That’s about the gist of it. Personally, I don’t worship God just because He is ontologically perfect (which is what G means). I worship Him because He is morally perfect. Were this the only convincing evidence of His existence, I would hate Him.
Fortunately, it’s not convincing. If modal logic accepts petitio principii as valid then modal logic is fatally flawed. I think the reason that arguments based on propostions such as the existence of a greatest possible island are easily seen to be fallacious is because the subjects have clear attributes the nature of which can be disputed. Given that this so-called greatest possible being does not have these easily definable attributes there is nothing to grab hold of to show how ludicrous the argument is.
Faldage, the conclusion is G. I do not see G asserted in any premise. It is not logically circular as far as I can tell.
All propositional calculus logics accept petitio principii as valid. That’s because of the definition of validity:
In any case, the MOP is not circular. Nowhere does any premise state the conclusion, G.
And yet, some people feel compelled to grab something — anything — for no reason other than that the conclusion is unacceptable to them. Speaking of circular: “the argument is ludicrous; therefore, it must be invalid”.
hmmm, i’ve been as big a critic of this as any, but I don’t see many people calling this argument invalid.
The closest I would come is that, even when talking with people who are well-versed in boolean logic, the argument may be invalid without assuming the soundness of S5. Then, the argument, when in the confines of symbols, is valid.
However, there are two huge gaping loopholes, or three, depending on how you decide to use this argument.
One, is it sound? 'nuff said.
Two, if it is sound, are you prepared to call g God? If so, why?
Three, if you personally are prepared to call g God, will you go into other threads and claim that God has been proven (which in English is a supernatural, sentient being, while in the proof is neither of these necessarily,) when this is far from the case? Will you intentionally equivocate the usage of g and God, and imply to your audience that the existence of an Om3I God has been proven by this proof?
Excellent questions, Ludovic! And decidedly on point! 
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It is sound if both <>g and g -> g are true. I believe they are.
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Yes, I would call g God because I have always called supreme being God.
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As I’ve said many times, all I ask for is intellectual respect. I ask that it not be assumed that a man who believes in God is “a stupid fuck”. (To reference the thread you keep referencing.) All I ask on behalf of the MOP is that you acknowledge that it is a reasonable argument, just as I acknowledge that those who believe it to be valid but unsound do so reasonably — even if I disagree with them. And now a question for you. Is this too much to ask?
Am I missing something? G is not a being, it’s a proposition. I don’t understand how we can assign a truth value to a being.
What is G? Something like:
G = the greatest possible being that can exist exists
and how do we define “greatest possible”? Why, as existing in all possible worlds, so:
G = a being that exists in all possible worlds exists
Now, obviously, we don’t know if such a being exists or not, which is why we set out to try to prove that he does.
Or: “in some possible world a being that exists in all possible worlds exists”. Is that not the very definition of circularity? We weren’t sure if there was a being that existed in all possible worlds, so we assumed that there was.
Though nobody seems to care, I’ll keep pointing out that this premise is (G -> G), otherwise the proof is not valid. Here is the countermodel where G -> G, <>G, and ~G are all true:
World 0 World 1
G -> []G G
<>G
~G
Nothing requires G to be true in World 1 (and thus, nothing requires G to be true in World 0) in this model. You would need to assert (G -> G) in World 0 to require G -> G in World 1.
You’re missing nothing. This is exactly why this argument fails out of the starting block. To define existence as a “greatness”, then to posit that G reflects all greatnesses, or perfections, or whatever you want to call it, is essentially starting with your conclusion, i.e., God exists, which is of course a fallacy.
I was once engaged in a discussion of whether religion views are a choice, and you said something to the effect of “my belief in God/Jesus is not something I chose”, and made reference to experiences you’d had which compelled you to have the religious beliefs that you have.
I found that to be a powerful and meaningful spiritual statement, which I respected. You are an (obviously) intelligent and reflective person who is Christian and believes in God.
That does not make you a “stupid fuck”, and anyone who thinks it does is, well, a stupid fuck.
