The modal ontological argument
Well i have been having a discussion with a theist and he has just brought up the modal ontological argument. I have now done some research on modal logic and have sites marked to further educate myself on it, but i am still way to new to it to have any clue whether my argument holds water or not, and i would really apreciate some help.
the argument he used goes like this
"1. It is possible that a maximally great being exists.
2. If it is possible that a maximally great being exists, then a maximally great being exists in some possible world.
3. If a maximally great being exists in some possible world, then it exists in every possible world.
4. If a maximally great being exists in every possible world, then it exists in the actual world.
5. If a maximally great being exists in the actual world, then a maximally great being exists.
6. Therefore, a maximally great being exists."- him
to which, after very little research i replied with
"Now the modal ontological argument is not proof of anything .The modal ontological argument applies a string of logic but fails to test the logic. If the same string of logic can be used to come to an opposite conclusion, then the logic has been disproven through contradiction.
1) It is possible that a maximally great being does not exist.
2) If it is possible that a maximally great being does not exist, then a maximally great being does not exist in some possible world.
3) If a maximally great being does not exist in some possible world, then a maximally great being does not exist in any possible world.
4) If a maximally great being does not exist in every possible world, a maximally great being does not exist in the actual world.
5) If a maximally great being does not exist in the actual world, then a maximally great being does not exist.
6) Therefore maximally great being does not exist.
This uses the exact same logic to reach an opposite conclusion that is at odds with the original conclusion. This proves that the logic of the MOA is completely faulty and as such, illogical."-my reply
To which he replied
"The issue I hold that you does not effectively deny the rationality of there existing God. Here I would re-enter the absence of evidence ,does not, = evidence of absence argument. Due to the nature of the atheist's presuppositional base for the arguments against the existence of God, it undermines the evidences that are provided for the existence of God because to say there is no evidence for the existence of God suffices to say that the atheist's knows all possible proofs that God exists, which is logically absurd. This is what I meant with my ontological argument as a preface for the evidence of absence. There is enough rational proof for the existence of God and that's where Plantinga's argument comes into play. Philosophically, it is possible. Yes, you can flip the logic but I don't believe that's sufficient enough to prove the argument holistically false. The difference here is I am saying that a maximally great being is necessarily possible and not simply possible. The reason for providing Plantinga's argument in the first place is because I am meaning to exhibit that there are no logical objections to the maximally great being unless the objector can prove that to be false. Rendering us back to premise 1. that it is possible. " - hes reply
Now this is where i am at the moment. now form my limited understanding it seems the major problem with this argument is that it uses two different meanings for the word possibility and only gets away with this argument by confusing them. the one type of possibility has to do with something that is either true or false but which the laws of logic cannot say one way or the other . such as the possibility england will win tomorrows rugby match.
The other possibility seems to be a logical possibility, something that has always been either true or false and always will be either true or false and so then has to be neccesarily true or false. and the only reason we can call it a possibility is because we do not have the answer yet.
Now this is what i have come up with so far to answer back to what he replied just and i would like to know if it is valid or not
" what i am saying is that this argument proves nothing. lets us replace god with some other proposition which is possible and if true is neccaserily true for all possible worlds , but that we do not know the answer to. lets call it (x) and (x)= the statement that the 12 billionth and first digit of pi is a 7. now we dont know the answer so it is possible that (x) is true , and if true in any world it would be true in all worlds,so if true it is neccaseraly true. now i will use your exact same argument
1. It is possible that (x) is true
2. If it is possible that(x) is true , then (x) is true in some possible world.
3. If (x) is true in some possible world, then it true in every possible world.
4. If (x) is true in every possible world, then it true in the actual world.
5. If (x) is true in the actual world, then (x) is actualy true
6. Therefore, (x) must be true
Now we do not need to know the actual answer to be able to say this does not prove (x) is true. yes it is possible (x) true, there is a 1/10 chance it is, but this does not prove it is true and we do not need to be able to prove (x) is untrue to be able to say this does not prove anything."
Now this seems fine to me and the only objection i can think of is if , in modal logic, it is possible for worlds to exist where logical and mathematical truths are not true any longer. ie if there is a world where 2+2=563 or something
Replies to This Discussion
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Permalink Reply by Nelson on -
Just because something is possible does not make it probable or likely.
To criticize the argument you have to have some understanding of modal logic. Not even a complete understanding (because I sure as hell don't have that. lol), but just some understanding. According to modal logic, that something is possible means that it is actual in some possible world. It more than makes it probable or likely, it makes it an absolute dead certainty... in some possible world.
And: "What can be asserted without evidence can also be dismissed without evidence."
It's a great quote, and we skeptics throw it around a lot. But when we do we often do so haphazardly. Darwin had ZERO evidence for his theory of natural selection when he proposed it. He reasoned rhetorically, making an analogy between the artificial selection of animal husbandry to the truth of natural selection (saying "If we can do this in the course of a few generations, imagine what nature can do over the course of millions of years!"). But he could point to absolutely no actual evidence that natural selection happened. The Origin never offers a single piece of actual evidence to support the theory. It's all just argument. And so, if the quote is true, no one should have believed it unless and until there was evidence. And yet we're forced to admit that the argument has power and that people were justified in believing he'd made the case. So let's try to leave off the pithy sayings that come off as excuses for not addressing the actual argument and admit that we are sometimes (often, even) convinced of things (and at least led to think that those things are probably true) by the force of argument alone even in the absence of evidence.
What makes the argument fail is that it is a failure as an argument, not that it is an argument in the first place (as opposed to some piece of evidence).
