I read a post here from a mathematics student, in which he reasoned that claiming God is infinite does not fit the other things theists claim about God. Honestly I, though being a theist, agree with him. I don't start, as people often do, with the problem of evil and from there either defend or reject the concept of God; I rewrite the model for God, -according- to what I'm pretty sure mathematics tells us about infinity.

At my current stage of thinking, the idea of an omniscient, omnipotent, omnibenevolent god that is also transcendent of all known finite entities is itself contradictory, regardless of whether such entities are considered evil. The error is in the thought that infinity only moves in one direction -- that an object can only be infinitely great or large. However, I like to use particle theory to demonstrate the falsehood of such a thought.

One can take any object visible to us, and examine its apparent infinitely-thorough texture. However, we know that with close enough examination, what becomes apparent is that the object is really a sort of cloud of smaller objects -- atoms. These atoms, we realize now, are themselves groups of particles smaller than the whole of the atom itself. Physicists speculate by a priori logic that one will find a smaller class of matter beyond those particles ("quark" is such a fun word, I love that). I think it's safe to say that there -is- a pattern of increasingly smaller classes of matter, until one realizes that smallness also moves toward infinity.

When applied to models for God, then, one can no longer claim that God is infinite and that this only means certain things, such as that God is above all moral evil (moral entities too small to equal any part of God), or that God is greater than the universe (physical entities too small to equal any part of God). If God can be said to be infinite in size, then God must be infinitely small as well as infinitely great; if God can be said to be infinite in 'holiness', or transcendence from finite moralities, then God must be infinitely close to them as well as infinitely distant from them -- and that's the kicker, there. In order to be infinitely close to something, one must -be- that something, or at least that something must partially compose oneself. Anything less and one is distant from the object. (Side-note: a finite object, then, is never infinitely close to itself, because it is constantly becoming something slightly different.)

Infinity itself, then, if defined positively as "the sum of all things" or "thing-ness (being) itself" would have to be synonymous with the whole of existence. A few theologians have accepted this definition as the proper one for God, and further nuance it into pantheism (such as Spinoza's model) or panentheism (such as Hegel's model).

Many theologians, of which I have only read the Jewish and Christian ones, would rather consider God to be limited in some ways, defining God as did Anselm the medieval theologian -- "of which one can conceive nothing greater" -- and not infinite in the sense I describe. Reasons for doing so often include the concern for God's 'holiness' (or transcendence from evil or finite entities) or their conviction that such definition of God is necessary for human free will to exist.

However, now I don't see how this is logically plausible; as far as I can tell from what I think mathematics teaches us -- unless the mathematicians have been false in their thoughts so far (and I doubt that) -- only infinity itself is 'above' the possibility or reality of a greater (or lesser) entity. (I disagree with the concept of 'possibility' as separate from reality, but I use those terms because people know what I'm talking about when I use them.) I wish I could remember enough from my calculus class, but there are two definitions of infinity, and one is infinity in a practical sense (which I think is what mathematics describes as "transfinite" ) and the other is to simply state, for lack of a better phrase, the infinity that is 'already there' and is not expressed as a stairway moving toward infinity to which there is no conceivable last step, though never itself reaching infinity (because there can always be a higher step). For this reason, in order to say that God is "of that which no greater thing can be conceived," God must be -- again -- either 1) a name for everything or thing-ness/being itself (pantheism) or 2) composed of all things (panentheism).

Of course, dang near all Christians who have heard or read my thoughts about the matter have protested this definition, because logically it not only points to God as the creator of evil things, but eliminates the distinction between creator and creation; God's 'creation' is the developing self of God, though as the infinite whole God is 'unchanging'. Therefore, God is partially composed of all that which humans consider evil. As far as I can see this view of God/existence makes a human conception of morality as relative (some actions are simply better than others; some things are greater than others).

The objection from Christians that conversed with me is the same as some atheists' objection to the existence of God; these objections seem to come from the concern to keep their ideals of morality as distant or transcendent from entities they consider unacceptable, or those things from which they desire to keep distant. If God is 'good' or the greatest thing conceivable, then God as represented by their ideal must keep as far distant from things conceived of as unacceptable as can be conceived. Concerning this, the atheist rejects the usual creator-god model of the monotheists and argues that probably only an extension of the heavens exist beyond what is observable; the theist argues that God created the possibility but not the reality of evil (which finite self-conscious beings created through their actions) or that God created evil to somehow point to the superior goodness of God.

My model (Hegel's model, really) acknowledges both, however -- that God cannot be good and fit the traditional theist model for God, which the atheist also affirms (and concludes that God cannot exist) -- and that God creates evil to point to the goodness of God, because God's goodness is a holistic goodness (morality as a whole by necessity includes those things we would consider insufficient morality for human living).

Now any naturalist-pantheist ("sexed-up atheists" as Richard Dawkins calls them) could look at this and say, "You can stop calling infinity by the name of God, then, if you want, because you no longer believe that the universe was created by a great person." I don't think it's that easy, however. According to Spinoza, God-or-Nature -- rather, God-or-existence, as he might have called God if he knew people would interpret his use of "nature" as only the planets and stars -- is the "being of infinitely many attributes" (slightly revising Wikipedia's term for Spinoza's model for God). Why would it be assumed that in the unity of those infinitely many attributes, there would not be infinite self-consciousness, morality (however it should now be properly understood), and energy/power -- all the things attributed to God in most of the traditional monotheist models? Perhaps the famous paradox of Epicurus should not lead to rejection of God, but to a reworking of how one would understand God.

I'm trying to base all this on a correct understanding of infinity, along with the basic structure of Hegel's panentheistic "Absolute." I am curious as to whether I have understood infinity accurately, at least as far as modern mathematics knows.

Otherwise, please discuss with me what I've said, what it means to you -- whether you agree with it, what you may wonder about any of its implications or logical conclusions that should derive from it.