I will report on recent work with Chris Isham on the application of topos theory to physics. The Kochen-Specker theorem shows that a naive realist description of quantum systems is impossible. This can be understood as the inapplicability of Boolean logic to quantum systems. In order to arrive at a more realist description, one can use the internal logic of a certain topos of presheaves. The choice of this topos is directly motivated from the Kochen-Specker theorem. I will show which structures within this topos are of physical significance and how propositions about physical quantities are assigned truth-values. The whole topos scheme is not bound to quantum theory, but allows for major generalisations, potentially in the direction of a future theory of quantum gravity.