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14.5: Scope ambiguities

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    138703
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    As noted in Chapter 4, when a quantifier combines with another quantifier, negation, or certain other kinds of elements, it can give rise to ambiguities of scope. For example, the sentence I did not find many valuable books allows for two readings, as shown in (31). The first reading could be paraphrased as ‘there were many valuable books which I did not find’. The second reading could be paraphrased as ‘there were not many valuable books which I found.’ The difference in the two readings depends on the scope of negation: it takes scope over the quantified NP in reading (b), but not in reading (a).

    (31) I did not find many valuable books.

    a. [many x: BOOK(x) ∧ VALUABLE(x)] ¬FIND(speaker,x)

    b. ¬[many x: BOOK(x) ∧ VALUABLE(x)] FIND(speaker,x)

    This is a real semantic ambiguity because the two readings have different truth conditions. For example, suppose that a library contains 10,000 books, of which 600 are considered valuable. One day the library catches fire. The next day the librarian goes in to search for the surviving books, and finds 300 which are considered valuable. In this context, 300 books could plausibly be described as “many”, in which case the first reading would be true while the second reading would be false.

    In Chapter 4 we noted that the proverb All that glitters is not gold actually has two possible readings. Once again the ambiguity arises from the interaction between the quantifier and clausal negation: either may occur within the scope of the other, as shown in (32). However, many English speakers are not aware of any ambiguity in this proverb. The mock syllogism in (33) has been proposed as an example of fallacious reasoning. In fact, the reasoning is sound under one possible reading of the proverb (the (a) reading), but not under the intended reading of the proverb (the (b) reading).

    (32) All that glitters is not gold.

    a. [all x: GLITTER(x)] ¬GOLD(x)

    b. ¬[all x: GLITTER(x)] GOLD(x)

    (33) All that glitters is not gold.
    This rock glitters.
    Therefore, this rock is not gold.10

    Part of the reason that speakers do not feel the proverb to be ambiguous is that only one reading is consistent with what we know about the world. However, it also seems to be the case that the (b) reading is generally preferred in sentences of this type. On the other hand, naturally occurring examples of the (a) reading can be found as well, such as those listed in (34). (In each case the context makes it clear that the intended reading gives widest scope to the quantifier; so (34c) for example is intended to mean that no person is perfect.)

    (34) a. All social features are not working.
    b. All external storage devices are not being detected as drives.
    c. Every person is not perfect.

    Example (35) illustrates how ambiguity can (and frequently does) arise from the interaction between the two quantifiers: either may occur within the scope of the other. The (a) reading says that there are many individual linguists who have read every paper by Chomsky. The (b) reading says that for any given paper by Chomsky there are many individual linguists who have read it. It would be possible for the (b) reading to be true while the (a) reading is false under the same circumstances.

    (35) Many linguists have read every paper by Chomsky.

    a. [many x: LINGUIST(x)] ([every y: PAPER(y) ∧ BY(y,c)] READ(x,y))

    b. [every y: PAPER(y) ∧ BY(y,c)] ([many x: LINGUIST(x)] READ(x,y))

    A similar example is presented in (36). The (a) reading says that every student in some contextually-determined set, e.g. all those enrolled in a certain course, knows two languages; but each student could know a different pair of languages. The (b) reading says that there is some specific pair of languages, e.g. Urdu and Swahili, which every student in the relevant set knows. (Another example of this type was mentioned in Chapter 4, ex. 28a.)

    (36) Every student knows two languages.

    a. [every x: STUDENT(x)] ([two y: LANGUAGE(y)] KNOW(x, y))

    b. [two y: LANGUAGE(y)] ([every x: STUDENT(x)] KNOW(x, y))

    Scope ambiguities can also arise when a quantifier combines with a modal auxiliary, as illustrated in (37–40). (The symbol ♢ stands for ‘possibly true’ and the symbol □ stands for ‘necessarily true’.) As we will see in Chapter 16, many modals appear to be lexically ambiguous, but that is not the source of the ambiguity in these examples. As with negation, the modal operator can either be interpreted within the scope of the quantifier (the (a) readings), or it can take scope over the quantifier (the (b) readings). Try to paraphrase the two readings for each of these sentences.

    (37) Every student might fail the course.11

    (38) ∀x[STUDENT(x) → ♢ FAIL(x)]

    (39) ♢ ∀x[STUDENT(x) → FAIL(x)]

    (40) Some sanctions must be imposed.

    (41) ∃x[SANCTION(x) ∧ □ BE-IMPOSED(x)]

    (42) □ ∃x[SANCTION(x) ∧ BE-IMPOSED(x)]

    We will mention just one more possible source of scope ambiguity, namely the interaction between a quantifier and a propositional attitude verb. Consider the example in (43):

    (43) John thinks that he has visited every state.

    a. [all x: STATE(x)] (THINK(j, VISIT(j,x)))

    b. THINK(j, [all x: STATE(x)] VISIT(j,x))

    The (a) reading could be true and the (b) reading false if John has no idea how many states there are in the United States, but for each of the 50 states, when you ask him whether he has visited that specific state, he answers “I think so.” The (b) reading could be true and the (a) reading false if John believes that there are only 48 states and knows that he has visited all of them, and he knows that he has not visited Alaska or Hawaii but doesn’t believe that they are states.

    It is possible to analyze many cases of de dicto-de re ambiguity (Chapter 12) as scope ambiguities involving propositional attitude verbs, if we treat the indefinite article as an existential quantifier. An example is presented in (44). The (a) reading says that there is some specific individual who is a cowboy, and Susan wants to marry this individual. This is the de re reading. It could be true even if Susan does not realize that her prospective husband is a cowboy. The (b) reading says that whoever Susan marries, she wants him to be a cowboy. This is the de dicto reading. It could be true even if Susan does not yet have a specific individual in mind.

    (44) Susan wants to marry a cowboy.

    a. ∃x[COWBOY(x) ∧ WANT(s, MARRY(s,x))]

    b. WANT(s, ∃x[COWBOY(x) ∧ MARRY(s,x)])

    Based on this analysis, the de re reading is often referred to as the “wide scope” reading, meaning that the existential quantifier takes scope over the propositional attitude verb. The de dicto reading is often referred to as the “narrow scope” reading, meaning that the quantifier occurs within the scope of the propositional attitude verb.12


    10 http://www.fallacyfiles.org/scopefal.html

    11 Abbott (2010: 48).

    12 Some scholars argue that de dicto-de re ambiguity cannot always be reduced to scope relations; see for example Fodor & Sag (1982).


    This page titled 14.5: Scope ambiguities is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Paul Kroeger (Language Library Press) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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