Neg-Raising — 2
When discussing a problem that has proved so refractory as NR, we should first of all be systematic. One way of being systematic is to distinguish which questions are on the table. I distinguish four of them: (1) How do we identify true cases of NR? (ii) What evidence will show that NR is or is not a rule of syntax? (iii) If so, how does NR fit into a theory of syntax? (iv) What triggers NR and how do we delimit the class of possible NR predicates? In the vast literature on NR, these questions are usually not clearly distinguished, which is not good. So let’s look at them briefly one by one.
The most common criterion for the identification of NR is semantic: I don’t think he is safe is normally felt to mean the more committal ‘I have the belief that he isn’t safe’ and not the less committal ‘I do not have the belief that he is safe’. But that is not enough. How do we know, for example, that a sentence like They are not anxious to move in, when used to conceal the blunter message ‘they are anxious not to move in’, or a sentence like He is not the sort of man to pick a quarrel with, used to convey the message that he is the sort of man it is wise not to pick a quarrel with, are not cases of NR but rather of litotes or understatement? The answer is complex. To exclude a sentence S from the NR category one will have to show that S does not fit into a pattern of regularities and other phenomena that are associated with clear cases of NR. And that again requires at least an initial theory of NR.
But let’s let this question rest for the moment and pass on to question (ii). To argue that NR as we know it is a rule of syntax, we will have to appeal to “phenomena involving rule interaction, mood, complementizer type, opposite polarity tags, object case marking, sentence pronominalization, anaphoric destressing, sluicing, subject-aux inversion, queclaratives, or the syntactic reflex of De Morgan’s Law” (Horn 1989, p. 313). The best known criteria have been the occurrence of strict (i.e. same-clause) negative polarity items (NPIs) in the lower clause, as in I don’t think he was in the least interested, where the NPI in the least, which normally requires a preceding negation in the same clause for the sentence t0 be grammatical, has seen its not promoted to the higher clause. Another, perhaps stronger, criterion is derived from the theory of island constraints: not in a lower clause cannot be raised to the main clause when the former is part of an ‘island’ as this notion is known in the theory of syntax. This criterion has recently been elaborated to great effect in Chris Collins & Paul M. Postal, Classical NEG Raising: An Essay on the Syntax of Negation, Linguistic Inquiry Monographs, MIT Press, to appear May, 2014. The authors argue, for example, that a sentence like *I don’t have the expectation that they will find a living soul there is ungrammatical because the strict NPI a living soul has had its required negation moved upward across the island boundary set by the complex NP the expectation that.
In Horn (1978, 1989)—two classics that are indispensable for any proper study of NR phenomena—a large range of arguments are discussed for and against a syntactic status for NR, but Horn comes to incompatible conclusions. In his (1978, p. 216) he concludes: “… the result is that, faute de mieux, NR must be regarded as a rule in the synchronic grammar of English and other languages.” Yet in his (1989, p. 313) we read: “In the end, I see no reason to repeal my conclusion in the 1978 paper: the strongest positive arguments on behalf of a syntactic rule of NR prove to be untenable, indecisive, or dependent on additional (often tacit) assumptions which are at best theoretically and/or empirically dubious.” Not only are these two conclusions, which are based on largely the same material, mutually incompatible, there also seems to have occurred a rather crucial lapse of memory, besides a significant shift over time, away from syntax and towards pragmatics. Horn never mentions the island argument mentioned by a number of earlier authors, including myself in my 1974 paper, and elaborated by Collins & Postal in their recent monograph. Nor does he mention in his (1989) my plural-were argument, as in I don’t think either Harry or John were late (see the previous posting), still treated as a strong argument in his (1978). In any case, opinions as regards the possible grammatical status of NR have been heavily influenced, over the past forty years, by ideological parti pris: Chomskyans don’t like it because it smacks too much of Generative Semantics; pragmaticists don’t like it because their aversion to syntax increases as the syntax becomes more abstract; formal semanticists hate it because it complicates semantic compositionality. I will take it that NR is indeed a rule of syntax, even though there is no unanimity on how to integrate it into the machinery of grammar. Which brings us to question (iii), which I won’t further discuss here, other than by saying that I expect some mileage from a precyclic notion of NR in terms of Semantic Syntax. Wim Klooster wrote an article specifically addressing question (iii), ‘Negative Raising revisited’, in Germania et Alia. A Linguistic Webschrift for Hans den Besten, edited by Jan Koster & Henk van Riemsdijk, 2003, available on the internet. Rejecting the Semantic Syntax way of accounting for NR, he proposes a Minimalist account. I won’t go into the details of that, since on general grounds I can’t see how Minimalism could pass muster as a theory of grammar, and also because I don’t want to cross swords in public with a close friend of five decades’ standing. I would have needed expert help anyway for a proper understanding of the minimalist grammatical technicalities.
What I want to focus on here is question (iv): What triggers NR and how do we delimit the class of possible NR predicates? Horn devotes many pages to this question. He lists as “potential NR triggers” predicates of (1) opinion, (2) perception, (3) probability, (4) intention/volition, (5) judgment / (weak) obligation (1978, p.187; 1989, p. 323). What binds this class together is, according to him, the fact that its members occupy an intermediate position on a set of “pragmatic scales” (1989, pp. 324–5), characterized by the property that its negation “will be an intermediate value on the corresponding negative scale” (1989, p. 325). This property is based on the observation that in scalar contexts, as a general rule, the negation represents the weaker relation of contrariety, not the stronger one of contradictoriness.
