Abstract
Some expressions of English, like the demonstratives ‘this’ and ‘that’, are referentially promiscuous: distinct free occurrences of them in the same sentence can differ in content relative to the same context. One lesson of referentially promiscuous expressions is that basic logical properties like validity and logical truth obtain or fail to obtain only relative to a context. This approach to logic can be developed in just as rigorous a manner as David Kaplan’s classic logic of demonstratives. The result is a logic that applies to arguments in English containing multiple occurrences of referentially promiscuous expressions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
My use of ‘referential promiscuity’ differs from Arthur Sullivan’s [29, ch. 4.4]. He uses ‘referentially promiscuous’ to characterize context-sensitive expressions generally, whereas I reserve it for those expressions distinct occurrences of which can differ in content relative to the same context. See the formal definition of referential promiscuity in the next section.
I am not claiming that Frege’s puzzle or the phenomenon of cognitive significance is merely a matter of logic. The logical difference between the two uses of (6) is evidence for a difference in cognitive significance between the two uses. But to identify a logical difference between them is not to give an account of the cognitive significance of either.
There are also arguments A such that relative to some but not all contexts of use, A is intuitively invalid, but A is simply valid in Kaplan’s logic. Iacona’s example above is such an argument. But the existence of such arguments is the result of two factors: (i) failure to recognize that an expression is referentially promiscuous (a semantic issue, as I emphasized above), and (ii) the main claim in this paragraph. Thus I take the main claim in this paragraph to be the heart of the problem for Kaplan’s logic.
Stanley and Zoltan Szabó develop this view into a systematic semantic theory of quantifier domain restriction [27]. On their view, the noun phrase complement of the quantifier in a quantifier phrase is associated with a pair of variables that can either be bound by operators scoping over the quantifier phrase, or be assigned a value by a context. Strictly, however, it is occurrences of noun phrases that are associated with variables. It is thus a subtle question whether quantifier phrases count as referentially promiscuous on their view, because what appear to be distinct occurrences of the same noun phrase turn out to be occurrences of distinct noun phrase-variable pairs. Yet insofar as different contexts can assign different values to the distinct variables associated with distinct occurrences of the same noun phrase, the results will be as though the quantifier phrase in which the noun phrase occurs was referentially promiscuous.
See Yagisawa [32] for an early attempt to grapple with the referential promiscuity of quantifier phrases. Yagisawa’s negative conclusions reflect his reluctance to part with Kaplan’s logic.
The data about definite descriptions, in particular, are difficult to sort out. Jeff King, for example, though sympathetic to the view of Stanley and Szabó mentioned in footnote 6, cites an apparent failure of referential promiscuity in definite descriptions as one important semantic difference between them and complex demonstratives [15, 27, 28].
I borrow the terms orthodox and heretical from Peter Ludlow [17, 476].
I am not suggesting that Yagisawa himself would object to my claim that \(\ulcorner (2)\), therefore \((3)\urcorner \) is valid in this way. I am merely arguing that one might be inspired by this passage to object along these lines.
I thank an anonymous referee for emphasizing this kind of example.
There is a wrinkle here, in that there are two very different views of logic to be found in the literature. It may be appropriate, for some projects, to investigate some of these optional constraints. See Section 4.
A similar principle considered in Iacona [12, 195] is the following:
Any two occurrences of the same expression in an argument must be interpreted in the same way.
This principle, again, is at best an optional constraint on interpretation. The example we considered above shows that this constraint does not always apply. In the context of our example, the two occurrences of ‘that’ in (3) differ in content.
I thank Paul Hovda for the suggestion of incorporating coordination schemes into the logic of demonstratives. In addition to the obvious inspiration from Kit Fine’s work on semantic coordination [7, 8], the view is inspired by a conversation with James Higginbotham, who suggested that I incorporate his ‘common reference intention’ (defended in an unpublished manuscript, “Anaphoric reference and common reference”) into my formal theory. But it was Paul who showed me how to do it. I do not, however, mean to suggest that he agrees with either the details of the implementation or the consequences I draw from it.
