It is quite commonly believed by contemporary logicians that contraposition, strengthening the antecedent and hypothetical syllogism fail for counterfactuals. In their (2008), Brogaard and Salerno argue that the putative counterexamples to these principles are actually no threat, on the grounds that they involve a certain kind of illicit contextual shift.
Here I suggest that this particular kind of contextual shift, if it is properly so called, is not generally illicit, and therefore the counterexamples cannot be blocked with the kind of blanket restriction Brogaard and Salerno appear to advocate. This sort of restriction, I suggest, ought to be made at the level of particular inference rules.
Brogaard and Salerno conduct their discussion within the framework of the standard Lewisian account of counterfactuals, which says that
a subjunctive of the form ‘if A had been the case, B would have been
the case’ is true at a world w iff B is true at all the A-worlds closest (or
most relevantly similar) to w.1
They introduce the term 'background facts', by which they mean to designate 'the respects in which A-worlds are relevantly similar to w'. Thus every counterfactual, once understood on the standard theory, is attached to a set of background facts. Now, the central claim of their article is that 'the set of contextually determined background facts must remain fixed when evaluating an argument involving subjunctives for validity'. One set of background facts per argument. Let us call this the Brogaard-Salerno Stricture. Brogaard and Salerno say that to break this stricture is to commit an illicit contextual shift, and since the putative counterexamples to contraposition etc. break the stricture, they should not be accepted.
For an argument to comply with Brogaard-Salerno Stricture, all counterfactuals occurring within it have to be alike in background facts. What I wish to point out is that this condition is plainly unsatisfied by a great many arguments, including the following:
If Mary hadn't had breakfast, she would have lunched sooner.
If John had worn black shoes, he would have worn black socks.
Therefore, if Mary hadn't had breakfast, she would have lunched sooner, and if John had worn black shoes, he would have worn black socks.
For the first premise, one of the background facts might be that Mary has a normal appetite. Another might be that she does not like to go hungry. These are plainly irrelevant to the second premise, i.e. these are plainly not background facts for the second premise. Conversely, John's sense of style has nothing to do with the first. We cannot stipulate that these premises are attached to the same set of background facts without doing obvious violence to their meaning. These two premises, if they are to be understood the way they are meant to be understood, cannot figure in the same argument without breaking the Brogaard-Salerno Stricture. But the above argument is obviously valid. Therefore the stricture is not generally appropriate. I suggest that a better course would be to restrict particular rules - starting with contraposition, strengthening the antecedent and hypothetical syllogism - in respect of background facts pertaining to counterfactual evaluation, rather than deductive argumentation in general. Other rules may be fair game too. In this connection, consider this passage:
But suppose we are wrong about this. Suppose shifting context mid-inference is no fallacy at all. Then a rather surprising consequence follows. Modus ponens - which many possible world accountants love and cherish - fails too. (2008, p. 44).
On my suggestion, the evidence for the claim of the last sentence might motivate the view that modus ponens needs to be restricted too - but still, not all deductive argumentation. Conjunction introduction, for example, is prima facie OK without such a strong restriction.
The University of Sydney
Brogaard, B. and Salerno, J. 2008. Counterfactuals and context. Analysis 68.1: 39–46.
Lewis, D. 1973. Counterfactuals. Oxford: Blackwell.
1 This is the formulation used by Brogaard and Salerno. It is adapted from Lewis (1973).