Fallibilism and Omniscience

[Meow Mix]

Q: What happens when an irresistible force hits an immovable object?

A: Mu. If there is an irresistible force, there can't also be an immovable object. If there's an immovable object, there can't also be an irresistible force.

This trite piece of paradox crops up every now and then when some people talk about omnipotence: the argument goes that, well, omnipotence is clearly an incoherent property because if God can do anything, can God make a rock so heavy it can't lift it?!

Of course, this is a silly argument because rational theists don't define omnipotence as "the ability to do anything" -- it's typically defined as the ability to do any logically possible thing. Since it's absurd for God to create both an irresistible force and an immovable object in the same cosmos, the question becomes absurd rather than the property of God the theist is attempting to expound upon.

The purpose of this thread is to look a little bit into omniscience as a property, which in my opinion is poorly defined.

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The problem with omniscience is that it deals with knowledge, which therefore means metacognition will come into play here: in order to know x, you must also know that you know x. If you really want to get sticky then it can be pointed out that in order to know that you know that you know x... (you see where this is going).

Humans are fallible beings -- we don't have a perfect epistemic method and we don't have access to all of the facts (we often don't even have access to the same facts as each other). Since we know we're not perfect, problems with this infinite regress of metacognition are just sort of shrugged off ultimately; though problems like this are the root of the major schisms in epistemic approaches (e.g., foundationalism vs. coherentism vs. infinitism, etc.)

But how does an omniscient being deal with this sort of problem?

Well, that seems to depend. I'm not even sure whether or not omniscient beings have an epistemic method or if they have something more direct, like some sort of perception of knowledge.

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Let's deal with omniscience as being without a method: as something raw and direct. Ostensibly an omniscient being's perception of knowledge would be perfect: any truths which could be known would be known, and no falsities would be believed. Is such a being safe from the ravages of fallibilism, infinite regresses, and otherwise skepticism?

I'm not sure, actually. Suppose God believes that God is omnipotent and omniscient -- but isn't, but has rather instead only been made to think so by an omnipotent demon.

"Well, then God would just omnisciently know there isn't an omnipotent demon to worry about," you might say.

But what if THAT is another ruse?

Aren't we right back to an infinite regress and fallibilism here? For every iteration of the cycle that God convinces itself there is no omnipotent demon messing with its mind since its mind is omniscient and omnisciently KNOWS so; there is another iteration of the cycle where, no, the demon MIGHT exist and just make God THINK nothing is wrong (falsely). Ad infinitum.

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So, how about the other possible version of omniscience with some sort of perfect epistemic method? Let's say that -- just as a hypothetical illustration -- that omniscient knowledge is to have justified true belief + O (henceforth JTB+O) where O is a Gettier defeater, a perfect fact analyzer and perceiver, so on and so forth.

"Aha!" we might think. Now an omnipotent demon can't mess with God by making God think it's omniscient when it really isn't -- because God has a perfect method which justifies the belief that there is NOT an omnipotent demon and that God really is omniscient.

Well... there still seems to be a problem actually, at least with the "JTB+O" example given (though the same sort of fundamental problem will crop up, I'm pretty sure, no matter what method is used by God).

Suppose the omnipotent demon attacks God's metacognition instead. Say God forms a true belief that Jefferson City is the capitol of Missouri, and believes it has knowledge since it THINKS it has perfect justification for this belief through O.

But how does God know an omnipotent demon hasn't implanted this belief that Jefferson City is the capitol of Missouri -- and the false feeling of the belief being justified? Suddenly the belief, while true, doesn't qualify as knowledge anymore since it isn't justified and there's an infinite chain of metacognition missing; leaving God *thinking* it's omniscient -- but isn't.

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So the problem here is that it seems even omniscience suffers from infinite regresses and fallibilism. While it seems easy to say "well nah, if God is actually omniscient then it would simply omnisciently know that it's omniscient," that doesn't appear to work because it's just starting an infinite regress of "omnisciently knowing I am actually omniscient" vs. "being tricked by an omnipotent demon into only THINKING I'm omnisciently knowing I am actually omniscient."

