Pandendeism is a fairly recently coined term to describe a sort of ``open'' pandeism similar to what I more specifically mused upon at the end of the previous section. According to the panendeist website, any deist who believes that the universe is a part (but not the whole) of God can be considered a panendeist. More explicitly, it asserts that ``panendeists believe in a god that is present in everything but extends beyond the universe... In other words, god is the universe but is also greater than the universe.''

I have to confess, these words on a site supposedly devoted to rational religion give me a bit of a headache. Let's eliminate the use of the term ``god'' and ``universe'' per se, and reduce these statements to pure set theory.

Suppose is ``the set of all things that exist''. Suppose some set
exists. Then it is *absolutely certain* that ( is a strict subset of ) or (where
could conceivably be all of ).

Fine, so now assert . One *cannot* at that point, also
assert (set is a *strict subset* of ), so that
is a *larger* set than the set that contains it. Or rather, one
can assert it all you want but it is obviously mathematically and
logically impossible no matter *what* particular existential set
is asserted to be.

Note that honestly we don't even need to assert that is the set of
everything that *exists*. Any set specifier could be used in place
of existence and the observation above would still hold - no set can at
one time be a strict subset, equivalent to, and a strict superset of any
other set, any more than a number can be at once strictly greater than,
strictly less then, and equal to any number. To assert such things
destroy all meaning; it is pure nonsense.

This is *especially* true in the case of the *Universe*, because
the set of all things *that exist* has special properties. Again,
consider the more obvious case of numbers. The set of *all natural
numbers* is reasonably well defined, with or without an axiom of
infinity. If I assert a set that is a *superset* of the natural
numbers, such as the real numbers, I am basically saying that there
exist real numbers that are not natural numbers, which is perfectly
true.

Now consider the problem when we try the same thing with the set of all
things that exist. If I assert a *strict superset* of all things
that exist, I am stating that in this set there are entities that *don't exist*. To assert that God is ``greater than'' the Universe is
thus equivalent to stating that God is at least partly *imaginary*,
unreal, nonexistent, because the Universe is *already* everything
that exists.

I find it vaguely irritating when people use words in this sort of way.
I imagine that the problem is that they are being sloppy in their usage,
and perhaps they mean to say *Cosmos* where they instead say *Universe*, where of course the Cosmos might well be a strict subset of
the Universe, although we have no sound empirical reason to think that
it is at this point. Or, perhaps they mean to use the term ``greater
than'' in some subjective and arbitrary way - as a way of saying ``has
a more complex structure than one might naively expect'' or the like.

The site does attempt to explain it further with vaguely poetic
metaphors, such as the idea that the whole is more than the sum of its
parts, but this of course breaks down given that the Universe *is*
the whole; the question is only whether God is *also* the whole or
just one of its parts as it is impossible that the Universe could be
only a part of God. It attempts to suggest that we are *more* than
just our cells, and in a similar (also very sloppy) way God might be
*more* than just the Universe. But this is doubly treacherous - we
are not more than our cells, the ``we'' of our self-awareness is far
*less*. High level awareness is *always* enormously
compressive; our thoughts and feelings, however sublime, are a tiny,
tiny bit of information compared to the vast sea of information
self-encoded within our cells and constantly updated by dynamical
interactions with the entire Universe. Also, this more or less assumes
that there is something inherently mystical or spiritual about
complexity or awareness, that it is ``greater than'' the microscopic
interactions that give rise to it. More important *to us*, I agree
- the only place where ``importance'' can exist - but ordinal
arguments of ``greatness'' smack of Descartes failed arguments for a
cause (God) that is ``greater than'' the effect (Descartes). To
ourselves we are enormously important - to the Universe, from the point
of view of physics, we are simply particularly efficient generators of
entropy.

Let me attempt to replace the poetry and set-theoretic and
information-theoretic contradictions with a more concrete and consistent
definition of panendeism. In physics and mathematics, there is a
profound difference between open sets and closed sets, between finite
sets and infinite sets. Let us suppose that the Universe does, in fact,
consist of *only the one Cosmos we seem to live in* - so that there
*are* no more actual Cosmi, there are no hidden dimensions or hidden
variables, so that the actual spacetime we inhabit plus the mass-energy
in it are pretty much ``it'' as far as existence goes. Let us assume
further that the Universe isn't much bigger than what we can see - that
there really is a boundary to it or that it closes topologically in some
way that lacks a boundary (such as a toroidal boundary condition). In
this case spacetime is *closed* and *finite*. The information
content of the Universe, however large, is not unbounded (especially if
spacetime is granular on some microscopic scale, e.g. the planck scale)
and the information *density* of the Universe is actually remarkably
low.

In this case it is difficult to sensibly postulate God at all, even a
God that is the Universe. To the best of our ability to see, all the
way out to the limits of our ability to see, the Universe appears to be
lifeless and mechanical, with a fair bit of ``disorder'' but in a *well defined state* that clearly has zero *global* entropy. If the
stars or the rocks are parts of God's Brain, there is no obvious way
they could be thinking of much of anything at all besides *what they
are* and *what they are doing*, with all of reality the collective
result of their microscopic collective motion. The motion might *appear* to be random or reasoned and ordered, in much the same way that
Monte Carlo computations *appear* to sample interaction spaces
randomly that exhibit phase transitions and other highly organized
behavior, but in reality both reality and the random number generators
used in the computations aren't random at all. The kind of ``free
will'' exhibited by an e.g. Ising model computation leading to an
``organized choice'' of a predominently spin up or spin down system is
an illusion, an artifact of the *appearance* of non-deterministic
outcomes, and our own free will or God's free will is similarly an
illusion, something that disappears if the Universe is a closed finite
state system with zero entropy.

