Position paper: Proof-Theoretic Semantics as a viable alternative to Model-Theoretic Semantics for natural language

This paper is a response to the last question in the CFP, about alternatives to model-theoretic semantics (MTS). I do not present any specific results, just argue for proof-theoretic semantics (PTS) as such an alternative. PTS is well-established within Logic (e.g., [8]). See [11] for an overview. I have extended PTS to fragments of English. The paper has two parts: 1. a brief exposition of PTS, and 2. criticism of MTS as a theory of meaning and advantages of PTS as such a theory. 1. In a nutshell, the PTS programme can be described as follows. I. Sentences: replace the received approach of taking their meanings as truthconditions (in arbitrary models) by taking their meanings as canonical derivability conditions (from suitable assumptions) within a “dedicated” natural-deduction proof-system in which the derivability conditions are formulated. Such a system is presented in [3]. In a sense, the proof system should reflect the “use” of the sentences in the considered fragments, and should allow recovering pre-theoretic properties of the meanings of sentences such as entailment, assertability conditions and consequence drawing. II. Subsentential phrases (down to lexical units): replace their denotations (extensions in arbitrary models) as meanings by their contributions to the meanings (canonical derivability conditions) of sentences in which they occur. This adheres to Frege’s context principle [5], made more specific by the incorporation into a typelogical grammar [6] for the fragment considered. This is elaborated upon in [4]. Dummett introduces ([1], p. 48) an important distinction between content and ingredient sense. The content of an (affirmative) sentence S is the meaning of S “in isolation”, on its own. The ingredient sense of S is what S contributes to the meaning of an S in which S occurs as a sub-expression, a component. This distinction is incorporated in the PTS in [4]. A grasp of the ingredient sense always includes a grasp of the meaning, but not necessarily vice versa. This distinction, incorporated in the PTS in [4], is propagated to sub-sentential phrases too. The success of PTS is manifested in [2], where conservativity of determiners is proved rather than stipulated as a universal. 2. There is a vast literature containing critical arguments against MTS as a theory of meaning. I present here briefly only some of the main ones, those pertaining directly to NL. Some involve philosophical considerations, and others not. My