@kamikazegymnast0 - Not a problem.
"Therefore the equation (infinity-infinity=infinity) still holds!"
Yes, but it's a different infinity as I explained, so the equation is misleading (too simplistic). It's really "an infinity - a particular infinity may still = infinity."
"It creates the paradox "Can God make a rock so big he can't move it?"...God is able to see infinity, so doesn't that make it less than infinity?"
If God can see a bear, does that make it not a bear? Why would God's view affect the reality of the situation? The "paradox" is created by presuming an actual infinity cannot exist. If you allow for one to exist, then there is no paradox. If you believe in immortality and in God's ability to know everything, then you are stuck with an actual infinity. There's no getting around that, as I said.
"If he can see the end, then there should be one more marble at the end...and one more after that...etc."
Again, this is the same error already addressed of applying the rules of finite numbers to an infinite set. Obviously if we are dealing with immortality, there is by definition no "end." Do you expect eternal life to stop? Makes no sense. If you think it continues and if you think God knows all that will be on it, it is an actual infinity. I don't see how you can mystery your way out of that. Good luck though, I guess. But I get to claim anything you don't understand about atheism is just as mysterious. hehe ;)
@WAR_ON_ERROR - I don't believe I will "breathe air" in heaven because we honestly don't know what heaven will be like. One thing is for certain -- it isn't a physical infinity. It's something completely different. We've been given word-pictures in the Bible, but since the finite human mind cannot comprehend infinity, it's not even a glimpse of what eternity holds.
Nonetheless, we aren't truly "infinite" as it would be in spiritual terms because we had a beginning. We will live forever if we are in Christ, but that doesn't make us infinite. That just makes life un-ending. The only infinite is God.
In your example using red and blue marbles, the two infinities existed before they were divided. There was an infinite number of red and an infinite number of blue, and after they were divided, there was still an infinite number of red and an infinite number of blue. That delineation was already there. All that changed was who possessed the different infinities. However, in Craig's example, a separate infinity didn't exist before it was subtracted from the first.
@gabrielpeter - The air breathing is a technicality. Merely an example. You will think thoughts in heaven right? Surely, surely, surely there is at least one definitive action you can reason you will do over and over again for eternity even if you cannot be absolutely sure you know which it is.
And if God doesn't know what will happen, then he's not quite God is he? Why couldn't he know? Won't it happen? Won't it ALL happen? Which point in time of your immortality would he be unaware of? Every single point in eternal time is known already by God or he doesn't know everything and that's not your definition of God.
"One thing is for certain -- it isn't a physical infinity."
I'm sure you believe in a physical resurrection of Jesus, right? Even though he had a suped up body, he could still be definitively touched, right? Perhaps the story of doubting Thomas is a myth? If not, that's not spiritual enough to wiggle out of the conclusive demonstration that from your own perspective you are logically forced to accept an actual infinity, in my opinion.
"Nonetheless, we aren't truly "infinite" as it would be in spiritual terms because we had a beginning. We will live forever if we are in Christ, but that doesn't make us infinite. That just makes life un-ending."
Rays are just as infinite as lines in geometry. A yellow brick road that starts and goes off in one direction forever is infinite in that direction.
"In your example using red and blue marbles, the two infinities existed before they were divided. There was an infinite number of red and an infinite number of blue, and after they were divided, there was still an infinite number of red and an infinite number of blue. That delineation was already there. All that changed was who possessed the different infinities. However, in Craig's example, a separate infinity didn't exist before it was subtracted from the first."
The odd marbles in the bunch of odd and even marbles could have been painted red by an infinite fleet of gnomes with paint brushes and the even ones could have been painted blue. So that odd infinity definitely already existed in the example either way. Does painting them change their number? It doesn't matter whether we tagged things or not. The mental assignment of even and odd was sufficient and the coloring was just my device to keep your mind on target and point out there's no contradiction.
It was not categorically different since in the original WLC conception, we could still say that we could not give someone else the exact same odd marbles that were previously given out since they are no longer in our possession. We gave them away! We have a whole new fleet of odd marbles in our odd and even bunch, but those were all previously the actual even marbles.
We could in fact do the same move with the color coated marbles by merely having our gnomes paint every other one of our new batch of only red marbles blue. But they wouldn't be the same blue ones we gave out previously. Hence there is no contradiction at the marble level as I've been saying and there's no way to change that.
I think I've sufficiently made my case from my perspective on the main issue and the conversation requires going in several different directions on contentious issues. I'm going to let this be my closing statement and we can move on to talk about other things some other time. I'll be sure and post any follow up of yours on my repost of these comments (link) and leave it at that. Fair deal?
@WAR_ON_ERROR - You state, "We have a whole new fleet of odd marbles in our odd and even bunch, but those were all previously the actual even marbles." Yes, I'd said that, too. I guess your example really isn't different than Craig's then. Painting the marbles different colors or numbering odds and evens (or even adding gnomes), we still get the same result.
When you first redefined the equation, you said, "infinity - a particular infinity may = infinity." The slight-of-hand here is that we're not subtracting just any random infinity. We are subtracting infinity from itself. In this particular case, infinity - infinity = infinity. But this is all still, what? Conceptual.
You mentioned that because I said infinity is conceptual, I've therefore proven that an infinite God is only a concept -- which was your first argument when I look back on it. In hindsight, if I'd said, "You're applying the physical to the nonphysical," which is really all I needed to say, would we be here now? ;) God created time and space. He transcends them both. Once He's created the universe, He can enter time, which you touched on in part of your argument, but that's a different topic altogether.
In summary, everything I need to say is contained within both of these posts, here and here. I started typing something else and realized I'd just be rehashing the same thing. I encourage you to read them again. Don't stop at some point you disagree with something and formulate a new argument for yourself. It's been thoroughly explained -- I promise. I appreciate the discussion. You never cease to challenge. Always a pleasure.
I'm glad I got around to addressing this issue since it is an important distinction that modern theists try to make. It clearly doesn't work without seriously backfiring unless you bury it in implausible ad hoc mysteries. If you do that, to be fair, it seems atheism doesn't really need to address the theistic complaints about apparent philosophical contradictions after all. If we can all agree that we don't really know how metaphysics works even when it really, really, really seems like there's a definitive contradiction, then why are we making arguments from that non-knowledge against anything? "Atheism doesn't make any sense because...
[insert supposed philosophical problem here]"
is no longer valid coming from theistic philosophers. If nothing else, I wish that's the lesson Christian thinkers would take away with them even if they don't get any of my points on understanding the basic nature of infinity.
I'm an agnostic humanist first and an atheist philosopher second, so having a worldview without a greater metaphysical conception (if I turn out to be wrong about something well outside the realm of human expertise) works perfectly well for me and my core beliefs about what is important in life. I'm not so sure the Christian can say the same. Feel free to disagree though!