This isn't that much of a problem actually, but it does reiterate my point that I think omniscience as a concept is poorly defined and poorly understood. I'm not saying it's a nonsensical property, or that "therefore God doesn't exist," or anything remotely like that -- I'm just saying I think some care and attention should be given to the definition of omniscience to clean it up from silly little absurdities like the "rock so big" shennanigans with omnipotence.

 

[InformedIgnorance]

I would assume that no entity can be omniscient in such as framework where the data is separate to awareness of data.

Would there not be data that describes the data itself (i.e. metadata) and indeed metadata for that (as well as for the combination of the two) - or might perhaps these be characteristics along with some sort of native consciousness or awareness of the data itself - perhaps as some sort of self organising system.

The problem with such an approach is that the more complex the divergence from the raw data used to represent ____ (for example data which represents the possible states of all possibilities in our universe) is that there exists increasing complexity which can be described by data - one must therefore acknowledge at the absolute least that the scope of omniscience is limited to _____ and thus does not describe the omniscient entity/force etc; indeed in such a case the entity MUST be ignorant to some extent of knowledge of itself.

 

[LegionOnomaMoi]

"(1) There is for every knower a set that contains precisely the propositions that this knower knows.
(2) An omniscient knower would know every true proposition.
(3) (The Power Set Axiom) There is, for every set S, a power set Pow(S) that is the set of all subsets of S.
(4) (True Propositions About Subsets of Sets of Known Propositions) For every knower and every set K composed of propositions known to him, for each member K
' of the power set Pow(K) of K there is a true proposition kn(K
') that of him and of K'
says precisely that he knows each of its members; and, for any distinct members K'
and K

'' of Pow(K), any proposition, kn(K'
), that of him and of K'
says precisely that he knows each of its members, is distinct from any proposition kn(K''

) that of him and of K''

says precisely that he knows each of its members. Now comes a lemma that presupposes (3).
(5) (Cantor’s Theorem) The power set Pow(S) of any set S contains more things than does that set S: That is, Pow(S) is of greater cardinality than is S.
Conclusion
(6) There is not an omniscient being."

Sobel, J. H. (2004). Logic and Theism: Arguments for and against Beliefs in God. Cambridge University Press.


(1') There is for every knower a totality that contains precisely the propositions that this knower knows.
(2) An omniscient knower would know every true proposition.
(3') (Subtotalities of Totalities) For every totality T: (i) For each member x of T, there exists the singleton totality {x}; and (ii) for every mapping Mof T onto a totality Sub(T) composed only of subtotalities of T, there exists a totality T* that is a subtotality of T such that T* includes x of T if and only if x is not a member of M(x), the totality in Sub(T) with which x is paired by M.
(4') (True Propositions About Subtotalities of Totalities of Known Propositions) For every knower and for every totality K composed of propositions known to him, for each subtotality K’ of K there is a true proposition kn(K’) that of K’ and of him says precisely that he knows each of its member propositions; and, for any distinct subtotalities K’ and K’’ of K, any proposition kn(K’) that of him and of K’ says precisely that he knows each of its members is distinct from any proposition kn(K’’) that of him and of K’’ says precisely that he knows each of its members.
Now comes a lemnma that follows from (3
) and a More-Than rule to be explained.
(5') (Cantor for Totalities) Every totality has more subtotalities than
members.
Conclusion
(6) There is not an omniscient being.
(ibid)

These are just two formulations of two proofs in a single chapter on one issue with omniscience and theism without the counter arguments. The literature is rather extensive on both sides. You aren't alone in your thinking here (what is it they say about great minds?)

 

[Aquitaine]

I'm not even 1/4th of the way through the OP, yet my brain already hurts.

Looking at Post #2..... what is this I don't even.....

