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A Philosophical Guide to Conditionals$

Jonathan Bennett

Print publication date: 2003

Print ISBN-13: 9780199258871

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0199258872.001.0001

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The Subjectivity of Indicative Conditionals

The Subjectivity of Indicative Conditionals

Chapter:
(p.78) 6 The Subjectivity of Indicative Conditionals
Source:
A Philosophical Guide to Conditionals
Author(s):

Jonathan Bennett

Publisher:
Oxford University Press
DOI:10.1093/0199258872.003.0006

Abstract and Keywords

Discussion of reasons for approaching indicative conditionals in terms of subjective rather than objective probability. The reasons include stand‐offs of the sort Gibbard has presented: cases where two right‐thinking people with partial information accept conflicting conditionals. Discussion and rejection of the view that subjectivity comes in because in asserting an indicative conditional one says that one has such and such a probability for the consequent given the antecedent. What remains, and seems to be right, is the view that in asserting such a conditional one is expressing a conditional probability without asserting anything.

Keywords:   conditionals, Gibbard, indicative conditionals, objective probability, subjective probability

32. Trying to Objectivize the Ramsey Test

6. The Subjectivity of Indicatives 32. Objectivize the Ramsey Test?

Faced with the Ramsey test thesis, which links

the degree of credence that a given person gives to A→ C

with

that person's probability for C on the supposition of A,

one naturally wants first to filter out the mentions of a person, replacing the thesis by something that links

the degree of credence that ought to be given to A→ C

with

the objective probability of C given A.

This offers to free us from the person‐relativeness which permeates the Ramsey test thesis—to take us away from subjective and over into objective probability, promising cooler air to breathe, less cluttered ground to tread.

No analyst of indicative conditionals has adopted or even explored this ‘objectivized Ramsey’ approach (as I shall call it), which indicates that it is not a live option. Still, we need to understand why it is dead. I shall devote this section to trying to make it breathe.

This conditional might be a reasonable thing for someone to accept: ‘If he sold his shares before last Wednesday, his idea of friendship is different from mine.’ (For discussion's sake, pretend the pronouns are replaced by proper names.) Even when that is reasonable, though, no probabilifying relation links this A to this C. For objectivized Ramsey to cover Shares → Friendship, it must link the probability of this conditional with the probability of Friendship given (Shares (p.79) & P), where P is some fact not stated in the conditional. We might think of P as including a complex fact about the relations between the two people.

For this to be one of our results, we need objectivized Ramsey to provide a general account of what the facts P are such that the probability of A→ C is tied to the probability of C given A&P. What account can this be? Well, try this:

  1. OR1: P(A→ C) is proportional to the value of π(C/(A&P)) for some true P.

This will not do, because it will bestow different probabilities on a single conditional, through different selections of P. Wanting uniqueness, we might try:
  1. OR2: P(A→ C) is proportional to the highest value that π(C/(A&P)) has for any true P.

Different Ps yield different conditional probabilities, but to get the objective probability of the conditional we take the P that yields the highest probability—thus says OR2. This could look promising only to someone who accepted the following:

We can consider the probability of C relative to values of P that are increasing in strength (each one containing its predecessors as conjuncts, so to speak); as the Ps get stronger, the probability of C given A&P increases; and the highest such probability reflects the strongest input of fact—which is why we are to think of this as the objective probability of A→ C.

This assumes that as the factual input grows so does the probability; but that is wrong, because reasoning with probabilities is not monotonic—a term I now explain. In mathematics, a function is monotonic if with increasing arguments (inputs) its values (outputs) either always increase or always decrease. On a loose analogy with that, a system of reasoning is called ‘monotonic’ if, as the pre‐misses of any argument are strengthened, the set of inferable conclusions either stays the same or increases. That is, adding to the premisses never implies removing anything from the set of conclusions. No probabilistic system of reasoning is ‘monotonic’ in this sense, because adding to a body of evidence may detract from the probability of some conclusion. Thus, settling for the highest probability of C given A&P may involve bringing in a sparse factual P, when a richer P would yield a lower probability. So we have no reason to tie the objective probability of A→ C to the highest probability C has relative to A&P where P is true; and therefore OR2 has nothing to recommend it.

