564 Lecture 10 Sept. 23, 1999

Last time, we saw that one approach to capturing the semantic ambiguity of scopes for quantifiers in English was to create two optional representations for a sentence, by assuming that quantified phrases can move like wh-phrases. Each representation is unambiguous, corresponding to a particular translation into the predicate logic, and the optionality arises because the two quantified expressions can move in either order, creating the two different scopes.

The key element of this approach is that a certain structural representation is mapped to a particular semantic representation, and any single structural representation will have only one interpretation.

Let's contrast that with a "quantifying-in" approach, where any given argument position of a verb can be filled with an unbound variable (represented in the derivation tree as a pronoun) and bound later by indicating a coindexing between the variable and some quantified or referential NP. In this type of approach, rather than interpreting the final representation, one interprets as one goes, constructing the semantic representation and the syntactic representation in parallel. In many respects the two approaches are equivalent.

If the predicate denoting "love" is Love(x,y), then we can represent the property of being a person that Harold loves as membership in the set {y | Love(h,y)}. Similarly we can represent the property of being a person who loves Maude as membership in the set {x | Love(x, m)}.

1. Predicate logic allows more natural units than the syntax of natural language

(a) {y | Love(h,y)} = the property of being a person that Harold loves

(b) {x | Love(x, m)}= the property of being a person who loves Maude

2. Constituency tests, e.g., treat the VP as a unit but not S+V:

(a) Harold loves Maude, and Bill does, too.

(b) *Harold loves Maude, and does Mary, too

3. Harold loves Maude and hates it. [it anaphoric on loving Maude]

In the syntactic tree for "Harold loves Maude", there's no node that corresponds to the set of things that Harold loves, while there is such a node for the set of things that love Maude (the VP).

However, if you allow NPs to be represented in your syntactic tree by free variables (pronouns, or equivalently, traces), and make the final syntactic operation the binding of those variables, you can create the same effect, creating the open proposition Love(h,y) at some stage of the derivation.

4. Quantifying-in

Now, note: in some sense, this would be equivalent to allowing general "NP-raising" in GB syntax. However, the representation at the end is not structurally different from a representation which is derived via simple insertion of Mary at the object position (see the bracketed structure created by the final operation of binding at the top node); the difference is in how you got to the representation. Now here, allowing variable insertion and binding doesn't make any interpretive difference, because binding a variable by a constant is equivalent to just inserting the constant in the first place (it's a spurious derivational ambiguity, in de Swart's terms).

However, if you allow this process of variable insertion and binding, you have the mechanism you need to give two different translations to a sentence with two quantifiers in it, by building the sentence in two different ways.

First, you could just insert the quantifiers as you come to them, just like inserting the constants as you come to them. This will produce the scope relation which is reflected by the linear order of the quantifiers in the sentence:

5.

On the other hand, you could choose to put a variable in object position, and bind it with the universal quantifier as the last operation of the derivation:

6. Quantifying-in resulting in scope difference

This will give you the reverse scope. The derivation constructs the same representation, but the way in which it constructs it differs, and because different rules apply in constructing 6 than in constructing 5, a different interpretation is produced.

Questions (which we saw last time involve movement on a GB-like theory) also behave as if they bear scope, and exhibit scope interactions with quantifiers. Consider 7:

7. Which woman does every man love?

a. reading 1: Which woman is such that all men love her?

Clearly, treating questions as a type of quantification can capture this type of fact very well, and since question words appear in a position displaced from the position in which they're interpreted, the fact that they take scope like quantifiers is (simple-minded) support for the position that quantifiers and questions should receive a unified treatment (i.e that Quantifier Raising exists). These scope differences can be treated in a quantifying-in framework, easily, as deSwart shows (although on a quantifying-in approach it's not clear why the wh-words appear in a different place in the sentence than quantified words – of course, this is not so clear on the QR approach either, but at least the different surface structures are merely a difference in timing, not a difference in kind, which they have to be on the quantifying-in approach).

