Abstract
I resolve the major challenge to an Expressivist theory of the meaning of normative discourse: the Frege–Geach Problem. Drawing on considerations from the semantics of directive language (e.g., imperatives), I argue that, although certain forms of Expressivism (like Gibbard’s) do run into at least one version of the Problem, it is reasonably clear that there is a version of Expressivism that does not.
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Notes
Here and throughout, I will understand the notion use as follows: U is a (conventional) use for ϕ iff a speaker (conventionally) expresses U with an utterance of ϕ. U is ϕ’s (conventional) use iff (i) U is a use for ϕ, (ii) ϕ has no use besides U. Three notes about this understanding. First, what the notion of conventional expression amounts to is something about which I will say very little here, beyond the fact that (a) it is a conventional, rather than conversationally implicated, relation that (b) holds by default, but defeasibly (cf. Asher and Lascarides 2001). Second, though it is standard for Expressivists to type uses as states of mind, I does not assume this. For all I will say, uses may be typed as proposals to update the conversational scoreboard (Lewis 1979c), speech acts, and so on. Finally, formal objects like propositions can, in a sense, count as uses (since a speaker can conventionally express a proposition in uttering a sentence). But this sense is to be understood as derivative: a speaker expresses a proposition by expressing a state of mind or speech act that can be at least partly individuated by its representational content.
A related example: in theorizing about the semantics of interrogatives, partitions of logical space—sets of disjoint, mutually exhaustive propositions—are generally assigned as the semantic values of interrogative sentences (the classic references are Hamblin 1973; Karttunen 1977; Groenendijk and Stokhof 1984). Partitions do not represent the world as being some way, rather they present alternative ways the world might be as candidates for actuality.
Proof By the saa, (2a) and (2b) must express A toward inconsistent contents (respectively: ϕ and some ψ such that \(\phi,\psi\models\bot\)). Similarly, (3a) and (3b) must too (respectively: \(\neg\phi\) and some χ such that \(\neg\phi,\chi\models\bot\)). Since \(\phi,\psi\models\bot\), it follows that \(\psi \models \neg\phi\). And since \(\neg\phi,\chi\models\bot\), it follows that \(\chi\models\phi\). Whence it follows that \(\psi,\chi \models \bot\). That is to say, ψ and χ are inconsistent. So, since A is inconsistency-transmitting, bearing A toward ψ and χ is inconsistent. Therefore, since (2b) expresses A toward ψ and (3b) expresses A toward χ, (2b) and (3b) are inconsistent.
The way to block this argument, while still holding onto a version of the saa, is to suppose that the contents of the attitudes expressed by (2a) and (3a) are not inconsistent. Indeed, Schroeder (2008a) suggests an Expressivist semantics—a “Being For” semantics—that does exactly that. I will not be interested in this response here. As Schroeder (2008a) discusses in detail, it runs into empirical difficulties. Thankfully, given its technical complexity, this dialectic is irrelevant, since I reject the pressures that would lead an Expressivist down this road.
Although I think Schroeder’s criticism of Gibbard is broadly correct, I should note that it has lately come in for criticism from Silk (2013) (who argues, in effect, that disapproval and toleration are logically related).
Portner builds on Lewis’ (1979b) classic account, although there are important differences. For other accounts that agree with Portner on at least Claims 1–2, see Charlow (2010, 2011); Mastop (2005, 2012); Starr (2011). The differences between these accounts are not relevant for my purposes here. Portner’s account is chosen simply as an illustrative example.
There are many accounts that fit this bill. For instance, some accounts analyze imperatives with explicit performatives (\(!\phi\, \approx\) I command you to see to it that ϕ) and assign the latter satisfaction conditions (Lewis 1970). Others analyze them in terms of future-tense indicatives (\(! \phi\, \approx\) you’ll do x) (Geach 1958). Still others say the semantic value of !ϕ is its fulfillment-condition (i.e., the proposition that ϕ) (Jørgensen 1937–1938; Hare 1952, 1967; Bennett 1970).