The following semantics is adapted from David Braun’s work on the semantics of demonstratives, particularly his context-shifting semantics [2]. The primary difference between the semantics presented here and Braun’s is that where I treat the occurrence tracking parameter as a separate parameter, Braun incorporates it into contexts in the form of a focal demonstratum [2, 153]. The result for Braun is that the evaluation of a demonstrative induces a ‘shift’ to a new context, with a new focal demonstratum. This seems to me to introduce a philosophically loaded interpretation that the formal mechanism of an occurrence tracking parameter does not require (see Section 2.1). But the logic I present here would work equally well for Braun’s context-shifting semantics, or indeed any semantics according to which the evaluation of some expressions induces a shift in context.
Note that for simplicity I am ignoring the possibility of referentially promiscuous predicates in this rule. No account is made for any predicate to have an effect on the occurrence tracking parameter. For languages with more than one referentially promiscuous expression, we could either introduce multiple occurrence-tracking parameters, or modify the condition on c D so that its elements could include appropriate contents for other kinds of expressions.
Note that this is only half of the complete semantic characterization of ‘ =’, since we must also specify its effect on the occurrence tracking parameter.
I leave the characterization of a context showing this as an exercise for the reader.
My rejection of reflexivity is not motivated by what, in the introduction, I called an overgeneration claim. The problem is not that if reflexivity were true, some arguments that are intuitively invalid would come out valid. The problem, again, is that if reflexivity were true, some arguments whose validity varies from one context to another would be ruled valid simpliciter.
In particular, another way one might achieve similar results is by replacing coordination schemes and sequences of demonstrata with sequences of demonstrations, understood as indexical definite descriptions. See [3] and [23] for discussion of some of the semantic and epistemological issues raised by such a view.
As stated, this definition of logical truth K appears nowhere in ‘Demonstratives’, but (with the unimportant exception of the occurrence-tracking parameter) is an immediate consequence of the definitions of content in Remarks 1 and 2 on the formal system LD [13, 546–547]. In more familiar Kaplanian terms, a sentence is logically true K if and only if its content in any context (of any model) is true at the circumstances of evaluation determined by the context.
More carefully: let \(a^{\prime }\) be the context such that \(a^{\prime }_{A} = a_{A},{\kern 1pt} a^{\prime }_{T} = a_{T}, {\kern 1pt} a^{\prime }_{W} = a_{W}, {\kern 1pt} a^{\prime }_{D} = c_{D},\) and \(a^{\prime }_{S} = c_{S}\), and let \(M^{\prime }\) be the model such that \(C^{\prime } = C \cup \{a^{\prime }\}, {\kern 1pt} W^{\prime } = W, {\kern 1pt} U^{\prime }= U \cup \{x|\exists i \ x = c_{i}\}, {\kern 1pt} T^{\prime } = T\), and \(I^{\prime } = I\).
I thank an anonymous referee for discussion of this paragraph.
To fully implement this idea would require further changes to the semantics, such as relativizing the function I to contexts and occurrence-tracking parameters.
Ludlow calls this an apostate view [17, 480].
I want to thank the late James Higginbotham, Paul Hovda, Barry Schein, Scott Soames, the referees for this journal, and the audiences of the Arché Conference on Logical Consequence, the 2012 Northwest Philosophy Conference, and the 2014 Logic, Grammar and Meaning conference for comments, suggestions, and feedback that led to improvements to this paper.
References
Beall, J., & Restall, G. (2006). Logical pluralism. Oxford: Oxford University Press.
Braun, D. (1996). Demonstratives and their linguistic meanings. Noûs, 30(2), 145–173.
Caplan, B. (2003). Putting things in contexts. Philosophical Review, 112(2), 191–214.
Corazza, E., Fish, W., Gorvett, J. (2002). Who is I Philosophical Studies, 107, 1–21.
Dodd, D., & Sweeney, P. (2010). Indexicals and utterance production. Philosophical Studies, 150(3), 331–348.