A third try for uniqueness:

  1. OR3: P(A→ C) is proportional to the value of π(C/(A&P)) where P is the whole truth.

(p.80) This fails too, because when A is false, ¬ A is part of the whole truth; so that this latest proposal will confer on A→ C (when A is false) whatever probability C has given (A&¬A& Q), where Q is the rest of the whole truth. If you want to tell a story about the probability of C given a contradiction, go ahead and tell one. But it will have to assign the same probability (presumably either 0 or 1) to every C in relation to any contradiction; so that OR3 gives the same probability to every indicative conditional whose antecedent is false.

Bad as OR3 is, it points to something more promising:

  1. OR4: P(A→ C) is proportional to the value of π(C/(A&P)) where P is the strongest portion of the whole truth that is compatible with A.

In this, we must understand ‘compatible’ to involve causal as well as logical compatibility. The idea will have to be that we get the probability of A→ C by taking the whole truth, minimally adjusted (if need be) so as to make the conjunction of it with A logically and causally coherent, and we then investigate the probability of C given this conjunction.

Why causally as well as logically? Well, in a situation where there was no high tide last night, the conditional ‘If there was a high tide last night, the beach will be clear of driftwood this morning’ may well be highly probable. This requires, according to OR4, that its consequent is probable relative to its antecedent together with a portion of the entire truth; and that fragment must omit not merely There was no high tide last night but also the likes of The driftwood stayed firmly on the sand throughout the night.

Of the versions of objectivized Ramsey that we have looked at, OR4 is structurally the most similar to the subjective Ramsey test with which we started. Each of them says: take a certain body of propositions, add A to it, adjust the rest in a minimal way so as to give A's high probability a comfortable fit, and then see whether the resultant body of propositions implies a high probability for C. They differ only in the initial body of propositions: for subjective Ramsey, it is everything the speaker believes; for OR4 it is the whole truth.

33. Davis's Theory

6. The Subjectivity of Indicatives 33. Davis's Theory

I shall discuss OR4 by considering Wayne Davis's account of indicative conditionals, which is close to it (1979; see also his 1983). He asks what makes a conditional true, rather than what makes it probable, but this difference does not matter here. My topic is Davis's attempt to evaluate indicative conditionals objectively.

Where the (subjective) Ramsey test has you evaluating A→ C by adding A to your present system of beliefs . . . etc., Davis says that you should add A to the (p.81) whole truth about the actual world . . . etc. Both approaches say that after adding A you make the smallest adjustments you need for the resultant set of propositions to be consistent, and then see whether the resultant set implies C or a high probability for C. In the Ramseyan approach, there is a subjective element in the input, and so the resultant judgement on C is subjective also. Davis, on the other hand, admits no subjectivity anywhere: he aims to give a procedure that will assign to the conditional an objective truth value. He expresses his theory in the language of ‘worlds’: A→ C is true just in case the A‐worlds most like the actual world are also C‐worlds. (A‐worlds are worlds at which A is true, similarly for C‐worlds etc.) I formulate it differently—not to expose Davis to further criticism, but to postpone worlds until I am ready for them.

Consider this:

If the British did not attack Suez early in 1956, the Israelis rigged the situation to make it look as though they had.

Davis will call this true because of all the evidence the world contains that the British did attack Suez. A world‐description that does justice to that evidence and yet includes The British did not attack Suez early in 1956 will imply—logically or causally—that there was an Israeli frame‐up. This is one half of Davis's ingenious Y‐shaped analysis of indicative and subjunctive conditionals (§4), which I shall examine in §138. My present topic is the account of indicatives taken on its own.

Jackson thinks that Davis's analysis falls to counterexamples (1987: 72–4). He adduces ‘If I have misremembered the date of the Battle of Hastings, it was not fought in 1066’. Davis's theory implies that this acceptable conditional is false, Jackson alleges, concluding that the theory itself is false. Here is the argument, in my words:

Suppose that I do not misremember the date of the Battle of Hastings. Then there are two ways to adjust the truth about the actual world so that I can consistently add I misremember the date of the Battle of Hastings to it. (1) I can delete the truth that the battle was fought in 1066. (2) I can delete the truth that I remember the date of the battle as 1066. For Jackson's conditional to be true by Davis's standards, the most conservative adjustment must be 1. But by any reasonable standard, the most conservative adjustment is 2—changing the truth values of a few propositions about a few neurons, rather than the facts about the date of an important battle. So our intuition clamorously says True, while Davis's theory says False. The theory is wrong, therefore.

