Scope — 2

by pieterseuren

Sentence (6a), at the end of the previous posting [For two years the sheriff jailed Robin Hood], strikes one as a bit comical, as it evokes an imgage of the sheriff putting Robin Hood in and out of jail repeatedly for two years. This oddness is of a pragmatic nature, as it is due to prevailing circumstances in life as we live it. It disappears when we change the lexical items, as in (7a) (McCawley discussed these examples in his 1971 paper “Prelexical Syntax”, republished in his book Grammar and Meaning, Taishukan Publishing Cy, Tokyo, 1974, pp. 348-9):

(7)       a.       For two months Harry lent me his bike. (unambiguous)

—       b.       Harry lent me his bike for two months. (ambiguous)

It is perfectly normal to lend someone one’s bike, say, every Tuesday and to do so for two months, as expressed in (8a):

(8)       a.      For two months Harry lent me his bike every Tuesday. (unamb.)

—       b.       Every Tuesday Harry lent me his bike for two months. (absurd)

Remarkably, if every Tuesday is preposed, as in (8b), eyebrows are raised, since a period of two months is far longer than one week, so how can Harry allow me every Tuesday  to use his bike for two months?! (8b) can only be saved by giving a sentence-final intonation to lent me his bike and starting a new sentence intonation at for two months. In writing, such an intonational break is best indicated by a comma or perhaps an m-dash.

Scope phenomena as illustrated here give rise to at least two questions: (a) how do we represent the different scope relations, and (b) how do we account for the fact that some scope readings are legitimate for some surface structures and others are not.

As regards the first question, I know of no better way of representing scope relations than in terms of hierarchical tree structures or, equivalently, bracketing structures as used in logic, preferably with labelled brackets. (The bracketing in logic is never labelled, but we have learned from linguistics that bracket labelling—that is, node labelling—is a useful additional device.) In linguistics, McCawley was the one who drew attention to the formal identity of these two methods of representation and subsequently proposed that meaning representations (I speak of semantic analyses or SAs) are best cast in the terms of a language closely akin to that of modern predicate logic. This proposal has gained universal acceptance in all varieties of formal linguistics. (In formal semantics it didn’t have to be accepted, as FSx is itself directly derived from modern predicate logic.) The general format of logical structures would then be that of operators functioning as (abstract) predicates taking a sentential (propositional) term as their scope, as shown in Figure 1.

When he wrote on prelexical syntax, McCawley did not know yet of generalized quantifiers, but it has meanwhile become clear that quantifiers are best treated as higher-order binary predicates, that is, as predicates over pairs of sets: the universal quantifier expresses an inclusion relation and the existential quantifier expresses a relation of nonnull intersection of two sets. The sentence Not all flags are green is then semantically analysed as ‘it is not the case that the set of green things includes the set of flags’ and represented as the tree structure in Figure 1a (ignoring tense and other nonessential elements). And the sentence All boys admire some footballer(s) is analysed as ‘the set of those who admire some footballer(s) includes the set of boys’, or more explicitly ‘the set of x such that there is a nonnull intersection between the set of footballers and the set of those admired by x includes the set of boys’. The corresponding tree structure is given in Figure 1b. (The label “NP/S” stands for constituents that have the syntactic form of an S-node but the semantic status of an NP-argument standing for a set of objects. Thus, the propositional function NP/S[flag,x] has the semantic status of an NP standing for ‘the set of flags’ but the structure of an S as it consists of a predicate and an NP-argument.)

blog15b-fig1

It will be clear that the (dominant reading of) the sentence Some footballers are admired by all boys requires an SA where all and some have swapped scope compared with Figure 1b. (Try drawing the corrsponding SA tree structure: it’s a useful exercise.)

Of course, the above is only a rough outline and quite a few questions are still to be answered, but the overall idea will be clear. That being so, the question arises of how to represent the scope relations in the pragmatically normal reading of (6b) of the previous post [The sheriff jailed Robin Hood for two years] or in (7b) above in the reading in which Harry gave me a permission valid for two months to use his bike. On the face of it, there is only one scope-bearing operator in these sentences: for two years in (6b) and for two months in (7b). For the corresponding (a)-sentences there is no problem, as the operator has highest scope over the rest of the sentence. But how do we render the meaning of the (b)-sentences that is not shared with the corresponding (a)-sentences in such a way that the scope difference is expressed in the systematic terms of scope-bearing operators? For this we need at least two operators in each sentence. So, where is the other one? This difficult question will force us to tread on ground that has so far remained largely unexplored.

