Should we treat indicative and counterfactual conditionals differently?
Justify your answer.
Now of course we are always free to slice up the universe of discourse in any manner that suits the convenience of our current cognitive purposes. So it is obvious that something can be used to slice the universe of conditionals into indicative versus counterfactual conditionals. Otherwise, we could not have created the two classifications. But the title question, in the context of a course on the philosophy of logic, inquires whether there is any principled reason for doing so, from the point of view of logical analysis. And it is at that point that the debate begins. But before I explore some of the arguments on either side of this question, I will elaborate a little on just what commonly is used to distinguish indicative from counterfactual conditionals
A conditional is a statement of the form “If A, then B”. 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. 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 “counterfactual” conditional. 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”).
Both of these kinds of conditional statements need to be distinguished from the class of conditionals called “material conditionals” (also known as material implications or truth-functional conditionals). Material conditionals are defined as those conditionals that satisfy a particular rule of logic namely that the conditional is defined as false when A is true and B is false, otherwise it is defined as true. The rules of logic apply no other constraints. Unfortunately, the behaviour of material conditionals does not correspond very well to the usual English understanding of the “If-then” construct, resulting in what are loosely described as “paradoxes of implication”. For example, any material conditional statement with a false antecedent is true. So the statement “if 5 is even, then pigs fly” is true. Similarly, any material conditional with a true consequent is true. So the statement “if pigs fly, then 5 is odd” is true. It is quite acceptable, within the rules of logic, to have an antecedent and a consequent that are totally unrelated to each other and indeed, like these examples, would normally be considered nonsensical. Such conditionals appear intuitively “unreasonable” because normal English usage of the conditional form somehow implies that the consequent is true (when it is true) because of the truth of the antecedent. Material conditionals do not adhere to that intuition. They are therefore of interest primarily within the limited scope of propositional or predicate logic. So from here on I will ignore the material category of conditionals.
Many philosophers approach the analysis of conditional statements from the perspective of linguistic usage, and focus on the conditions under which the conditionals would be intuitively evaluated as true. They argue that the truth-conditions of the two kinds of conditionals are demonstrably different. This is claimed to be s a sufficiently significant distinction to count as a “principled” reason for treating the two kinds of conditionals differently.
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.
However, contrast these two examples with –
(c) If Booth doesn’t kill Lincoln then someone else will.
(d) If Booth hasn’t killed Lincoln, then someone else will.
(e) If Booth won’t kill Lincoln, then someone else will.
(f) If Booth had not been going to kill Lincoln, someone else would have been going to.
Into which category each of these latter examples fall has been the subject of some debate. They are also closely similar to the first two examples. And they do not clearly fit the three-way categories of classification described above.
Analyzing the truth-conditions 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 – on the premise 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 on the premise that if Booth did not kill Lincoln, then Lincoln was not killed. And if Lincoln was 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 analyzing the truth-conditions for counterfactual conditionals amounts to analyzing “¦ what? There is nothing actual, no “facts of the matter”, no “State of affairs” that can be examined if the premise is that Lincoln was not killed.
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 (somehow, means unspecified) appears that it is not (the closest possible world in which Booth did not kill Lincoln is one in which no one else did), the (b) conditional is false.
Assuming that the “possible worlds” understanding of counterfactual conditionals is an acceptable approach, it is then argued we now have two fundamentally different means of establishing the truth of the two sorts of conditionals. Since the truth status of each statement is analyzed differently, and the subject matter being analyzed is different, and the two different analyses arrive at different truth values for otherwise closely similar conditionals, it must be the case that the two sorts of conditionals are fundamentally different. Therefore, we should indeed treat indicative and counterfactual conditionals differently. We have to treat them differently in order to determine whether they are true or false.
Unfortunately, relying on the truth-conditional analysis as the principle justifying the differing treatment of indicative and counterfactual conditionals suffers from two significant difficulties. Significant enough to put in doubt the appropriateness of the truth-conditional approach to the distinction.