Thus Jackson. This argument is slippery. Suppose I entertain ‘If Henry has misremembered the date of the Battle of Hastings, it was not fought in 1066’. For (p.82) me, the thought of Henry's misremembering the date is the thought of his not remembering it as 1066, because I am sure that this is the correct date; so for me the conditional is unacceptable. Jackson's first‐person version trades on my knowing for sure what I remember the date as, so that for me the thought of my misremembering the date has to be the thought (not of my remembering it as something other than 1066, but rather) my remembering it as 1066 and being wrong about this. That gives the conditional the truth value Jackson wants it to have, but only by pummelling it into a shape that makes it tantamount to ‘If I am wrong in thinking that the Battle of Hastings was fought in 1066, then it was not fought then.’ This is boring, logically true, an independent conditional (§ §7, 62), and not fit to help in refuting Davis.

Even if Jackson's example were fatal to Davis's analysis, it would not explain its error. If we are to gain understanding, we need a proper diagnosis, enabling us to see why the analysis is wrong and what makes it plausible.

Davis makes indicative conditionals seem to have objective truth values by considering only cases (Oswald and Kennedy, Booth and Lincoln) where much relevant evidence is known to all of us, and it virtually all favours one side. In each case we have the public death of a world‐famous figure: the world shouts at us that if Booth didn't kill Lincoln, someone else did. But this is an accident of the examples. Furthermore, even in those cases there could in principle be overwhelming evidence—out there in the world, though not known to us—that goes the other way, making it almost certain that nobody other than Booth killed Lincoln. (I am here following Warmbröd 1983: 250. His way of tackling indicative conditionals through the notion of subjective truth is worth thinking about, though I choose not to discuss it here.)

I now vary the example so as to filter out the distracting fact that Lincoln's death was a world‐famous event. Toxic chemicals are found in the creek, and there is strong and widely available evidence that one of two local people dumped it there. In fact, the culprit was a local manufacturer named Capone; the other suspect is a right‐wing radical activist named Siegel. The well‐informed Speaker One says:

  1. C: If Capone didn't poison the creek, then Siegel did.

You might think this to be objectively true, so that any sufficiently well‐informed person will accept it. But now consider Speaker Two: he has all the evidence that Speaker One has, and also has powerful evidence (there is plenty of it lying around) that Siegel did not do the deed. Speaker Two will not accept C, and may put in its place:

If Capone didn't poison the creek, it was poisoned by someone from out of town,

(p.83) or the like; or, if he does not have strong evidence that the creek was poisoned,

If Capone didn't poison the creek, it wasn't poisoned.

The illusion of an objectively true indicative conditional was created by taking one that would be acceptable to someone with a certain distribution of knowledge and ignorance, in a case where that distribution is common property, shared by all concerned. This makes it ‘objective’ in the sense of inter‐subjective: all the relevant ‘subjects’ have it. But it is still a contingent generalization of something that is basically personal, and thus ‘subjective’ in the strongest sense.

34. Gibbardian Stand‐Offs

6. The Subjectivity of Indicatives 34. Gibbardian Stand‐Offs

A famous example of Allan Gibbard's (1981b: 231–2) gives us a clearer view of the subjectivity of some conditionals, or at least of their resistance to being objectivized in Davis's way. The example concerns a stand‐off—a case where one person is fully entitled to accept A→ C while another is fully entitled to accept A→ ¬ C. I stress fully entitled; these acceptances are intellectually perfect. Here is the story.

A hand of poker is being played, and everyone but Pete and one other player have folded. Two onlookers leave the room at this point, and a few moments later each sees one player leave the gaming room. Winifred sees Pete without the scowl and the trembling cheek that he always has after calling and losing, and concludes that if Pete called, he won; Lora sees Pete's opponent caressing more money than he owned when Lora left the room, and concludes that if Pete called, he lost.

As well as changing the names for mnemonic reasons, I have altered each person's basis for her conditional. Here is why I changed Lora's. In Gibbard's example, she judged that if Pete called, he lost because she had evidence that Pete had a losing hand. That basis for the conditional also supports:

If Pete were to have called, he would have lost, and

If Pete had called he would have lost,

which are subjunctive conditionals, which almost nobody has thought to be subjective or person‐relative—the exceptions being Chisholm (§120) and Lycan (§37). Gibbard's conclusion did not depend on this detail in his example, his handling of which is philosophically flawless. In the subsequent debate about it, however, the pure signal of his argument has sometimes been invaded by noise coming over the wall from the subjunctive domain. I have suppressed that clamour by changing the bases for the two conditionals so as to protect them from being thought of as subjunctives in disguise.

