October 26, 2004

Too Too Too To Put A Finger On

In considering Achille Varzi's paper about this sentence:

(1) If Alf went to the movie then Beth went too, but only if she found a taxi cab

Brian claims that the word "too" is usually semantically inert. He points out that

When we’re doing propositional logic (7) and (8) are of the same form.

[2] If the Red Sox win the Patriots will win too.
[3] If the Red Sox win the Patriots will lose.

Varzi thinks that (1) should come out false when Alf does not go, Beth finds a cab, and Beth does go--because Beth can't go "too" if Alf doesn't go in the first place. Brian thinks this is wrong, because "too" is semantically inert, and I agree. (Though it seems to me that in that case (1) is true vacuously, and we don't need to evaluate "Beth went too.")

That seems fine, but what does "too" do?

I'm going to throw out a bunch more sentences, with judgments.

(4) If I am stupid, you are stupid too.

(5) *I may be stupid, and you are stupid too.

(6) Kerry will probably win New Jersey, and he will win New York too.

(7) ?The Steelers will lose decisively to the Patriots, or they will beat the Eagles too.

It seems that (4) can clearly be true if I am not stupid but you are--which at least casts doubt on Varzi's contention that (1) is false if Beth goes but Alf doesn't. In (5) I mean to assert unconditionally that you are stupid (contrast (4) and (1)), I don't mean to assert outright that I am stupid, and it seems that "too" is inappropriate. But in (6) I do outright assert that Kerry will win New York, and I don't assert outright that he will win New Jersey. So the theory that (5) seems to support is refuted by (6).

An interesting case is (7). If it's acceptable, I think the "too" isn't semantically inert; it means either that the Steelers lose decisively to the Patriots or they beat both the Patriots and the Eagles. I think. And I think it presupposes that, if the Steelers don't lose decisively to the Patriots, then they will beat the Patriots (well, that just follows from the reading I just gave). But I'm really not sure that it is acceptable.

That might provide a bit of support for the idea that "too" isn't semantically inert, and that what's going on in (1) and maybe in (4) is that, if the antecedent is false, the conditional is vacuously true, not that the consequent (with "too" thrown in) is true. This is all at the logic-textbook level Brian mentions; I'm not going to try anything at the level of Brian's explanation of the pragmatics of "but only if." And, I should say again that I'm not at all sure about (7), so it may provide no evidence of anything. Still, it seems like a somewhat interesting question what "too" does and when it's OK.

Posted by Matt Weiner at October 26, 2004 01:36 PM

I think (7) depends a lot on context.

(7') I think the Giants will beat the Eagles, but I'm not sure how good the Steelers are. They will lose decisively to the Patriots, or they will beat the Eagles too.

(7') is far from perfect, but I think we understand the idea - the Steelers as well as the Giants will beat the Eagles.

My gut feeling is that we interpret your (7) as elliptical, and that's because 'too' is inappropriate unless there's some antecedent it attaches to. But I'm going out on a limb a bit here - to say the least.

Posted by: Brian Weatherson at October 26, 2004 01:41 PM

Absolutely right about (7')--I meant everything to be discourse-initial. [And I think it can be made perfect; try this:

(7'') Any team that can beat the Patriots can beat the Giants. The Patriots absolutely destroyed the Giants. Either the Steelers will lose decisively to the Patriots, or they will beat the Giants too.

Well, maybe not perfect.]

I also get the feeling that "too" has to refer to something possibly suppressed that is somewhat parallel--that's why I think there's some pressure to say that (7), if it makes sense and is discourse-initial, means what I said it did. But that doesn't really explain why (5) is bad, I don't think.

Posted by: Matt Weiner at October 26, 2004 02:39 PM