Some will need need a prompt here. Two sentences are contraries when they cannot both be true but may both be false at the same time (e.g. Caesar is a man and Caesar is a dog); they are subcontraries when they cannot both be false but may both be true at the same time (e.g. John is dead and John has not been murdered); they are contradictories just in case they can neither be true nor be false at the same time (e.g. John lives in Paris and John does not live in Paris). It follows that a proposition p under contradictory not1 ENTAILS the same proposition p under contrary not2: if p and not-p can be neither true nor false together, it follows that they cannot be true together. Logicians consider not to be a guaranteed producer of the contradictory of what forms its scope. If this distinction is applied to the raised not, when taken literally (i.e. as if it had not been raised), the semantic result in common language use is the contrary not2, not the contradictory, not1.
The question is, of course, WHY. Why is not reduced to the weaker contrary not2, in NR contexts? Horn gives two answers to this question. One is (1989, p.333) that the use of the weaker contrary not2 is more guarded or polite, in that it leaves it to the listener to infer the more precise contradictory not1, and that this pragmatic politeness convention has spread to other categories, to different degrees in different languages. The other answer, given in (1978, p. 215–6) is: “The view proposed here is that NR originates as a functional device for signalling negative force as early in a negative sentence as possible.” Yet despite the many pages devoted to this topic, neither answer is shored up with precise criteria. One hardly manages to form a concise idea of what is meant and, beyond rough outlines, it remains obscure what exactly prohibits or allows NR in any given predicate. So what we are left with is a series of more or less useful and certainly intuitively appealing but informal suggestions as to what may or will be, or have been, behind the facts of NR.
I find this altogether unsatisfactory. For one thing, the scales that are invoked (1989, p. 324–5) are anything but self-evident and no empirical criteria are given for their validity. For example, what to think of a scale (ranging from weak to strong) “be legal/ethical — want/choose/intend/plan — order/demand/require” (1989, p. 325)? It seems to have been put together pour le besoin de la cause. Consequently, it remains opaque why, in particular, predicates of wanting or liking are such extremely strong Neg-Raisers in all languages, even to the point that some linguists have considered a sentence like I want not to go ungrammatical. So let me try to bring a little more light to the entire question of NR, which is both crucial to the theory of language and, apparently, extremely hard to solve.
I take as my cue the intuition expressed in Horn (1978, p. 215–6): “NR originates as a functional device for signalling negative force as early in a negative sentence as possible.” It seems to me that we may come a little closer to a solution if it is assumed that NR is the grammaticalization of a cognitive trend to give the negation operator largest scope over assertive propositions that have negative import, which is either indirect or psychologically qualified. I have no formal definition at hand for the notion of negative import, but the informal definition is that what has been said in the end amounts to an overall negative conclusion or evaluation. Perhaps the notion is to be defined in psychological or cognitive terms, but even then it would be desirable to have criteria that are a little more precise. With this proviso, I think we may tentatively proceed and accept that negative import is gradable in that it can be more or less indirect and more or less qualified. Correspondingly, we see that different languages and dialects draw the line for NR at different places in a partially ordered gradability scale, leading to cross-linguistic variation in this regard. Verbs for ‘hope’, for example, are Neg-Raisers in some languages (e.g. German, Dutch) but not in others (e.g. English). The ‘original’ function of NR would then be to alert the listener straight away that s/he should be prepared for a negative message, which might not be altogether welcome.
Let us see first what is meant by indirect negative import, the question of what is meant by psychological qualification being left hanging for the moment. Cases of indirect negative import are those where the truth of the proposition logically implies the reality of a negative fact not-f without the falsity of the proposition referring to f being expressed directly by the negation operator taking paramount scope: ‘cause [not p]’ results in the imagined fact f referred to by p not becoming a real fact; ‘necessary [not p]’ means that f cannot be a real fact; ‘and [[not p], [not q]]’ means that both p and q are false; ‘all x [not PRED(x)]’ amounts to ‘no x[PRED(x)]. I argue that placing the negation operator in highest position is psychologically functional in that it prepares the listener for the overall negative import of the utterance at hand. Lexical switch to the logical dual (from all to some, from cause to allow, from necessary to possible, etc.) is called for in such cases to avoid communicative breakdown. The point is that negative import should be signalled by the negation being at the top of the semantic tree.
A little note is called for about the notion of duality. Two operators (predicates) K and L are considered duals just in case not-K-not is equivalent with L and not-L-not is equivalent with K. Thus, all and some are duals because not-all-not is equivalent with some and vice versa. Likewise for order and (deontic) allow, and a few other predicate pairs, such as (epistemic) necessary and possible. The internal negation can swop places with the external negation, provided one dual is replaced with its opposite number.
A note also about the Square of Opposition, the classic traditional schema of predicate logic (not quite correctly attributed to Aristotle, but that is a different issue). Around 1900, the old Square was replaced with modern (Russellian) predicate logic, as it was widely believed that the old Square was logically faulty. In a number of recent and forthcoming publications I argue that this attitude is misguided in that the Square is not simply logically defective and is of great value in the study of language, more so, actually, than standard modern predicate logic. The Square is traditionally represented as a geometrical square, whose four vertices or ‘corners’ have the traditional type names A (for ‘all R is M’), I (for ‘some R is M’), E (for ‘no R is M’), and O (for ‘not all R is M’), as shown in Figure 1 (where arrows indicate entailment, the cross in the middle stands for contradiction, “C” means ‘contraries’, and “SC” means ‘subcontraries’).
It has not, or at any rate not often, been observed (a) that one may have a Square without duality, but complete with all its logical relations, and (b) that the Square without duality has a wide application outside logic in the lexicon as a whole. Square structures with one or more lexical predicates but without duality are, for example: [A: be murdered], [I: be dead], [E: be alive], [O: not be murdered]; or [A: believe(p)], [I: not disbelieve(p)], [E: disbelieve(p)], [O: not believe(p)]. Why this is both relevant and interesting I hope to show in the next post. … to be continued