The first, and less serious of the two, is that the truth-conditional classification scheme does not offer any means of distinguishing between “reasonable” and “unreasonable” conditionals of either variety. Both indicative and counterfactual conditionals would still be vulnerable to the challenges facing material conditionals, as described above. The truth-conditional classification scheme results in conditionals of both sorts that do not correspond very well to the usual English understanding of the “if-then” construct. For example the conditionals “if 5 is even, then pigs fly”, “if pigs fly, then 5 is odd”, “if 5 had been even, then pigs would have flown”, and “if pigs had flown, then 5 would have been odd” are all as acceptable. It is quite acceptable, by this classification scheme, to have an antecedent and a consequent that are totally unrelated to each other. And while this deficiency is not fatal for the truth-conditional approach, it at least demonstrates that there must be some other classification scheme that can distinguish “reasonable” from “unreasonable” antecedent-consequent pairings.
The second, and more serious difficulty with the truth-conditional classification scheme, is that the possible-worlds theory, posited as the means of evaluating the truth-conditions of counterfactual conditionals, has its own difficulties. The entire concept 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-conditions of counterfactual conditionals, that will not do. (But it does point the way towards a better alternative that I will explore shortly.)
In contrast to those who argue for a clear distinction between indicative and counterfactual conditionals, other philosophers argue that the truth-conditions of the two kinds of conditionals are actually identical, and arguments to the contrary are flawed. The claim is then that there is therefore no sufficiently significant distinction to count as a “principled” reason for treating the two kinds of conditionals differently.
There are actually two different lines of reasoning to this conclusion one that argues that the two kinds of conditionals are alike in that they are both not truth-apt; and one that argues that there is a common way to analyze the truth conditions of both kinds of conditionals.
There are philosophers, like Mackie, who argue that conditional statements 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-conditions 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 the various versions of the Booth-Lincoln conditionals is what is assumed to be part of the “ceteris paribus” and what is assumed part of the “mutatis mutandis” into which falls the assumption that “Lincoln was killed”. So on the basis of this understanding of conditionals, there is no reason we should treat indicative and counterfactual conditionals any differently.
The other line of reasoning that denies there is any reason we should treat indicative and counterfactual conditionals differently, was implied by my critique of the possible-worlds theory. This is the analysis of conditionals on the basis of causal relationships (natural laws, rules, linkages, flows-of energy, or however else one might choose to understand the notion of a causal relationship). Or alternatively, on the basis of our causal expectations (our subjective beliefs about the causal laws, rules, etc.). Some writers prefer objective causal relationships. But a few rely only on our subjective causal expectations. Personally, I prefer the latter as it demands only a loose Humean notion of a causal relationship, and avoids the problems inherent in specifying just exactly what “causation” amounts to.
Either way, this approach to analyzing conditionals focuses on the causal relationship between the antecedent and the consequent. The motivation is provided by our strong intuition that when we frame a conditional “if A, then B” we somehow imply that it is B because of A. As was pointed out by Achourioti, that intuition is strong enough that we frequently reason from “if A, then B” and “not-A” to “not-B”. According to the rules of logic, this is the logical fallacy of denying the antecedent. It is supposed to be invalid. The truth-conditional approach to conditionals would agree with this judgement. But if the analysis is causal, then the results are somewhat different. If it is among the “ceteris paribus” that A is the only cause of B, then the reasoning is in fact valid. And even if A is only one of many possible causes of B, if “not-A”, then one of the possible causes of B is not the case, and so B is probably less likely. Thus the reasoning is still partially valid. Hence our strong intuitive draw to such logically invalid reasoning.
The causal based analysis of conditionals shares a great deal of similarity to the calculus of conditional probabilities employed by the likes of Mackie in his analysis of conditionals as conditional assertions. The great advantage of the causal approach is that it makes a clear distinction between “reasonable” and “unreasonable” conditionals. If there is some manner of a causal relationship (even if only in a broadly Humean sense) 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 conditionals. If the causal relationship is such that given A, B is necessary or more likely, then the conditional is true. Otherwise, it is false. Quite different from the truth-table for the both the material conditional analysis, and the truth-conditional analysis. But more in line with our normal English usage of the if-then construct.
Most importantly for this discussion, the approach draws no distinction between indicative and counterfactual conditionals. From the basis of a causal analysis of conditionals, there is no principled reason for maintaining the distinction between the two kinds of conditionals, and we should not treat indicative and counterfactual conditionals any differently.
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