Validity without Reference

Christopher Gauker (Cincinnati) gives a talk at the MCMP Colloquium (9 Feb, 2012) titled "Validity without Reference". Abstract: Two definitions of logical validity for a simple first-order language will be compared in order to decide which one provides a better model for the semantics for natural language. One of these is the standard model-theoretic definition. The other defines contexts as structures of linguistic objects and then defines validity as preservation of truth-in-a-context. The disadvantage of the model-theoretic definition is that it commits us to explicating the reference relation, which no one has ever been able to do. The context-logical definition avoids this commitment, although it takes on others. It particular, it commits to explaining what it takes for a given context to be the context that pertains to a conversation. As a three-valued theory, the context-logical definition generates a non-classical logic; this consequence will be defended. Inasmuch as it employs a substitutional interpretation of quantifiers, the context-logical definition faces a technical problem having to do with the omega rule. This will be addressed by arguing that even for purposes of defining logical validity, natural languages may be individuated in such a way as to contain no fixed number of singular terms.