(p.84) Winifred's and Lora's conditionals cannot both be true, because their being so would conflict with the principle of Conditional Non‐Contradiction:

CNC : ¬ ( ( A C ) & ( A ¬ C ) ) ,
which is almost indisputably true. According to the horseshoe analysis, CNC is false, because exactly half of the conjunctions of the form (A ⊃ C) & (A ⊃ ¬ C) are true, namely those where A is false. But on no other account of indicative conditionals has CNC any chance of coming out false.

It is conspicuously true according to any analysis which, like Davis's, ties the truth of A→ C to C's being true at a certain ‘world’; because on no viable account of what worlds are can C and ¬ C both be true at a single world. CNC is true also according to theories that include the Ramsey test thesis. Suppose CNC is false. Then sometimes A→ C and A→ ¬ C are both true, in which case one person could coherently accept both. Such a person would have a belief system such that adding A to it and conservatively adjusting to make room for that leads to a probability > 0.5 for C and to a probability > 0.5 for ¬ C. Obviously, it would be irrational to think it more likely than not that C and also more likely than not that ¬ C. So the two conditionals could not rationally both be accepted by one person at one time, so they cannot both be true. Nobody has been so bold as to suggest that they may both be true although no rational person could accept both at once.

We can take it as settled, then, that Winifred's and Lora's conditionals are not both true. Then is at least one false? Gibbard says No, because: ‘One sincerely asserts something false only when one is mistaken about something germane. In this case, neither [Lora] nor [Winifred] has any relevant false beliefs . . . and indeed both may well suspect the whole relevant truth.’ Gibbard must mean that one sincerely asserts something false only if one is mistaken about some relevant nonconditional matter of fact. That is plausible, so this argument has force.

The final clause in what I have quoted from Gibbard points to a way of strengthening his argument. Suppose you are on the scene; you trust both speakers not to have hallucinated evidence, or to have been muddled about its significance, and are thus led to conclude that Pete folded, which indeed he did. In this case you take a coherent route from your informants' correct evidence and sound thinking to your true conclusion. Can we believe that this route runs through at least one falsehood? Sometimes one does coherently get from falsehood to truth, but only through luck, and in our present case luck has nothing to do with it.

That tells against either conditional's being false. The stronger thesis that one is true and the other false is also open to a different objection, namely that there is no basis for choosing the culprit. You may think: ‘On the contrary: a certain (p.85) fact favours one conditional over the other, though we may not know what fact it is or, therefore, which conditional should be crowned. The deciding fact concerns whether Pete had a losing hand. If he did, then Lora's conditional wins; if he did not, Winifred's.’ I have encountered this in debates about Gibbardian stand‐offs; it is to be found in Pendlebury 1989: 182–3; and it is treated with respect in Lycan 2001: 169. The idea must be that if Pete had a losing hand, then Winifred's conditional—however soundly based and sincerely accepted—is doomed by a fact she does not know about the hands.

To see how wrong this is, let us turn to Gibbard's original story (pp. 226–7), in which Winifred watches the game for a while, sees the opponent's (very strong) hand, signals its contents to Pete, and then leaves the room. Standing outside, and reflecting on Pete's competitive nature, Winifred has powerful grounds for thinking ‘If Pete called, he won’. Our objector has to say ‘Nevertheless, her conditional is doomed by the fact about the hands’; but this looks weaker than ever, because in this version of the story she herself is pretty sure of that fact. Knowing the strength of the opponent's hand, she correctly infers that Pete's hand is a losing one, which leads her to accept that if Pete were to call he would lose. Our objector must say not merely that her confident ‘If Pete called, he won’ is condemned by the fact about the hands, but further that in accepting it she exhibits a muddle, because she knows better. It is an unlikely tale.

Still, we can avoid the distracting need to deal with such objections, and let the pure signal of Gibbard's point come through, by moving to a new example where subjunctives cannot get under our feet and trip us up:

Top Gate holds back water in a lake behind a dam; a channel running down from it splits into two distributaries, one (blockable by East Gate) running eastwards and the other (blockable by West Gate) running westwards. The gates are connected as follows: if east lever is down, opening Top Gate will open East Gate so that the water will run eastwards; and if west lever is down, opening Top Gate will open West Gate so that the water will run westwards. On the rare occasions when both levers are down, Top Gate cannot be opened because the machinery cannot move three gates at once.