An obvious way to detect a second scope-bearing operator in the sentences in question is by breaking up the predicates jail and lend into component parts. Jail would then be analysed into ‘cause to be in jail’ and lend into ‘allow to use’, as proposed in McCawley’s theory of prelexical syntax. Let us provisionally pursue this line of thought for a moment, leaving open the possibility that there are alternative ways of accounting for the relevant facts. The theory doesn’t say that jail is semantically equivalent with ‘cause to be in jail’ or lend with ‘allow to use’. All it says is that the lexical verb jail entails ‘cause to be in jail’, but not vice versa, and analogously for the lexical verb lend and ‘allow to use’. Let us, for the moment, assume that these analytical paraphrases make up what we may call the core meaning of these predicates. Once a semantico-syntactic complex has been unified into a single lexical predicate, that predicate is likely to assume further semantic refinements. A clear example is the English verb fell, which is historically the causative of fall (‘cause to fall’, with Germanic causative umlaut on the vowel), but which is now typically restricted to the felling of trees and exists along with other specialized verbs whose meaning can be described as implying ‘cause to fall’, such as trip, push over, knock over, etc. (which does not mean that these verbs should also be considered to have ‘cause to fall’ as their core meaning).

In the same way, jail and lend, being lexical predicates, may be seen as having additional idiosyncratic semantic elements associated with the items themselves and not expressed in their core meanings. Thus, jail implies that the referent of the subject term has the power or authority to cause the object referent to be in jail and that it is through this power or authority that the jailing takes place. And lend implies additionally that the lender is the owner or possessor of the object lent, not, say, the guardian, even though a guardian may well allow one to use some object in his custody. Clearly, such distinctions and conditions will have to be elaborated in a general theory of the lexicon, a general lexicology. But if such a theory could be developed, it would provide the structural space for a second operator and thus for a scope swap. This is shown in Figure 2, where the meaning that is common to (6a) and (6b) is represented in Figure 2a, and the meaning that is unique to (6b) is represented as Figure 2b. And analogously, of course, for (7a) and (7b), where lend would be broken up into ‘allow to use’. In Figure 2, the two scope-bearing operators of (6a,b) are for two years and cause. For (7a,b), the two operators are for two months and allow.

blog15b-fig2

The theory of prelexical syntax clearly makes some sense, but it also poses serious difficulties, as is to be expected from a radically new theory that opens new and promising horizons. The proper answer to this is, of course, not an immediate cold dismissal on grounds of trivializing arguments (which is what happened to it in the early 1970s), but an open-minded, positive reception and a serious willingness to look into its potential for the science of language. In any case, one of the positive consequences of this theory is that the nonlogical, merely lexical verbs cause and allow can now be taken to be scope-bearing operators ‘inside’ causative verbs such as jail or lend. Which in turn may provide an opening to our original problem of how to define the notion of scope, as we may envisage the possibility of saying that, in general, the complement of a complement-taking predicate is its scope—a highly significant generalization that would bring logic and language a great deal closer to each other. So let us defer the question of prelexical syntax for the moment and focus again on the question of scope in general, seeing if we can uphold the generalization that all scope-bearing operators are abstract predicates—that is, predicates at SA-level—with their own predicate-argument structure.

I have shown above that at least the quantifiers are naturally treated as predicates. This move will now have to be extended not only to the operators of propositional logic (not, and, or, if) but also to those prepositions that can occur in high peripheral position, such as for indicating temporal extension, or because of, or during, or after, etc., and then also to subordinating conjunctions like because, unless, although, while, etc. In general, it pays to consider all lexical items with semantic content to be predicates in SA-structures, as proposed in my Semantic Syntax of 1996 The lexicon of a language L will then define for each semantic predicate what its surface category will be: verb, noun, adjective, preposition, affix, etc. and the grammar of L will then deal with each such item according to the procedures fixed for verbs, nouns, adjectives, prepositions, affixes, etc. This is how what is a predicate of causation at SA-level may turn up in surface structure as, say, a causative affix of the kind found in a large number of languages.

Some linguists have expressed bewilderment at this approach, but that seems to me to be due merely to their lack of imagination. There is nothing wild or exotic about it. On the contrary, it constitutes a significant generalization over logico-semantic structures and throws an explanatory light on the fact that, for example, negation is an auxiliary verb in Finnish, that what are prepositions in European languages are verbs in Korean, and other such unexpected grammatical category shifts in various languages. (It will also help to maintain the generalization that it is semantic predicates that induce presuppositions, given that because, although, while and quite a few other subordinating conjunctions induce a factive presupposition.) … to be continued

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