O and U contradict each other, so one doesn't exist. Why not U?

O has infinite knowledge, it's a part of its definition. Does it even have to check to knowledge? If yes, what if it can check multiple (infinite) things at once?

What is a better question is, how does O know it's O?

O and U contradict each other, so one doesn't exist. Why not U? — BlueBanana

Good point. My answer is it isn't possible to determine the nonexistence of a U because there are an infinite number of possible universes.

O has infinite knowledge, it's a part of its definition. — BlueBanana

Here I draw a distinction. We can have knowledge of infinity only as a concept, like we have.

I ask: What is the largest natural number?
O: There is no largest natural number.

O's answer doesn't make him non-omniscient because there's only one way of knowing infinity - as a concept.

What is a better question is, how does O know it's O — BlueBanana

That can be reduced to the U we're discussing.

Here I draw a distinction. We can have knowledge of infinity only as a concept, like we have. — TheMadFool

So how much does O know? It knows everything, and the amount of information is infinite.

So how much does O know? It knows everything, and the amount of information is infinite — BlueBanana

O can't know everything. That's my argument.

Because you define it that way. O can know infinite amount of information and everything because that is its definition.

Because you define it that way. — BlueBanana

How do you define an omniscient being then?

U is possible because there's no contradiction in positing a U. — TheMadFool

There is if there's an omniscient being. So your argument begs the question. You have to assume that there isn't an omniscient being to claim that an unknown thing is possible.

A being with absolute and infinite kowledge. That is, it knows absolutely everything, even if that means an infinite number of things.

U contradicts itself. "U is something about which nothing can be known" tells us something about U. In other words, I gain knowledge about U and what U is. Therefore, U is logically contradictory.

There is if there's an omniscient being. So your argument begs the question. You have to assume that there isn't an omniscient being to claim that an unknown thing is possible. — Michael

I haven't said U exists. My argument depends only on the possibility of U existing.

it knows absolutely everything, even if that means an infinite number of things. — BlueBanana

How will O answer the question:

What is the largest natural number?

The expected answer is that O will say ''no such number exists''. For me this answer doesn't disprove omniscience because infinity isn't a number. It's just a concept that represents, not ignorance, but limits of omniscience.

U contradicts itself. — Chany

U can't be known but U can exist. My argument depends only on the possibility of U's existence.

U can't be known but U can exist. My argument depends only on the possibility of U's existence. — TheMadFool

If U can't be known at all, then how can we talk about U?

If U can't be known at all, then how can we talk about U — Chany

We just did.

Yes, we did, but if U is unknowable, then we shouldn't be able to talk about U. We should not even know if U is logically possible, as, again, this is a fact about U, meaning we know something about it.

I haven't said U exists. My argument depends only on the possibility of U existing. — TheMadFool

And I'm saying that if an omniscient being exists then U isn't possible. So your claim that U is possible begs the question by assuming that an omniscient being doesn't exist.

And I'm saying that if an omniscient being exists then U isn't possible. So your claim that U is possible begs the question by assuming that an omniscient being doesn't exist. — Michael

It's not that U isn't possible. O isn't possible.

But why? Why should U take precedence over O?

But why? Why should U take precedence over O? — Chany

Because O is the assumption. U is a real possibility.

What's self-contradcictory about O?

Also, you didn't address my point. I know something about U- that U is logically possible.

Because O is the assumption. U is a real possibility. — TheMadFool

U is the assumption. O is a real possibility. We can both play this game.

How will O answer the question:

What is the largest natural number?

The expected answer is that O will say ''no such number exists''. For me this answer doesn't disprove omniscience because infinity isn't a number. It's just a concept that represents, not ignorance, but limits of omniscience. — TheMadFool

That is the answer it will give and it does not disprove omniscience. I fail to see your argument with that point. Is it that because infinity is a concept and not a number, it can't be an amount of anything? Or is the argument that that is an example of limit of omniscience, and comparable of O having a finite maximum amount of information?

Either neither exists; or O exists and the possibility of U disproves it; or U exists and the possibility of O contradicts itself.

Either neither exists; or O exists and the possibility of U disproves it; or U exists and the possibility of O contradicts itself.

No, if O exists there is no actual possibility for U to exist; it would only exist for our incomplete knowledge.

The mistake in the reasoning is that for all things T there is a group of things K (K1, K2, ...) which includes the properties of T. There is such O that for all T it knows all K, and there is such T=U that its Kx cannot be known. Can O know Kx? It's simply a contradiction, like unstoppable and unmovable objects. As well as you can say O doesn't know Kx, you can say it does so U can't exist.

That's what I pointed out in my next comment. The reason I first argued against TheMadFool, then Michael and then TheMadFool, reaching the same conclusion as Michael, was that the premises set by OP were incorrect. Because of that the whole discussion was based on the fallacy of false premise, and Michael only reached the right conclusion due to another fallacy. My last comment fixed the original premises and reasoning.

OK.

It does sound a lot like the immovable object and the unstoppable force problem. The object which cannot be known (or infinity, a useful mathematical concept) vs. the being who knows everything (omniscience). One is a useful mathematical concept, the other a common religious conception.

When it comes down to it I don't think omniscience (or omnipotence for that matter is a useful religious conception.

The omnipotent being who can see all the suffering in the future especially if the same being is omnipotent (could change the future if it chose) immediately becomes a responsible for the problem or existence of evil ( a major traditional religious problem and prominent source of disbelief).

Better to regard G as powerful (but not all powerful) giving other entities some degree of agency. Also better have G take in the experience of the world and respond to it by offering possibilities for progress. G is persuasive but not coercive. See process theology or open theology or Whitehead (consequent and primordial nature of God, dipolar theism or best of all Charles Hartshorne's Ominpotence and Other Theological Mistakes (Omniscience is one of them). So the Omnipotent and Omniscient conceptions of God have more problems than just infinity and U.

Firstly, the omniscient being/God isn't a common religious concept outside of the Abrahamic religions. Secondly, it's a very useful religious concept since it gives us a true arbiter of Truth, Reality, and morality. Without that omniscience, we cannot and will not have that.

As to changing the future, it would be truly terrible to give humans free will and then take that away from them by nullifying their choices, particularly when that will just lead to different miseries. So S/he does not become the source of evil, humans making evil choices do.

And it's not better to regard God as not all powerful, as he no longer is god and all his views are flawed and could be as bad as or worse than ours.

Well when it comes to religious conceptions, I think everyone is entitled to their own (assuming they are not persecuting or otherwise harming others of a different belief). I just find the problems inherent in omniscience and omnipotence so severe (regarding evil and free will) that I am happy to entertain conceptions of a somewhat lesser God. One who is persuasive and not coercive, a companion instead of a ruler, one of love not law.

But I showed those problems weren't severe and a lesser God isn't God anymore

And Christ, who is all things you mentioned, is an omniscient God.