LINGUIST List 5.114

Wed 02 Feb 1994

Qs: Quantifier scope

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Date: Wed, 02 Feb 94 12:25:32 SSQUANTIFIER SCOPE
From: David Gil <ELLGILDNUSVM.bitnet>

The following (longish) comments/query may be construed as
either substantive, pertaining to issues of quantifier scope
(related to the ongoing discussion of Aoun and Li's "Syntax of
Scope"), or, alternatively, sociological, concerning the ways in
which we do things in our discipline.

Consider the following sentence:

(1) Every man loves a woman

Almost all syntacticians and semanticists appear to accept the
following two claims:

Claim A: sentence (1) has two potentially available readings
(though individual speakers may vary with respect to the
degrees to which they accept either of these two readings):

Reading I: every man loves a different woman
Reading II: every man loves the same woman

Claim B: Reading I results from the subject NP "every man"
having wide scope over the direct object NP "a woman";
conversely, reading II results from the direct object NP "a
woman" having wide scope over the subject NP "every man".

Quite some time ago, I published an article ("Quantifier Scope,
Linguistic Variation and Natural Language Semantics",
Linguistics and Philosophy 5:421-472, 1982) in which I argued
explicitly against Claim B above (specifically, the second half
thereof). Briefly, the argument consisted of the following points:

Point 1:
If, instead of looking at sentences with universal and existential
quantifiers, such as (1), we turn our attention to sentences with
generalized, eg. numerical quantifiers, such as (2) below, a more
complex picture emerges:

(2) Two men love three women

Sentence (2) has the following four readings:

Reading I: two men each love three women
Reading II: three women are each loved by two men
Reading III: each of two men loves each of three women
Reading IV: two men love three women between them

Whereas readings I and II result, respectively, from the subject
and direct-object NPs having wide scope, readings III and IV (in
which there are exactly two men and exactly three women)
result from both NPs having equal scope; in particular, reading
III may be represented using the notation of branching

Point 2:
Extensive empirical evidence (presented in that article) shows
that for sentences such as (2), readings III and IV, in which both
NPs have equal scope, are much more readily available than
readings I and II, in which one of the NPs has wider scope than
the other.

Point 3:
It is a fact of logic that when generalized quantifiers are
replaced by universal and existential ones, readings in which
both NPs have equal scope become equivalent to readings in
which one of the NPs has wider scope than the other. In
particular, a quantifier prefix consisting of branching existential
and universal quantifiers is logically equivalent to a quantifier
prefix in which the existential quantifier has wide scope over the
universal quantifier. Accordingly, Reading II of sentence (1)
may be represented in either of two ways: (a) assigning the
existential quantifier wide scope over the universal quantifier,
or (b) with branching existential and universal quantifiers.

Point 4:
Given the strong preference for readings in which both NPs have
equal scope as compared to readings in which one NP has wide
scope over the other (as evidenced by sentences with
generalized quantifiers, cf. Point 2 above), Reading II of sentence
(1) should accordingly be represented not with wide scope for
the existential quantifier (as per alternative (a) Point 3), but
rather with branching universal and existential quantifiers (as
per alternative (b) Point 3) -- contrary to Claim B above.

End of argument. Now in the 12 years that have ensued since
the publication of the above argument, most or all linguists
working on quantifier scope have continued to accept Claim B
above, apparently unquestioningly. Indeed, I am not familiar
with a single discussion of quantifier scope that has
acknowledged the existence of the above argument, let alone
addressed its substance -- even to refute it. (Apologies if I have
missed anybody.)

In principle, this could be for any of the following reasons: (a)
the argument is incoherent; (b) the argument is badly worded;
(c) the argument is irrelevant; (d) nobody bothered to read it.

The main purpose of this query is to satisfy my own personal
curiosity as to which of the above 4 reasons is closer to the truth.
Reasons (a) and (b) are of course difficult for me to judge myself
-- though at least the two anonymous reviewers of "Linguistics
and Philosophy" must have thought otherwise. Reason (c)
strikes me as implausible given the elaborate theoretical edifices
that have been and are continuing to be built on the foundations
of Claims A and B. And Reason (d) is hard to believe, given that
the article appeared in such a highly respected journal. So why,
then, has the above argument against claim B gone totally
ignored for the last 12 years? Somebody enlighten me, please.

I would be extremely grateful for any comments with regard to
the above query. Perhaps if the opinions are in support of (a)
and (b) they would be more appropriately sent to me directly --
I promise to accept the most damning criticism graciously (after
all, I am sticking my neck out and asking for it). Alternatively,
substantive comments pro and contra the above argument might
be posted directly to the list -- given the ongoing discussion of
quantifier scope in the context of Aoun and Li's book. Similarly,
comments on the reading habits (or lack thereof) of our little
community might also be of some general interest.

Thanks for bearing with me,

David Gil
National University of Singapore
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