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Thursday, March 01, 2007

On Adam's Counterexample to Modus Tollens

Ernest W. Adams famously offered the following counterexample to modus tollens:

If it rained, it didn't rain hard.
It rained hard.
So, it didn't rain.

Obviously, this is not a counterexample, given a logic 101 reading of the indicative conditional. Rather, it is a counterexample, given an intuitive assignment of truth-values to the premises and the conclusion. On an intuitive assignment, it seems that 'if it rained, it didn't rain hard' and 'it rained hard' may both be true. But the conclusion seems false, given the premises.

Notice that we get the same result with a subjunctive instead of an indicative:

Should it rain, it won't rain hard.
It is raining hard.
So, it is not raining.

The subjunctive in the first premise is a so-called future subjunctive, which differs pragmatically from the past and pluperfect subjunctives, for example the past and pluperfect subjunctives introduce a counterfactual implicature). With a future subjunctive, the argument seems invalid. But the appearance is an illusion. If it is raining hard in reality, it is not true that it doesn't rain hard at the closest worlds at which it rains. For the closest worlds at which it rains will include the actual world. So, if the second premise is true, then the first premise is false. Now, on a possible world account of the indicative conditional, Adams' argument fails for the very same reasons. I take that to be a virtue of a possible worlds analysis of indicative conditionals. But obviously more needs to be said about how to avoid certain problems that arise on a possible worlds analysis of the indicative.

Here is one such problem: if subjunctives and indicatives have the same truth-conditions, why is 'if Oswald didn't kill Kennedy, someone else did' acceptable when 'if Oswald hadn't killed Kennedy, someone else would have' is not? Edgington suggested that the difference turns on a difference in the tenses. I think that story is plausible.

Another problem is to account for the difference between pairs of conditionals such as 'If Kerry had won the election, the actual U.S. president would have been a democrat', which seems false, and 'if Kerry won the election, the actual U.S. president is a democrat', which seems true. Solutions have been suggested by e.g. David Chalmers, Brian Weatherson and Daniel Nolan. Weatherson and Nolan suggest that the evaluation world (the "A-world") may fix the reference of the expressions in indicative conditionals. That's an interesting idea but it does seem to have some odd implications. For example, 'If language didn't exist 80,000 years ago, then language existed 80,000 years ago' comes out true. Chalmers' two-dimensional account seems to fare better, as it avoids this consequence. On his account, language doesn't have to exist at the scenarios used to evaluate indicative conditionals.

Reference:
Adams, E. W. "Modus Tollens Revisited", Analysis 48 (1988) 122-128.

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