Abstract

A framework is introduced in which categories play an essential role in the foundations of physics. The work of F.W. Lawvere is exploited to provide axiomatizations for the relevant mathematical objects in a way which does not depend on set-theoretical foundations. An axiomatization of the category of complete atomic Boolean algebras is sketched as an example. These results are then used to give an explication of "truth in a (classical) physical theory" in terms of a commuting diagramme. This explication is then generalized to quantum theory and shown to capture, not truth, but necessity in the sense of van Fraassen.