February 02, 2004

If, then, and

[Note: Due to blogging with half my mind while doing other things at the same time, my original post on this topic contained an elementary logical error. I hope I've now fixed it -- the conclusions and examples haven't changed, just a piece of the discussion. I've also added another post with some pointers to background information that may make the discussion more accessible to outsiders. As usual, we stand behind our our offer to refund your subscription fees in full in case of less than full satisfaction.]

Allan Hazlett has further thoughts about odd ifs, following up on my post here. The money quote from Hazlett: "If we can say the same thing with a conjunction of the two clauses, it's not a conditional, but a masked conjunction ..." He's talking about examples like

(1) If you're a good citizen, then I'm Donald Duck.
(2) You're a good citizen? And I'm Donald Duck.
(3) Yeah, you're a good citizen. And I'm Donald Duck.

I don't think that this is right. For one thing, the argument runs at least as well in the other direction. The interpretation of and in (2)-(3) requires some extra pragmatic work, while the interpretation of if in (1) is rather closer to its putative logical meaning. So we might with at least equal justice say "if we can say the same thing with a conditional expression, then it's not a conjunction, it's a masked conditional..." We really have to look at what and how the particular uses of if and and (and then) mean. My own (provisional) opinion is that each of these examples is itself, not a masked version of one of the others, even if the interpretations sometimes overlap in meaning.

Another problem is that the if in (1) is probably not the same case as the if in the original NYT quote, which (edited for brevity and clarity) was a sentence like

(4) But if this dramatic move was necessary, it was (nevertheless) risky.

Both (1) and (4) are certainly non-vanilla-flavored uses of if, but the extra flavor seems to be different in the two cases. We can make a Gricean argument for the extra flavor being concocted on the spot out of thin pragmatic air, so to speak, but the recipes must at least be different.

(4) is an example of the OED's sense 4.a. for if, glossed "Even if, even though; though; granted that". We can render (4) as "but even though this was necessary, it was nevertheless risky", with roughly the same meaning as the original. (In my earlier post, I sketched a neo-Gricean story about how this might develop). But we can't render (the intended sense of) (1) as "even though you're a good citizen, I'm nevertheless Donald Duck." And turning it around, we (or at least I) can't use then in (4), in the original NYT example, or in the OED's examples for sense 4.a., such as

If Mozart was a life-long admirer of J. C. Bach, (*then) his views on Clementi were disparaging, to put it mildly.

Nor does and have the same force as the "concessive" or "excessive" uses of if:

 If Mozart was a life-long admirer of J.C. Bach, his views on Clementi were disparaging, to put it mildly.
≠Mozart was a life-long admirer of J.C. Bach, and his views on Clementi were disparaging, to put it mildly.

 Virtual colon dissection is promising, if flawed.
≠Virtual colon dissection is promising, and flawed.

 Dr. Lee's behavior was curious, if not criminal.
≠Dr. Lee's behavior was curious, and not criminal.

Hazlett's (2)-(3) are examples of the rhetorical device most famously illustrated by Dorothy Parker's little verse

Oh, life is a glorious cycle of song,
A medley of extemporanea;
And love is a thing that can never go wrong;
And I am Marie of Roumania.

Such examples seem to be ordinary coordinations, interpreted with respect to a Gricean version of the (logically fallacious) pragmatic maxim falsum in uno, falsum in omnibus ("(if) false in one thing, (then) false in all things". That is, the speaker asserts "A and B", but B is obviously false, so the speaker must mean to cast doubt on A as well.

What about Hazlett's case (1)? The speaker says "if A (then) B". B is obviously false. The truth table for the (standard, "material implication" logical version of) "if A then B" is


so if the whole sentence is true and B is false, then A must also be false. As usual, there is more to be said about what the speaker communicates by choosing this (roundabout) form of expression over other simpler and more direct ones, and also about what rhetorical niches it's adapted to. For example, intuition suggests that one common context is for K to assert "A", and L to respond with "if A then (nonsensical) B", implying that K has not thought enough about the elementary implications of A. (Alas, there is no easy way to query internet search engines for rhetorical patterns).

A more general comment... Similar flavored interpretations of if and and were the occasion of Grice's original work on how speaker's meanings can be created out of sentence meanings. This work has been deservedly influential, and among all its intellectual progeny there may well be a whole body of writings on the cases we've been discussing. As a simple phonetician, I don't keep up with such things very systematically. But it seems to me that it might be worthwhile to revisit the original problem of explaining the diverse uses of if and and and or.

Among the things I (somewhat naively) wonder about: To what extent is relevance logic relevant? Are these uses always just the same in different languages, as one would expect on the Gricean account? Do common cases become conventionalized as new senses for the words involved? If so, do these senses then gather additional (non-Gricean) moss? Are such cases subject to priming effects, either in terms of speed of interpretation or in terms of frequency of use? Does conventionalization make a difference in this respect?

And what about then, anyhow?

I look forward to learning about this from various friends and colleagues who actually know something about it.

Posted by Mark Liberman at February 2, 2004 12:33 PM