How can one justifiably distinguish true counterfactual conditionals from false ones,
given that all such conditionals have false antecedents?
A conditional is a statement of the form “If A, then B”. If the antecedent is assumed to be actually (or probably) true, or is assumed will (probably) become true, then the conditional is called an indicative conditional (this statement is an example). But if the antecedent is assumed to be actually (or probably) not true, or is assumed will (probably) not become true, then the conditional is called a “counter-factual” conditional. An indicative conditional speaks to what is (in fact) the case if its antecedent (“A”) is in fact true. A counterfactual conditional speaks to what would be the case (the consequent – “B”) if its antecedent were true.
Counterfactual conditionals are also called “Subjunctive” conditionals, because the verb form of the antecedent and consequent clauses are in the subjunctive mood. Another means of distinguishing the two kinds is based on the observation that in indicative conditionals, the antecedent and consequent clauses can be used as stand-alone sentences. In counterfactual conditionals, on the other hand, because of the nature of the subjunctive mood, the two clauses cannot be used as stand alone sentences. Now these three modes of classification (verb tense, verb form, and clause structure) are not entirely coincident, and there is much debate about whether some of the incongruities should be classed in one category or the other. This is especially the case when consideration is extended to English sentence forms that are not in the “if-then” format, yet are clearly conditional statements in a different guise (eg. “When in Rome, do as the Romans” or “He would have done as the Romans, had he been in Rome”).
Consider the pair of statements –
(a) If Booth didn’t kill Lincoln, then someone else did.
(b) If Booth hadn’t killed Lincoln, then someone else would have.
Conditional (a) is an indicative conditional, because it is about what is the case. And the two clauses “Booth didn’t kill Lincoln” and “Someone else did” can be used as stand alone sentences. Conditional (b) is a counterfactual conditional, because it is about what would be the case. And the two clauses “Booth hadn’t killed Lincoln” and “Someone else would have” cannot be used as standalone sentences. But despite their otherwise close similarity, the two are said to differ in their truth conditions and their truth-value.
Analyzing the truth-status of indicative conditionals amounts to analyzing the status of the facts of the matter. The facts are that Lincoln was killed. If Booth didn’t do it, then it is necessary to the concept of “Lincoln was killed” that someone else did. Statement (a) is hence usually considered to be true – given that Lincoln was killed by somebody, if that somebody was not Booth, it has to have been someone else. Statement (b) on the other hand, is arguably false – assuming that Booth did not kill Lincoln, then Lincoln was not killed, and if Lincoln not killed, then he was not killed by anyone. Yet all that we have done in going from (a) to (b) is change the verb-form to the subjunctive mood. But distinguishing a true counterfactual conditional from a false ones amounts to analyzing . . . what? There is nothing actual, no “facts of the matter”, no “State of affairs” that can be examined to determine whether the counter-factual conditional in (b) is true or false.
It is at this point that the “possible worlds” approach of Lewis makes its contribution. Lewis argues that what is available for analysis in counterfactual scenarios are the various possible worlds. The truth of (b) is established by determining whether or not the closest possible world in which Booth did not kill Lincoln is also one in which someone else did. Since it appears (somehow, means unspecified) that it is not (the closest possible world in which Booth did not kill Lincoln would seem to be one in which no one else did), the (b) conditional is false.
Unfortunately, relying on the possible worlds analysis as justifying the distinction between true and false counterfactual conditionals suffers from two significant difficulties. Significant enough to put in doubt the appropriateness of the possible worlds approach to the distinction.
The first, is that the possible worlds approach does not offer any realistic means of distinguishing between “reasonable” and “unreasonable” conditionals. It is quite acceptable, by this scheme, to have an antecedent and a consequent that are totally unrelated to each other. For example the counterfactuals “if 5 had been even, then pigs would have flown”, and “if pigs had flown, then 5 would have been odd” are both plausibly acceptable by the possible worlds analysis. Possible worlds analysis demands only that the truth of “if 5 had been even, then pigs would have flown” is established by determining whether or not the closest possible world in which 5 is even is also one in which pigs fly. Given the outlandishness of the two conditions, it is questionable whether any estimate of their relative “closeness” can be entertained. If it becomes problematic in such outlandish cases, what recommends it for cases more mundane?
