There has been an intensive debate about whether modus ponens fails for indicative conditionals. Less attention has been paid to the question of whether similar examples can be constructed for counterfactuals as well. This is insofar surprising as McGee claimed that the Import/Export principle (which leads to the counterexamples for indicatives) holds also for counterfactuals. So, are there counterexamples to modus ponens for counterfactuals?
Let us recall the setting of McGee’s counterexample. There are three candidates for the 1980 election: the two republicans Reagan and Anderson, and the democrat Carter. The polls see Carter far behind Reagan, with Anderson a distant third. Prima facie, McGee’s counterexample can go counterfactual. Suppose I know about the polls but do not receive any relevant information afterwards, perhaps because I go on a safari trip or because I just don’t care. After the time of the election I consider the following argument:
(1) If a republican had won, then if it had not been Reagan, it would have been Anderson.
(2) A republican won.
(3) Therefore, if Reagan had not won, it would have been Anderson.
Given the polls, I will find the premises highly probable although I will dissent from the conclusion. This comes as a surprise: if an inference is classically valid, the uncertainty of the conclusion cannot exceed the sum of the uncertainties of the premises. This puts pressure on the validity of modus ponens for right-nested counterfactuals.
Posted by Moritz.
Yet intuitions are quite shaky when it comes to the evaluation of counterfactuals with a true antecedent. Since modus ponens is such a valuable tool, we may happily pay the prize of blaming some intuitions which are not stable anyway to be misleading. This strategy would be appealing if the putative counterexamples were simply an idiosyncrasy of our language. But there seems to be a systematic principle in the background which serves to generate the counterexamples, namely the infamous Import/Export principle:
(IE) Counterfactuals of the form (A > (B > C)) are logically equivalent to the corresponding counterfactuals of the form ((A & B) > C).
The Import/Export principle sounds fine for many counterfactuals. Consider for instance its application to (1):
(4) If a republican had won and it had not been Reagan, then it would have been Anderson.
It seems natural to take (1) and (4) to be equivalent. Now, hardly anyone thinks that the inference from ((A & B) > C) and A to (B > C) is valid for counterfactuals. But by the Import/Export principle, any invalidating sequence for this pattern of inference generates a counterexample to modus ponens. Thus, the Import/Export principle may provide a systematic reason of why counterexamples to modus ponens occur. Modus ponens can only be saved if Import/Export fails in all the relevant cases.
In a recent talk, David Etlin considers the following counterexamples to the Import/Export principle for counterfactuals (you can find the corresponding paper here).
(5) Even if this match had lit at noon today, it would not have done so if it had been soaked in water last night.
(6) If this match had lit at noon today and had been soaked in water last night, then it would not have lit at noon today.
(7) If this match had lit at noon today, then even if it had been soaked in water last night it would have lit at noon today.
(8 ) If this match had lit at noon today and had been soaked in water last night, it would have lit at noon today.
(5) seems to be true whereas (6) is false, and (7) seems to be false whereas (8 ) is true. If this is so, then we have counterexamples to Import/Export for both of its directions. But the counterexamples are not as clear as one would like them to be. Both (5) and (7) contain an extra “even” (note also that in (5) the counterfactual in the consequent is presented in reversed order). Let us remove these additional features. We would then arrive at the following sentences:
(5′) If this match had lit at noon today, then if it had been soaked in water last night, it would not have lit at noon today.
(7′) If this match had lit at noon today, then if it had been soaked in water last night, it would have lit at noon today.
(5′) sounds quite bad, and even if (7′) is somewhat pointless, it does not seem to be false. This might be because we would probably assent to
(9) If this match had lit at noon today, then if it had been soaked in water last night, it would have had to have dried rather quickly.
Thus, it does not seem that Etlin has given us clear counterexamples to Import/Export, which is not to deny that there isn’t a challenge here.
Now, “even if”-conditionals may very well differ semantically from the corresponding conditionals in which “even” is dropped. Typically, we take an “even if”-conditional to imply its consequent. But I do not see how this feature could explain why inserting “even” in the counterfactuals under consideration effects our judgement. As you can check, the relevant implications seem to be o.k. What else can be said?
For a start, consider the following conditional which comes from (5) by turning the past past in the antecedent into a simple past tense:
(10) If this match lit at noon today, it would not have done so if it had been soaked in water last night.
This seems indeed to be true. But this is because the outer conditional is now an indicative one which only has a counterfactual in its consequent. Now, a past past in the antecedent does not necessarily command a subjunctive consequent:
(11) I had a look at this match in the afternoon. If it had lit at noon, it had not been soaked in water last night.
To my ears, the indicative conditional sounds grammatical. Since there is no double subjunctive, nested counterfactuals may be syntactically ambiguous between a counterfactual within a counterfactual and a counterfactual within an indicative. Clearly, the first interpretation is the default one. But context may sometimes favour the outer indicative interpretation. It would be nice if the pragmatics of “even” could be shown to support the indicative interpretation. Compare the following two sequences:
(12) I looked at this match in the afternoon. Probably, it had not lit at noon. Even if it had, it would not have done so if it had been soaked in water last night.
(13) I am certain that the match did not light at noon. Even if it had, it would not have done so if it had been soaked in water last night.
In (12) “probably” invites an “even” within an indicative construction. In (13), however, “certain” forces a counterfactual interpretation. Interestingly, (12) seems to be o.k. whereas (13) appears to be odd. Isn’t this evidence that “even” favours an indicative interpretation with respect to the example under consideration?
Perhaps there is also an alternative explanation. Proponents of Import/Export sometimes hold that the antecedent of the conditional within the consequent of the outer conditional restricts the antecedent of the outer conditional. So, the syntactic structure of an embedded conditional is something like this: [if A: if B] [C]. Perhaps “even” influences the syntax of a sentence by interfering with the default binding structure which then becomes [even if A] [if B: C].
Anyone out there with a better explanation?