 

[idea]

infinite regressions and cycles are only daunting to finite temporal beings... God has no beginning, no end - is infinite in and of Himself.

eternal - no beginning - means there was no divergence, no initial point to diverge from. It's not like God just showed up on the scene one day, not knowing what happened before He was there - He was always there.

 

[LegionOnomaMoi]

The problem comes in with what kind of knowledge an omniscient being would have. Need it have propositional like knowledge broken into discrete "bits" of knowledge? Need an omniscient being have in mind the truth of every proposition or just access to knowledge of it? And so on. It's kind of difficult to understand how an omniscient being might comprehend. And mathematically we can deal with uncountable sets and mappings between these. Infinite regress is possible for us to model, just not to keep in mind the way an omniscient being would be required to.

 

[LegionOnomaMoi]

infinite regressions and cycles are only daunting to finite temporal beings... God has no beginning, no end - is infinite in and of Himself.

eternal - no beginning - means there was no divergence, no initial point to diverge from. It's not like God just showed up on the scene one day, not knowing what happened before He was there - He was always there.

The problem with the easy out is why we should believe that a being exists whom is so far beyond our comprehension that we deem that entity logically impossible.

 

[idea]

The problem with the easy out is why we should believe that a being exists whom is so far beyond our comprehension that we deem that entity logically impossible.

We know we exist, we know that infinity and eternity exist (and those concepts are partially outside our comprehension.) If infinite and eternal anything exists, then everything logically possible exists.... it's kind of an all or nothing deal imo, that something exists, means everything exists to me.

 

[LegionOnomaMoi]

If infinite and eternal anything exists, then everything logically possible exists....

That doesn't follow. And even if it did, the question is whether and how omniscience can be logical.

 

[Aquitaine]

The problem with the easy out is why we should believe that a being exists whom is so far beyond our comprehension that we deem that entity logically impossible.

As well as why such a vast omnipotent being would be subject to feeble human-like ego, and thus desire to be worshiped by it's inferior creations.

 

[idea]

That doesn't follow. And even if it did, the question is whether and how omniscience can be logical.

Do you not believe in anything being eternal and infinite? (You don't believe in basic conservation laws - conservation of mass/energy... do you think there was a time of nothingness? or will ever be a time of nothingness? then you have to explain how something came from absolute nothing, or could disappear into absolute nothing? etc.)

And if you do believe that "eternal" and "infinite" exist, then how are they not all-encompassing?

In an infinite amount of time, everything would eventually happen and exist.

 

[LegionOnomaMoi]

Do you not believe in anything being eternal and infinite? (You don't believe in basic conservation laws

Not all infinities are the same. I'm not sure about eternal as currently it seems to be that time has not always existed and it is not clear what eternal might mean. More importantly, just because I believe in some concepts of unendingness does not mean that I believe everything must exist.

And if you do believe that "eternal" and "infinite" exist, then how are they not all-encompassing?

Imagine a single particle traversing an infinite distance for all eternity. Why would this entail that everything would happen?

 

[idav]

Omniscience wouldnt need to be defined as the knower knowing they know. That would be helpful though if god is supposed to be a consious being. The first step of awareness is in itself knowing which is what I think makes life and consciousness even remotely possible.

 

[idea]

Not all infinities are the same. I'm not sure about eternal as currently it seems to be that time has not always existed and it is not clear what eternal might mean. More importantly, just because I believe in some concepts of unendingness does not mean that I believe everything must exist.



Imagine a single particle traversing an infinite distance for all eternity. Why would this entail that everything would happen?

Strange, everyone can imagine something that has no end, but most people have a hard time with the concept of "no beginning".

It's not a single particle of coarse, that's the point, we don't live in a singularity - we live in something that is unbounded, that seems to undergo perhaps countless cycles of crunching and exploding and crunching again with infinite combinations and permutations of everything.

