Abstract
In the past decade various linguists and philosophers (e.g. Pagin, Pelletier, Recanati, Westerståhl, Lasersohn) have proposed a weakening of the standard interpretation of compositionality for propositional content. Their move is motivated by the desire to accommodate radical forms of context sensitivity within a systematic account of natural languages. In this paper I argue against weakening compositionality in the way proposed by them. I argue that weak compositionality fails to provide some of the expected benefits of compositionality. First, weak compositionality fails to provide systematic meaning-rules which can handle forms of context-sensitivity that are not amenable to explanation in terms of a fixed and limited set of contextual parameters. Secondly, I argue that weak-compositionality fails to play any role in explaining speakers’ ability to calculate the semantic values of complex expressions. I conclude that weak compositionality is not a viable alternative to standard interpretations of compositionality, and that it doesn’t offer an acceptable way to accommodate radical forms of context-sensitivity within a systematic account of natural languages. Given the central role that weak-compositionality plays in recent approaches to natural language (e.g. in truth-conditional pragmatics) this also casts doubt on the viability of these projects.
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Notes
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See Kaplan (1989, 507) where both varieties are given informally. For their formal rendering see Pagin and Westerståhl (2010, 259–260), Dever (2006, 634), Szabó (2010, 258–260). Given that linguistic meaning is a property of expressions themselves, linguistic meaning will be assigned directly to expressions, and given that propositional content is a property of expressions at contexts, content will be assigned to expression-context pairs. Furthermore, since linguistic meaning is a function from contexts to propositional content, and propositional content is a function from circumstances to extensions, a semantics I* which assigns linguistic meaning directly to expressions is the curryied version of a semantics I which assigns propositional content to expression-context pairs. That is, for any expression e and any context C, I(e,C) = I*(e)(C).
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Strong compositionality is a proper generalization of weak compositionality, which, in its turn, is a proper generalization of linguistic meaning compositionality. For proofs see Westerståhl (2012). For an alternative proof and a further discussion of how weak and strong compositionality for content interact with various types of context-sensitivity see Briciu (2018).
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According to skeptics, radical context-sensitivity affects virtually any natural language sentence. Arguments similar with Travis’ have been put forward concerning rather pedestrian sentences like (2) “It is raining” (Recanati 2002), or (3) “The cat is on the mat” (Searle 1978), or (4) “The ham sandwich stinks” (Recanati 2010), or (5) “The snow is white” (Moravcsik 1994). This skepticism is also shared by linguists like Chomsky (2002). For discussions of many more such examples see Bezuidenhout (2002), Recanati (2004), Cappelen and Lepore (2005), Szabó (2007), García-Carpintero (2006).
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Obviously some of these claims were contested. For example Kennedy and McNally (2010) argue that (1) is ambiguous because color terms are ambiguous between gradable and non-gradable interpretations. Given that there are many other similar arguments put forward by skeptics that do not involve color terms and that TCP accepts, for the sake of the argument I will go along with skeptics and truth-conditional pragmatists and accept their claim that no vagueness, ellipsis or ambiguity is involved in (1).
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Needless to say, defenders of formal semantics try to resist the above argument by rejecting some of its premises. Borg (2004a, b) and Cappelen and Lepore (2005) deny that the data put forward by skeptics are semantically relevant, Predelli (2005) denies premise (B) and argues that (1) expresses the same content at the two contexts where the difference in truth-value is the result of evaluating the content for truth at different circumstances; Szabó (2001) and Rotschild and Segal (2009) deny premise (C) and argue that “is green” is context-sensitive after all.
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Pagin and Pelletier (2007, 32) are explicit about this.
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For this purpose Recanati (2004, 23–37) distinguishes two types of pragmatic operations: primary (they play a role in the determination of truth-conditions) and secondary (they play a role solely in the derivation of conversational implicatures).
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This phenomenon was first discussed in Nurnberg (1995). Of course, the first-blush reaction that defenders of formal semantics have in the face of these examples is to deny their semantic significance: to deny that intuitions about metonymic uses of (4) are to be treated on a par with those of literal use, and that a common treatment of both is desirable. For a discussion along these lines see Stanley (2007, 206–207).
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As Recanati puts it, “modulation itself is context-sensitive: whether or not modulation comes into play, and if it does, which modulation takes place, is a matter of context” (Recanati 2010, 19). In their formal apparatus both Pagin and Pelletier (2007) and Recanati (2010) make use of a general modulation function mod which sole purpose is to determine the particular, context-specific modulation functions: mod takes pairs of expressions e and contexts C as arguments and delivers, for each such pair, the contextually appropriate modulation function mod(e,C).
