Explanatory and Inferential ConditionalsAuthor(s): Ian WilsonSource: Philosophical Studies: An International Journal for Philosophy in the AnalyticTradition, Vol. 35, No. 3 (Apr., 1979), pp. 269-278Published by: SpringerStable URL: http://www.jstor.org/stable/4319287 .

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IAN WILSON

EXPLANATORY AND INFERENTIAL CONDITIONALS

(Received 19 December, 1977)

A conditional sentence may be employed to express and understood to express a number of different claims. Of course a given sentence may express different claims on different occasions of its use because of changed assign- ments to proper names and indicator words or because of ambiguous predicates or grammatical construction. A conditional sentence shares such indeterminacy with other types of sentence, for it allows altemative interpre- tations of its antecedent and consequent. But, even after the interpretation of its component sentences is regarded as given and fixed, a conditional sentence may be interpreted in more than one way and hence regarded as expressing now one claim, now another, possibly not even materially equivalent to the first. And, conversely, distinct conditional sentences may each express the same claim.

It is, I think, this freedom or looseness of fit between expression and what is expressed which in part explains how writers on conditionals can (ap- parently) disagree on such central matters as the validity of contraposition and conditionalisation, the compatibility of opposite conditionals 'if P then Q' 'if P then -Q' and the compatibility of their negations, and can disagree about the relationships between indicative, subjunctive and counterfactual conditionals. And such disagreements are, I think, fostered by a misleading simplification which tends systematically to distort our intuitions. The sim- plification is this. It is often assumed that whatever is expressed by a sentence such as

If Mary was there (then) it was a good party

is expressed equally by the corresponding

If it is true (the case) that Mary was there (then) it is true (the case) that it was a good party.

It is assumed that these sentences are mere linguistic variants of one another,

Philosophical Studies 35 (1979) 269-278. 0031-8116/79/0353-0269$01.00 Copyright ?3 1979 by D. Reidel Publishing Co., Dordrecht, Holland, and Bostoa, U.S.A.

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270 IAN WILSON

that they express exactly the same claims with the same presuppositions and

implications. Now it is at least not obvious that this assumption, concerning

the indicative, is correct, but when it is extended to the subjunctive it is

fairly clear that it is incorrect. For it is then assumed that whatever is expres-

sed by a sentence such as

If Mary were there (then) it would be a good party

is expressed equally by the corresponding

If it were true (the case) that Mary was there (then) it would be

true (the case) that it was a good party.

It is assumed that these two sentences express exactly the same claims - and

indeed that the second, in which the modal elements have been extracted

from antecedent and consequent, is more perspicuous and gives the form of

the first. But this assumption is incorrect and misleading.'

Suppose we are discussing a party thrown by some friends of ours. We

might consider the claim, concerning some one person called 'Mary'

(1) If Mary was there it wvas a good party

Story A: We hold (1) to be true because Mary is an irresistable ice-breaker,

the life and soul of any party. We think, that is, that (1) is true because we

think that in the circumstances which will have prevailed, if Mary was there

the party will have been a good one, if for no other reason, because Mary was

there. If we let 'P' abbreviate 'Mary was there' and 'Q' abbreviate 'It was a

good party', we believe not only that P is a reason for thinking that Q but,

further, that P is a reason why Q.2

Story B: We hold (1) to be true because Mary is well known not to go to parties unless they are good ones. (Friends telephone and tell her if they are at a good party and then she sometimes goes.) We think, that is, that (1) is true, becauge we think that in the circumstances which will have prevailed

if Mary was there the party must have been good because she wouldn't have

gone if it wasn't. We believe, then, that P is a reason for thinking that Q but

in this case we do not believe that P is a reason why Q, but rather that -Q is a reason why -P. ('Only if' has come under a good deal of pressure from

logicians taking P only if Q to be equivalent to If P then Q, and hence taking P if and only if Q to be symmetrical. If we resist this pressure, and retain

the discriminatory force which English supplies, then we will, I suggest,

regard

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EXPLANATORY AND INFERENTIAL CONDITIONALS 271

(2) Marv was there only if it was a good party

as justified, just as (1) is, by story B, but not justified by story A.) Story C: We hold (1) to be true because, in circumstances like those under

discussion, it always tums out to have been a good party if Mary was there. No doubt there is a reason for this but we have no particular opinion about what that might be. Nonetheless we hold ourselves justified in inferring from the supposition that Mary was there that, in the circumstances which will have prevailed, it was a good party. We believe, that is, that P is a reason for thinking that Q, but do not believe that P is a reason why Q nor that -Q is a reason why -P.

