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Why Indefinites?

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Redefining Indefinites

Part of the book series: Studies in Natural Language and Linguistic Theory ((SNLT,volume 85))

Abstract

The chapter contains a brief overview of the main arguments in favor of the hypothesis that indefinite DPs are neither referential nor quantificational expressions, but rather a third type of DP. We then present the various analyses that can be found in the formal semantics literature over the past 30 years, which treat indefinite DPs as free variables, choice functions, Skolem terms or properties. We then attempt to define the main semantic properties of indefinite DPs and finally we present the interpretation problems raised by this class of DPs.

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Notes

  1. 1.

    We will not differentiate between the terms quantified and quantificational.

  2. 2.

    It is currently assumed that DPs associated with the copular verb be function as predicates. This issue will be examined in detail in Chap. 2.

  3. 3.

    sm is the weak (i.e., unaccented) form of some.

  4. 4.

    Most semantic models assume at least one additional rule, predicate modification. But it is primarily for reasons of simplicity of exposition that this choice is made, since technically, one can limit oneself to functional application (cf. Heim and Kratzer 1998: 61ff).

  5. 5.

    The domain of truth values, notated Dt, is composed of two elements, true and false, notated 1 and 0 respectively.

  6. 6.

    The formal representation of cardinals (see (8c′)) requires first-order logic with identity.

  7. 7.

    If the same sentence contains more than one quantified DP, their relative scope may vary (see Chap. 6).

  8. 8.

    This mapping may be affected by contrastive stress.

  9. 9.

    The need for such a rule is generally assumed in models of the syntax-semantics interface: see Montague’s rule of “Quantifying in” or May’s (1985) “Quantifier Raising”. However, it is not clear whether this rule obeys general constraints on syntactic movement, as claimed by May (1985). Cf. Chap. 6.

  10. 10.

    A detailed analysis of donkey sentences will be provided in Chap. 8.

  11. 11.

    In Kamp’s discourse representation structures, an indefinite DP contributes a discourse referent and a condition on that discourse referent. Although technically different, free variables and discourse referents are comparable at the stage of evaluation.

  12. 12.

    According to Reinhart, a subset of indefinite DPs does not behave like generalized quantifiers and should be represented by means of choice functions. Winter, on the other hand, maintains that all indefinites should be represented by choice functions.

  13. 13.

    In the literature, this point is known as the empty restriction problem or the Donald Duck problem.

  14. 14.

    Steedman insists that Skolem terms do not denote functions (a constant Skolem function is merely part of their representation) but are referential terms (type e) that are assigned structured representations.

  15. 15.

    According to Steedman (2006) the scope of indefinites is always assigned in situ and depends on ‘generalized Skolem term specification’, which is an “anytime” operation, in the sense that it can apply at any point in a derivation: a Skolem term is specified as a constant if the specification operation applies as soon as the DP constituent has been formed, i.e., before the DP combines with, e.g., some quantified expression; it is specified as a dependent Skolem term if the specification operation applies only after the indefinite DP combines with the main predicate and other arguments of that predicate.

  16. 16.

    An alternative solution is to say that many takes a third argument, one that corresponds to the norm. This argument must be contextually instantiated. Once the norm is determined, many becomes conservative.

  17. 17.

    Formally, a determiner Det is said to be extensional if and only if for all A, B, E and E′ such that E′  Ê  E and Det A B is true in E, then Det A B is also true in E′.

  18. 18.

    Here, we are not taking presuppositions into account.

  19. 19.

    This point is still under debate. Thus, Keenan (1996) notes that, unlike other proportional determiners, every is not necessarily defined as a relation between the cardinality of (AÇB) and the cardinality of A. Knowing the cardinality of A is not necessary to verify that Every A is B, since it is enough to check whether the set of A’s that do not verify B is empty.

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Authors and Affiliations

  1. Laboratoire de Linguistique Formelle, University of Paris 7 UMR 7110-CNRS, Paris, France

    Carmen Dobrovie-Sorin

  2. Jean Nicod Institute, UMR 8129 CNRS, ENS, EHESS, Paris, France

    Claire Beyssade

Authors
  1. Carmen Dobrovie-Sorin
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  2. Claire Beyssade
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Dobrovie-Sorin, C., Beyssade, C. (2012). Why Indefinites?. In: Redefining Indefinites. Studies in Natural Language and Linguistic Theory, vol 85. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-3002-1_1

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