Something that might make us wary of my claim here is the fact that the imperative is of a different clause-type than the permission-grant (which is declarative). It should not. It does seem clear that the English imperative don’t jaywalk is inconsistent with the English permission-grant you may jaywalk. It is, moreover, easy to imagine a language with a single, “directive” clause-type, which permitted canonical formations of both commands and permission-grants, with sentences of respective forms !ϕ and
ϕ (Lewis 1979b, see, e.g., the language defined in).If we model commanding in terms of some sort of Boolean operation on plans (e.g., addition to the To-Do List, or restriction of the “permissibility sphere” to worlds where the command is satisfied), commanding and permitting are notoriously non-inter-definable; see Lewis (1979b) for discussion.
Portner actually says it is properties that are added. This is a wrinkle we can ignore.
There are other semantics for imperatives/permissions that are consistent with this. Starr (2011), for instance, takes this to motivate an update semantics for imperatives. The dialectic for such theories will be basically the same as for the static view that I entertain here. For discussion, see my (to appear).
My reply draws on my understanding of Dreier (2009)’s understanding of the disagreement problem.
On the view under consideration, \(\neg\) expresses an operation that can apply not only to propositions, but arbitrary sets of objects. There is no reason, from the point of view of the semantics, to forbid \(\neg\) from scoping over an imperative. For purposes of this discussion, I will suppose that this view makes sense.
A related worry: what kind of use a certain kind of language has, by default, is a question for empirical linguistics. But the considerations the proponent of the disagreement problem uses to motivate propositional semantics are wholly a priori. Since the connection between a propositional semantics and a representational use is plausibly a priori (see, e.g., Burge 1993), the disagreement problem appears to furnish a way of making empirical “discoveries” about language a priori. Obviously, it does no such thing.
For the same reason, it seems the familiar technique of exploiting disquotation—e.g., inferring from the fact that ‘a ∧ b’ holds at X the fact that both ‘a’ and ‘b’ hold at X—as a tool of proof in the metalanguage will be unavailable. If X is a state of mind, disquotation in this sense is simply invalid.
The notion plan (like the notion of, say, belief) does admit of an abstract, rather than simply psychological, interpretation. Talk of a ‘belief’ can refer to an abstract object (the thing believed), and talk of a ‘plan’ as well (the actions or goals planned). Still, to highlight the shift away from a Psychologistic Semantics, I have chosen terms here—‘possibility’ and ‘strategy’—that tend toward an abstract, rather than psychological, interpretation.
The characteristic use of different kinds of language may warrant the introduction of more kinds of entities into the semantics. Since epistemic modals quantify over (epistemic) possibilities, a semantics of epistemic modals will have sets of (epistemic) possibilities providing verdicts for sentences. More interestingly, Swanson (to appear), Yalcin (2007) suggest that the characteristic use of the language of subjective uncertainty (including but not limited to epistemic modals) will warrant the introduction of probability functions (sets of which encode a probabilistic perspective) as a basic semantic entity. I ignore such complexities here.
The meaning of a specific verdict will depend on the kind of sentence in question. When an imperative receives a verdict of 1 at a strategy, we will not be inclined to say it is true at that strategy. For discussion of how to interpret a positive verdict for an imperative relative to the relevant semantic entity, see Lemmon (1965), Segerberg (1990).
I develop the empirical and conceptual foundations for this sort of account of imperatives in detail elsewhere (Charlow 2011, to appear). Three things that I want to highlight here. (1) There are many ways to define truth conditions for modal sentences from objects like strategies. For the most influential, which uses a strategy to determine an ordering of possibilities according to strategy-relative desirability, see Kratzer (1981). (2) The question of how to interpret the modal notions \(\square\) and ⋄ is a hard one. Standardly \(\square\) is interpreted as a universal quantifier, ⋄ existential, over strategically most desirable possibilities. For many reasons, these definitions are too simple (cf. Kratzer 1981; Cariani, to appear). (3) On some ways of resolving (1) and (2), my view formally resembles one independently developed by Silk (2013). (Despite the formal similarity there are major differences between our theories.)