Story D: We hold (1) to be true because we believe that it was a good party and the supposition that Mary was there does not conflict with that belief. Though if Mary's presence does tell to some extent agaist its being good then we shall to a related extent prefer to express our opinion as

(3) Even if Mary was there it was (still) a good party

That is, we regard the truth of Q as sufficient for the truth of (1) provided only that P is not (by suitable criteria) incompatible with Q.

Story E: The material implication story. Now each of these stories provides a different justification for holding (1)

to be true and I have presented them as though the sentence (1) expressed a single claim which could be justified in five different ways. I wish to argue, however, that to each of these different justifications there corresponds a distinct interpretation of the conditional sentence (1). That is, to each story there corresponds a distinct claim. (If this contention is established then the justificatory stories would each require rewriting in the form: 'We hold the claim we now take the sentence (1) to express to be true because ...'.) Only if one adopts such a view, it seems to me, is it possible to explain how we can save anything at all of contraposition without again sliding all the way down the slippery slope into the material implication account of conditionals.

Let us call conditionals related as If P then Q and If P then -Q 'opposite' conditionals, and conditionals related as If P then Q and If -P then Q 'al- ternative' conditionals. (Downing's Argument.)3 If there is a type of condi- tional such that alternative conditionals of that type are compatible but opposite conditionals of that type are incompatible, then conditionals of that type do not entail their contrapositives. For the contrapositives of alternatives are opposites. But now consider any genuine or informative empirical condi- tional which conveys what is, will or would be if ..., say,

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272 IAN WILSON

(4) If you touch the wire you will get a shock.

(4) is incompatible with its opposite. What would the world have to be like for both (4) and its opposite to be true? Would the wire both be at high potential relative to you and not? It will not do to say that it would simply be that you are not going to touch the wire. For both (4) and its opposite purport to convey what would happen if you did. But (4) is compatible with its alternative. It may well be that things have been so arranged that if you don't touch the wire a shock will be administered to you in some way anyway. And in these circumstances both (4) and its alternative would be true. Hence (4) does not entail its contrapositive, and, if all genuine empirical conditionals share the properties described (and what reason have we for thinking otherwise?) then no genuine empirical conditional entails its contrapositive.

[Incidentally, it is sometimes said that if a conditional and its alternative are both true then this shows that the antecedents are irrelevant to the con- sequent. But this is misleading. Admittedly, if a conditional and its alternative are both true then their common consequent is true whatever the truth-value of either antecedent. But it doesn't follow from that that either antecedent is irrelevant. Either or both may constitute reasons for thinking the consequent true. And one (at most one) may be a reason why. Thus it may be both that (1) expresses a true claim justified by story A and that

(5) If Mary was not there it was a good party

also expresses a true claim which is justified by a story C', viz: If Mary didn't go she would have made sure that Harry went and Harry ... etc. So there may be causal or other links both for (1) and for (5) and neither antecedent is then irrelevant. Such considerations may be of great importance when, for example, we are concerned to ensure that a system fails safely.]

