"finite matter" = the ~3.5lbs of squishy grey stuff between your ears and all the material stuff that leaves an impression upon it

"visions of the infintite" = can mean many things that approach that limit = Pi = recursion of indefinite length = time "before" matter = the number of possible synaptic connections ...

What makes them interesting "visions" - to me - is our intellect can just about get our fingers those concepts and then...indeed, I know not the bounds of this inquiry

And studying semantic memory in the brain, I have no idea where a concept like "infinity" comes from. Sure it might come from the brain? It must! Right? Right!? :)

I don't see a coherent argument here, which further suggests that it doesn't mean anything.

Our having a concept of infinity has no metaphysical significance. All our definitions are phrased negatively, by what it's not:

Infinite: That which has no limit. From the Latin 'infinitas', meaning 'unboundedness'.

Try and see if you can define infinity by what it is rather than what it isn't.

"Infinity is that which can be put in one-to-one correspondence with a subset of itself."

If you're saying that infinity is not directly realizable in what we perceive, then I agree. But this has little to do with how it's defined (or even its metaphysical significance); positive and negative definitions are for all intents and purposes equivalent.

What, exactly, do you think I'm trying to argue? To me the question is exactly whether having a concept of infinity has metaphysical significance. I think no good answer is humanly possible. Your definition is just as tautological as anything offered in the positive. That's exactly the problem.

That's the problem, it's hard to tell what you're saying.

Then I've failed... :)

Seriously, I'm not trying to proselytize nor argue. I just find atheism to be an untenable position. It's an attempt to say something while really saying nothing. Problem is, I know the same can be said of theism. But I think the latter is that much more compelling because it starts and ends with one question - "God" - that we can pose to ourselves. Where the answer leads is up to us to decide.

That infinite things can be stored in finite space isn't weird at all. Programmers do it all the time (e.g. circular lists). The trick is that you cannot store all infinite things in finite space (circular lists can only store repeating sequences). There are only a finite number of infinite things you can think of.

For example, the number 0.33333 is infinite if you write it this way. If you use another representation (1/3) then it isn't. Similarly, you can use a computer program that generates the digits of pi as a representation of pi.