Caveat: To be perfectly honest, I'm not really qualified to comment on the two methods of treating quantification. I was trained in a QR (Quantifier Raising) framework, and I've seen the work QR can do, and the desirable linguistic generalizations that can result in a QR framework, while I've not read very much at all in frameworks that quantify-in, e.g. categorial grammar (which admits the constituent [Harold loves] as a reasonable possibility -- but on its plus side, the relationship between the semantics and the syntax of structures is extremely transparent), or HPSG (Head-Driven Phrase Structure Grammar). So I can see what is beautiful and good about QR, but I know there are many beautiful and good things about quantifying-in that I know nothing about (some of which may be the same as the QR things!)

But from the sketchy understanding I have of quantifying-in, here's some prima facie objections I have. (I can guarantee that smarter people than I have treated these generalizations in quantifying-in frameworks successfully, so it's not necessary to take these objections too seriously.)

9. If any NP may be replaced by a free variable and later bound, perhaps the close relationship between quantifiers and wh-words that is captured by the QR analysis is not captured as well by the theory. For example, both wh-words and quantifiers exhibit "Weak crossover":

9. "Weak crossover"

(a) Whoi does Bill think ti loves hisi mother?

(b) *?Whoi does Bill think hisi mother loves ti ?

(c) Bill thinks every boyi loves hisi mother.

(d) *?Bill thinks hisi mother loves every boyi.

Under the QR theory, the bound variable reading for the pronoun is unavailable because the pronoun intervenes between the wh-word or quantifier and its trace, creating a Relativized Minimality effect. Crucially, the same principle can predict the ungrammaticality in both cases. In the derivational theory, this type of interpretation difficulty would have to be captured by some other type of constraint, because, for instance, there's a derivation available for (d) in which the quantifier introduces its bound variable right away (as we saw in 5 above) and no later binding is necessary. If it's the "wide scope" of the quantifier over the pronoun that creates the weak crossover effect in (d), then (d) should only have a derivation where a variable is introduced and then later bound.

10. Cross-linguistically, there are languages where quantifier scope is disambiguated at surface structure (what Simin called scrambling languages).

10. (Get Larson and Segal Hungarian example)

That is, two different readings are assigned two different surface representations, with the quantifiers in the order in which they take scope – representations that clearly reflect structural differences. In a theory where a single representation may be derived in two different ways, providing two different readings, the parameterization that creates a scrambling language must have something to do with the syntactic derivations allowed in those languages. For instance, if we assert that scrambling languages do not allow derivational ambiguities created by free variable-insertion and binding, then we will force the different scope interpretations to have different syntactic structures (for there will be no other way to represent the different scopes and remain compositional). This seems problematic on a number of levels. First, wh-expressions will still need to be treated with quantifying-in, so the derivation required by quantifying-in will be available for some parts of the language and not for others. Second, any account of weak crossover that depended on the wide-scope interpretation of a quantifier will disappear, so if such languages exhibit weak crossover with quantified expressions, it will have to be treated in some other fashion (which it might anyway, see 9). Third, in comparing the two theories, the QR-type theory allows a much easier way to parameterize: scrambling languages merely pronounce their sentences after QR has applied, but are otherwise interpretively and structurally identical to non-scrambling languages at LF. The parallells between wh-containing and quantified structures are still predicted to exist (and, luckily, seem to).

11. No weak crossover in non-quantified expressions:

a) Hisi mother loves Haroldi

Quantifying-in, as presented, can apply to any NP (creating a spurious derivation when the NP is a proper name). This might, perhaps, predict that weak-crossover effects should exist in a sentence like "Hisi mother loves Haroldi". They don't, and of course this is consistent with a derivation where Harold is interpreted immediately, and quantifying-in doesn't take place – but perhaps it's inconsistent with the equally available derivation where quantifying-in did take place?

12. It seems to me that the sentence "Harold loves Maude" is a statement about a property that Harold has, not a statement about a property that Maude has. If we wished to discuss the property that Maude has in the situation described, we'd say "Maude is loved by Harold". Yet, the derivation illustrated in 4 has a sub-interpretation in which we are talking about a property of Maude's, and "Harold loves Maude" should be appropriate for talking about either a property of Harold's or a property of Maude's, depending on the context.

