I borrowed a copy of The Triumph of the Straight Dope, and I really love it, so I thought I would check out the message board.
Okay, on to my idea.
If the Bible says (or at least implies) that God has infinite knowledge, does it not imply that the universe is infinite?
Knowledge has to be of something, of course. So to have knowledge, something must exist. For anything that exists, be it a concept, theory or object, there is a finite number of things that can be known about it.
If God has infinite knowledge, must there be an infinite number of things for him to have knowledge of, and thus be an infinite material universe. If there were a finite universe, God would have a finite number of things to know.
Could there be non-material things that God draws infinite knowledge? Perhaps. God could draw knowledge from himself, knowing of his own infinite ability. Perhaps he has knowledge of the infinite complexity of the Mandelbrott Set, or some other complex fractal. There might be a few more things God might be able to have infinite knowledge of. However, I certainly hold to my idea that belief in any kind of infinite knowledge also requires a belief in another, seperate infinity.
Well, yes, except that unless I’m mistaken, the Bible doesn’t actually describe any of God’s attributes as infinite, but rather ultimate, which isn’t quite the same thing.
Only if God exists within the universe, since the universe would have to be infinite in order to contain an construct that holds infinite information (i.e. God).
If God exisst outside the universe, then He could have infinite knowledge even if the universe incredibly small and completely empty.
“I know that the universe is empty.”
“I know that I know that the universe is empty.”
“I know that I know that I know that the universe is empty.”
“[(I know that) * n] that the universe is empty.”
There you go. An infinite amount if knowledge about a finite universe.
If having knowledge of your own knowledge, knowledge of -that- knowledge, etc is infinite knowledge, then anything capable of having knowledge of it’s own knowledge has infinite knowledge.
The “thought universe”, or “mindscape”, is infinite. (Joe Random conveys it perfectly.) Check out Infinity And The Mind by Rudy Rucker if you are interested in infinity as a concept.
I almost broke my brain reading that one. Rudy posits that, in the hierarchy of the infinities, God is the “Ultimate Infinity.”
I haven’t thought of that book in a decade. Just thinking back on it now makes my brain ache.
Think of this one as well.
If you put two dots on a piece of paper for example.
How many different positions exist allong the imaginary line between those two dots?
Though we know there are atoms and a finite number of them, there may be an infinite number of different differntiable points between those two dots. So it would take an infinite amount of knowledge to know the location of every one of those points.
This shows a problem of the concept infinity, an infinite knowledge might only know about the points between two dots on a piece of paper.
God having ultimate knowledge, or all knowledge, or omniscience are all stronger concepts than infinite knowledge.
Mathematics, at least, is infinite… We can keep on identifying bigger and bigger prime numbers…forever…
And so can God…
(I once had a notion that super-advanced, near-godlike-people – maybe like the “Q” in Star Trek – would trade mathematical theorems as a form of currency… It’s the only thing that can never run out…)
God could have infinite knowledge and the universe can be finite. God’s knowledge includes things outside the finite universe. However, even God’s knowledge of a finite universe is infinite, since He is aware of things to the infinitesimal level.
If the universe is finite, then mathematics won’t actually be infinite. We’ll eventually run out of ways to represent new numbers and perform calculations.
If there isn’t enough stuff in the universe to continue mathematics, then can we really say there’s any more to it than that?
TVAA, Your statement that “If the universe is finite, then mathematics won’t actually be infinite.” Was in (I assume) response to the point that Dogface made in his post “God can have infinite knowledge of a finite universe,”
If your position is accurate then, is it proper to infer that if the universe is finite, there will be a “largest” possible number, a “hottest “possible temperature, a “furthest” possible distance, etc, and if it is infinite, none of these will exist?
Dogface, If God has infinite, or ultimate knowledge, of everything (all things), why did he react to Adam and Eve’s disobedience the way he did? If he knew they would fail, why did he expect more?
Isn’t a characteristic of a living God the ability to learn, that is, to grow in knowledge of all things?
It might be the case that there is still one thing/state/extreme/etc. that is greater than all others in an infinite universe. Or, it might be the case that there’s always something greater/larger/whatever.
Transinfinite mathematics always confused me, but I’ve been assured by people who (presumably) understand it that in an infinitely large set, there might be no such “extreme” things.
I am not convinced that mathematics cannot be minfinite even within a finite universe. The Mathematics is it self infinite pretty much by definition that infinity is a mathematical concept. Our limitation is that we can only ever explore or process finite amounts of mathematics. That is not saying that we cannot explore infinity itself, it is that we can only explore a finite amount of any concept.
ie we can know that pi is infinite string of digits,
but we can never calculate it to more digits than their are corresponding quantum states in the entire universe (think that value was about 10[sup]10[sup]40[/sup][/sup] binary digits in length remembering from the thread on possible repeating quantum states in an infinite universe)
So we can know something is infinite, and that the math is infinite, but we can only express a finite amount of any infinity.