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Binding, Compositionality, and Semantic Values

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Binding, Compositionality, and Semantic Values volume 19, no. 2 I. Introduction: the plan1 january 2020 Assume that propositions — things that are or determine functions from possible worlds to truth-values — are the objects of the attitudes, the possessors of modal properties like being possible or necessary, the things we assert by uttering sentences in contexts, and perhaps more. Suppose we have a compositional semantics that assigns se- mantic values relative to contexts to the well-formed expressions of Binding, Compositionality, a natural language.2 What is the relation between the proposition ex- pressed by a sentence in a context and the semantic value assigned to the sentence in that context? Surely the simplest view, and so the one we should prefer, other things being equal, is that the relation is and Semantic Values identity: the proposition expressed by a sentence in a context just is the semantic value of that sentence in that context. We’ll call this the clas- sical picture. Lewis [1980] claimed that the proper semantics for certain expressions precluded identifying the compositional semantic values of sentences relative to contexts with propositions as the classical pic- ture does. King [2003, 2007] and Glanzberg [2011] argued that Lewis’s argument ultimately fails and that the classical picture can be upheld. Call this exchange the old debate. It is worth noting that the dialectic of 1. Thanks to Chris Barker, Ezra Cook, Josh Dever, Geoff Georgi, Hans Kamp, Peter Pagin, Bryan Pickel, Brian Rabern, Anders Schoubye, Dag Westerståhl, Malte Willer, Seth Yalcin, Juhani Yli-Vakkuri, Zoltán Szabó, and two anony- Michael Glanzberg & Jeffrey C. King mous referees for many discussions of the ideas in this paper, and comments on earlier drafts. Versions of this paper and its ancestors were presented at Northwestern University Rutgers University the Workshop on Tense, Modality, and Semantic Values, Center for the Study of Mind and Nature, University of Oslo, 2013; the Conference on Philosophy of Language and Linguistics, Interuniversity Center, Dubrovnik, 2013; the Philosophical Linguistics and Linguistical Philosophy Conference, Tarrytown, NY, 2013 and 2014; the Language, Logic and Cognition Center, Hebrew Uni- versity of Jerusalem, 2014; the American Philosophical Association Eastern Division Annual Meeting, Philadelphia, 2014; the Workshop on Operators © 2020 Michael Glanzberg & Jeffrey C. King vs Quantifiers, Facultat de Filosofia, Universitat de Barcelona, 2016; the Mid- Atlantic Philosophy of Language Workshop, West Virginia University, 2016; This work is licensed under a Creative Commons and the University of Edinburgh, November 2016. Thanks to all the partici- Attribution-NonCommercial-NoDerivatives 3.0 License. pants at those events for valuable questions and discussions. <www.philosophersimprint.org/020002/> 2. Some people think that a semantics may not assign semantic values to some well-formed expressions, (this is mentioned in Westerståhl [2012] and Pagin and Westerståhl [2010a]). But we’ll ignore that here since this issue is or- thogonal to those we are concerned with. michael glanzberg & jeffrey c. king Binding, Compositionality, and Semantic Values the old debate was that reasons needed to be given for abandoning II. The classical picture the classical picture. Absent such reasons, we should retain it, as it is We begin with what the classical picture says about propositions. They the simpler alternative. are the objects of the attitudes. They are the things we assert in utter- Recently, a number of philosophers have revived the Lewis-style ing sentences in contexts. They are the bearers of truth and falsity, as argument for the claim that propositions cannot be identified with well as modal properties like being possible or being necessary. They sentential semantic values in contexts. They too have argued that the are the semantic values of sentences taken in contexts.5 Here we focus 3 proper semantics for certain expressions precludes this identification. on this last property of propositions. We assume that semantic values In the present work, we want to consider one instance of a new Lewis- (relative to various parameters) are compositionally assigned to sen- style argument we find particularly interesting, in Rabern [2013], and tences. In defending the classical picture, we then argue that these se- respond to it. Call this the new debate. We begin by reviewing the old mantic values are propositions; or perhaps better, we resist arguments debate since we think the morals that should be drawn from that de- that they are not. In the end, we think these come to the same thing, bate are essentially the same ones that should be drawn from the new since, as mentioned above, we think the classical picture is the one we debate. should adopt unless we are for some reason unable to. We return to Along the way, we’ll touch on a number of additional issues that these points below. we think have independent interest. Chief among them will be issues One assumption we will make