Cantor himself was a very religious man, and believed that after his endless hierarchy of infinities, the ultimate infinity was God. He called it the Absolute infinite, and denoted it Ω. Cantor's mathematics is universally accepted now, while his theological ideas are forgotten by everyone except historians — fishfry

An idea regarding infinity I’d like your feedback on, since you’re far more knowledgeable regarding mathematics:

“Infinity” is fully synonymous to “unlimitedness”. All mathematical infinities (e.g., 0, 1, 2, 3, … infinity) are bounded by being other than what they are not (e.g., 0, -1, -2, -3, … infinity) and so are bounded infinities, or infinities limited to that subject of contemplation addressed. There is always something other relative to such infinities which demarcates them as such. Here, infinities are quantitative.

Boundless, or complete, or absolute infinity, however, (though I’m not certain if this is in line with Cantor’s works) is not limited nor bound by anything; it is the same as absolute unlimitedness. It is therefore nondual in every conceivable sense of the word: there is nothing other relative to it. Hence it is not, nor can it be, numerical, for it is not quantitative. Nor can it be a quantitative understanding of “greatest” for this always stands in contrast to that which is lesser as other, as can be exemplified by X > Y, which limits the greater to X by excluding Y as the lesser other.

(In terms of the overall thread: Other than boundless infinity’s possible correlation to the notion of omnipresence, I don’t see how this can make the case for God as typically conceived: e.g., the greatest being among all other beings.)

An idea regarding infinity I’d like your feedback on, since you’re far more knowledgeable regarding mathematics: — javra

“Infinity” is fully synonymous to “unlimitedness”. [/quote]

One hears this a lot since it's a dictionary definition. But it's not the mathematical definition. In math, a quantity is infinite if it can't be put into one-to-one correspondence with some natural number like 1, 2, 3, ...; or else it's infinite if it can be placed into one-to-one correspondence with a proper subset of itself.

Now that's mathematical infinity. There's also physical infinity, the question of whether anything in the world is actually infinite. And there's metaphysical infinity, God, the absolute, the everything of the everything. Those aren't mathematical infinity.

All mathematical infinities (e.g., 0, 1, 2, 3, … infinity) are bounded by being other than what they are not (e.g., 0, -1, -2, -3, … infinity) and so are bounded infinities, or infinities limited to that subject of contemplation addressed. — javra

Yes, I agree. Mathematical infinity is the most limited or constrained or trivial kind of infinity, because it's the one we can reason symbolically about. And you are right, the set of natural numbers 1, 2, 3, 4, ... is infinite, but it doesn't contain any ocelots or pomegranates. So it's infinite but it's not everything. That's why I agree with you that the mathematical infinity is a very trivial and limited kind of infinity.

There is always something other relative to such infinities which demarcates them as such. Here, infinities are quantitative. — javra

Yes, agreed. In fact just the even numbers alone, 2, 4, 6, 8, ... are infinite in number, yet missing all the odd numbers. A poor excuse for infinity. I agree. But we still have a fascinating mathematical theory of infinity, which doesn't tell us anything at all about the universe or God.

Boundless, or complete, or absolute infinity, however, (though I’m not certain if this is in line with Cantor’s works) is not limited nor bound by anything; it is the same as absolute unlimitedness. It is therefore nondual in every conceivable sense of the word: there is nothing other relative to it. Hence it is not, nor can it be, numerical, for it is not quantitative. Nor can it be a quantitative understanding of “greatest” for this always stands in contrast to that which is lesser as other, as can be exemplified by X > Y, which limits the greater to X by excluding Y as the lesser other. — javra

I don't know anything about God or whether the physical universe is infinite, so I can't say. I agree with you though that mathematical infinity is subject to the constraint of being limited to mathematical objects only, and doesn't tell us anything about God or the physical universe.

And even Cantor's absolute infinity was a mathematical infinity, it was just the class of all ordinal numbers. So I don't even know how he got God from that. Probably why his theological ideas are long forgotten.

(In terms of the overall thread: Other than boundless infinity’s possible correlation to the notion of omnipresence, I don’t see how this can make the case for God as typically conceived: e.g., the greatest being among all other beings.) — javra

I don't know anything about boundless or metaphysical infinity, only mathematical infinity. As a sign I once saw on a math prof's door said: Good sense about trivialities is better than nonsense about things that matter!

Cool post, thanks.

As a sign I once saw on a math prof's door said: Good sense about trivialities is better than nonsense about things that matter! — fishfry

:up:

there is nothing to prevent God being both imaginary and self-contradictory.
— Herg

If god is self-contradictory then god renders himself unavailable for discussion.

(p & ~p)⊃q

If god is self-contradicting, anything follows, and so anythign can be asserted. Conversation ends; truth becomes falsehood.

Hence, if you assert that god is, and is self-contradictory, you are not worth talking to. — Banno

I don't assert that God is. 'God is imaginary' means the same as 'there is no God'. So any assertion about an imaginary God is talk about nothing, and it doesn't matter what it asserts.

I mean, no ontological argument can get you to god and especially doesn't connect you to any specific god.