Omniscience is impossible
Argument A: Infinitely many possible universes
Let us take a mathematical variable x and assign to it values from the set of natural numbers {1, 2, 3,...}
For x = 1, one possible world exists. Let's call it A1. Now, x = 2 can't exist in A1 because that would entail the contradiction x = 1 and not x = 1 (where x = 2). So, x = 2 must be in another possible world A2, and so on, ad infinitum
Argument B: Omniscience is impossible
U = a thing about which nothing can be known
U is possible because there's no contradiction in positing a U. So, it is possible for U to exist in one of the infinitely possible worlds (argument A)
Imagine now an omniscient being O. What does O know about U?
Either such a thing as U exists or not.
If U exists then by definition nothing can be known about U. So, O is not omniscient because there exists something about which nothing can be known viz U.
O can't know U doesn't exist because there are an infinite number of universe O must check before O can determine the nonexistence of O. That's not possible because infinity has, by definition, no end. So, O is not omniscient.
Therefore, O, an omniscient being, cannot exist.
Is my argument sound? Is there a simpler proof for the nonexistence of an omniscient being?
Let us take a mathematical variable x and assign to it values from the set of natural numbers {1, 2, 3,...}
For x = 1, one possible world exists. Let's call it A1. Now, x = 2 can't exist in A1 because that would entail the contradiction x = 1 and not x = 1 (where x = 2). So, x = 2 must be in another possible world A2, and so on, ad infinitum
Argument B: Omniscience is impossible
U = a thing about which nothing can be known
U is possible because there's no contradiction in positing a U. So, it is possible for U to exist in one of the infinitely possible worlds (argument A)
Imagine now an omniscient being O. What does O know about U?
Either such a thing as U exists or not.
If U exists then by definition nothing can be known about U. So, O is not omniscient because there exists something about which nothing can be known viz U.
O can't know U doesn't exist because there are an infinite number of universe O must check before O can determine the nonexistence of O. That's not possible because infinity has, by definition, no end. So, O is not omniscient.
Therefore, O, an omniscient being, cannot exist.
Is my argument sound? Is there a simpler proof for the nonexistence of an omniscient being?
Comments (69)
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?
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.
Quoting 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.
Quoting BlueBanana
That can be reduced to the U we're discussing.
So how much does O know? It knows everything, and the amount of information is infinite.
O can't know everything. That's my argument.
How do you define an omniscient being then?
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.
I haven't said U exists. My argument depends only on the possibility of U existing.
Quoting BlueBanana
How will O answer the question:
[B]What is the largest natural number?[/b]
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.
Quoting Chany
U can't be known but U can exist. My argument depends only on the possibility of U's existence.
If U can't be known at all, then how can we talk about U?
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.
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.
It's not that U isn't possible. O isn't possible.
But why? Why should U take precedence over O?
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.
U is the assumption. O is a real possibility. We can both play this game.
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?
No, if O exists there is no actual possibility for U to exist; it would only exist for our incomplete knowledge.
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.
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.
In any event I, like Thomas Jefferson, admire the moral and ethical teachings of Jesus while having considerable doubts about his divinity. To many, of course, this means I am not a Christian, but I think following the teachings is more important than believing in God taking human form, and what one does in this life is more important than precisely what one believes..
In any event I don't think this will be a productive conversation. Strange because I actually regard myself as a theist (and have strong religious inclinations) but who do dogmatic theists hate more than atheists? Other theists with competing religious views.
I was lost/wandering in the wilderness. I can attest this is the best site (posters) after some experience elsewhere.
You seem to be saying God must be omnipotent and omniscient and that any other conception is not God. You seem to be saying also that Jesus is God in the flesh and omnipotent and that other conceptions have to be in error. If you are saying something else please elaborate otherwise I find these proclamations, although orthodox, also dogmatic.
I never said either of those things and you haven't shown I have. Try to stop straw-manning me and read my posts better.
You've just shown you read my posts poorly, so what you find is irrelevant and doesnt' matter to me.
Just because you know something is possible doesn't mean you know it in the general sense of the word ''knowledge''. Knowledge is a justified true belief. As you can see U isn't known to be true (it's only possible) and so doesn't count as knowledge or something known.
Quoting Chany
O can't check all universes, which I've shown is infinite, for the existence of U. So, O is NOT omniscient. If U exists then O is not omniscient.
Quoting Michael
This can't be done because the possibility of U derives no contradiction. However the existence of O results in one.
Please read my OP.
O can do anything it wants, and it doesn't have to check infinite universe, for the existence of U, as it knows everything at all times and knows there is no U.
The existence of O doesn't result in a contradiction. Or at least you haven't presented an argument that it does. All you've shown is that the existence of O is incompatible with the possibility of U. But whereas you're asserting that U is possible and so O can't exist, I'm turning it around and asserting that O exists and so U can't be possible.
