Content and Depth Revisited

Abstract

In this paper I will compare depth relevance to what has come to be called depth hyperformalism. Ordinary formality, is typically taken to require closure under uniform substitutions. Depth hyperformality requires closure under depth substitutions—not-necessarily-uniform substitutions that are allowed to vary with depth. As it turns out, all depth hyperformal logics are depth relevant but not vice-versa.

So we’re left to ask the following question: for the particular projects Ross Brady is engaged in, should it be depth relevance or depth hyperformalism that should set the pace? More to the point, I’ll be interested in the following two claims:

• Logics of meaning containment are necessarily depth hyperformal.
• Logics of meaning containment are necessarily depth relevant.

The first entails the second. Brady seems to endorse the second. I’ll argue in this paper that he should also endorse the first.