But Downing's compelling argument (last paragraph but one) fails as it stands to secure complete conviction. If (4) is true, in its natural interpreta- tion, then so also is its contrapositive

(6) If you don't get a shock then you won 't have touched the wire

I do not pretend to be able to prove this - but nor do I believe it possible coherently to conceive of circumstances in which the claim expressed by (4), in its natural interpretation, is true and yet the claim expressed by (6) (as

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EXPLANATORY AND INFERENTIAL CONDITIONALS 273

contrapositive of (4)) is false. But then things must stand otherwise with the alternative to (4)

(7) If you don't touch the wire you will get a shock

and its contrapositive

(8) If you don't get a shock you will have touched the wire,

How shall we proceed? In the end the conclusion of Downing's argument will, I believe, be vindicated. No genuine empirical conditional entails its con- trapositive. And yet something must be saved if we are to account for the truth of (6) given (4). To do this we will employ the distinction between P is a reason why Q and P is a reason for thinking that Q and in the light of this distinction reconsider the compatibility of alternative conditionals and the validity of contraposition.

A situation or state of affairs, described or reported in a certain way, may be explanatory of another. That the water froze explains (in part, but, it may be, sufficiently for our purposes) why the pipes burst. That Mary was there explains (in part ...) why it was a good party. These claims are factive. The first, for example, presupposes that the pipes burst (to be explained) and that the water froze (to explain it). But the explanatory relationship which holds between the freezing of water and the bursting of pipes in virtue of which the former is a potential partial explainer of the latter, holds, if it holds at all, independently of those presuppositions. The claim that such a relation- ship holds between the situations reported (truly or falsely) in a sentence P and a sentence Q I have expressed by 'P is a reason why Q'.

And a situation or state of affairs, described or reported in a certain way, may be a sign or indicator of another. That the pipes burst is a sign (more or less reliable) that the water froze. That Mary was there indicates (more or less reliably) that it was a good party. These claims also are factive. But the inference justifying relationship which holds between the bursting of pipes and the freezing of water holds independently of whether they are facts. The claim that such a relationship holds between the situations reported (truly or falsely) in a sentence P and a sentence Q, such that its being true that P would be a reason for thinking that that Q also, I have expressed by 'P is a reason for thinking that Q'.

Let us now abbreviate 'P is a reason why Q' as 'P rw Q' and 'P is a reason

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274 IAN WILSON

for thinking that Q' as 'P rt Q'. P rw Q is incompatible with all other simple reason-why claims involving both and only P and Q (except, con- ceivably, -P rw -Q). For present purposes we need only that P rw Q is incompatible with -P rw Q and with -Q rw -P so we confine our atten- tion to these. (i) Incompatibility of P rw Q and -P rw Q: Any concept of explanation or reason-giving which allowed both to be true would be at- tenuated beyond applicability, would have lost all connection with under- standing. That which can be 'explained' as well by the absence of some

property as by its presence, as well by the occurrence of some event as by its non-occurrence, can be 'explained' by anything whatever. (ii) Incompatib- ility of P rw Q and -Q rw -P: Explanation or reason-giving has a direc- tion. If we would regard the lateness of his train (if it were late) as explaining Smith's standing on the platform (if he were still standing there) we could not at the same time regard Smith's not being still on the platform (if he were no longer there) as explaining his train's being on time (if it were to be).

Conversely if we would regard Smith's standing on the platform (if he were still standing there) as explaining the lateness of his train (if it were late - he is the driver, say) then we could not at the same time regard his train's being on time (if it were to be) as explaining Smith's not being still on the platform (if he were no longer there). In general, if we regard P as explanatory of Q we cannot at the same time regard -Q as explanatory of -P.

P rt Q, on the. other hand, is compatible with -P rt Q and with -Q rt -P and is incompatible with P rt -Q, as already maintained. Further it seems clear that P rw Q entails P rt Q and -Q rt -P. Let us suppose this.

And let us correlate with each of our justificatory stories for what is expres- sed by a conditional If P then Q a distinct type of claim, as follows:

(A*) P rt Q&P rw Q (B*) PrtQ &-Qrw-P (C*) P rt Q (D*) Q&-(Prt-Q) (E*) -(P& -Q)

Now (A*) and (B*) both entail -Q rt -P and we have saved the appearance of contraposition without regenerating the problem posed by Downing's argument. For (A*) thus entails -Q rt -P &P rw Q which has the form of (B*). And (B*) entails -Q rt -P & -Q rw -P which has the form of (A*).

