In the first part of the talk I present my work on the framework of semantic constraints. In the second part I discuss two questions that arise, the first regarding criteria for semantic constraints, and the second regarding the relation between logicality and analyticity.
Logical consequence is viewed by many as depending on the distinction between logical and nonlogical terms. The new proposed logical framework does not lean on the distinction between logical and nonlogical terms. The framework, couched in model theory, is conservative with respect to the conventional view of logic as necessary and formal, and provides a conceptual wealth rising from a generalization of standard logic. A semantic constraint for L is a sentence in the metalanguage that somehow constrains or limits the admissible models for L (and can be viewed as a meaning rule). Logical terms (or more precisely, rules defining logical terms) are merely a special case of semantic constraints, while all the semantic constraints in a system are involved in determining logical consequence for L. I shall present some definitions and results in the framework, and move on to discuss further issues that arise.
The first issue is that of criteria for semantic constraints. In previous work I left open the question of whether there is a “correct” set of semantic constraints. Criteria for logical terms have been discussed extensively in the literature. Invariance criteria for logical terms have proved to be of special interest. I shall present a natural way of generalising invariance criteria to apply to semantic constraints.
The second issue I shall discuss, and for which I would be especially interested in the group’s thoughts, has to do with the relation between logicality and analyticity. A common way of distinguishing between analytic truth and logical truth is by referring to the former as truth in virtue of meaning (of all terms) and to the latter as truth in virtue of meaning of just the logical terms. I shall discuss the question of whether the framework of semantic constraints should be considered as a framework for analytic truth rather than logical truth, and more generally the significance of the distinction between the two notions of truth.