Omniscience as actual infinity

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Omniscience as actual infinity

Postby sepia » Thu Jan 10, 2013 10:06 pm

I thought, I've written this argument already here, but then I noticed, that I have confused 2 communities. This argument is an idea I had to show, that William Lane Craig's God is incoherend with his point on actual infinities.

Craig defines god as all knowing. And he claims that an actual infinity can't exist.

Now in maths there are some infinities. Craig would say, that numbers don't exist and therefor infinite numbers aren't an actual infinity. But the knowledge of all those numbers would be. There are for example infinite prime numbers. Knowing all of them would be an actual infinity.

In the other forum, I've got one objection: God could know a way to calculate all prime numbers.
But this would need an infinite long calculation. In this case the actual infinity of this calculation must be possible, or it can't be used to calculate any prime number.

Therefor Omniscience is an actual infinity.
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Re: Omniscience as actual infinity

Postby Nitz Walsh » Mon Jan 14, 2013 1:28 am

Yeah, William Lane Craig`s God can`t exist because it contradicts itself.
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Re: Omniscience as actual infinity

Postby TomSmith » Mon Jan 14, 2013 9:38 am

You ever notice the double standard employed by W.L.C?
On one hand he asserts an actual infinity cannot exist and then promptly goes on to claim that god is infinite...special-plead-much?
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Re: Omniscience as actual infinity

Postby sepia » Mon Jan 14, 2013 3:41 pm

Seems so, but I find it hard to prove it. One good strategy would paraphrase one of Craig's arguments against an actual infinity by using God.

I can think about one example but I'm unsure if it is correct:

If God knows X then his knowledge of X is a fact. Therefor there is one fact more to know. God has to know it because he must be omniscient.

But If God knows to know X, then his knowledge about his knowledge is a fact too. Again he has to know this as well and so on. Every knowledge is a fact and should be known by an all knowing being. So every knowledge increases the number of facts by 1. And this leads to the same conclusion Craig draws with his infinite library or infinite cycling planets: The 2 infinite numbers shouldn't be the same but are the same and therefor it is paradox.
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Re: Omniscience as actual infinity

Postby TomSmith » Tue Jan 15, 2013 7:22 am

sepia wrote:Seems so, but I find it hard to prove it.

Another possible problem is the problem of experiential knowledge. That is knowledge which can only be acquired through certain experiences.
As an example, knowledge of what it is like to 'sin', or if you prefer, knowledge of what it is like to do or say an evil thing.

This is problematic for the theist who asserts that god is all loving and all good because it entails that the god cannot have the knowledge of what it is like to do or say an evil thing, this renders the god not omniscient.

Here's an interesting read: http://www.patheos.com/forums/unreasona ... php?id=134
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Re: Omniscience as actual infinity

Postby sepia » Tue Jan 15, 2013 9:36 pm

That is more a question of how god knows something. Yes in this case I find it strange too. Let's take the definition of knowledge as justified belief (you can replace other definitions if you wish): God beliefs something and this fits perfectly to the reality. Why? It is possible too, that a supernatural creator has wrong beliefs too.
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