Analyticity and Possible-World Semantics

The aim of this paper is to consider how the notion of analyticity can be dealt with in model-theoretical terms. Standard approaches to possible-world semantics allow us to define necessity and logical truth, but analyticity is considerably more difficult to account for. To explain this difficulty, we first provide a simplified sketch of possible-world semantics. After defining necessity and logical truth, we describe how a two-dimensional variant of that approach is used to define the notion of a priori. The subsequent section is focused on analyticity. As is suggested, the source of the difficulty in defining that notion lies in the received model-theoretical conception of a language interpretation. In intuitive terms, analyticity amounts to truth in virtue of meaning alone, i.e. solely in virtue of the interpretation of linguistic expressions. However, the received conception of a linguistic interpretation as a mapping from language to a model frame makes it impossible to keep the interpretation constant, while varying other components of the model. To make room for analyticity, the concept of an interpretation should therefore be revised: Interpretations should be made richer in content than it has usually been assumed. As a by-product, this revision also gives us a one-dimensional analogue of the two-dimensional account of a priori. We are thus able to map out the network of formal connections between analyticity, apriority, logical truth and necessity.