Title: Higher Theory and the Three Problems of Physics,
Abstract: According to the Butterfield--Isham proposal, to understand quantum gravity
we must revise the way we view the universe of mathematics. However, this paper
demonstrates that the current elaborations of this programme neglect quantum
interactions. The paper then introduces the Faddeev--Mickelsson anomaly which
obstructs the renormalization of Yang--Mills theory, suggesting that to
theorise on many-particle systems requires a many-topos view of mathematics
itself: higher theory. As our main contribution, the topos theoretic framework
is used to conceptualise the fact that there are principally three different
quantisation problems, the differences of which have been ignored not just by
topos physicists but by most philosophers of science. We further argue that if
higher theory proves out to be necessary for understanding quantum gravity, its
implications to philosophy will be foundational: higher theory challenges the
propositional concept of truth and thus the very meaning of theorising in
science.