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EXPLANATORY AND INFERENTIAL CONDITIONALS 275

But since (A*) and (B*) were incompatible anyway there is, so far, no problem here. And the A- claim and B-claim for the alternative If -P then Q viz.

(A*') -P rt Q&-P rw Q (B*') -Prt Q&-Q rwP

are incompatible with (A*) and (B*) (respectively). Thus although both (A*') and (B*') entail -Q rt P, again the problem is'avoided.

Strictly speaking it is only the appearance of contraposition which has been saved. None of these claims entails its contrapositive (except E*!). Indeed (A*) and (B*) are incompatible with theirs (if, that is, we regard their contrapositives as the A-claim and B-claim respectively for If -Q then -P. (C*) cannot entail its contrapositive -Q rt -P by Downing's argument. And (D*) is not a candidate. But both (A*) and (B*) entail the contrapositive of (C*) and this, while possibly less than we hoped for, is, I suggest, all we were entitled to assert in the first place (plus, of course, the validity of contraposi- tion, for the material conditional). And it is enough to take account of the conviction that given the truth of (4) then (6) must also be true. For (4) is naturally interpreted as expressing an A-claim whereas (6), given that inter- pretation of (4) will be, in that context, interpreted as expressing as C-claim.

It seems likely that this approach could be extended to cover disputed matters other than the validity of contraposition. Is the so-called law of conditional excluded middle

(9) (If P then Q) v (If P then -Q)

valid? Or, what comes to the same thing, are the internal and external nega- tions of a conditional equivalent? Are conditionalisation and strengthening-the- antecedent valid? Is hypothetical syllogism valid (does transitivity hold)? In reply to these questions one would answer that it depends on the interpre- tation selected - and it may be that further interpretations would be required in addition to those mentioned, or, at least, further refinement of those mentioned. But I do not pursue these matters now but rather turn to some questions concerning the subjunctive.

I shall not concern myself here with the question whether English (really) has a subjunctive. There is a construction commonly called 'subjunctive' which we can isolate for discussion by the use of that term whether or not it is in every way properly applied. The construction I have in mind is exhibited in the difference between

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276 IAN WILSON

(10) If Mary was there it was a good party (1 1) If Mary had been there it would have been a good party

the second of these being subjunctive. Nor shall I concern myself (directly) with the relationship between the choice of the subjunctive to express one's conditional claim and counterfactual claims or presuppositions. The fruit- fulness of this study (at least as an investigation lying within logic or semantics) has remained unclear to me.

Consider the following pairs of examples

(1 2)(a) If Jones built it then it was soundly constructed (b) If it was soundly constructed then Jones built it

(1 3)(a) If Jones had built it then it would have been soundly constructed (b) If it had been soundly constructed then Jones would have built it

(14)(a) If it was edible then Jones ate it (b) If Jones ate it then it was edible

(1 5)(a) If it had been edible then Jones would have eaten it (b) If Jones had eaten it then it would have been edible

Now there is no difficulty in attaching interpretations to these sentences, except in the cases of (13)(b) and (l5)(b), which read extremely oddly. And it is interesting to ask why this should be.

To simplify the exposition let us ignore D-claims and E-claims. Then (1 2)(a) and (14)(a) may both be regarded as expressing A-claims or merely C-claims but cannot be regarded as expressing B-claims. (12) (b) and (14) (b) on the other hand may both be regarded as expressing B-claims or merely C-claims but cannot be regarded as expressing A-claims. (These limitations on admis- sible interpretations result from properties if the verbs 'build' and 'eat' and the existence presuppositions carried by the predicates 'soundly constructed' and 'edible' - but be that as it may ...). (13)(a) and (15)(a) may both be regarded as expressing A-claims. Whether they may be regarded as expressing C-claims is not so clear. Now since the subjunctive correlate to (12)(b) is (13)(b) and the subjunctive correlate to (14)(b) is (15)(b) one might expect that these latter subjunctives could be regarded as expressing B-claims and possibly on other occasions merely C-claims. But that seems not to be the case - one is hard put to it to see what (13)(b) and (l5)(b) might mean. And this strongly suggests that at least one role of the subjunctive is to block B- claim (and C-claim?) interpretations.

