Originally posted by twhitehead
... If Gods knowledge was infinite it would not imply he knows everything. Merely knowing every natural number would suffice without having to know every real number.
a good point. I was think about how, even when we move a fraction of an inch, we have covered infinite points. Most people think of infinity as something overwhelmingly large, like the fact that there are infinite natural numbers - an amount that is literally immeasurable. But even in the finite we find infinity. The number of real numbers between 1 and 10 are infinite, even though none is smaller than one or greater then 10.
So knowledge could be infinite (theoretically) and still not be comprehensive. That's really interesting.
The Jews did not use the expression infinite in the Hebrew Old Testament (or use Calculus of indefinite integration). But Psa 147:5, the Hebrew "ayin mispar" is translated infinite in the New King James. The phrase means literally "beyond number". But this does not mean something that is without limit. The Bible uses the same phase in several passages as a hyperbole to describe things that are to numerous to count - but are clearly finite like the sands of the sea (Gen 41:49), the men and camels of Israel's army like locust (Jud 6:5). So I can only determine of Scripture support the premise that God's knowledge is without limit. I can't do it with the Hebrew phrase in Psa 147:5.
Anyhow, I've read others say the infinite knowledge is a kind of contradiction. I'm not sure. It is true that no human or man-made mind is able to hold infinite facts.
I can easily write a computer program that lists the natural numbers starting at one that could go on infinitely. There would be no logical stopping point withing the programs logic. And I could write a similar program that could take a given length and list different ways it could be divided up - which could go on forever. There is potential infinity there if not actual.
But is it a contradiction to propose an infinite divine mind (assuming the divine mind is part of an omniscient and omnipotent and eternal being)? I am looking at infinity as it is defined mathematically - as boundless or without limit. I think the point of conflict is in saying God is "all knowing" and has "infinite knowledge". Maybe the potential contradiction is between "all" and "infinity".
Just thinking out loud.