As regular readers will know, I tend to be a quivering Milquetoast when it comes to philosophical disputes. And most of the time I tend to expect my colleagues in the profession to behave similarly. So I was shocked, _shocked_, to see this paragraph in Gil Harman’s “review of Peacocke’s _The Realm of Reason_.”:http://www.princeton.edu/~harman/Papers/Peacocke.pdf.
bq. At another point, Peacocke says, There is no plausible truth-conditional content for the indicative conditional. with a footnote reference, See D. Lewis, Probabilities of Conditionals and Conditional Probabilities, _Philosophical Review_, 85 (1976), 297-315, and Probabilities of Conditionals and Conditional Probabilities II, _Philosophical Review_, 95 (1986), 581-9. Peacocke gives no further explanation. This completely misrepresents the content of the two papers and Lewis view about indicative conditionals.
I had mostly forgotten about this bit of the book. (And it took me a while to find it again because the index references to Lewis don’t include the relevant page. 14, if you’re wondering.) When I first saw it I didn’t make too much of it. Here’s a quick telling of the back story to say why.
What Lewis proved in those papers was that (given some more or less undeniable assumptions) there is no function _f_ from pairs of propositions to propositions such that the probability of f(p, q) always equals the probability of _q_ given _p_.
One might go on to reason the following way. If the conditional _If p then q_ has “truth-conditional” content, then the probability of that content being accurate, i.e. of the conditional being true, is the probability of _q_ given _p_. But then there would be such an _f_, since f(p, q) could just be _If p then q_. So we conclude that the conditional does not have “truth-conditional” content. (The scare/quotation quotes are because I’m not really sure what the effect of this modifier is meant to be. Are relativist contents like MacFarlane assigns to various claims, and Egan, Hawthorne and I assign to epistemic modal claims meant to be truth-conditional or not? I honestly don’t know, which makes me a little wary of _using_ this locution.)
One might argue this, and to a very rough approximation Dorothy Edgington has argued this, so it’s not like there’s no connection between Lewis’s results and the idea that conditionals don’t have “truth-conditional” content. (Edgington’s views are of course much more subtle and detailed than this, but unless I’m entirely misremembering her position, she isn’t entirely unsympathetic to a this line of argument.)
But Harman is _entirely right_ to point out that it’s not what Lewis argued. Lewis denied the premise that if the conditional _If p then q_ can be true or false, the probability of it being true is the conditional probability of _q_ given _p_. Lewis acknowledged that that position has some intuitive plausibility, but suggested that it could be explained by either Gricean or Jacksonian mechanisms. In fact Lewis thought that _If p then q_ was true just in case _p_ was false or _q_ true, so the probability of _q_ given _p_ is just a lower bound for the probability of _If p then q_ being true.
When I first started out here, I sorta meant to write a post saying that each side had some merit and some demerit. The idea was that Peacocke was wrong to not note the discrepancy between his position and the position of the papers he was using to support that position, but Harman’s comment might leave a misleading impression that there was no connection between Lewis’s results and Peacocke’s conclusion. But having actually tried to spell out the connection, that seems a little ridiculous. Harman was obviously space-constrained in a review, and couldn’t go into this level of detail. Peacocke wasn’t so constrained in a _book_, and could have easily added a few lines pointing out the differences between his position and Lewis’s, and maybe even name-checking the papers that have run the kind of argument I sketch above. (Especially since it seems rather doubtful that he thought up the whole connection on his own, given the lack of detail in the book.) So basically I’m on Harman’s side here, and I regret a little not making more of a fuss about this line when I first read it.
Maybe I should be less of a Milquetoast sometimes!
By the way, I’ve never thought much of the “extra” premise in the argument from Lewis’s formal result to the claim that conditionals don’t have truth conditions. That premise, remember, was
bq. If the conditional _If p then q_ has “truth-conditional” content, then the probability of that content being accurate, i.e. of the conditional being true, is the probability of _q_ given _p_.
I have _never_ seen an argument for this premise that strikes me as even remotely plausible. The _only_ argument that I’ve ever seen for it consists of noting that it seems like a plausible equality in a few examples noted followed by what I imagine is an inductive generalisation to the claim that it always holds. The problem with this argument is that the cases examined are rarely representative of the whole class of conditionals. In particular, they never seem to include cases where either _p_ or _q_ are conditionals. So the only generalisation that would be supported is that when _p_ and _q_ are conditional-free, the probability of _If p then q_ being true is the probability of _q_ given _p_.
Now there are many reasons for *not* generalising beyond that. First, Lewis’s results all turn on what happens with conditionals containing conditional constituents. Second, a broadly Stalnakerian semantics for indicative conditionals suggests that the probability of the conditional should be the probability of _q_ imaged on _p_. And, coincidentally enough, provided you set up the imaging properly, that equals the conditional probability of _q_ given _p_ in all cases where _p_ and _q_ are not conditionals, but not in other cases. Third, it just isn’t so clear that the intuitions are particularly strong in cases where _p_ and _q_ contain conditionals. So the generalisation to support this premise has for a long time struck me as very suspect.