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Descriptions as variables

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Abstract

On a popular view dating back to Russell, descriptions, both definite and indefinite alike, work syntactically and semantically like quantifiers. I have an argument against Russell's view. The argument supports a different picture: descriptions can behave syntactically and semantically like variables. This basic idea can be implemented in very different systematic analyses, but, whichever way one goes, there will be a significant departure from Russell. The claim that descriptions are variables is not new: what I offer is a new way of defending it. The argument centers on attitude reports. I argue that we should recognize a new reading of descriptions under attitude reports, which I call ‘singular opaque’. The existence of this reading cannot be explained on the traditional Russellian view, and demands a switch to the variable view. Along the way, some interesting new facts about attitude reports come to light.

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Notes

  1. I assume in the background a view on which the and a are generalized quantifiers in the style of Barwise and Cooper (1981). Hence the and a, on a par with every, some, most, many, and so on, are two-place functions taking as argument two predicates and returning a proposition. Notice that the is a controversial case: several linguists who buy into generalized quantifier theory still want to treat the as an operator which, combined with a predicate, refers to an individual, in the style of Frege (1892/1997). (For example, see the treatment of definites in Heim and Kratzer 1998.) All my main points apply to a view of this sort; I stick to a uniform quantificational treatment just for expository convenience.

  2. The idea of treating attitude verbs as modal quantifiers is due to Hintikka; see his (1962) and (1969).

  3. In line with Heim and Kratzer (1998), I’m assuming a background syntax on which quantified phrases like a stockbroker undergo movement leaving behind a trace (which I represent as ‘x’). But I take the liberty of not representing this kind of movement when it’s not important for my purposes (as in the schematic representation just below this footnote).

  4. At least, the intensional paradigm as it stands. Cresswell (1990) points out that, by supplementing a language with enough intensional operators, we obtain a system with expressive power analogous to extensional systems.

  5. For a useful summary of the problems for the intensional theory, see chapter 1 of Keshet (2008). For discussions and criticisms of the extensional framework, see also (among many) Percus (2000) and Romoli and Sudo (2009).

  6. Using variables ranging over worlds allows us to let the indefinite have narrow scope with respect to the attitude verb, and at the same time evaluate the noun stockbroker with respect to the actual world. In schematic terms, here is the logical form of (4):

    Stacey intends [to marry w 1[a stockbroker w @]]

  7. Fodor connects the two axes of variations to the two standard tests for opaque contexts, namely failure of substitutivity of coreferential terms and and failure of existential generalization. Here I want to remain neutral on this point.

  8. Here I take discourses to be just concatenations of sentences and call a discourse ‘true’ just in case all the sentences it involves are true.

  9. Heim’s discussion is focused on the following examples, which she attributes to Barbara Partee:

    1. (a)

      I dropped ten marbles and found all of them, except for one. It is probably under the sofa.

    2. (b)

      ?? I dropped ten marbles and found only nine of them. It is probably under the sofa.

  10. See, among many, Heim (1990), Neale (1990), and Elbourne (2005).

  11. In particular, D-type approaches diverge on whether the ‘picking up’ process is semantic (as in Chierchia 1992) or syntactic (as in Heim 1990; Elbourne 2005).

  12. Also, Heim (1990) notices that mention of the noun phrase earlier in the sentence is not sufficient for successful anaphora; it is necessary that the noun phrase be part of an indefinite or a definite noun phrase. This also concerns noun phrases embedded under attitude verbs; consider:

    ?? Jason believes that the husband-wife relation requires trust. As a husband, he always trusts her.

    It’s perfectly clear what is meant, yet the occurrence of her is still infelicitous.

  13. This idea was strongly pushed by Jenn Wang (in written comments) and Mark Richard (in Q&A). Many thanks to both of them.

  14. Incidentally, the rule as I stated is actually still in simplified form. We would also need more explicit provisions about how the binding works, once we move the article. (Essentially, we will need exactly the moves that Gendler Szabó 2010 makes in trying to specify the split quantifier account.) Moreover, some further provisions seem needed for the case of counterfactual attitude verbs like hope or wish, which aren’t accommodated properly by a rule of this kind.

  15. For simplicity, I ignore the part of the meaning of she that concerns gender.

  16. Notice that his won’t automatically give rise to singular truth-conditions. For Heim, definites and indefinites are bound a the discourse level by an existential quantifier, hence (at least at one level of analysis) the final truth-conditions associated to a statement involving a description will be still existential.

  17. For current purposes, just think of presuppositions as the information that is ‘backgrounded’ by an utterance, without being part of what is asserted.

  18. In short, it requires supplementing our model of shared information in communication with a set of discourse referents. Following Heim’s metaphor, you can think of discourse referents as ‘file cards’ that speakers use to track which objects are being talked about. An utterance involving a definite works as an instruction to add information to an existing card. An utterance involving an indefinite works as an instruction to open a new file card.

  19. The basic idea in this case would be that definites and indefinites are indeed quantificational, but have a silent restrictor that (a) includes a covert variable ranging over individuals and (b) restricts the domain of quantification to a singleton set. For a well-developed version of this view, see Schwarzschild (2002).

  20. See Cumming (2008), Ninan (2012), and Santorio (2012).

  21. Also, this view is incompatible with the general account in Santorio (2012), according to which attitude verbs obligatorily bind singular terms in their scope. I still find arguments for that account compelling. Hence I’m genuinely uncertain that the suggestion made in this section is on the right track, at least in the present form.

  22. Moreover, there is no easy patch. We know (via a formal result in Barwise and Cooper 1981) that there is no way to define the meaning of a quantificational phrase like More than half of the Fs in terms of More than half of the things, plus first-order logic resources. So the comparative understanding of proportional determiners is necessary to capture the meaning of most, more than half, and the like; moreover, there is no way to recover it starting from the non-comparative one.

  23. Examples of this sort have been discussed in the debate on indefinites and scope islands: see in particular Reinhart (1997), and Schwarz (2011) for an overview of this debate. The basic observations about the problems one get when widescoping existential operators out of antecedents of conditionals goes back to Heim (1982).

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Acknowledgments

For lively discussions and feedback thanks to Raul Saucedo, Jenn Wang, and audiences at the 2012 AAP conference in Wollongong and the 2012 BSPC. Thanks also to Paul Elbourne for a brief but useful email correspondence on D-type theories. Finally, special thanks to Zoltan Gendler Szabó for extended email exchanges on descriptions and the fourth reading.

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  1. University of Leeds, Leeds, UK

    Paolo Santorio

  2. Australian National University, Canberra, Australia

    Paolo Santorio

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Santorio, P. Descriptions as variables. Philos Stud 164, 41–59 (2013). https://doi.org/10.1007/s11098-013-0095-9

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