Just after the lever‐pulling specialist has stopped work, Wesla knows that west lever is down, and thinks ‘If Top Gate opens, all the water will run westwards’; Esther knows that east lever is down, and thinks ‘If Top Gate opens, all the water will run eastwards’.

Each has a sound basis for her conditional. Someone might rightly trust both speakers and soundly infer that Top Gate will not open; and it would be absurd to think there must be some asymmetrical fact making one conditional true and (p.86) the other false. This example contains nothing analogous to the winning‐or‐losing‐hand feature of Gibbard's example, which has misled some students of it.

Objection: ‘In your example, both conditionals are wrong. Top Gate could not have been opened while both levers were down; each conditional implies that it could have been; so both are false.’ This response leads to fatal conclusions. In particular, for any false A whose falsity was causally determined by the antecedent state of the world, every instance of A→ C will be judged false (except perhaps ones where A entails C). ‘If the avalanche that we heard came over the crest into this valley, we shan't get home tonight’, ‘If there was a specially high tide last night, those logs will have been floated off the beach’, ‘If she fought off the infection, it will be such a relief’—and so on, a swath of falsity will be cut through the middle of what we had thought were innocent conditionals. This defensive objection leads to disaster.

35. How Special Are Stand‐Offs? Does It Matter?

6. The Subjectivity of Indicatives 35. How Special Are Stand‐Offs?

In stand‐offs like Gibbard's and mine, we have two conflicting indicative conditionals neither of which is objectively false or objectively true. How special, how unusual, are such pairs? If they are a tiny enough subset of the whole, they may be a misleading guide to the analysis of indicative conditionals generally.

If a ‘stand‐off’ requires two people who actually do accept respectable though conflicting conditionals, such cases may be rare; but that does not answer the question we should be asking. Suppose my Top Gate story is true except that Esther is not on the scene, and nobody actually accepts ‘If Top Gate opens, all the water will run eastwards’. The basis for this conditional is there in the concrete situation, but nobody does with it what Esther does in my story. This difference cannot affect the status of Wesla's ‘If Top Gate opens, all the water will run westwards’. In the original story, the real obstacle to calling that conditional objectively true, or objectively false, came from the fact that the rival conditional was equally supported by the concrete situation; it did not need someone to have actually accepted it.

Perhaps the noun ‘stand‐off’ is appropriate only when two people accept rival conditionals. If so, reword the question, and ask about the prevalence of stand‐off situations—by which I mean states of affairs containing adequate bases for two conflicting indicative conditionals.

I shall address this question as it arises for indicative conditionals with false antecedents. When an antecedent is true, the picture changes (§ §46–7), and in the meantime I set that aside. Ever so many of our indicative conditionals do (p.87) have false antecedents, and we want to understand how they work—which involves coming to understand how they should be evaluated. So bear patiently with this temporary restriction in the scope of the enquiry.

Without having any statistics, I confidently assert that the vast majority of acceptable F→ C conditionals (that is, instances of A→ C where A is false) are based upon stand‐off situations. Virtually all the ones Davis has in mind are like that (§33). These are conditionals to the effect that if A obtained at some earlier time then so did C, accepted on the strength of evidence that A& ¬ C did not obtain. But ex hypothesi A&C did not obtain either, and the world is probably cluttered with evidence against that conjunction too; in which case someone who noticed it and nothing else would be justified in accepting A→ ¬ C.

This also holds for many conditionals saying that if A comes to obtain in the future then so will C. Such a conditional can be accepted on the strength of present evidence that A& ¬ C will not come to obtain; and, as before, there may often be equally strong evidence that A&C will not come to obtain either. My Top Gate example is like this.

What about the many Future → Future conditionals that are accepted at a time when the world does not contain strong evidence that A will not come to obtain? When a physician justifiably says ‘If you take this drug, you will recover’, could a rival conditional be equally justified? Probably not, but we need to grasp why not. (I labour this because it took me so long to clear my thoughts about it.) We are confining ourselves to F→ C; so we want to evaluate the physician's conditional on the understanding that the patient will not in fact take the drug. Now, if the causes of her not taking it already exist—are lying around in the world so they could in theory be known—then someone might learn of some of them as part of an evidential package that does not assure him that the patient won't take the drug, but does assure him that the conjunction (She will take the drug & She will recover) will not come true. This person would be entitled to accept ‘If she takes the drug, she will not recover’, which would create a stand‐off. My Top Gate story illustrates the simplest kind of instance of such a package; if it is all right, then more complex examples are also possible, and they may spread over much of the conditionals territory.

