> > It would seem that even if there were no physical universe -- no matter, energy, or physical laws, the higher realm of potentiality would remain. There would still be "possible universes" that could be created (by God, if God exists). Even higher than that is the realm of absolute logical truth. No matter what the universe is like, and higher up, no matter what a divine creator might wish, nothing can change absolutes such as the Pythagorean theorem, the infinite size of the set of primes, and even subtler things like Fermat's Last Theorem. Non-mathematical examples could probably be thought up as well, I suppose. We might suppose that the universe could lack the proper framework to make it likely that those truths would ever be discovered, or even, in the lack of a physical universe, that any entity *could* contemplate them, but they'd be truths nonetheless.
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> I think limiting God's abilities to a set of mathematical rules that He created is really putting Him in a box. Whether you believe in God or not, the very concept of an omnipotent being implies the ability to do anything, regardless of physical or mathematical laws.

I don't think most people who believe in God truly think he is omnipotent in a pure sense. They would say he has the power to do anything which is logically possible (he can't make himself non-existent, he can't make a rock which is heavier than itself, etc., etc.) This is not really any significant sort of limitation. Perhaps you could even define omnipotence this way (being able to perform a maximal set of actions). I happen to believe that among these logical limitations are the sort of things bound by mathematical/logical truths that I mentioned in my last post.

>As we discussed in a previous thread, God is outside of time and can change the past, present, or future. In the same way, I'm sure He could design a triangle that doesn't match up with the Pythagorean Theorum.

Same sort of logical limitation. Of course it's possible that the Pythagorean Theorem *isn't* true, but that for some reason or by some incredible chance every person who has thought about the problem has made some fundamental flaw. Then God could make said non-conforming triangle and amaze us all, I guess. But I doubt this would happen. It would seem to be against God's nature to deceive us that way.

>So what if it's beyond the grasp of *our* reason, *our* way of perceiving the truths of reality? This is what makes us mortal, and really pretty stupid in comparison to an ultimate deity.
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The point is not that there might be truths which are too complex or abstract for humans to perceive, but that there *are* truths which are *simple* enough for us to perceive. Again, sure, God might have made us critically flawed to make the same stupid mistake over and over and over throughout all of history, but why?


> Scientists and mathematicians use numbers and formulas to describe the way things work around them. They certainly don't MAKE the physical laws, but only try to predict how objects operating within these laws will behave. If, in an experiment, something acts totally different from the scientists' predictions, the scientists realize that maybe they didn't understand that law as well as they thought they did. Then they go back and tweak their formulas to reflect the new information they've discovered. It's obvious that our understanding of physical laws is only temporal, a compilation of observations amended over time. Usually our guesses are pretty accurate. But since when did we decide that these rules are "absolute logical truth," even higher than the power of a divine God?
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I have no idea where you got the idea that I said physical laws were included with absolute logical truth. In fact, I put them on opposite extremes of the existential spectrum, with God in the middle.

> Granted, you said you weren't talking about physical laws, but the "higher realm" of potentiality. Basic mathematical stuff.

The way I phrased it, the realm of potentiality would describe possible sets of physical laws and physical universes which God could implement. I put this on a level below the absolute to signify that logical requirements place strictures on potential universes, just as the realm of potential universes places obvious strictures on the nature of the *actual* universe. The mathematical stuff I would throw in to the absolute realm (above the realm of potentiality). These are just terms I came up with for my own use, by the way. They're in no way standard definitions.

>Maybe even things as simple as the basic number system. Whether you say "one two three," "uno dos tres," or anything else, numbers have a specific meaning for us... they are abstract representatives of concrete objects: whatever we might be counting at the time. A number is not a "real" thing like a frisbee or a glass of lemonade. It's a concept which doesn't do much outside of the realm of math.

Yes, they are mere concepts that we come up with -- unless you follow the school of Platonic realism in which such things were thought to really "exist" on a plane of existence above our own.

There's a subtle distinction though. I don't claim that the numbers themselves are absolute. I claim that the truth of theorems one can derive from axiomatizing these basic concepts, "common-sense" logical rules (such as the law of transitivity: if (A implies B) and (B implies C), then (A implies C)), and other necessary set-theoretic axioms, *are* absolute. Yes, yes, assuming of course that our analysis isn't flawed and destined to go wrong every single time.

>When you consider the true nature of numbers, it's a stretch to say that God is bound by them. I'd say that He created them just like He created gravity, light, and cytoplasm.