Elbourne, P. (2008). Demonstratives as individual concepts. Linguistics and Philosophy, 31, 409–466.
Fine, K. (2003). The role of variables. Journal of Philosophy, 80(12), 605–631.
Fine, K. (2007). Semantic Relationism. Malden: Blackwell Publishing.
Gamut, L. (1991). Logic, Language, and Meaning. Chicago: University of Chicago Press.
Georgi, G. (2012). Reference and ambiguity in complex demonstratives In Campbell, J. K., Kabasenche, W., O’Rourke, M. (Eds.), Reference and Referring: Topics in Contemporary Philosophy, vol. 10. Cambridge: MIT Press.
Groenendijk, J., & Stokhof, M. (1991). Dynamic predicate logic. Linguistics and Philosophy, 14, 39–100.
Iacona, A. (2010). Truth preservation in any context. American Philosophical Quarterly, 47(2), 191–199.
Kaplan, D. (1989). Demonstratives In Almog, J., Perry, J., Wettstein, H. K., Kaplan, D. (Eds.), Themes from Kaplan. New York: Oxford University Press.
Kaplan, D. (1989). Afterthoughts In Almog, J., Perry, J., Wettstein, H. K., Kaplan, D. (Eds.), Themes from Kaplan. New York: Oxford University Press.
King, J.C. (2001). Complex Demonstratives: A Quantificational Account. Cambridge: MIT Press.
King, J.C., & Stanley, J. (2005). Semantics, pragmatics, and the role of semantic content In Szabó, Z. (Ed.), Semantics vs. Pragmatics. Oxford: Clarendon Press.
Ludlow, P. (1997). Review of Semantic Ambiguity and Underspecification by Kees van Deemter and Stanley Peters. Computational Linguistics, 23(3), 476–482.
Perry, J. (1977). Frege on demonstratives. Philosophical Review, 86(4), 474–497.
Predelli, S. (1998). ‘I am not here now’. Analysis, 58(2), 107–115.
Predelli, S. (2005). Contexts: Meaning, Truth, and the Use of Language. Oxford: Clarendon Press.
Reyle, U. (1996). Co-indexing labeled DRSs to represent and reason with ambiguities In van Deemter, K., & Stanley, P. (Eds.), Semantic Ambiguity and Underspecification. Stanford: CSLI.
Romdenh-Romluc, K. (2006). ‘I’. Philosophical Studies, 128, 257–283.
Salmon, N. (2002). Demonstrating and necessity. Philosophical Review, 111(4), 497–537.
Salmon, N. (2006). A theory of bondage. Philosophical Review, 115(4), 415–448.
Schubert, L.K., & Pelletier, F.J. (1989). Generically speaking, or, using discourse representation theory to interpret generics In Chierchia, G., Partee, B. H., Turner, R. (Eds.), Properties, Types, and Meaning II. Dordrecht: Kluwer Academic Publishers.
Sidelle, A. (1991). The answering machine paradox. Canadian Journal of Philosophy, 21(4), 525–539.
Stanley, J., & Szabó, Z. (2000). On quantifier domain restriction. Mind & Language, 15(2 & 3), 219–61.
Stanley, J., & Williamson, T. (1995). Quantifiers and context-dependence. Analysis, 55(4), 291–295.
Sullivan, A. (2013). Reference and Structure in the Philosophy of Language: a Defense of the Russellian Orthodoxy. New York: Routledge.
van Benthem, J. (1995). Language in Action: Categories, Lambdas, and Dynamic Logic. Cambridge: MIT Press.
van Deemter, K. (1996). Towards a logic of ambiguous expressions In van Deemter, K., & Stanley, P. (Eds.), Semantic Ambiguity and Underspecification. Stanford: CSLI.
Yagisawa, T. (1993). Logic purified. Noûs, 27(4), 470–486.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Georgi, G. Logic for Languages Containing Referentially Promiscuous Expressions. J Philos Logic 44, 429–451 (2015). https://doi.org/10.1007/s10992-014-9335-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10992-014-9335-5