12. Can a transitive clause describe a property of either the subj. or the object?

a) Describing Harold, with neutral intonation:

"Harold is eighteen. He is unemployed. He drives a hearse. Harold loves Maude."

b) Describing Maude, with neutral intonation:

"Maude is seventy-nine. She likes to dance. She steals cars. Harold loves Maude."

(Perhaps it is: Describing Harold, with neutral intonation: "Harold is eighteen. He is unemployed. He drives a hearse. Harold loves Maude." Compare to, describing Maude, with neutral intonation: "Maude is seventy-nine. She likes to dance. She steals cars. Harold loves Maude." – it could be that the derivation difference is signalled by the intonational contour necessary in the second example.)

13. And, finally, a prima facie problem for QR: in a sentence like "Which woman does every man love?" QR seems to be counter-cyclic on the reading where the wh-word takes wide scope. If Wh-movement adjoins to S, and QR adjoins to S, but Wh-movement happens before the sentence is pronounced and QR happens after, then in order to get the wide-scope wh interpretation, the quantifier will have to adjoin inside the wh-word.

13. (a) [CP Every mani [CP Which womanj [C' does [IP ti [VP love tj ]]]]]

(b) [CP Which womanj [CP Every mani [C' does [IP ti [VP love tj ]]]]]

This is not a problem if it doesn't matter whether LF is cyclic or not (the same problem obtains in a slightly less visible form with respect to the crossing vs. nested paths of the quantifier movement in the two-quantifier sentences), but since cyclicity is the more natural theoretical stance, QR could be problematic.

I'll just discuss these briefly because deSwart does; they're interesting but they'll be more interesting when we have the tools to really go to town on them.

Two different ways of asking "how many books have you read?" in French:

14. a) [Combien de livres]i as-tu lus ti ?

Howmany of books have-you read?

b) Combieni as-tu lu [ ti de livres] ?

Howmany have-you read of books?

Two ways of asking "how many books have they all read?" in French

15. a) [Combien de livres]i ont-ils tous lus ti ?

Howmany of books have-they all read?

b) Combieni ont-ils tous lu [ ti de livres]?

Howmany have-they all read of books?

Now, interestingly, when you leave the NP in place, moving only the wh-word and not taking (pied-piping) all the NP material along with it, you wind up with a question in which the question word has to take narrow scope with respect to the quantifier in the subject position. So, 15a) has got two interpretations, one where it's asking for a pair-list and one where it's asking for a simple number, while 15b has only got the pair-list interpretation:

16. a) Cleopatra read 5, Sue read 3, Felicity read 8, etc.

Five.

b) Cleopatra read 5, Sue read 3, Felicity read 8, etc.

*Five.

Our structure-to-meaning mapping will explain the difference between the readings available for 15a and 15b in terms of a particular derivation for each. 15a will have a derivation like the corresponding English sentence, while 15b will only allow the derivation where the question-word has narrow scope (presumably because the restriction ("of books") on the variable it binds remains in object position).

If this is the effect of the split construction, then we can construct a purely semantic explanation for why 17b, below, is ill-formed:

17. a) [Combien de livres] est-ce qu'aucun étudiant n'a lus?

How many books (has) no student read?

b) *Combien est-ce qu'aucun étudiant n'a lu de livres?

How many (has) no student read of books?

Consider the interpretation of the question in 18:

18. Which woman does noone love?

a. Mary (Question word has wide scope)

b. #John doesn't love Mary, Cleopatra doesn't love Antigone, ...

(b) is not an appropriate answer to 18. There doesn't seem to be any obvious structural reason why (b) should not be available; we've treated "no one" as a quantifier+negation so there ought to be a wide-scope reading for that quantified expression, giving a question to which there should be a pair-list answer. However, consider what the paraphrase of the wide-scope quantifier expression would mean: "For no person x, which woman does x love?" which basically amounts to asking nothing. Language (according to Grice) is a cooperatively used, functional tool, so 18b is an ill-formed interpretation just because we couldn't find out anything or accomplish anything by intending it.

For the same reason, then 17b will be ill formed, or rather uninterpretable or unfelicitous, because the use of the split construction forces exactly the wide-scope quantifier interpretation for aucun étudiants, and that's exactly the interpretation which is ill-formed for Gricean-type reasons.