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Permalink Reply by Albert Bakker on -
1. It is possible that I win the lottery.
2. If it is possible that I win the lottery, then I win the lottery in some possible world.
3. If I win the lottery in some possible world then I win the lottery in every possible world.
4. If I win the lottery in every possible world then I win the lottery in the actual world.
5. If I win the lottery in the actual world then I have won the lottery.
6. Therefore I have won the lottery.
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Permalink Reply by Nelson on
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Did you mean to reply to me with this? I can't tell why if so. I certainly don't think that the argument is successful if that's what you think. I'm merely pointing out that it says nothing against the argument to critique it without critiquing it on modal grounds. I agree with Greg above that axiom S5 is the problem and that the argument, even disregarding the problems with S5, could only ever be considered successful by someone who already believes the proposition the argument aims to prove.
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Permalink Reply by Albert Bakker on
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No it wasn't a reply to you, I just plugged it in here. And no I see no way by which I could possibly have concluded that you agree with it's validity.
I just thought maybe my suggestion of substituting the mass of an up quark is (apparently) still too abstract to show what it I think what is wrong with this particular form in addition to premise 2 not necessarily following, premise 3 does not follow, except in the singular case that this is actually true. This is the clearest example by which to show this that I could think of.
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Permalink Reply by Nelson on
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I disagree when it comes to premise 2. If you posit a logically possible being, there is a world in which that being exists. It's a numbers game at that point. Since the sheer number of possible worlds is massive, the chances that a logically possible being exists in some world is a virtual certainty, and is a certainty if the number of possible worlds is infinite.
On premise 3, yes. That's the version of the S5 axiom used in the argument. If the axiom doesn't hold up then the argument fails since the argument assumes the validity of the axiom.
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Permalink Reply by Albert Bakker on
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Okay that is where I am wrong, within modal logic as far as I understand it now, you are right.
If the set of all possible worlds is infinite, it must necessarily be true. (edit: removed objection that I doubt is valid.)
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Permalink Reply by Albert Bakker on
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The obviously flawed form here used:
1. It is possible that a maximally great being exists.
2. If it is possible that a maximally great being exists, then a maximally great being exists in some possible world.
3. If a maximally great being exists in some possible world, then it exists in every possible world.
4. If a maximally great being exists in every possible world, then it exists in the actual world.
5. If a maximally great being exists in the actual world, then a maximally great being exists.
6. Therefore, a maximally great being exists."Or from 1 follows 6, what's in between is just a ritualistic formula and doesn't really matter: whatever you fill in at 1 will come out at 6.
Is a derived form, with copy of terminology, of that of Plantinga:
1. A being has maximal excellence in a given possible world W if and only if it is omnipotent, omniscient and wholly good in W; and
2. A being has maximal greatness if it has maximal excellence in every possible world.
It is possible that there is a being that has maximal greatness. (Premise)
Therefore, possibly, it is necessarily true that an omniscient, omnipotent, and perfectly good being exists.
Therefore, (by axiom S5) it is necessarily true that an omniscient, omnipotent and perfectly good being exists.
Therefore, an omniscient, omnipotent and perfectly good being exists.In this form the objection to wrongful use of modal logic is much more in place. In the first argument it isn't pointed out that a "maximally great being" is only a "maximally great being" if and only if premise 3 is true, a tautology. Then indeed you are just begging the question and it isn't an argument at all.
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Permalink Reply by erik112358 on -
dumb question, and may open a can of logic worms that none may want to bother with, but...
...in this context, what does the phrase "in some possible world" mean? Any imaginable space which we cannot prove impossible?
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Permalink Reply by Nelson on
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Not a dumb question at all!
Modal logic has to do with the concept of possible worlds. The idea is this: the actual world (the one we inhabit) is just one of many logically possible worlds that could exist; in varying the features of a logically possible world (the features that differentiate it from World 1, 2, 3...) you can see that you can conceive of many logically possible worlds. The phrase "in some possible world", then, refers to one of these logically possible worlds.
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Permalink Reply by erik112358 on
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Thanks. I guess what is hanging me up is the word "possible". By Greg's definition, "some is logically possible if it is not logically impossible," wouldn't a "possible world" then be any world that is not logically impossible?
For example, unicorns are not logically impossible, therefore they exist in some possible world. Yes?
Is the argument here then that if a "A maximally great being exists" in one world, then, by virtue of its maximal greatness, spans all possible worlds, and therefore exists in our actual world?
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Permalink Reply by Nelson on
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Precisely right. Since there's nothing about unicorns that makes them logically impossible, according to modal logic, they exist in some possible world.
The argument here is not that a maximally great being that exists in some possible world spans all possible worlds in the sense of transcendence (as if one being exists over all worlds) but that if a (not THE, "a". as in one of many) maximally great being exists in some possible worlds, a maximally great being exists in all possible worlds. Hence, a maximally great being exists in the actual world.
The key is the S5 axiom. The axiom leaves off qualifiers as assumed. So if written fully out including the missing qualifiers it would be "If a maximally great being is necessarily, possibly, necessarily possible, then a maximally great being is possible". The only one that actually gets expressed in the axiom is the underlined one. So it functions to keep premises short and easier to understand. When someone trained in modal logic sees the S5 they understand what is being said even though it's not all being written out. The problem, however, is the counterintuitive nature of the implication that once we admit that unicorns exist in some possible worlds, they are necessary, and if they are necessary, they are necessary in all possible worlds (for this is what it means to be necessary). And if they are necessary in all possible worlds, they are necessary in the actual world (being included in the set "all possible worlds"). Hence, they exist in the actual world.
So like all ontological arguments it seeks to *POOF* god into existence by sheer wordcraft. And Albert is right to reformulate the argument with regard to lotteries because it shows off just how silly the conclusion is when it comes to the lottery. And if the conclusion is silly there, it seems that the same conclusion with regard to god is silly.
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