But not over all of it. Presumably in many Future → Future cases where the antecedent will turn out to be false, the present state of the world does not contain sufficient conditions for this falsity; or if it does, they are—as in my doctor–patient example—so remote from anything we can know that it seems perverse to think of them as possible bases for a stand‐off. It would be rash to contend, as I did until warned by Dorothy Edgington, that every well‐supported F→ C belongs to a stand‐off situation.

(p.88) Nevertheless, I do contend that they are all subjective. Whether a given instance of F→ C could be party to a stand‐off depends entirely upon what the outside world contains, not on the frame of mind of the person who accepts or asserts it. The person's input into the conditional is just what it is for any conditional—a high subjective probability for C given A. The world may be laid out in such a way that the high value for π(C/A) is backed up by the causal impossibility of A's becoming true without C's becoming true, or by some high objective relative probability; but that does not affect what the person means by what he says, what kind of semantic item he produces.

Compare two cases in each of which someone accepts ‘If Top Gate is opened, the water will flow eastwards’. (1) The one described in my example, where sufficient conditions exist for Top Gate not to open, and . . . etc., yielding the stand‐off. (2) It is causally possible for Top Gate to be opened, but impossible for it to be opened without the water flowing eastwards. In 1 there can be a stand‐off, in 2 there cannot. But the very same conditional sentence is used in each to express something the speaker accepts. The conditional in 1, we have seen, cannot be understood as objectively true or false; how can we treat the conditional in 2 differently? Notice that for all I have said to the contrary, Esther1 (so to speak) may think she is in 2, and Esther2 may think she is in 1. The difference between 1 and 2 that affects their capacities for stand‐offs are entirely external to the Esthers; it should not influence our accounts of what these two people are doing in accepting their conditionals.

Last stand: ‘Esther2 might believe she is in 2, and might build this belief into the meaning of her conditional. When she says “If Top Gate is opened, the water will flow eastwards” she means that it is causally possible for Top Gate to open and causally impossible for it to do so without the water's flowing eastwards. Is there anything subjective about what she is saying?’ No. What she means by her conditional is an objectively true proposition about the world, with no covert reference to her belief system. But this is not a permissible meaning for her conditional to be given; it is not a meaning that it conventionally has. In §134 I shall discuss certain related claims attributing to conditionals an array of different meanings, and shall give reasons for dismissing nearly all of them.

36. Subjectivity through Self‐Description

6. The Subjectivity of Indicatives 36. Subjectivity through Self‐Description

Indicative conditionals, I conclude, do not have objective truth values. Well, then, do they have subjective truth values? What could that mean? We could stipulate that if P(A→ C) is high for you now we shall say that A→ C is ‘true for’ you now. But this would merely allow the word ‘true’ to come on stage; it wouldn't let it do any work once it got there.

(p.89) The only way to combine real subjectivity with real truth is to suppose that when someone asserts A→ C, the proposition he asserts has a truth value in the normal way, but that what proposition it is depends not only upon A and C and the normal meaning of → but also on some unstated fact about himself. Analogously, if I hold up a painting and say ‘May Smith painted this’, I express a proposition, but which one depends not only on the sentence I utter but also on what I am holding up while uttering it. If I say to you ‘You have been helpful to me’, the proposition I express depends not only on the sentence I utter but on who I am, who you are, and when I speak.

So we have to consider the idea that what someone means by a sentence of the form A→ C depends in part upon his overall epistemic state, that is, upon how probabilities are distributed across the propositions on which he has opinions. This opens the door to the possibility that when Winifred asserts Called → Won while Lora asserts Called → Lost, each woman says something true, just as they might if one said ‘May Smith painted this’ and the other, holding up a McCahon, said ‘May Smith didn't paint this’.

This amounts to the proposal that → is not a binary but a ternary operator, involving A, C, and the overall belief state of the speaker. So Winifred's conditional applies a triadic relation to the triple {Called, Won, Winifred's belief system}, while Lora's applies the same relation to the triple {Called, Lost, Lora's belief system}. These do not conflict.

