Neg-Raising — 3
So what is the significance of the classic Square of Opposition in the context of NR? First, it seems significant that all NR predicates occupy the A-position in the Square (not conversely: it is not so that all predicates in A-position are Neg-Raisers). But what does it mean to say that a predicate L occupies the A-position in the Square? This way of looking at lexical predicates is not found in the literature, but it is, in fact, fairly simple and straightforward, and, I hope, enlightening. I distinguish two classes of cases. The first class does not take an embedded complement-S as an argument but takes only nominal arguments, such as hit or eat. These predicates form a Square structure when there is a different predicate entailed by, or a different predicate contrary with, them, or both. Thus, as we saw in the previous posting, since murdered entails dead, murdered is in A-position, with dead in I-position. The rest follows automatically: not dead now stands in E-position, and not-murdered in O-position. For not dead we can read alive: Square structures are valid under constancy of presupposition; given that, alive is the contradictory of dead within the universe restricted by the presupposition that the subject is animate. In this case, there are different predicates both in I-position (dead) and in E-position (alive). (Apparently, there never is a special lexicalization for the O-position; the reason for that is discussed in P.A.M. Seuren & D. Jaspers, ‘Logico-cognitive structure in the lexicon’, to appear in Language, some time in 2014). All those well-known pairs of contraries, such as good–bad, polite–impolite, hot–cold, inside–outside, etc., etc., form Square structures with the simple positive in A-position and the contrary term in E-position. Litotes forms, such as not bad, not impolite, thus occupy the I-position, as they are the contradictories of their opposite number in E-position. Perception predicates like see or hear, when they take simple nominal object arguments, are in A-position with regard to, for example, be aware of in I-position: the rest of the Square follows in virtue of the negation standing over these predicates.
The second class of A-position predicates takes a complement-S as one of its arguments. The complement-S can itself be negated, in which case we speak of the internal negation, as opposed to the external negation which stands over the main predicate. Now, to say that a complement-taking predicate L(p) (where p stands for the nonnegated embedded argument-S) occupies the A-position in the Square means that L(p) entails not-L(not-p), which will then occupy the I-position. Sometimes there is a special, mostly optional, lexicalization M(p) for not-L(not-p). When there is such an M, we say that L and M are duals. There may also be a special lexicalization for the E-position, as with say(p) in A-position and deny(p) (= say(not-p)) in E-position, which makes say(p) and deny(p) contraries.
Given the entailment from A-position to I-position—the so-called positive subaltern entailment—the rest follows again automatically, in virtue of the contradictories of both positions formed by means of a higher negation. Thus, given that L(p) stands in A-position, not-L(p) is in O-position and not-not-L(not-p), which equals L(not-p), in E-position. When there is a dual predicate M(p) standing for not-L(not-p), the E-position is filled by not-M(p), equivalent with L(not-p). When there is a contrary predicate K(p) standing in E-position, the I-position is filled by not-K(p).
Given the positive subaltern entailment from L(p) to not-L(not-p), it follows, by contraposition, that L(not-p) (the E-corner) entails not-L(p) (the O-corner). This is known as the negative subaltern entailment. The I and O corners, not-L(not-p) and not-L(p) respectively, are subcontraries, since if the former is false, its contradictory L(not-p) is true, and if the latter is false, its contradictory L(p) is true; but L(not-p) and L(p) are contraries, which means that they cannot both be true at the same time. It follows that not-L(not-p) and not-L(p) cannot be false together. They may be true together since no logical clash occurs when they are. This means that not-L(not-p) and not-L(p) are subcontraries. Voilà a Square structure (salva presuppositione), complete with all logical relations of the classic Square, but not necessarily with the Conversions.
Examples of I-predicates are nondeontic allow(p), with force(p) as its dual in A-position, or approve(p) in I-position, with disapprove(p) in E-position, disapprove(not-p) in A-position and approve(not-p) in O-position. Accept(p) is likewise an I– predicate, with accept(not-p) in O-position, not-accept(p) in E-position and not-accept(not-p) in A-position. It is a bit of a puzzle, but you will see that the pieces fit nicely together.
In some cases, again, there is a separate lexical form for some composition with the internal and/or external negation. Thus, for example, the predicate believe(not-p), in E-position, is optionally lexicalized in English as disbelieve, so that we get the Square configuration [A: believe(p)], [I: not disbelieve(p)], [E: disbelieve(p)], [O: not believe(p)]. Likewise, as has been said, for say(not-p), which optionally lexicalizes as deny(p), so that we have: [A: say(p)], [E: deny(p)], [I: not deny(p)], [O: not say(p)]. Yet, although both believe and say are A-predicates, believe is an NR predicate whereas say is not. Other A-predicates are, for example, force(p), which has allow(p) for a dual—that is, in I-position—and disallow(p) in E-position, assert(p), plan(p), hope(p), prefer(p), (with disprefer(p) as an optional lexicalization for the E-position).
