An axiom set is given which purports to formalize the notion of a “theory involving measurement.” The abstract objects satisfying these axioms are examined, and some candidates for measures of complexity are considered.

This framework allows us to discuss some forms of a degree of confirmation. Both “complexity” and “degree of confirmation” appear to be intimately bound up with geometrical aspects of these “theories” which derive from measurement considerations, suggesting that the concepts may be inapplicable to more “general theories.”

The view is taken throughout that the well known paradoxes indicate inadequacies of the linguistic apparatus and that the axiomatization here presented is an attempt to construct an adequate language for the relevant portion of the world. This position is not defended in the paper.