The basic point is that the possibility of U not deriving a contradiction isn't sufficient to assert that U is possible. Even if the possibility of U doesn't derive a contradiction, it might nonetheless be impossible – which it is if O exists. Therefore your assertion that U is possible begs the question by assuming that O doesn't exist.
Aside, your definition of knowledge is highly suspect. I'll roll with it for now.
Modal facts about possibility, contigency, necessity, and impossibility are facts.Take a unicorn, a horse-like being with human cognitive abilities, a horn on its head, and magical powers. Unicorns are logically possible, as they are concievable and not self-contradictory. To use possible world semantics, there exists a possible world in which unicorns exist. This possible world does not have to be the actual world. Unicorns may not be contigent (actual), but they are possible. From this, we can list a number of things about unicorns. Unicorns:
1) are horse-like beings.
2) have horns.
3) have human cognitive abilities.
4) have magical powers.
5) are logically possible.
All these statements are true, per how I defined unicorns. Just because something is logically possible does not mean we cannot have justified true beliefs about it. Onto U. Assume U is true. U:
1) is something about which nothing can be known.
2) logically possible.
The first statement is true by the definition provided. The second statement, according to you, is true because there is nothing self-defeating about U. Therefore, in the same way I know about unicorns, I know facts about U. I can add another fact to the list of facts about U. U:
3) is something about which something is known.
The third statement contradicts the first statement. Therefore, U is logically impossible, as U is self-contradictory.Quoting TheMadFool
If the omniscient being is similiar to God, then the being does not need to search for any true statement. The being just knows it all already.
U isn't self-contradictory. That's why you accepted it as a possibility. About possibility consider this: ''It'll rain tomorrow'' is a possibility but it isn't true. We're merely entertaining possibilities here. Truth comes later. Truth needs to be established with evidence.
However, U contradicts O. And O being the weaker assumption compared to U it becomes necessary to abandon O. Why is O weaker? Because the mere possibility of U is enough to contradict O. The converse isn't true because U can't check infinite universes.
Quoting Chany
Infinity can't be known like the number 2 or 3,000. It simply extends without end. Asking O to give us the largest natural number will elicit the response that no such number exists. So, there are limits to knowledge but that, in my opinion, doesn't devalue omniscience. It's simply the nature of infinity.
You don't read replies, do you?
Sorry. Perhaps I misunderstood but...
1) Your claim that U is self-contradictory is false.
2) Infinity doesn't have an end. So I don't know what you mean by ''Quoting Chany
Can you clarify.
Also thanks for your criticism. I think it would be better to define U as something about which something can't be known instead of U = something about which nothing can be known. If you like we can go with definition viz. U2 = something about which something can't be known.
I provided an argument showing U is actually incoherent when you analyze it. Modal facts about logical possibility are facts. The statement "it is logically possible that it will rain tomorrow" can be true or false. "Unicorns are logically possible" can be true or false.
"U is logically possible" can be true or false. If this statement is false, then it is no threat to omniscience. If it is true, my argument shows it self-contradicts, as I know facts about U.
Quoting TheMadFool
God (under common definitions) cannot gain knowledge via learning. To do so would mean God did not know something at some point in time, meaning God was not omniscient at some point in time. God's knowledge is simply known. There was never a time when God had to work to access knowledge.
Quoting TheMadFool
If there is nothing, there is not something. They operate indentically. U2 is a rephrasing of U.
Knowing infinity and knowing an infinite amount of things are two completely different things. O can't know infinity as a number but infinity can logically speaking refer to an amount and O can possess an infinite amount of knowledge.
Thanks again for your valuable criticism. I offer you two options:
1. Let's change the definition of U as something about which something can't be known. If U is defined this way then O can't exist because either U exists or U does not. If U exists then there's something which O can't know. And O can never know that U doesn't exist because there are an infinite number of universes to check.
2. Let's stick to the original definition of U i.e. U = something about which nothing can be known. The only thing we know about U is that it is possible. I'll agree with you in that we do know that U is possible. So, it is a fact which is true. However I have a small problem with this counting as knowledge of U. Take for example the case of unicorns. Unicorns are logically possible. This is a fact and I admit we know it. However, in the general sense of the term "knowledge" it doesn't pass muster. From the fact that you know unicorns are possible can you describe any of its real properties? Take another example: We know angels are possible.. Does this count as knowledge of angels?
In essence, I'm drawing a distinction between knowledge of possibility and knowledge of existence. The former is meta-knowledge, if you will and the latter is what we actually refer to when we say knowledge is true justified belief.
There are ineffable numbers.
Just look at Richard's paradox. The short of the story is that language expressions are countable, while real numbers are uncountable. Hence, there are real numbers that exist but cannot be expressed in language.
