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

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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.

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?

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?

Okay, yet I am still confused about one thing though.

The difference between these sentences: 1. It is possibly necessarily true that unicorns exist and 2. it is possible that unicorns exist. If I understand correctly by S5 in 1. you leave out the qualifier possibly and retain the sentence that it is necessarily true that unicorns exist and with 2. that (if it is possible that unicorns exist) it is necessarily possible that unicorns exist.

What does this mean with respect to the set of logically possible worlds? Well I would think that 1 then becomes unicorns exist in all logically possible worlds and 2 that is (necessarily) possible (but not necessary) that unicorns exist in all logically possible worlds.

What am I overlooking here?

In addition I must apologize to James, because it appears I stole the example from him. (In fact I am ashamed to admit that it is even worse than that because I didn't. I'm just busy with way too many things and I suck even at serial multitasking.)

So if there's nothing special about the "maximally great" being that allows this to work, then you can just shoe-horn in anything you want, like unicorns or winning the lottery, right? To make a generic example, it essentially becomes "if something is not demonstrably impossible, then it exists."

If so, I fail to see why experts consider this legitimate.  If anything, it just demonstrates a flaw in modal logic.  But maybe I'm still missing something.

So does the S5 axiom have legitimate uses in other contexts?  Is that why it is not rejected outright?

OK, I've been reading this page that Albert posted later in the thread.

Based on this:

Plantinga defines God as necessary... God, then, either does not exist or he exists in all possible worlds.

...

Axiom S5 requires a proposition that, if true, can only be necessarily true, and which is possibly true, to be necessary. In other words, Axiom S5 states that if something's definition only allows it to be true or to exist necessarily, then if there is a possible world in which it is true or exists, it is true or exists in all possible worlds.

It sounds like this argument only works for things that are by definition necessary (exist in all worlds), which would not apply to unicorns or winning the lottery, right?  Those things are just possible, but not "possibly necessary" like Plantinga's God.  If so, then you can't just substitute any old silly thing in this argument for "God" like a lot of people are trying to do.

If you have no clue what something means, you probably should not voice your opinion on it. Also, if the experts think an argument is serious and you are not an expert and think it is easily defeated, you are probably dead wrong and just don't understand the topic.

Modality requires at least 2 years of logic classes to understand well. I have taken a lot of philosophy in my undergrad (2 logics, 8 other) and I was not comfortable talking about modality and possible worlds until last year. If you have not even taken symbolic logic, then there is no way you understand it well enough to dismiss it. If you would like learn about logic, I suggest you get a symbolic logic textbook and after you have worked your way through the whole book, go buy one on modal logic. 

This may sound condescending, but non-experts simply have no place openly dismissing concepts from a legitimate field of study. This puts you in the same camp as anti-vaxers, 9/11 truthers, and creationists.

(friend me and ask my for books on formal logic and I would be very happy to help you).

Damn that sounded a lot meaner than I intended. Note that I do not think anyone here is a fool or that I am even smarter or wiser than you are (I am probably not).Sry if it came off another way.

they aren't real worlds. they are possible worlds. BIG DIFFERENCE. and you do not have to define every such detail of a world. Nelson already explained this earlier. Without possible world semantics, not even the basic axioms of logic work.

"Few people without some knowledge of modal logic will know that arguments using modal logic are representative of a legitimate field of study."

Just reading this thread made my phreakin' head hurt! I am completely ignorant about a lot of subjects and modal logic is there at the top.

But I do have one simple honest question: Are there practical applications for modal logic? If so, what would be a layman's example? Thanks.

Also computer science to an extent I think. I'm pretty sure it's the Matrix.

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