 

[LegionOnomaMoi]

It's not a single particle of coarse

For conceptual simplicity. Eternity and infinity do not imply or entail everything. Instead of a single particle travelling an infinite distance for eternity we have lots and lots of "particles" (the scare quotes are because arguably we have no particles but for all intents and purposes it doesn't matter). But the logic still holds. There is no reason to believe that adding to the number of particles suddenly makes a difference. An infinite set entails infinitely many finite subsets. It does not entail all infinities. A denumberable infinite set does not contain an uncountable set. No set, including all possible infinite sets, can contain its power set.

we live in something that is unbounded

Really?

 

[idea]

Eternity and infinity do not imply or entail everything. ...

In other words, you do not believe that eternity, or infinity exists... that's ok, as I said before, these concepts are partially outside our comprehension, as other things are too.

You ask questions about the nature of God, how about asking questions about the nature of yourself? You know you are not "all-knowing", that you cannot be "all-knowing", so belief is a choice, not choosing between "known" facts... there are no "facts" if you do not know everything.... so everyone makes a choice - to believe in something larger than themselves, or not.

 

[LegionOnomaMoi]

In other words, you do not believe that eternity, or infinity exists

No, that's not what I mean at all. I absolutely do believe that infinities exist. I simply don't see how any concept of unendingness entails everything exists.

how about asking questions about the nature of yourself?

I ask this constantly. I study (as my field) knowing and the mind, after all, from everything from a philosophical basis to a neurophysiological basis.

You know you are not "all-knowing"

WHAT!!?? How can you say that!

Whatever appearance to the contrary, I know this. I am finite like anyone else, and more than most. But that doesn't mean I can't understand what is entailed by what or must necessarily accept that illogical things should exist.

there are no "facts" if you do not know everything

Why not?

 

[idea]

Why not?

There are no facts if you do not know everything - because part of what you do not know can always counteract what you think you did know.

Either you "know" it all, or you "know" nothing.

Google "Perry Model of Intellectual and Ethical Development", it outlines the cognitive stages where people go from being dualist (believing facts exist, and knowledge is possible) to being able to embrace uncertainty, and knowing how to rely on their personal conscience.

I have to sleep (party over here tomorrow night, I need to be awake for

It was fun chatting with you!

 

[LegionOnomaMoi]

There are no facts if you do not know everything - because part of what you do not know can always counteract what you think you did know.

This simply means I have imperfect access to facts/truth. It doesn't mean it doesn't exist.

Either you "know" it all, or you "know" nothing.

This doesn't follow.

it outlines the cognitive stages

This involves my field (I mean my actual field, not the studying I do as a hobby): cognitive neuroscience. I don't believe there is evidence for any such stages.

party over here tomorrow night

Have fun! I hope it goes well

It was fun chatting with you!

Likewise. I hope to do so again.

 

[Slapstick]

I would assume that no entity can be omniscient in such as framework where the data is separate to awareness of data.

Would there not be data that describes the data itself (i.e. metadata) and indeed metadata for that (as well as for the combination of the two) - or might perhaps these be characteristics along with some sort of native consciousness or awareness of the data itself - perhaps as some sort of self organising system.
The problem with such an approach is that the more complex the divergence from the raw data used to represent ____ (for example data which represents the possible states of all possibilities in our universe) is that there exists increasing complexity which can be described by data - one must therefore acknowledge at the absolute least that the scope of omniscience is limited to _____ and thus does not describe the omniscient entity/force etc; indeed in such a case the entity MUST be ignorant to some extent of knowledge of itself.

I haven’t read the entire OP, only to the part about properties and then skipped to your post. However, I would like to say this:

Trying to assign metadata to an entity that doesn’t have clearly defined attributes or “properties” would leave you in an infinite loop and leave you with an unlimited amount of possibilities without ever clearly defining those attributes. It would be like trying to pin the tail on a donkey without ever knowing what the property or attribute actually is, where it goes or how it fits into the equation, which is why metadata would be useless. If an entity is not an atomic entity then it would not be possible to describe its characteristics, rendering metadata as being essentially useless, because you would not be able describe the data itself without first knowing what type of data it is that you are actually working with. Whether it be analyzing, or trying to describe.