That obviously says something about the tool of language. It therefore says something about the users of the tool of language, i.e. humanity.
There exists ineffable knowledge.
This knowledge is not accessible if you are limited to using the tool of language, but not necessarily so, if you happen not to be subject to that limitation.
No they arent. Knowledge of what someone is going to choose to do doesnt effect whether or not they have a choice. If you think they have a choice to start with, someone else knowing what they will choose doesnt magically take that away.
For example, if offered vanilla or chocolate ice cream and I choose chocolate cuz I hate vanilla, thats my exercise of free will (if you believe we actually have it to start with). Foreknowledge doesnt change that, how would it (unless you share your foreknowledge with me and that effects my choice but then thats MY foreknowledge of my choice effecting things.)?
Come again? If it is predetermined what you chose, how is it still a choice? Think!
You first lol
How about you address the rest of my post? The part you quoted is my claim, what follows is the reasoning for that claim. That reasoning is what you need to address.
My point is, knowledge of what someone is going to choose does not predetermine what they will choose. Its just knowledge of what they will choose.
Ill try another example.
If you come up to me and ask me for a cookie, and I know that you are sincere in your desire for me to give you a cookie, then I know you are going to take the cookie when I take it out of my cookie bag and offer it to you. I know you will take the cookie because you sincerely asked me for the cookie. You’ve still made the choice, i just knew what it was going to be.
The knowledge and the free will are not mutually exclusive, as you claimed.
Now, maybe you do not believe in free will in which case your initial statement makes no sense. Omniscience is mutually exclusive with something you dont think exists? That would be gibberish. (Im just covering the bases, im not saying you dont believe in free will but in case you dont’t...your statement is nonsense).
I actually agree with this. I guess the better way to put it is if the lady across the table is better than everyone else at chess and she consistently beats everybody including the big name software A.I. programs, i would imagine her winning streak will continue on for a very long time.
The most common way professional chess players win is through essentially memorizing millions of patterns on the board (and also knowing the game rules), and the much less used method is calculating a vast majority of the future patterns at crunch time. You don't have to know everything, you just have to run faster than the other guy being chased by the bear.
The "reasoning for the claim" is a repetition of the same claim, not proof of any sort.
So again: Yes, me knowing what you are going to choose by definition means that what you going to chose is already determined, ergo no free will.
Are you restricted to a one paragraph reading limit? Respond to the rest of what I said. At least show you understand the analogy. Thats literally the least you could do and have it still be considered a discussion.
The "rest of what you said" was:
For example, if offered vanilla or chocolate ice cream and I choose chocolate cuz I hate vanilla, thats my exercise of free will (if you believe we actually have it to start with). Foreknowledge doesnt change that, how would it (unless you share your foreknowledge with me and that effects my choice but then thats MY foreknowledge of my choice effecting things.)?
As I said, that is simply a re-statement of the claim, and not proof of anything. You san"Foreknowledge doesnt change that" and I say yes it does.
By the way, this question has been argued many times before (see Wikipedia entry on "argument from free will"), and I think you see which side I find convincing and which not. And trust me, others have presented your view better than you with your vanilla ice cream.
Nothing wrong with vanilla ice cream.
There is a question in there. Do you have an answer?
Also, Im not arguing for or against free will. We can discuss that if you want but its not what Im getting at.
Do you read before posting? I simply pointed out that omniscience and free will are mutually incompatible.
Lol, ok. So an answer to my question?
I did not see a question. All I saw was that you changed your metaphor from "vanilla ice cream" to "cookies". You can change it to pickled fish if you want... that does not turn it into an argument.
Then you should pay more attention, a clear question (a few actually) was asked, in simple english. My second analogy was better than my first attempt I thought. Better illustrated the point Im making.
Post your "clear question in simple English".
Sorry, I got sidetracked. Mathematical infinity per se doesn't prove the impossibility of omniscience because a question like "what is the greatest natural number?", having no answer, under the condition that one knows the set of natural numbers is infinite, is inconsistent.
However, take a physical constant of the universe; it can take on any value i.e. its domain is infinity itself and since each value assumed is a universe itself, it follows that there are an infinite number of possible universes. Now, if a U such that nothing can be known of it must be ruled out, as required by omniscience, then a candidate being for omniscience must check each and every single possible universe but that's impossible because infinity, by definition, has no last element; no last element, no last universe.
Hello, new to the group. Just a point of order, really. The universe, by definition, is entirety. So, does it really make any sense to talk about "other universes" or "multiverses".
Could we refer to the unknown as any part of the (single) unobservable universe?
As to the general idea of omniscience, normally associated with "God", I believe it to be theoretically possible, provided it does not involve a logical contradiction, eg "Can you know what the highest prime number is?" [because that involves an infinity, which by its very nature, cannot be actualised.].