throughout is that truth-conditional about the nature of semantic composition and about the way syntactic contents are good candidates to be propositions. This is, perhaps, a environments can affect what semantic values are composed and how simplification. Many, including one of the authors,6 hold that proposi- they are composed. Our response to Rabern [2013] and our defense of tions are structured entities, individuating content more finely than the classical picture will involve invoking multiple modes of semantic truth-conditions can. But it is commonly assumed that however fine- composition and will allow for type-adjusting of semantic values to grained propositions are, they determine truth conditions. This is a take place in composition. variant of what Cresswell [1982] calls the “most certain principle of We wish to be explicit at the outset regarding the nature of our semantics,” that the content you express, plus the facts in the world, defense of the classical picture. It depends on making claims about determine a truth-value.7 As we will see below, the main challenge what syntax is actually like and about how semantic composition in to the classical picture is a compositional semantics on which seman- fact works. Hence, there is nothing “conceptual” about our defense of tic values for sentences are not truth-conditional at all. Hence, the the classical picture. Language could have evolved in such a way that propositions could not be identified with sentential semantic values and Glanzberg [2011]. To our surprise, some people seem not to have ap- in context. We just claim it didn’t. Thus, our defense of the classical preciated this. picture is empirical.4 5. To clarify a little further, by ‘semantic value in context’ we intend the meaning assigned to an expression in a context by the correct semantic theory. The question then arises whether this theory is compositional and in what sense 3. For instance, Ninan [2010, 2012], Rabern [2012], Weber [2012], Yalcin [2011, it is compositional. We discuss this extensively as we go forward. 2014], and Yli-Vakkuri [2013] (though Ninan mainly argues that it is impor- tant to recognize the possibility that propositions are not compositional se- 6. King [2007]. mantic values in contexts). 7. Cresswell [1982, p. 69] writes, “If we have two sentences A and B, and A is 4. This is also true of the defense of the classical picture in King [2003, 2007] true and B is false, then A and B do not mean the same.” philosophers’ imprint – 2 – vol. 20, no. 2 (january 2020) michael glanzberg & jeffrey c. king Binding, Compositionality, and Semantic Values simplifying assumption that propositions are truth conditions is a 1. a. Location: Somewhere [the sun is shining] helpful way to focus on the issue at hand. b. Tense: There have been dogs = It has been that [there are dogs] III. Lewis’s [1980] challenge to the classical picture c. Modal: Aunts must be women = It must be that [aunts Assume that sentences are (compositionally) assigned semantic values are women] relative to a context. Sentential semantic values (relative to a context) are then evaluated for truth at indices. This is a version of what Lewis d. Standard of precision: Strictly speaking [France is not [1980] calls the variable but simple semantic value approach to semantics. hexagonal] The semantic values of sentences are variable in the sense that they As indicated, Lewis thought these operators work by shifting the indices differ from context to context for at least some sentences. They are at which the semantic values (relative to context) of the sentences they simple in that they are, or determine, functions from mere indices to embed are evaluated. For instance, (suppressing contextual sensitiv- truth-values. (Lewis also considers what he calls the constant but com- ity) ‘Past [S]’ evaluated at (index) t tells us to see whether the semantic plicated semantic value approach on which sentential semantic values value of S is true at a time prior to t. For these operators to be non-vac- are functions from context/index pairs to truth-values, but we need uous, sentential semantic values (relative to contexts) must be able to not consider that here.) On the classical picture, these sentential se- vary in truth-value across shifted indices. But, Lewis claimed, since we mantic values assigned relative to context just are propositions. As we see that we have operators that shift time, location, standard of preci- mentioned, for present purposes we will assume, as Lewis [1980] does, sion and world features of indices, sentential semantic values (relative that propositions are functions from worlds to truth-values. Accord- to contexts) must be capable of varying in truth-value across times, ingly, on the classical picture, indices are nothing but possible worlds.8 locations, and standards of precision as well as worlds. That is, senten- Lewis’s [1980] argument that propositions cannot be identified tial semantic values (relative to contexts) must be functions from times, with sentential semantic values relative to context is deceptively sim- locations, standards of precision and worlds to truth-values.
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