  I would claim that we do not have a suitably general definition of what a
topological phase is, or more importantly, any robust understanding of how to
enter one even in the world of mathematical models. The latter is, of course,
the more important issue and the main subject of this note. But a good
definition can sharpen our thinking and a poor definition can misdirect us. I
will not attempt a final answer here but merely comment on the strengths and
weaknesses of possible definitions and argue for some flexibility. In
particular, I describe a rather simple class of ``quantum gravity'' models
which are neither lattice nor field theoretic but appear to contain strong
candidates for topological phases.
