(*) If Alf went to the movie then Beth went too, but only if she found a taxi cab.
He runs through six possible options for it. I’m inclined to think that by the logic textbook standards he’s using, the fourth is clearly correct, and I don’t really follow the objections to it, but I think it’s an interesting sentence. But it’s probably best to start with easier sentences, things like the consequent of (*). If you Google for but only if you get a lot of hits. (The link is to Google News to try and reduce somewhat the size of the target pool.) Here’s one typical example.
(G) American Express will try to help airline avoid bankruptcy, but only if deal with pilots is reached. (Atlanta Journal-Constitution)
I think that by Varzi’s standards, i.e. the standards at play in undergraduate logic textbooks, this is to be interpreted as
(G*) American Express will try to help airline avoid bankruptcy if and only if deal with pilots is reached.
I wouldn’t set this as a question, but if I was somehow grading it, that’s the answer I’d expect. And I’d grade the same way if this was a consequent not a full sentence. But logic courses are odd – what’s really being done with the sentence? I’m inclined to use a bit of cheap (and distorted) DRT to handle this.
The important point to note about (G) is the long pause between ‘bankruptcy’ and ‘but’. I think that’s a sign that two different things are being done with the sentence. The first is asserting (relative to the context in play) that American Express will try to help [the] airline avoid bankruptcy. Then the context is expanded (perhaps degeneratively, i.e. improperly, expanded) so that it’s an open question whether a deal with pilots will be reached. And relative to that wider context it’s asserted that American Express will try to help [the] airline avoid bankruptcy only if [a] deal with pilots is reached. From the truth of these two assertions (relative to their contexts) and the hypothesis that we really had to expand the context to include worlds where a deal where the pilots wasn’t reached, it follows that it’s true (in the original context) that if a deal is reached, American Express will try to help.
That’s my hypothesis about the pragmatic effects of the sentence, and it’s already a mouthful. As to the semantic content of the sentence, I’m completely at sea. (I hear a voice in my head telling me that “American Express will try to help airline avoid bankruptcy, but only if deal with pilots is reached” is true iff American Express will try to help airline avoid bankruptcy, but only if deal with pilots is reached, and that’s its semantic content, but that doesn’t seem helpful.)
One complication in Varzi’s original sentence is ‘too’. He suggests in places that this should affect the breakdown into logical form. I think this is wrong. When we’re doing propositional logic (7) and (8) are of the same form.
(7) If the Red Sox win the Patriots will win too.
(8) If the Red Sox win the Patriots will lose.
Once we notice that ‘too’ is usually semantically inert, it becomes a lot easier (though still not easy!) to interpret Varzi’s (*).
By the way, does anyone else find the crown icon in the address bar on Columbia sites kinda strange? I thought that when I arrived in America I left royalism behind. Heaven forbid that I be sounding like a Republican a week before an election, but still crowns seem kinda creepy.