Abstract

Classical physics and ‘classical’ mathematics (ie, mathematics based on set theory) fit together naturally with the Boolean algebra of the subsets of a set serving perfectly as a model for propositions in physics. However, this is known to fail in quantum theory, where the inherent logic is non-distributive. In this lecture I will describe some recent work that aims to construct a new way of looking at quantum mechanics in which the theory ‘looks like’ classical physics, but in a topos other than the topos of sets. In fact, we go well beyond this and claim that any theory of physics should/can be expressed in a pseudo-classical form in which each system has its own topos in which the physical theory is formulated.