• TheMadFool
    13.8k
    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?
  • BlueBanana
    873
    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?
  • TheMadFool
    13.8k
    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 OBlueBanana

    That can be reduced to the U we're discussing.
  • BlueBanana
    873
    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.
  • TheMadFool
    13.8k
    So how much does O know? It knows everything, and the amount of information is infiniteBlueBanana

    O can't know everything. That's my argument.
  • BlueBanana
    873
    Because you define it that way. O can know infinite amount of information and everything because that is its definition.
  • TheMadFool
    13.8k
    Because you define it that way.BlueBanana

    How do you define an omniscient being then?
  • Michael
    14k
    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.
  • BlueBanana
    873
    A being with absolute and infinite kowledge. That is, it knows absolutely everything, even if that means an infinite number of things.
  • Chany
    352
    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.
  • TheMadFool
    13.8k
    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.
  • Chany
    352
    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?
  • TheMadFool
    13.8k
    If U can't be known at all, then how can we talk about UChany

    We just did.
  • Chany
    352


    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.
  • Michael
    14k
    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.
  • TheMadFool
    13.8k
    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.
  • Chany
    352


    But why? Why should U take precedence over O?
  • TheMadFool
    13.8k
    But why? Why should U take precedence over O?Chany

    Because O is the assumption. U is a real possibility.
  • Chany
    352


    What's self-contradcictory about O?

    Also, you didn't address my point. I know something about U- that U is logically possible.
  • Michael
    14k
    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.
  • BlueBanana
    873
    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?
  • BlueBanana
    873
    Either neither exists; or O exists and the possibility of U disproves it; or U exists and the possibility of O contradicts itself.
  • John Harris
    248
    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.
  • BlueBanana
    873
    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.
  • BlueBanana
    873
    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.
  • prothero
    429
    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.
  • John Harris
    248
    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.
  • prothero
    429
    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.
  • John Harris
    248
    But I showed those problems weren't severe and a lesser God isn't God anymore
  • John Harris
    248
    And Christ, who is all things you mentioned, is an omniscient God.
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