Metasemantics and Possible Expressions

Theories of meaning addressing natural language consist of both semantic and metasemantic claims and features. The former has to do with pairing the expressions of a language with values, where the statement of those pairings and their interrelations is understood as central to semantics proper. The latter has to do with explaining the basis of those pairings, linking the semantics of the language with the reality of the speakers that are purported to use it, which is an aspect of theories of meaning that is variously referred to as metasemantics, foundational semantics, the theory of meaning itself, or as defining a full-blooded theory of meaning (see, e.g., Dummett, 1996, Chapter 1; García-Carpintero, 2012; Kaplan, 1989a, p. 573; Lewis, 1970, p. 19, 1975; Stalnaker, 1997; see also Burgess & Sherman, 2014). This work is a development of these metasemantic aspects of theories of meaning – it aims to establish the need for broader consideration of possibilities at the intersection of the basic structures of natural language, our conceptions of meaning, and our capacities as speakers to engage with them. The pursuit of that aim rests upon idea that the nature of words and sentences in natural language may be used to problematize theories of meaning with explicit metasemantic commitments by exposing them to the theoretical possibilities those expressions appear to facilitate. The suggestion is that our metasemantics need to account not only for the expressions used in the language but also for the expressions that could be used, for the structural possibilities that our natural languages provide us. This can be demonstrated most clearly in the context of the meaning of individual words, both for theories that take word meaning to be primitive and explanatorily primary and for theories that see word meaning as derivative from their place in sentences, where sentences are taken to be explanatorily primary.¹

The guiding intuition here is that the possibilities surrounding the words we could have in our language and the sentences available to us are just as much part of a complete picture of language as the words we do have in our language and the sentences we actually use. The words of we communicate with had to come from somewhere and at some point must have been merely possible expressions, and the sentences available to us are a product of the incredible expressive power that languages exhibit when words are paired with syntactic rules, providing a set of sentences that are available to us whether or not we ever use them. The implications of this intuition are far reaching, one of which is explored in this work. Namely, it motivates the idea that theories of meaning need to account for the possibilities of language in equal measure as they need to account for its actualities. It invites the extension of how we assess the plausibility of different theories of meaning to the matter of how their characterizations of meaning and their foundational mechanisms play out with respect to those possibilities.

As such, this is not so much a work about meaning as it is about theories – it does not pursue any particular view of meaning, but rather aims to demonstrate the significance of those possibilities by confronting theories of meaning with them. This is done through an explication of lexicalization and compositionality, where the former concerns the process of introducing new words into a language and the latter concerns the syntactic and semantic relationship between words and sentences. This basic understanding of each is then developed into a framework characterizing possibility with respect to each of them and detailing the interrelations between them. These possibilities can be mapped out with a rudimentary recursive procedure and a few minor assumptions, allowing us to produce transparent and seemingly trivial examples of possible words and sentences. The procedure itself is not controversial or even particularly interesting, but it gives us an idea of how these possibilities can be elicited and ultimately adapted to the vernacular of specific theories of meaning, where they can be shown to lead to complications, particularly at a metasemantic level.

Two theories of meaning are examined here, corresponding to the two types of positions noted earlier – a theory that takes word meaning to be primitive and explanatorily primary and a theory that takes word meaning to be derivative from sentence meaning, with the latter being explanatorily primary. They are radically different perspectives, providing us with two very different and even opposing theoretical contexts. The first is represented by Jerry Fodor’s atomism (1998, 2008) and the second is represented by Robert Brandom’s inferentialism (1994, 2001).

The former is shown to encounter significant issues with reconciling the primitive causal picture of meaning Fodor commits to with the possibilities of lexicalization – where taking the meaning of words to be simple concepts and the meaning of sentences to be complex concepts, we can generate possible simple concepts on the basis of the complex concepts available to us. In doing so, we can populate a vast field of well-defined concepts that can then be regimented under expressions to serve as their meanings, introducing a pervasive form of tacit, theory-bound polysemy and significantly complicating Fodor’s conception of communication. This ramification of the atomistic position has apparently gone unnoticed, with no similar arguments having been explored in the literature.

The latter is shown to have difficulty reconciling its paradigmatic normative character with the inferential chains that follow from the compositionality that Brandom accommodates in his theory. That is, we can generate inferential chains using the logical vocabulary that Brandom develops, moving from expressions like “This is green” to “This is not red” to “This is not very red.” Taken together with his conviction that the meaning of subsentential expressions derives from their place in sentences, we are quickly led to a situation in which even the most basic expressions apparently depend upon bizarre sentences for their meaning. This dependency is a problem in and of itself and also complicates his scorekeeping metaphor as well as his appeal to use as the locus of meaning.

Each case points to a failure to appreciate the possibilities projected by lexicalization and compositionality, which is to say that these theories were simply not designed to accommodate a specific and significant part of our linguistic potential, of the way we see language functioning as a complex representational system. The spirit of this endeavor may be likened to that of Michael Dummett’s (1996) criticism of Donald Davidson’s (2001) semantic holism. Davidson’s truth-conditional semantics is a significant achievement as a development of Alfred Tarski’s (1936/1956) formal work involving truth – where meaning is conceived of as consisting in the interrelations of sentences of the object-language and a metalanguage. That is, knowing the meaning of a sentence of a given natural language consists in being able to produce a sentence in a metalanguage that specifies what would make it true – for example, “Snow is white” is true if and only if snow is white, where the sentence on the left is given an interpretation by what follows. It is a holistic and compositional theory of meaning. Its holism derives from its treatment of subsentential expressions:

We decided a while back not to assume that parts of sentences have meanings except in the ontologically neutral sense of making a systematic contribution to the meaning of the sentences in which they occur. … One direction in which [this] points is a certain holistic view of meaning. If sentences depend for their meaning on their structure, and we understand the meaning of each item in the structure only as an abstraction from the totality of sentences in which it features, then we can give the meaning of any sentence (or word) only by giving the meaning of every sentence (and word) in the language. (Davidson, 1967, p. 308)

And Davidson produced a number of convincing and influential arguments to the effect that the semantics of natural language must be compositional, understood as the idea that “the meaning of a complex expression is a function of the meanings of its parts and its mode of composition” (Pagin, 2019, p. 76).² The most compelling of these arguments is from learnability:

When we can regard the meaning of each sentence as a function of a finite number of features of the sentence, we have an insight not only into what there is to be learned; we also understand how an infinite aptitude can be encompassed by finite accomplishments. For suppose that a language lacks this feature; then no matter how many sentences a would-be speaker learns to produce and understand, there will remain others whose meanings are not given by the rules already mastered. It is natural to say that such a language is unlearnable. (Davidson, 1965, pp. 8–9)