At least this is strongly suggested when the modal element occurs within

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EXPLANATORY AND INFERENTIAL CONDITIONALS 277

the sub-sentences it modifies as in the examples under consideration. If we now extract it and write it as an explicit quasi-sentential operator, thus

(16) If it were true (the case) thatP it would be true (the case) that Q

we obtain from (13)(b) and (1 5)(b) respectively

(17) If it were true (the case) that it was soundly constructed then it would be true (the case) that Jones built it.

(18) If it were true (the case) that Jones ate it then it would be true (the case) that it was edible.

And there is no difficulty in interpreting these sentence - they must be regarded as expressing C-claims (we are confining attention to A, B, C-claims). And this shows that extracting the modal operator in this way does not always yield a synonymous sentence.

We reach the same conclusions when we compare contrapositives rather than converses. Consider

(19)(a) If the water had frozen the pipes would have burst (b) If the pipes hadn't burst the water wouldn't have frozen

(20)(a) If it were true (the case) that the water froze then it would be true (the case) that the pipes burst

(b) If it were true (the case) that the pipes didn't burst then it would be true (the case) that the water didn't freeze

Now (19)(a) is naturally interpreted as expressing an A-claim, but, then, what can (19)(b) mean? One wants to try to make it (as it were) express a B-claim but the words seem not to be able to accept the thought. Of course there is a natural enough interpretation, though unusual, which can be revealed in this way - suppose that the water never freezes while in the pipe which is constantly hot and carefully protected. Then one might well assert (19)(b). But then in these circumstances (19)(b) will surely be regarded as expressing an A-claim and one will be in difficulties over the interpretation of (19)(a). But difficulties do not arise over the interpretation of (20)(a), (b) which, since they express C-claims, can receive natural interpretations both in the expected contexts for such claims and in the unusual one described.

Let us now, in conclusion let in D-claim interpretations. It is my impres- sion that the subjunctive conditionals in which the modal element is internal to the sub-sentences may not be regarded as expressing D-claims, while those

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278 IAN WILSON

in which it has been extracted, may. Thus, for example, (13)(a) may not, but (18) may, be regarded as expressing a D-claim. If I am right about all this then one can see how there can be disagreement about the 'law' of conditional excluded middle and how to resolve that disagreement. In the case of CEM for subjunctive conditionals, for someone who regards the forn of a subjunctive conditional as given by (16), since such structures may be regarded as ex- pressing D-claims, it will seem possible that CEM is valid. And it will seem possible to regard the inference

(21) P & Q l- If P then Q

as valid, even where the conditional conclusion is subjunctive. But if we deny that the form of a subjunctive conditional is given by (16) then our reaction to (21), for example, may be, and I suggest, will be, quite different, (at any rate if the modal elements are internal to sub-sentences of the condi- tional conclusion).

Suppose that it turns out that it is almost never the case that we have both bread and butter. If we have butter we tend to have no bread and if we have bread then we tend to have no butter. But that on Tuesday of last week, mirabilis dictu, we have both. Is it the case that

(22) If we had had butter last Tuesday we would have had bread?

Of course not!

University of Stirling

NOTES

1 The simplification is resisted by Wilfred Sellars in.'Counterfactuals', Minnesota Studies in the Philosophy of Science, ed. by Feigl, Scriven and Maxwell (Minneapolis, 1956), Vol. 2, pp. 227-48; reprinted in Sosa, E. (ed.), Causation and Conditionals (Oxford, 1975), pp. 126-46; in the latter see pp. 131, 142. 2 For related distinctions see Sellars op. cit., pp. 134, 139, 141, 144. 3 Peter Downing, 'Subjunctive conditionals, time, order and causation', Proceedings of the Aristotelian Society 59 (1958-59),. pp. 125-40, esp. p. 138. See also Downing's 'Con- ditionals, impossibilities and material implications', Analysis 35 (1974-75), pp. 84-91, esp. p. 90.

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