Two versions of this line of thought arise from two ways of referring to one's own belief system. One is (1) through an identifying description such as ‘my belief system’, the other is (2) through some device—a proper name, perhaps—that does not describe the belief system in question as one's own. Because I found this difference hard to get clear about, and because it is crucial in our present context, I shall stay with it for a few moments.

Here are two semantic myths. (1) Everyone uses the name ‘Natus’ to mean ‘the place where I was born’. (2) Each person uses the name ‘Natus’ to refer to a particular place; the places vary from person to person; and nothing in the meaning of ‘Natus’ enables one to read off from someone's use of the name any information about the place to which he refers. These are alike in that in each of them one person's ‘The aquifer in Natus is polluted’ need not conflict with someone else's ‘The aquifer in Natus is not polluted’. But they also differ. In 1 a person who says ‘The aquifer in Natus is polluted’ says something about himself, namely that he was born in a place with polluted water; whereas in 2 a person who says ‘The aquifer in Natus is polluted’ does not refer to himself at all. He asserts of a particular place that it has polluted water; but no information about the place can be read off from what he says. Let us first look into the 1‐like or self‐describing version of this story.

(p.90) We are to suppose that Winifred differs from Lora in the way that someone who says ‘I am hungry’ differs from someone else who says ‘I am not hungry’. When you assert an indicative conditional (on this view) you talk about yourself; when you say A→ C you are reporting that your value of π(C/A) is high. This brings in subjectivity through the reference to yourself, yet what you express is a normal proposition with a truth value.

This account of indicative conditionals has virtues. Sheer information about people's conditional probabilities can be useful: in the poker game example, if Winifred tells me that her probability for Pete won given Pete called is high, and Lora tells me that hers is low, I learn things giving me evidence that Pete folded. Similarly with the Top Gate example.

But this is not what indicative conditionals mean. Winifred tells me ‘If Pete called, he won’, and I say ‘Are you sure?’ She replies ‘Yes, I am pretty sure I'm right.’ If she had meant that her value for the conditional probability is high, then her reassurance to me would have meant that she is pretty sure it is indeed high. But confidence in a conditional is not like that. Common sense and the Ramsey test both clamour that Winifred is not assuring me that her value for a certain conditional probability is high, but is assuring me of that high value. She has not asked herself ‘How sure am I about the conditional probability?’ but rather ‘How high is the conditional probability?’ She aims to convince me of that probability, not the proposition that it is her probability. Also, if her probability for Won given Called is only a little above 0.5, she may be utterly certain that that's what it is, yet only mildly inclined to accept Called→ Won. None of this could be right if she and I took her to be simply reporting a fact about her belief system.

It is not useful to appeal to the theoretical hunches of folk who have not confronted the problems and wrestled with the difficulties; so one should not object to the ‘self‐description’ understanding of indicative conditionals on the grounds that the plain person would wrinkle his nose at it. I am not doing that. I appeal not to common opinion but to common usage, contending that the ‘self‐description’ account of indicative conditionals contradicts how they fit into our lives, the role they play in our thought and talk. So failure meets this attempt to show how indicative conditionals can have truth values yet be subjective in the way they are shown to be by the Gibbardian stand‐off.

37. Subjectivity Without Self‐Description

6. The Subjectivity of Indicatives 37. Subjectivity Without Self‐Description

If → is to be ternary, therefore, the belief system in question must be referred to other than through the description ‘my belief system’, which pretty clearly (p.91) implies that it must be referred to without use of any description. On this view, what Winifred asserts is not what Lora denies, but neither woman talks about herself. It is as though Winifred said that R3(Called, Won, Henry) and Lora said that R3(Called, Lost, James), with their names for their belief states not being replaceable by definite descriptions, and in particular not being replaceable by ‘my belief state’. This still makes indicative conditionals subjective, in that what is said by any instance of A→ C depends in part upon who says it, but it also gives what is said on each occasion a solid old‐fashioned truth value.