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Within this account literalness can be treated as a limiting case: the context-specific function that delivers the content of “the ham sandwich” in the context of sorting food is the identity function.
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This is but one of many compositional rules available to theorists. Other rules can introduce other types of operations for various complex expressions. For a discussion see Chung and Ladusaw (2004, 2–14)
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In a sense, meaning-rules interpret syntactic ones. Each syntactic rule states that expressions of certain syntactic categories can combine to form expressions of a certain syntactic category, and determine the operation by which they combine. And each meaning-rule states how (i.e. by which operation) the meanings of complex expressions with a certain syntactic structure are built from the meanings of their constituents.
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It is obvious that this rule is not strongly compositional. But it is weakly-compositional. Under the assumption that a fragment of English, of which Vertical English is an extension, is weakly compositional, it can be shown that Vertical English is weakly compositional too. If the initial language is weakly compositional then extending it with the above rule does not destroy its weak compositionality. In Vertical English for any two sentences e1˄e2 and e1˄e3 and any context C, if ac ≤ 1.60 m and I(e2,C) = I(e3,C) then I((e1˄e2),C) = I((e1˄e3),C) – the content of constituents combine through functional application. And for any two sentences e1˄e2 and e1˄e3 and any context C if ac > 1.60 m and I(e2,C) = I(e3,C) then I((e1˄e2),C) = I((e1˄e3),C) – the content of constituents combine through the complex operation described. Thus, the failure condition of weak compositionality, given in Sect. 1.2, does not obtain.
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That TCP can do with a small number of meaning operations already concedes a lot. It looks to me that TCP is committed to the claim that there are a potentially open-ended number of meaning-operations. This follows directly from two of its other claims: (a) that a sentence can, in principle, express an open-ended number of propositions, each particular to a given context, and (b) that this variation need not be traceable to a corresponding variation in the content of the simple constituents, but that it can be the result of combining the content of constituents by different operations at different contexts
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This is acknowledged also by Lasersohn. He writes with respect to such rules: “the contextual effects that threaten compositionality are of a much more thorough-going nature than the effect illustrated in [this rule], and do not lend themselves to an analogous treatment” (2012, 186).
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Moreover, there is another reason to doubt that TCP can successfully appeal to theories of demonstratives that rely on salience in order to make a case for rules which do not introduce meaning operations. Even if the explanation of how an object becomes salient within a context of utterance is beyond the scope of a theory of meaning, there is a substantive story to be told about this. But there is no substantive story to be told about how one meaning-operation becomes more salient than another one. To say that one way of combining meaning is more salient than another is just to say that one interpretation of a complex expression is more salient, or more readily available to than another one.
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In fact, this is closer to the organization of TCP that Recanati (2010) and Pagin and Pelletier (2007) work with. It is easy to see that the two ways of organizing TCP are formally equivalent. In the two-step version, the content of an expression α(e i,e j) at a context C is determined by a context-specific pragmatic function mod(α(e i,e j),C) which takes as argument what is determined by the lexical and syntactic properties:
I(α(ei, ej), C) = mod (α(e i, e j), C)(f(α, (I(ei, C), I(ej, C)).Notice that this is formally equivalent with I(α(ei,ej),C)) = f∘mod(α(e i,e j),C)(α,(I(ei,C), I(ej,C))
where f∘mod(α(e i,e j),C) is a complex function obtained by combining the composition function f and the modulation function mod(α(e i,e j),C).This corresponds to the way of building TCP where a context-specific meaning operation combines the content of constituents into the content of the complex in one fell swoop.
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TCP might point out that there are limits on what propositions a sentence can express, because there are limits on how much one can tinker with the meaning of sentences: even if a sentence can express indefinitely many propositions, it can express any proposition. This, though, doesn’t make its analysis of (1) more informative.
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Acknowledgments
Thanks to Emma Borg, Manuel García Carpintero, Zoltán Gendler Szabó, Max Kölbel, Josep Macià, Sara Packalén, Peter Pagin, Dan Zeman and to the audience at the first Context, Cognition and Communication Conference and the University of Warsaw for extremely helpful questions, comments and objections. I acknowledge the financial support received from the Spanish Ministry of Economy and Competitiveness, EXCELENCIA program, project no. FFI2016-80636-P: Foundations and Methods of Natural Language Semantics.
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Briciu, A. (2020). Compositionality in Truth-Conditional Pragmatics. In: Ciecierski, T., Grabarczyk, P. (eds) The Architecture of Context and Context-Sensitivity. Studies in Linguistics and Philosophy, vol 103. Springer, Cham. https://doi.org/10.1007/978-3-030-34485-6_11
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