It seems that all complement-taking NR predicates are A-predicates, though not vice versa. In the present context, this makes sense because an A-predicate taking scope over a negated proposition (or propositional function) has clear negative import, due to the universal character of the E-position. This negative import is indirect because, other than with the A-position, it is mediated by the internal negation over the embedded proposition p. This indirect negative import will, according to my hypothesis, have the effect observed in NR cases: the negation will tend to hop across the higher predicate and come out with highest scope. In sentences with the logical structure all-not, and-not, force-not, cause-not, and others of the same nature, this preference is easily realized, since all, and, force, and the others all have a single-item lexical dual available: some, or, allow, etc., respectively . All that has to be done to get the negation in highest position is to put it there and replace all, and and force, etc. with their respective duals. This is, presumably, why sentences with all-not, and-not, force-not, etc. are decidedly unpopular, though not altogether ungrammatical. Speakers don’t like Everybody did not leave; they prefer Nobody left. And likewise with John didn’t leave and Harry didn’t leave, and He forced me not leave, which are dispreferred in favour of Neither John nor Harry left and He didn’t allow me to leave, respectively. This seems to be the case in all languages.
But what if the predicate L over the negated p does not have a single-item lexical dual? Well, if raising not to the position over L changes the truth conditions in such a way that communicative havoc would result, there will be no NR. Thus, a sentence like I told John that it wasn’t raining does not allow for NR, since I didn’t tell John that it was raining conveys a very different message and saying the one while meaning the other will hardly make for useful communicative interaction. So the verb tell is not a Neg-Raiser, even though it is an A-predicate. In general, verbs that may serve as speech act verbs when used in the first person singular and in the present tense, such as say, tell, assert, claim, forbid, order, etc. do not allow for NR. The same for factive predicates, which presuppose the truth of the embedded clause. If the negation over the subordinate clause p is moved upward into the main clause, what is presupposed is no longer not-p but p: John realizes that not- p, with the factive predicate realize, presupposes the truth of not-p, but John doesn’t realize that p, under the default minimal negation that preserves presuppositions, presupposes the truth of p. Swopping the one for the other rather turns the entire communicative set-up upside down (and destroys any possible Square structure).
But what predicates are then left, which do allow for the negation in the lower clause to be raised to do service in construction with the main predicate? Here I fall back on the suggestion made by Horn and earlier authors to the effect that Neg-Raisers are those predicates that allow for use as a litotes or understatement, politely leaving it to the listener to infer the intended overall negative import, especially when they are in the first person and in the present tense. In this view, NR would then have its ‘origin’ in a polite, mitigating manner of speaking. The precise sense of the term origin in this context is unclear, but it is perhaps best taken to refer to a natural, preprogrammed tendency in the early formative stages of a language, such as the early Middle Ages for most Romance languages, or the immediate post-Conquest period for English. (It would be interesting to see what can be found out about NR in the early stages of Creole languages, some of which have been documented to some extent from very early on in their development, but I know of no work done in this respect.) NR would then quickly develop, in each language, into a grammaticalized construction, and it would fix on certain predicates allowing for NR but not on others, depending on ‘the will of the people’ (what I call settling in Chapter 1 of my book From Whorf to Montague, just out with OUP). Such processes are far from clear. They take place in the border area between language, cognition and society, an area that is still in need of much clarification and where things look as if they are more fluid than within the more strictly regulated boundaries of well-established language systems proper. And, of course, we would very much like to have some precise criteria for possible use as a litotes—again untrodden ground. Yet it does look as if the solution to the NR problem should be sought in this direction, hazy as most of all this still is.
It is anyway suggestive that there are sentences like I thought you would never come, that is, without NR, which are perfectly idiomatic and not interchangeable with their raised version: I didn’t think you’d ever come conveys a rather different message—an observation made by Wim Klooster many years ago. But note that the non-raised version does not have overall negative import but rather expresses the speaker’s satisfaction at the addressee’s arrival, late though it may have been, which makes the high negation as a warning sign for negative import inappropriate. Likewise for a sentence like You are not going to the supermarket, I suppose?, which, again, has no negative import but is, rather, a veiled request for a small favour, like a lift or an errand the addressee could run for the speaker. … to be continued