My particular approach is to base the universe on the idea that it is a
physical isomorphism of but one of a "set" of incomplete, finite,
consistent FAS [ifc-FAS]. Members of this "set" occasionally [no "time"
connotations] "freeze out" spontaneously from a growing, seething, foamy
fractal of bifurcations [say zeros and ones] I call a superverse. The
superverse itself spontaneously arose from no absolute information because
"no absolute information" is itself incomplete. It can not answer the
question of its own stability.
The simplest form of such a resulting initiating incomplete fc-FAS is one
with a single axiom containing relative information only and a set of rules
for operating on the axiom.
The incompleteness of this FAS makes it indeterminant - it continues to
grow by an ongoing Godelian type of "freezing out" process from the
superverse. I identify these logic growth events as isomorphic [in our
universe] to quantum perturbations. Aside from its incompleteness
resolution process, the only "dynamic" supportable by such an ifc-FAS is a
recursively enumerated cascade "set" of theorems that starts with the
The simplest SAS capable physical isomorphism seems to be a 3 space grid of
isolated points that can not migrate, but can "relocate" relative to
neighbor points within their region of the grid in a quantified way. Each
configuration is isomorphic to a theorem of the ifc-FAS.
While the points are "identical" they are distinguishable by their relative
position thus they seem to form a "set".
A "quantum mechanics" and a "relativity" seem easy to derive on such a base.
If I understand Russell correctly this may be a Hilbert space in the sense
that the superverse may be a "continuous" set of bifurcations, but I am not
a mathematician. However, each ifc-FAS describes a finite discrete subset
of this "space".
So it seems to me that the universe is a "set" on multiple scales.
If anyone is interested my model such as it currently stands is at: