Omniscience Argument Against God's Existence

[max-greece]

Set theory doesn't tend to get used much these days. Initially it was perceived to be a way of explaining everything but that was shot down by Bertrand Russell.

In essence Russell proposed "the set of all sets that do not contain themselves as a member." As you can see set theory breaks down because that set can't contain itself, whilst if it doesn't it must.

[Vincenzo Vinny G.]

I have two points so far. Tell me what you think:

My first point is about the logical compossibility of a GCB and an unknown unknown (UU).

But first some important points:
1) UU don't exist alone, but are predicated on a subject. Ie, something that is unknown is not merely "unknown" but "unknown to some entity", either "unknown to Vinny" or "unknown to MFM" or "unknown to God", eg. There is always a "to + subject(s)". In this case it is "UU to God" we are concerned about.

2) The existence of any "UU to God" relies on the existence of an epistemic threshhold. Ie, there is a limit, before which are all real or hypothetical KKs, KUs. Then beyond the limit is the UUs.

If (1) is true, I think UUs are incoherent. Why?

If God is indeed conceived as a GCB (or MGB depending on your preference) then that by definition rules out unknowns. Postulating UUs thus entail a contradiction.

It's like saying "Imagine a bachelor. Now imagine the bachelor is married. A bachelor cannot be married. Therefore, the concept of a bachelor is incoherent."

You will respond "But, your conception of a marriage bachelor is the problem, not the definition!"

So if there is indeed an MGB/GCB (as the ontological argument, for example goes to show), then it is by definition non-compossible with a set of UUs.

I have a second response based on the status of the confirmed UU claimed by Noel. He postulates three sets of propositions

1) {Known unknowns}. Known question, unknown answer. These are confirmed "to us", presumably not "to God" (notice how the "to + subject" is so important).
2) {Unknown unknowns}. Unknown question, unknown answer. These are confirmed to us, not confirmed to exist to God. If it has to exist to a God, then God does not exist.
3) But we have a special third one: "The status of the set of an unknown unknown". Noel concludes that this is a confirmed existence of unknown unknown to us, but also to God.

And thus, given (3), Noel concludes that God has an unknown unknown, and therefore omnipotence is incoherent.

But I think Noel gets (3) wrong. If you recall, a known unknown is like "How many atoms are in my body?" You know the question but you don't know the answer. An unknown unknown is where you don't know the question or the answer.

But given "What is the status of the set of unknown unknowns?" we know the question, even if we don't know the answer!

So (3) is not UU, but KU.

Now, we have UU beyond the threshold, even for God. But given omniscience, God would know all the answers to KU. So God would know the answer to (3).

So God would have to know the answer to "What is the status of the set of unknown unknowns?"

I have to go to bed, but I love this argument and I'd love to work on it more. Tell me what you think of my responses.

[MindForgedManacle]

Good response. Actually, I think the question with regards to unknown unknowns would be something like "Who is a member of the set of unknown unknowns?" The problem is that you can't even know if the set itself has any members or what those members are, because otherwise they're no longer Unknown Unknowns. I suppose that does make it a strange UU, if one at all. Perhaps it's something else entirely? ("known unknowable" maybe?)

[Vincenzo Vinny G.]

Or, the question could be "Are there any members in the set of UUs?" I think the question can be tweaked appropriately to cover the various issues.

A third response I thought of, as a quick and dirty one is this:

Noel takes a GCB, and then postulates something the GCB cannot do. And this is meant to be a legitimate problem.

What stops us from using an identical method of reasoning but in a Moore shift kind of way?

We can take a UU, and then postulate a GCB who cannot NOT know it. And pose it as a legitimate problem for the concept of UUs.

If the reasoning can be identical to Noel's argument, it would work equally well as Noel's argument, right?

[MindForgedManacle]

Actually, that's not a problem at all. Clearly, Christians think there are things God cannot do (anything against his benevolent nature). I could perhaps argue that doesn't make him the GCB, but otherwise there doesn't seem to be a problem there specifically.

However, the problem is I don't think it makes sense to say you can conceive of a being who can conceive of that which is inconceivable by definition. Does it? Otherwise, my GCB can conceive of a square-circle.

[Vincenzo Vinny G.]

I think you can, and here's why.

If you read my response, I said that when we say UU, we must always have a subject to whom something is an UU. So using the word "Inconceivable", we must say "Inconceivable to some subject." This is the first premise. (1)

(2) In Noel's example he used the notion of a big God who creates a little God who has UU. Presumably to the big God these UUs are known in some way. Quite possibly KKs.

Given 1 + 2, we can use the same principle from Noel's example. Just as Noel conceived of a big God to whom these UUs were KKs (or KUs), why can't we conceive of a greater being who has access to these UUs?

Aren't we doing the same thing done in Noel's example?

[MindForgedManacle]

I wasn't clear I guess. What I mean is that you cannot conceive of a being who can conceive of an incoherent idea (square-circle) or possess an incoherent attribute. I don't mean inconceivable to any subject in particular, but to all of them.

In regards to UUs that are such for a particular subject(s): that doesn't rule out UUs. That simply means the being in question knows our UUs to be KKs, but it couldn't rule out any UUs to itself, could it?

Heh, you're making me less sure of the argument... well done.

[FallentoReason]

Seems like things have become more productive in this thread

[Vincenzo Vinny G.]

I wasn't clear I guess. What I mean is that you cannot conceive of a being who can conceive of an incoherent idea (square-circle) or possess an incoherent attribute. I don't mean inconceivable to any subject in particular, but to all of them.

In regards to UUs that are such for a particular subject(s): that doesn't rule out UUs. That simply means the being in question knows our UUs to be KKs, but it couldn't rule out any UUs to itself, could it?

Heh, you're making me less sure of the argument... well done.

I wanted to be sure of my reasoning, so I looked at it again, along with Noel's reasoning in the video.

If you want to verify it yourself, look at 4:50 in Noel's first video where he starts explaining his scenario. You will notice the following features:

1) A greater God who creates a lesser God
2) The lesser God has one or more UUs.

In this situation, the UU is only UU "to the lesser (created) God". It's not UU to the greater God. After all, the greater God explicitly created the lesser God to have UUs.

You cannot create a lesser being who has UUs unless these UUs are known to you, I think.

I'm sure it won't be a singular one-shot defeat of the argument. After all, Noel is a smart guy, and can revise his argument. Can you get in touch with him? Is he still active on youtube?

[MindForgedManacle]

I'll respond specifically later, but as for your last question, yes he's still active. He uploaded a video just the other day on another topic.