Do Counterfactuals Violate Modus Ponens?

9 08 2008

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.

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“Might”-Counterfactuals and Reversed Sobel Sequences

19 05 2008

To which extent are counterfactuals context-dependent? Lewis suggested that we can do without a systematic dependence on context by combining an invariant similarity relation with a variably strict analysis of counterfactuals. Recently, this approach has been challenged partly by drawing attention to the phenomenon of reversed Sobel sequences: sometimes it seems as if the order in which two counterfactuals are uttered makes for a difference in truth-value. Philosophers who take this phenomenon to be semantic in nature have reacted to it by allowing the similarity relation to vary from context to context (for instance, have a look at von Fintel’s semantics for counterfactuals, which you can find here). In this note, I’d like to challenge the semantic analysis of reversed Sobel sequences by arguing that it does not square well with a plausible link between “would”-counterfactuals and “might”-counterfactuals.

Here is the phenomenon. In an initial context, the counterfactual

(1) If she had been at the concert, she would have seen Mick Jagger

may be truly asserted, or so it is assumed. Subsequently, the counterfactual

(2) If she had been at the concert and got stuck behind a group of tall people, she would not have seen Mick Jagger

may be accepted, too. All this is to be expected on Lewis’s account: strengthening the antecedent is not a valid rule of inference. But now suppose that (1) and (2) are uttered in reversed order: it seems that asserting (1) after (2) is not o.k. There is something odd about saying

(3) If she had been at the concert and got stuck behind a group of tall people, she would not have seen Mick Jagger, but if she had been at the concert, she would have seen Mick Jagger.

So, can the order in which these counterfactuals are uttered affect their truth-values?

 Posted by Moritz.

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