The point I’m trying to make is that if you actually do encounter an even remotely thoughtful person who honestly thinks you’re a stupid fuck because you believe in God, the ontological argument (assuming they’re intelligent enough to understand it) is unlikely to make a difference to them, because what they’ll likely take issue with the aspect of your belief which is addressed by Ludovic’s third question, which is the aspect that is not addressed by the ontological argument at all.
The sleight-of-hand in the existence proof is that first proposition: <>G.
Considered before the premises are known, it’s tempting to agree with <>G because you don’t want to look unreasonable. However, when the premises are revealed, we must say ~<>G IF G = necessary existence and existence has yet to be established. In other words, you’ve already assigned ‘necessary existence’ to something that has not been proven to exist (a priori). It would be the same as calling ~G “necessary”. With that definition, we couldn’t say <>~G either.
Now if God = imaginary entity, then we can start with <> G. Good luck.
“In some possible world, a being exists with the ‘property’ that if its existence is actual, its existence is necessary.”
Well, as you like. Logical proofs, of course, are only done by manipulations through tautologies. All logical proofs are circular: their conclusions are always held within the premises. The question is whether you object to these premises, and if so, on what grounds. Though I’d imagine you don’t object to the manipulations of symbolic logic, one wonders…
Huh? The proof goes through two assumptions, one instantiated postulate, the law of the excluded middle, substitution, the modal modus tollens, and a disjunctive syllogism. Assuming these are valid, the proof is certainly valid. Your counterexample assumes ~G, which is far, far the stronger assumption than <>G. If you reject <>G, one wonders why ~G is any more persuasive to you.
Restrict our attention to beings that are not forbidden: <>G
Restrict our attention to a being with this property: G -> G
G? G!
OK, good. So G is the proposition
G = a being exists with the ‘property’ that if its existence is actual, its existence is necessary
And we set out to prove that G is true of this world, that is, in this world a being exists with the ‘property’ that if its existence is actual, its existence is necessary. In order to do so, it is we must assume in some possible world, a being exists with the ‘property’ that if its existence is actual, its existence is necessary.
Libertarian (and now you) will claim that you didn’t assume the conclusion. But you did—you assumed a being into existence. It doesn’t matter that you claim you assumed it about some metaphysically possible world, not necessarily the actual world; becuase you’ve defined this being so that it inhabits all possible worlds if it inhabits one.
The thing that Libertarian calls “modal modus tollens” is not valid. I have pointed that out to him in (at least) three of these threads, stretching back to almost two years ago.
He uses a rule like this (A -> B) -> ~B -> ~A, which is not valid. To see why, consider that A -> B and ~B are true in this world. Now, there are two kinds of possible worlds, those (like this one) where A -> B is true, and those where A -> B is false (nothing compels A -> B to be true at every possible world).
In the worlds where A -> B is true and ~B is true (by its necessity) then ~A is true by classical modus tollens. However, in the worlds where A -> B is not true and ~B is true by its necessity, we can conclude nothing about A (there is nothing inconsistent with A being true thus ~A being false).
To make this a valid rule of inference, he needs
(A -> B) -> ~B -> ~A
and he needs to amend his assumption to
(G -> G).
Well, it’s a countermodel. It’s one way to show how an inference is not valid: by demonstrating a consistent model in which the premises are true but the conclusion is false. I have demonstrated such a model. I did not “assume ~G”, I negated the conclusion and demonstrated that there is no contradiction, because that is the way that one constructs a countermodel.
I certainly don’t object to the manipulations of symbolic logic. As a professional theoretical computer scientist studying programming languages, I’m about as close as you get to a practical “logician”; and I certainly understand symbolic manipulations
Here is a really slick proof of Goldbach’s conjecture (that every even number greater than two is the sum of two primes).
Surely, the truth value of Goldbach’s conjecture is logically necessary. That is, if it’s true in one possible world, it’s true in every possible world.
