The Metalinguistic Theory of Counterfactuals

The basic idea of the metalinguistic theory of counterfactuals is that the counterfactual A>C is true if and only if C is entailed by A and some other relevant premises. This theory was proposed by Chisholm (1946 "The Contrary-to-Fact Conditional," Mind 55 289-307, reprinted with revisions in H. Feigel and W. Sellars (1949) Readings in Philosophical Analysis New York: Appleton-Century-Crofts, 482-97) and Goodman (1947 "The Problem of Counterfactual Conditionals," The Journal of Philosophy 44 113-28, reprinted in N. Goodman (1955) Fact, Fiction, and Forecast. Indianapolis: Bobbs-Merrill, and in Frank Jackson, Conditionals 9-27), and the tag of 'metalinguistic' comes from the observation that the theory seeks to specify truth conditions of counterfactuals in terms of (meta) linguistic notions such as entailment and premises. (But it is controversial whether there is anything essentially metalinguistic about this approach.)

This theory seems to capture well our intuition involving everyday counterfactuals. When we say that, for example:

(C1) If this match had been scratched, it would have lighted

we mean something like "this match lights" can be derived from "this match is scratched" in conjunction with the laws of nature and other relevant background conditions that the match is well made, it is dry enough, oxygen is present, and so on.

But what makes the conditions relevant? For example, what about the condition that the match is made in U.S? Any metalinguistic theories should be able to provide a principled way of characterizing the relevant conditions in order to be a genuine analysis or account. This is what Goodman calls "the problem of relevant conditions."

The first thing obvious is that the relevant conditions cannot be the whole actual truth, for among true sentences there is the negate of the antecedent, so that any consequence would follow from the contradiction. So it would be safe to say that the relevant conditions must be not only true but also compatible with the antecedent A. In addition, the conditions must also be compatible with the negate of the consequence C, for otherwise A and the laws would play no role in deriving C. Of course, the conditions must be compatible with C because the conditions, together with A and the laws, are to be chosen to imply C.

Goodman's Analysis

So Goodman's analysis, as a first approximation, goes as follows:

[GM1] A>C is true if and only if there is some conditions S such that (i) S is compatible with A, C, and ¬C, and entails C in conjunction with A and the laws (ii) there is no conditions S* such that S* is compatible with A, C, and ¬C, and entails C in conjunction with A and the laws.

Here the second condition is necessary because the analysis should be able to admit true counterfactual we are concerned with but also exclude the opposite conditional. We can see easily that [GM1] gets the foregoing counterfactual (C1) right. In (C1), we have the following A, S and C:

where, A, together with S and the laws, entails C. However, further investigation shows that [GM1] is not adequate. To see this, consider the following Goodman's example:

(C2) If this match had been scratched, it would not have been dry.

In this case, according to [GM1], we are forced to say that (C2) is true as well, because we also have the following A, C* and S*:

The problem is that the compatibility condition in [GM1] is not strong enough that [GM1] counts some counterfactuals such as (C2) as true which are false. It can be seen easily that the trouble is caused by the fact that S might include a true sentence which, though compatible with A, is not "eligible" for membership of S, whatever that might mean. Accordingly, we need exclude such an ineligible statement from the set of relevant conditions. So Goodman requires that S must be not merely compatible with A but also "contenable" with A.

Cotenability

Goodman distinguishes true statements that are cotenable with the antecedent and true statements that are not cotenable with the antecedent. For example, it is cotenable with A in (C2) that the match is well made, dry enough and oxygen is present; but it is not cotenable with A that it did not light. What is it then for a true statement to be cotenable with A? It seems obvious that defining the relevant criterion of cotenability is one of the major problems of the metalinguistic approach to counterfactuals. Goodman proposes the following definition: A is cotenable with S if it is not the case that S would not be true if A were true. Taking this into account, Goodman's analysis of counterfactuals amounts to:

[GM2] A>C is true if and only if there is some conditions S such that (i) S is cotenable with A and entails C in conjunction with A and the laws (ii) there is no conditions S* such that S* is cotenable with A and entails C in conjunction with A and the laws.

Here, compared with [GM1], the condition of S's being compatible with C and ¬C has been removed, for the condition has become redundant given the cotenability condition.

[GM2] delivers the right verdict for (C2). But, as Goodman notes, this account faces a serious difficulty, i.e. circularity, because cotenability is defined in terms of counterfactuals. That is, in order to determine the truth of A>C we have to determine whether there is a suitable S that is cotenable with A. But in order to determine whether S is cotenable with A, we have to determine the truth of the counterfactual A>¬S. This is, as Goodman acknowledges, "an infinite regresses or a circle."

One may attempt to find an independent characterization of cotenability which is not defined in terms of counterfactuals.