  We consider Hilbert's problem of the axioms of Physics at a qualitative or
conceptual level. This issue is more pressing than ever as we seek to
understand how both General Relativity and quantum theory could emerge from
some deeper theory of quantum gravity, and in this regard I have previously
proposed a `principle of self-duality' or `quantum Born reciprocity' as a key
structure. Here I outline some of my recent work around the idea of quantum
spacetime as motivated by this non-standard philosophy, including a new toy
model of gravity on a spacetime consisting of four points forming a square.