If the Universe is *open and infinite*, on the other hand, the game
is, as they say, afoot. Step right up and lay your bets. Nobody will
be able to say what the outcome is, because an *infinite* amount of
information is required to fully specify the state of an infinite
system, and no *part* of that system can have a complete knowledge
of the state information of the *whole*. Note that *now* we're
using set theory and information theory in the correct, ordinal way,
because for an open infinite system, *the whole is not specifiable*.
We can invent *symbols* such as to stand for the *concept*, and can even wrap our heads around the concept and learn to
use it in constructive ways, but one can no more grasp *the whole
real number line* than one can fly to the moon on the back of a pig with
wings.

If the Universe contains an *infinite number of Cosmi*, each with an
*infinite number of dimensions* and with at least some of those
dimensions *infinitely unbounded* and with nonrepeating behavior
evidence on *all length and time scales in all the dimensions of all
of the Cosmi*, well, we're starting to talk about something that is very
complex indeed. Infinitely complex. I for one don't feel comfortable
*rejecting* the notion that this infinitely infinite real Universe
might be able to function as its *own source of entropy* and yet be
everywhere locally perfectly defined and in a unique state. It could
possess awareness on an infinite set of utterly incommensurate scales.

Would the Universe in this case arguably be God? Could the Universe not
have enough ``processing power'', as it were, in the infinite exterior
of any finite domain to have *asymptotically* complete knowledge of
that domain in a high level symbolic form at the expense of its *self* awareness of the open exterior whereup that information is encoded
and dynamically flows as ``thoughts''? Note that this in no way asserts
that God is *greater* than the Universe, only that a Universe that
is *sufficiently* large and complex might have properties that are
more or less equivalent to those usually attributed to God *including at least a form of high-level self-awareness*.

To illustrate the point with a hopefully apropos metaphor, consider Hilbert's Grand Hotel, which has an infinite number of rooms. The way the metaphor usually is described is that although it is strictly forbidden to bring cigars into the hotel, every morning a fresh new cigar is delivered to your room. Where did it come from? Well, when the hotel was built, there was a cigar in every room left there compliments of the builder. Every day, after you smoke the one in your room, the person with the next highest room number than yours hands his cigar down to you, and gets a cigar from the person with the next highest number than his. Every day this goes on, and even if you stay there an infinite number of nights, smoking a cigar a day, there is no reason to think that you will exhaust the supply.

Now imagine that the owner of this hotel still wasn't happy. Even
though he can accommodate an infinite number of guests arriving every
day for an infinite number of days and *still* offer them all a
tasty cigar every day without ever having to have more cigars delivered,
he wants more. He adds on to every room an infinite number of doors to
an infinite number of corridors with an infinite number of rooms each on
them. The rooms aren't large enough - he wants his guests to have a
truly sybaritic experience - so he makes them all infinitely large and
fills them with an infinite amount of furniture so that they won't
appear too sparse. He wants to make the guest's experience Universal,
so that *everybody* is a guest in his hotel, so he does away with
the outside of the hotel altogether. Hotel guests may think that they
are leaving, but in a twilight zone-y sort of way they are merely
leaving one *room* that happens to be furnished so that it looks
like a hotel in favor of another room that happens to be tricked out to
look like an entire external Cosmos. Finally, he *still* isn't
satisfied, so he plays the cleverest trick of all. He puts his entire
Hotel into *every room* of the Hotel, which is possible because
(after all) they're infinitely big.

There is always room for more in Hilbert's Universal Panendeist Hotel,
where the rooms themselves are the latest in artificial intelligence and
anticipate your every need, reconforming themselves at will even as they
*simulate* your presence because *you* are just a part of the
furniture, a part of the contents of the inside of the Hotel itself,
every bit as much as you are a guest that came to spend the night. Or
is it the rooms that are the guests and you that are the artificial
intelligence? Nothing is as it seems, because underlying everything
there are layers within layers, overlaying everything are layers on top
of layers, in an infinite sequence of layers in both directions both
ascending and descending.

If you're going to assert a panendeist God, then, it appears to me that:

- It must be a pandeist God, identical to the Universe, but
- It is a
*very complex*- open, unbounded, infinite Hilbert Hotel of a*Universe*, one large enough to contain as many cigars as you ever might care to smoke.

This is all very speculative, of course, and not *much* better than
calling the whole greater than the sum of its parts, but at least we can
avoid that much. I would conclude that panendeism of *this* sort is
nothing but an ``open and complex'' pandeism and hence is completely
compatible with the theorem proven above, and indeed is much *more*
appealing, more congruent to the intuitive idea of God than ``closed''
pandeism, for anyone include to assert the existence of God in the first
place. The model is hardly provable, but I don't think it is actively
self-contradictory and it leaves *open* the possibility of a
``personal'' God that is much greater than the *visible* Cosmos.

Truthfully, though, if the theorem proven in this work proves anything,
it proves that one really has to do real mathematics in order to do
rational metaphysics. One has to precisely define one's terms, and
avoid making poetic and metaphorical statements in *English* unless
they are specific illustrations of points that you actually obtain
rigorously. To to be honest, I cannot prove that either pandeism itself
or panendeism are globally (conditionally) consistent, only that any
other model of God is (conditionally) *in*consistent. These two
models (and the various other theisms or non-theisms that are ``close''
to these two, possibly with some heretical tweaking) are at least
``possible'' models of Deity