(Apologies in advance for the techy nature of this post. The subject itself is pretty techy.)
Various philosophers have argued for a semantics for natural language that makes no use of the notions of truth and reference in its metalanguage—that is to say, a non-representational semantics. There are many ways in which one might attempt to develop such a semantics. One way is expressivism. While there is much that is distinctive about expressivism as an approach to the semantics of natural language, the most central idea is utterances of “complete” pieces of syntax do not assert propositions with cognitive (truth-conditional) content, but rather function to express attitudes of approval (something like full credence) or disapproval (something like zero credence) by the speaker.
There are many questions about how to formalize this central idea. One approach is to rewrite a standard truth-conditional semantics (e.g., the kind you’ll find in Heim and Kratzer’s Semantics in Generative Grammar) with “approval” standing in for “truth” and “disapproval” standing in for “false” in the metalanguage.
That is to say, we retain the standard lambda calculus, but now understand it as a formal representation of a calculus of attitudes, where the semantic value computed by our semantics for some tokening of some sentence is either approval or disapproval of the claim expressed by that sentence in the relevant utterance[*]. The semantic value of a proper name is a mental state that saturates a “functional” mental state, yielding approval or disapproval of some claim as an output. On this approach, it is natural to see the lexical entry for an intransitive verb like “barks” as being something like this:
(BARKS) ||barks||u,s,XP,c = λx ∈ DR . Appr[barks(x)] if s approves of the claim that x barks, Disappr[barks(x)] otherwise
Understand DR to be the set of semantic values of referential expressions; ‘Appr[barks(x)]’ to be a metalanguage expression such that for all x, Appr[barks(x)] iff s approves of the claim that x barks; and ‘Disappr[barks(x)]’ to be a metalanguage expression such that for all x, Disappr[barks(x)] iff s disapproves of the claim that x barks. Read the lexical entry, then, as follows: the semantic value of ‘barks’ in an utterance u by speaker s of some larger piece of syntax XP in context c is the function taking every element x of DR to Appr[barks(x)] if s approves of the claim that x barks, Disappr[barks(x)] otherwise.
Here is a major worry for this approach. Take a speaker A who disapproves of the claim that George Bush barks. Using this lexical entry for ‘barks’ to compute the semantic value of ‘George Bush barks’ (for all utterances u by A in all contexts c) yields the following result: Disappr[George Bush barks]. This seems wrong; Disappr[George Bush barks] seems as if it should be the result of computing the semantic value of ‘George Bush doesn’t bark’, not of ‘George Bush barks’. The expressivist who chooses (BARKS) as his lexical entry for ‘barks’ is thus forced to bite a pretty big bullet; intuitively speaking, the results of his computations for any of A’s utterances of ‘George Bush barks’ and ‘George Bush doesn’t bark’ will have to be identical.
Perhaps the following pragmatic response can help. It is presupposed by default that in uttering some sentence φ, a speaker means to express approval of the claim expressed by φ. The presupposition is, however, cancelable; usually one can cancel it merely by employing the negation operator. Roughly, the negation operator has a metalinguistic function; it indicates to a speaker’s interlocutors that he is in fact to be interpreted as disapproving of the claim expressed by the attached sentence.
This seems to amount to the suggestion that the role of negation is to cancel a pragmatic presupposition to the effect that in uttering some sentence φ, a speaker means to express approval of the claim expressed by φ. By asserting φ’s negation, a speaker makes it presupposed that she disapproves of the claim expressed by φ. That is to say, negation is a signal to one’s interlocutors, used by a speaker to make sure that she will be understood as she intends to be understood.
Consider, however, what happens when the speaker A attempts to reflect on the claims she endorses. Even in a private moment of reflection, A will refuse her assent to the sentence ‘George Bush barks’. But the suggested pragmatic story seems to predict that she will not so refuse. A perceives no risk that she will be misunderstood, since there is no audience to misunderstand her. The meaning of the sentence is, more or less, transparent to her, and yet she still refuses to assent to it. But why should this be? If the meaning of the sentence is more or less transparent to A, and the semantic value of the sentence is in fact the expression of disapproval by A of the claim that George Bush barks, these facts alone should be sufficient to defeat the relevant presupposition. Why then would A rationally refuse her assent to the sentence ‘George Bush barks’ in such a situation?
The following reply is possible. There is a pragmatic rule of assent, such that one may only assent to a sentence when one approves of the claim expressed by an utterance of that sentence. In all other cases—including cases that do not involve any conversational interlocutors—assent is inappropriate.
As far as I can tell, there is simply no motivation for positing such a pragmatic rule of assent. What reason could we have for supposing that there in fact is such a rule governing the linguistic behavior of ordinary English speakers? Generally, it is plausible to assume the existence of such rules concerning linguistic behavior only when it is possible to tell a story about why the rule is important for promoting efficient and felicitous communication between individuals. For the reasons articulated in the previous paragraph, it is not clear why a rule governing the linguistic behavior of a single, non-conversant individual in such a way would be important in this way, since there appears to be no risk of misinterpretation in such cases. This seems to follow from the following (seemingly plausible) general methodological principle of pragmatics: given some linguistic context c such that there is no reasonable basis for a speaker A to suppose that there is some risk that some linguistic performance P of hers will be misinterpreted, there is no pragmatic rule φ such that φ forbids A’s performance of P in c.
All this said, I think it’s safe to assume that (BARKS) is the wrong lexical entry for ‘barks.’ The broader point seems to be that there’s no easy way to directly adapt a standard truth-conditional semantics (that of Heim and Kratzer) to the expressivist project.
What would the right lexical entry for ‘barks’ look like? There are a few options, but all of them have some drawbacks. (Perhaps the worst drawback is that, in order to be even prima facie viable, a viable expressivist semantics for natural language will require us to rebuild even the most basic parts of our semantics from the ground up.) Depending on the response this post receives, I may have some more to say about those options in a later post.
[*] The notion of a claim is problematic for the expressivist. I use it here only for expository ease. You’ll have to trust me that there are ways of cashing out the expressivist project that don’t depend on the notion.