The price is too high. I have learned about the difficulties from Gibbard (1981b: 231–4) and Stalnaker (1984: 110–11). They present them in the context of a theory according to which A→ C says that C obtains at a certain A‐world. In this context subjectivity comes in through the proposal that what A‐world a speaker of A→ C selects depends in part on her belief system; so Winifred and Lora refer to different A‐worlds in their seemingly but not really conflicting conditionals. In one version of this approach, each means ‘the A‐world that relates thus and so to my belief system’; but that is the self‐description account, which we have seen to be false. In the other version—our present topic—each means something more like ‘the A‐world that relates thus and so to Henry’, where ‘Henry’ picks out a belief system, or a part of one, without describing it. The fatal flaws in this attempt at subjectivity, however, can be brought out well enough without mentioning worlds.

The account of the subjectivity of indicative conditionals that we are now considering has bizarre consequences for communication. I ask both Winifred and Lora ‘If Pete called, did he win?’ Winifred says ‘Yes’ and Lora says ‘No’, and both are right. Now four results emerge, in a crescendo of strangeness. They are not answering a single question. There is no single conditional question that I could have put to both. There is not even a coherent conditional question that I could put to either; for there is no privileged belief system for someone who has no probability for A→ C and is merely asking about it. And even if there were, I could have no way of putting to either of them the very question that she would answer. This is all too much to swallow, say Gibbard and Stalnaker, and who could disagree?

This speaker‐relative view might seem to be strengthened—to gain innocence by association—from the existence of indexicals. But the latter, as Alan Hájek has pointed out to me, count against rather than for the view. When someone speaks using ‘I’, ‘you’, ‘here’, ‘now’, or ‘this’, we are not left floundering to know what he or she is talking about. All we need is to know who is talking, or to whom, or where, or when, or indicating what. No such apparatus comes to our aid in understanding indicative conditionals on the view of them we are now considering.

(p.92) The comparison with indexicals fails in another way. When someone uses ‘I’ to express a proposition, Stalnaker points out, we can re‐express it in other ways; when Miles tells me ‘I am hungry’ I can report that Miles is hungry; and similarly with ‘you’, ‘here’, and the rest. But if someone asserting A→ C expresses a proposition that is determined by her beliefs but is not about them, there can be no speaker‐neutral way to express it. When you assert A→ C to me, I literally cannot say what you have told me.

William Lycan (2001) offers an ingenious account of conditionals through which he aims to give a unified treatment of indicatives and subjunctives, allowing conditionals of each kind to have truth values. I shall comment on the second part at the end of §84. The first part—the attempt to cover indicatives—requires Lycan to put something subjective into the truth‐conditions for such conditionals; which he does. According to his analysis, the truth of A→ C depends upon whether C obtains in a certain class of states of affairs in which A obtains, the class being partly defined by their being states of affairs that the speaker regards as real possibilities in a certain sense. This theory evaluates indicative conditionals subjectively, then, and from time to time Lycan does speak of some conditional as ‘true for’ this or that person. What brings his theory down in ruins, I believe, is his failure to address the issue I have discussed in these two sections. Lycan builds something speaker‐relative into what he calls the truth conditions of indicative conditionals; but he does not even ask whether speakers of such conditionals are always talking about themselves, or whether . . . and so on.

Objection: ‘You have jumped across something. Go back to your “Natus” stories. In one, (1) everyone uses “Natus” to mean “the place where I was born”; in the other, (3) everyone uses “Natus” as the proper name of some place, the places being different for different speakers. You have neglected to consider the intermediate story that (2) everyone uses “Natus” as the proper name of the place where he was born. Analogous to this is the possibility that Winifred means by her conditional something of the form R3(Called, Won, Henry), where “Henry” is a proper name for her belief system, and everyone knows that that's what it names. According to 2, communication succeeds because we all know that when someone accepts an indicative conditional of the kind here in question, she does so on the basis of a relation between A, C, and her present system of beliefs; but in asserting the conditional the speaker does not speak about herself, because she implicitly refers to the relevant belief system not as “mine” but through a proper name.’

Plausible as this is, I think it is wrong. If the information (P) that the relevant belief system is the speaker's own is something the hearer must know if he is to understand what the speaker says, does not that make P a part of what the speaker means by what she says?

(p.93) Even if this were not so, the proposed account of indicative conditionals still mislocates their point, purpose, and interest. On this latest account, if we allow it to survive, someone who says A→ C is giving news about a triadic relation holding amongst A, C, and a certain belief system. It follows that a hearer who says ‘You have convinced me’ or ‘I'm sure you are right’ or the like is not saying or even hinting that his own probability for C given A is high; he is merely agreeing that C is high given A within the belief system to which the speaker has somehow referred.