Assume Goldbach’s conjecture is true in some possible world…
<>G does more than restrict your attention to beings that are not forbidden, it asserts the existence of the being whose existence is in question.
…and if it doesn’t assert that, then <>G assumes the possibility of non existence of a being whose necessity has already been established…an invalid premise.
With all due respect to the impressive collective facility in formal logic. This all reminds me of the deadly serious debates concerning the number of angels that can fit on the head of a pin.
It seems to me that attempting to use formal logic to either proove or disproove the existence of god is innapropriate. Either God exists or God does not exist. I suspect that if God does exist he/she/it is laughing at all these attempts to Prove that which cannot be proven. All formal logic operations mmust begin with a premise. What possible basis could their be for choosing the premise of the possibility of gods existence over the premise of the possibility that god does not exist?
While there is certainly a place for logic in philosophy, and again I point out that the majority of those posting here have demonstrated a superior understanding of it, the questions with which philosophy is concerned are those which are unaproachable by means of syllagisms and operation of modus ponens. What is Good? What is right? What is wrong? What is Evil? these are not determined either inductively or deductivly.
If my comments are out of line, please accept my apology. I felt that it would be acceptable to interject what I intended to be a constructive criticism of the attempt to apply formal logic to that to which it does not apply. I reiterate I mean no disrespect to anyone.
A reasonable question and one answered quite eloquently by Eris and, somewhat more verbosely, by Newton.
The assertion ~<>G is a denial of a positive ontological proposition. How can there even be a denial of a positive ontological proposition? In other words, how can the statement “The greatest possible being cannot possibly exist” be defended? Clearly, that proposition is absurd. The more subtle assertion, <>~G, is equally absurd. “It is possible that the greatest possible being does not exist.” The only reasonable modal assertion with respect to G as a premise is <>G. “It is possible that the greatest possible being exists.”
Point well taken, Max. But wouldn’t you agree that it is untenable to hold both a respect for my views and an opinion that I am intentionally equivocating? (That’s what he said in his third point.) How can anyone intellectually respect a man who has not made a mistake, but rather has intentionally set out to deceive, manipulate, and well, basically troll?
In the general literature, the MOP is controversial, yes. But not because of the definition. Not because of some perceived circularity. Not because philosophers are suspicious of the symbology, the formulation, or the intent of Plantinga et al. The controversy is over whether <>G is a more reasonable premise than <>~G. It is unreasonable to the extreme to call for people simply to shut up about it because of inevitable recalcitrance and belligerence. Don’t you agree?
That is acceptable if, as in this case, you have postulated that if it is true in all possible worlds, then it is true in the actual world. Of course, there is nothing about the nature of the conjecture that makes any positive ontological proposition about it reasonable. In fact, it does not make an ontological commitment of any kind.
And as I have pointed out for as many years, the accessiblity relation of the MOP is Euclidean, not merely symmetric. You are NOT free to invalidate a proof by disregarding one of its premises. G -> G is a premise of the proof. Ignoring the accessibility relation is enthymemic.
That is rather like attacking an arithmetic proof by pointing out that 1 is not a number, it’s a numeral. I think you ought to know that when Eris refers to G as a proposition, he means “G”. G is indeed a being. “G” is a statement.
Then you are denying the possibility of non-existence, a priori. That absolutely equates <>G with G, a priori. There’s your circle.
This is equivocation; whether it is intentional or not is irrelevant. The possible in the phrase the greatest possible being is being used as the modal possible, the possible in it is possible is the normal street value of possible. There may not be a greatest possible being. It may be such that there is one being, A, that is greatest in attribute a, another, B that is greatest in attribute b, etc. Let’s roll out some attributes of this presumed G and discuss them.
Once again:
Every premise of every argument in every bivalent system denies the possibility of its opposite being true. For example, by declaring that the argument must be flawed, you are denying that it may be valid. Why does your own criticism not apply to your own argument?
In every case, the term “possible” and its variants are metaphysical, not epistemic, possibility. Those are the only two kinds. The only attribute of G is the nature of its existence: ontological perfection.