Basic Aspects of the Theory of Grammatical Form

Abstract

In his book The Logical Structure of Mathematical Physics Sneed analyzes the structure of a theory of mathematical physics through informal axiomatization. According to Sneed, a theory of mathematical physics is characterized by a matrix for the theory, which “‘determines’ the sort of mathematical entities the theory is going to employ”, and four other entities: the set of models, the frame, the core, and the expanded core of the theory. The latter entities are, in a sense, restrictions of the matrix determined by basic axiomatic considerations and by considerations determining the empirical content of the theory. Each of these entities, the matrix as well as the other four, are set-theoretically characterized in their general properties.

I wish to thank H.-H. Lieb for pointing out some problems in the original version of the article and helping me to work out some revisions.