several further considerations.I have not the space to consider the positive arguments here, but I would self-servingly note that DeRose and Grandy’s main argument fails.It is that the conditional-assertion view can offer a unified view of ordinary indicatives and “biscuit” conditionals (e.g., Austin (1961, p.158): “There are biscuits on the sideboard if you want them”) considered together, while “the best the leading theories can do by way of ‘handling’ biscuit conditionals… [is] to cordon off the abnormal [biscuit] cases for separate treatment” (p. 407).Ahem: Lycan (2001, pp. 206-10) offers a unified truth-conditional account of ordinary indicatives, biscuits, and a number of cases in between.

[23] “If, in the emergency ward, you’re told ‘If the patient is still alive in the morning, change the drip’, and you smother the patient, you can hardly claim to have merely carried out an order.”Of course you cannot.If you smother the patient you have committed murder or at least active euthanasia. That leaves open the question of whether you did obey the order; and I say you did obey it, however defectively.Perhaps there is a sense in which you did not carry it out, but that does not entail that no order was issued.

[24]Edgington herself uses the phrase “ad hoc” (p. 283).She also uses exactly my present sort of argument to impugn “irrelevance” counterexamples to TT (p. 269). 

[25] He thereby takes most of the sting out of the first of my ten arguments against NTV (Lycan (2001), pp. 73-74).I had said that NTV makes indicative conditionals a surd in truth-conditional semantics.But Bennett reminds us that many otherwise truth-conditionally minded philosophers are expressivists about moral judgments, aesthetic judgments, modal discourse,… , so NTV is no surd but is in fairly good company.(For highly developed expressivist views of such other sentences, see Gibbard (1992) and Blackburn (1995).)I had missed that, (a) because I myself am a compulsive metaphysical realist about nearly everything and (b) because qua philosopher of language I do not believe that an entirely well-formed sentence can lack a truth-value.