Filling in these lacunae is, I want to assure the reader, orthogonal to our purposes here. So long as:
For all ψ and χ that are contradictory (such that \(\chi \models \neg\psi\)): \(\square \psi \models \neg \diamond \chi\)
(χ is prohibited if it thwarts a requirement)
As they will on any semantics of \(\square/\diamond\), there is a canonical proof of the inconsistency of !ϕ and
χ.Proof Suppose that \(\chi \models \neg\psi\), and suppose for reductio that there is some σ such that \(\sigma \in [\![ !\psi ]\!]\) and \(\sigma \in [\![\)
\(\chi ]\!]\). Then \(\sigma \models \square\psi\) and \(\sigma \models \diamond\chi\). Then, since \(\square \psi \models \neg \diamond \chi,\, \sigma\models \neg \diamond \chi\) and \(\sigma \models \diamond\chi\). Contradiction.seccf improves on, e.g., coordinative views of the interface between semantics and communicative function (on which utterances function to coordinate speaker and addressee on a state of mind). Though I doubt he would endorse such a view, Seth Yalcin provides a helpful formulation of it:
The point of the speech act [is]\(\ldots\) to engender coordination among one’s interlocutors with respect to the property of states of mind the sentence semantically expresses in context. (2011, p. 311)
Coordinative views work well for sentences whose function is to assert, assertion’s function is to make addressee and speaker share an attitude (belief) toward a proposition; assertions transfer contents between agents (Burge 1993; Egan 2007). They work poorly for sentences whose function is to command: in commanding that you leave, I hardly propose that we coordinate on the perspective my utterance expresses (the property, roughly, of planning to leave).
Relevant precedents for the notion that sentences semantically encode their default uses are Asher and Lascarides (2001, 2003). I discuss this further in Charlow (2011, Ch. 2–3). Precedents for the notion that a sentence does this by expressing a property of a state of mind are Yalcin (2007, 2011), Swanson (to appear).
To say a sentence expressing a set of, e.g., worlds encodes a locational perspective (and thus a representational function) is not to say that expressing such an object can only function as a proposal for an agent to come to self-locate in a certain way. It is just to say this is how things work by default: the default function of a set of possible worlds is representational (Asher and Lascarides 2001, 2003). By default, an intelligible proposition is regarded as presented-as-true; as Burge has argued, “Understanding [propositional] content presupposes and is interdependent with understanding the force of presentations of content,” i.e., as true (1993, 481ff). Similarly for nonpropositional content; by default, an intelligible nonpropositional content presents, e.g., some object as desirable or worth pursuing.
Areas where Expressivists (and their sympathizers) can claim to have moved the semantic dialectic forward include modality (Yalcin), conditionals (Swanson), and imperatives (Portner, Charlow).
I am grateful to Alex Silk for helping me to think through this issue. For a similar (but much more detailed) take on the theoretical content of Expressivism, see Silk (to appear, Sect. 3).
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Acknowledgments
For feedback and discussion, I am grateful to Allan Gibbard, Benj Hellie, Nathan Howard, David Plunkett, Anders Schoubye, Alex Silk, Sergio Tenenbaum, Richmond Thomason, and Jessica Wilson. Thanks to Peter Ludlow for the inspiration for this project. Thanks also to audiences at Arché and Semantics in Philosophy in Europe III.
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Charlow, N. The problem with the Frege–Geach problem. Philos Stud 167, 635–665 (2014). https://doi.org/10.1007/s11098-013-0119-5
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DOI: https://doi.org/10.1007/s11098-013-0119-5