Logic without Model Theory

Arguably, model theory serves two main functions: (1) to explain the relationship between language and experience, and (2) to specify the notion of logical consequence. In this paper I shall propose the notion of`knowledge assimilation', the assimilation of new information into a knowledge base, as an alternative understanding of the way in which a knowledge base formulated in logic relates to externally generated input sentences that describe experience. I shall argue that the notion of logical consequence can also be understood within a knowledge assimilation framework, in terms of sentences that must hold no matter what stream of input sentences might arise in the future. Classical model theory can be understood as dealing with static relationships among individuals. It leads naturally therefore to possible world semantics and modal logic, in which models are understood as related to one another by accessibility relations. I shall argue in favour of a non-model-theoretic alternative to possible world semantics , an alternative which employs a syntactically rich vocabulary of terms representing time, events, situations and theories. Similarly to the way in which possible worlds can be viewed as arising from classical models, situations which cut across time and space in situation semantics can be viewed as arising from possible worlds. I shall argue for representing situations syntactically as theories and amalgamating object language and metalanguage as an alternative to situation semantics.