The second, is that the entire concept of the possible-worlds theory, as the means of evaluating the truth-status of counterfactual conditionals, is based on the notion of the (relative) “closeness” of any two possible worlds. But that is a notion that is undefined, and indefinable – despite the rigorous treatment of the notion by Lewis in his Counterfactuals. The idea seems to work only because it draws upon our prior expectations of causal relationships. The only way of discerning whether one possible world is closer to the actual world than another possible world, is to draw upon our pre-existing casual intuitions to guess which is the more causally likely. Since Lewis bases the theory of possible worlds on our intuitions about causation, and then attempts to analyze causation in terms of a possible worlds analysis of counterfactuals, the theory becomes quite circular. And as a means for discerning the truth-status of counterfactual conditionals, that will not do. (But it does point the way towards a better alternative that I will explore shortly.)
There are philosophers, like Mackie, who argue that conditional statements in general are not statements for which “True” and “false” apply. They argue that what they are is conditional assertions, rather than assertions of conditionals. One does not evaluate the truth of “if A, then B”. Instead, one evaluates the truth of “B, given A”. On this interpretation of conditionals, the evaluation of truth-status is modelled by the mathematics of conditional probabilities. The advantages of this approach are that the mathematics of conditional probabilities is well understood, and it nicely distinguishes “reasonable” from “unreasonable” conditionals of both kinds. The mathematics of conditional probabilities was also well established before the theory of possible-worlds was suggested, so it can make do quite nicely without the problems of understanding the notion of “closeness”. But the consequence most germane for this discussion is that it treats indicative and counterfactual conditionals identically. The only difference between them is an intuitively natural difference in what is part of the “given” and what isn’t. As Mackie points out, the English form “if A, then B” must be understood as including two additional assumptions – “if A, then (ceteris paribus and mutatis mutandis) B”. All that differs between indicative and counter-factual conditionals, according to Mackie, is what is assumed to be part of the “ceteris paribus” and what is assumed part of the “mutatis mutandis“. To go back to our outlandish counterfactual “if 5 had been even, then pigs would have flown” – this would have to be reformatted as evaluating the probability of “pigs have flown, given 5 is even”. It is reasonable to suppose (but on what basis?) that the probability is very near zero. And that, according to the conditional-probability math, means that we should evaluate the counterfactual as false.
But it is on the basis of our pre-existing causal intuitions that we find it reasonable to suppose that the probability of “pigs have flown, given 5 is even” is very nearly zero. So it seems that both the possible worlds and the conditional probability approaches rely on our pre-existing causal intuitions. And therein lies the key to a better solution. That is the analysis of counter-factual conditionals on the basis of our causal expectations (our subjective beliefs about the causal laws, rules, etc.).
This is not an analysis on the basis of actual causal laws (natural laws, rules, linkages, flows-of energy, or however else one might choose to understand the notion of a causal relationship). The concept of causal laws is itself well known to be problematic. Rather it is an analysis on the basis of a loose Humean notion of previously experienced and hence now expected causal relationships with a carefully unspecified level of detail. As such, it thereby avoids the problems inherent in specifying just exactly what “causation” amounts to, and what a “causal law” amounts to. By relying on our subjective expectations of causal relationships, it allows that each individual will have their own catalogue of expectations that they have learned through experience. Hence different people can come to different conclusions about the truth of a given counterfactual. It also allows “causal” relationships that transcend any conception of physical law. Hence one can evaluate as true (although misleading) the counterfactual “if Peter is not in the pub he is in the library” when Peter is known to be in the pub. Consider for example, a common causal expectation about a roulette table that has had a run of several reds. The common expectation is that a black is more likely on the next spin. The expectation is wrong, of course (its called the “gambler’s fallacy”). But it is common enough that casinos display running lists of the last ten or twenty red/black results to seduce the gamblers into drawing upon it.
The great advantage of the causal expectation approach over either the possible worlds analysis or the conditional probability approach, is that it makes a clear distinction between “reasonable” and “unreasonable” conditionals. If there is some manner of a causal relationship expected between the antecedent and the consequent, then the conditional is “reasonable”. Otherwise, it is “unreasonable”. And this too fits nicely with our intuitions about which conditionals are worthy of further consideration, and which are worthy of merely a chuckle or groan.
The causal approach provides a much more intuitively appealing, and English usage conforming, analysis of the truth-status of counterfactual conditionals. If the causal expectations are such that given A, B is expected to be necessary or more likely, then the counterfactual conditional is true. Otherwise, it is false. If there is no causal expectation linking A to B, then the evaluated probability of “B, given A” will not differ from the evaluated probability of “B, given not-A”. And that will mean that the counterfactual conditional is false. Otherwise, it is true.
The means of distinguishing true counterfactual conditionals from false ones on the basis of our causal expectations is a fully justified one because that personalized database of causal expectations is the foundation upon which we make all our evaluations of the likely consequences for any choice. We have lots of practice in forecasting that “if I do A then B will likely result”. It is only slightly different to forecast “if (counter-factually) A then B would have likely resulted”.
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