A thought: on one hand you're saying that numbers don't really exist as more than concepts in our mind. And perhaps God created those concepts in our mind just, as you say, he created physical laws and structures such as gravity, light, and cytoplasm. Yes, maybe he created the concepts of the number 0 and the number 1, and by placing the ideas in our heads, gave us the capability of creating those concepts for ourselves from our own viewpoints. And perhaps he created in our minds many other related concepts, such as all other integers, addition, multiplication, and taking integral powers of integers. From all that, we can derive for example that 1729 is the smallest integer which can be written as the sum of two cubes in two different ways (there's a famous story about Ramanujan coming up with this after a single moment's though). Did God create this numerical truth? Could he have created the idea that "583 is the smallest integer that can be written as the sum of two cubes in two different ways"? No, he couldn't! Even if you ascribe the creation of our number system to God (which I don't -- I put the philosophical existence of it in the absolute realm), you *still* must conclude that God is in some sense "bound" by numbers once you put all the axioms into play.


>And then all mathematics (prime numbers and the theorums you mentioned) build on this basic concept of the number system, and thereby also cannot limit the actions of God. To say these things are absolutes is only proof of the limitations of the human mind to perceive a world without them.
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In a way I addressed this in my previous post (second-to-last paragraph). We're certainly limited in the kind of concepts we can comprehend, and one could very well imagine a similar universe in which humans couldn't grasp the concept of number. But the fact is that the concept of number would *still* be a potential concept. It would still be the case that if someone *were* to come up with the concept of number and the same set of axioms that we have, that the same theorems would turn out to be true.

There are quite possibly infinitely many types of logically structured systems which could be used instead of the basic framework we use in our mathematics. Possibly in this universe (and even possibly in all potential universes) there would be no hope of any being grappling with them because of their complexity. I would say that the truths derivable from these systems *still* exist in the realm of absolutes.


> I see no reason why God couldn't create another universe, separate from ours, governed by a completely different set of rules. Different at a fundamental level: the dimensions of height, width, depth, and time wouldn't exist, but instead there would be radical alternatives that we can't even begin to comprehend. Simply put, God could start from scratch and create a new system, with new physical and mathematical laws (provided physics and math even existed in this place), and nothing that we know or percieve to be absolute would apply there. And most likely, the citizens of this place would also try to define these rules within some logical context -- of course they wouldn't have numbers -- and these beings would be as unable to comprehend the structure of OUR universe as *we* are to understand THEIRS.
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Okay, you're sort of going down the same lines as I was just above. I'm totally with you on the part about physical laws. God could make a universe with a different number of dimensions, or something even stranger with no concept of dimension at all. To reiterate the distinction I made earlier, it's not the number system we use that's absolute, but the truths derivable from the number system and all other logical axioms we've come up with. So yes, the inhabitants of an alternate universe might never think of our number system at all. And yes, the inhabitants, if they had mathematical laws, very well MIGHT have different ones than the ones we have. That *doesn't* mean that our mathematical laws are logically flawed in their universe or that their mathematical laws are logically flawed in ours. The differences would arise from the basic concepts (our number system in our case, or the equivalent thing they'd use in their case) and in the logical axioms. If, somehow, one of use could visit this other universe, communicate the idea of a number system and the other axioms we make up to derive theorems, then the inhabitants of the other universe would agree with us on the truth therein derived.

> In summary (deep breath), God makes the rules and can't be limited by them. What's to stop Him from breaking the rules any more than a soccer player can break the rules of that game? It surprises people and seems awfully out of place, but it certainly isn't IMPOSSIBLE by any means. Especially for the One who wrote the book. Just because our puny minds can't perceive any possible alternatives to the rules and order of this universe doesn't mean that they couldn't be created by God and/or function as well as the reality that we all know and love.
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> -useless"DUDE, that was HEAVY"ness

I'll just check at this point that you mean that God could very well break/change the rules of the game in that any *physical* law we go by could instantaneously be thrown out the window, since you state it as "rules and order". And of course I agree this is possible -- up to the previously stated logical strictures. God could instantaneously reconfigure the positions of all pieces of matter/energy in the universe...beyond that, change any physical law such as the inverse square law of gravity (assuming, of course, that it's true to begin with!)...beyond that, change the very nature of matter and energy itself...beyond *that*, change the very notions of time and space themselves. But still, the way I see it, *all* of that is bound to the realm of potentiality which is subject to the restrictions of absolute logic. I agree with all that you say in your summary paragraph, but you may be implicitly including logic and truth as components/facets of the physical universe. I'm not, so maybe we just differ in that regard.