  We discuss some conceptual issues that any approach to quantum gravity has to
confront. In particular, it is argued that one has to find a theory that can be
interpreted in a realist manner, because theories with an instrumentalist
interpretation are problematic for several well-known reasons. Since the
Hilbert space formalism almost inevitably forces an instrumentalist
interpretation on us, we suggest that a theory of quantum gravity should not be
based on the Hilbert space formalism. We briefly sketch the topos approach,
which makes use of the internal logic of a topos associated with a quantum
system and comes with a natural (neo-)realist interpretation. Finally, we make
some remarks on the relation between system logic and metalogic.
