Abstract

What is it that semanticists think they are doing when using formalisation? What kind of endeavour is the formal semantics of natural language: scientific; linguistic; philosophical; logical; mathematical? If formal semantics is a scientific endeavour, then there ought to be empirical criteria for determining whether such a theory is correct, or an improvement on an alternative account. The question then arises as to the nature of the evidence that is being accounted for. It could be argued that the empirical questions are little different in kind to other aspects of linguistic analysis, involving questions of performance and competence (Chomsky 1965; Saussure 1916). But there are aspects of formal accounts of meaning that appear to sit outside this scientific realm. One key issue concerns the precise nature of the formalisation that is adopted; what criteria are to be used to decide between accounts that are founded on different formal systems, with different ontological assumptions? Indeed, is it necessary to judge semantic frameworks on such grounds? In other words, are two theoretical accounts to be treated as equivalent for all relevant purposes if they account for exactly the same linguistic data? Broadly speaking, there are two related perspectives on the analysis of propositional statements, one “truth conditional” — reducing sentence meaning to the conditions under which the sentence is judged to be true (e.g. Montague 1973) — the other “proof theoretic” — reducing sentence meanings to patterns of entailments that are supported (e.g. Ranta 1994, Fox & Lappin 2005 ,Fox 2000). Variations of these perspectives might be required in the case of non-assertoric utterances. We may wonder what critieria might be used to decide between these approaches. This brings us back to the nature of the data itself. If the data is (merely) about which arguments, or truth conditions, subjects agree with, and which they disagree with, then the terms in which the theory is expressed may be irrelevant. But it may also be legitimate to be concerned with either (a) the intuitions that people have when reasoning with language, or (b) some technical or philosophical issues relating to the chosen formalism. The truth-conditional vs proof-theoretic dichotomy might broadly be characterised as model-theoretic vs axiomatic, where the model-theoretic tend to be built around a pre-existing formal theory, and the axiomatic involves formulating rules of behaviour “from scratch”. In some sense, fitting an analysis of a new problem into an existing framework could be described as providing some kind of “explanatory” power, assuming that the existing framework has some salient motivation that is independent of the specific details of the phenomena in question. In contrast, building a new theory that captures the behaviour might then be characterised as “descriptive”, as — superficially at least — it does not show how an existing theory “already” accounts for the data in some sense. Here we observe instead that the argument can be run in the other direction. that a reductive model-theoretic account merely “describes” how some aspects of a problem can be reduced to some formalisation, but may fail to capture a subject’s understanding or intuitions about meaning. It is surely appropriate for the formal theory itself to be at least sympathetic to the ontological concerns and intuitions of its subjects — if not inform them (Dummett 1991). The alternative amounts to little more than carving out otherwise arbitrary aspects of a system that mimics the required behaviour, without a coherent explanation of why some aspects of a formal theory characterise, or capture, the intended meaning, but not others (cf. Benacerraf 1965). That seems an impoverished approach, weakening any claim to “explain”. Any constraint this imposes on what is it to be an explanatory account of meaning then faces the same problem as naive notions of compositionality (Zadrozny 1994) — that is, what appears to be a meaningful restriction is, in reality, a mirage