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:
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) inconsistent. 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