I really wish you hadn’t skipped over my post, Lib. Especially since it was one of the first five or so replies, and I’d really like to see an answer to some of the more basic challenges to your argument. Basically, I don’t think anyone is simply “rejecting a strong argument” so much as pointing out the argument isn’t that strong at all. In fact, it has such wide-spread aplication to all sorts of unrelated and ill-defined topics that it is quite flimsy.
Anything that isn’t proven to be impossible or not exist, has some chance to exist. In english, it’s possible that it exists. Possible also can be used to say that something can be done. I don’t know much about modal logic, but just from reading this thread, I can tell that “possible” in modal logic means that something is true in at least one case. This is not the same as the english “possible”. “True in at least one case” != “could be true”. Your argument uses the english possible and modal possible interchangably, which simply doesn’t work. If you’re going to use the modal-logic “possible” for god’s existance, IE, that god exists in one world, you will need to demonstrate that a good does indeed exist in one world. Untill then, you’ve got a possible possible (English and modal, respectively) value, but not a definate one.
You’re also assuming definitions here. You presume to define got as the “greatest possible existance”, but there is neither any evidence for this, nor any definition of what the greatest possible existance is. In fact, you don’t even have any reasoning that there can be a “greatest possible existance”, instead of either existance or non-existance. As someone else pointed out, it sure seems to be an either-or thing, not a greater-or-less-than thing. But assuming for a moment that it is possible, you still need to show what the greatest possible existance is. It could be that whatever the greatest possible existance is, is so great that the entire universe is contained inside a single atom of a single cell of his body. Or he could simply be a human that’s just a hair ‘better’ than all the rest. Maybe he can jump a few inches further than any other human, or has a single-point higher IQ than anyone else. Which leads into the final point, you would have to show that god is the greatest possible existance, instead of something else. Without simply presuming he must exist, and is therefor the greatest possible existance. You (And most christians) would probably define god as being such, but that’s presuming his existance, which doesn’t logically work. It would be like me saying a great dragon is the greatest possible existance, and using that as proof that a great dragon must exist. The popularity of your opinion has no bearing on logic, after all, and the two have the same amount of logic (Very, very superficial and flawed logic, that is).
Even if you define god as being the greatest possible existance, that does not make god necessary exitance. I’m assuming you’re using the modal-logic possible here, because otherwise “greatest possible existance” has no solid meaning (It instead would mean that there’s a -chance- that god exists, which would also mean there’s a chance he doesn’t, which is even more fatal to your possition). But if we assume that god is the greatest (modal)possible existance, that would mean he exists in one world. You then have to define what a world is. At the very least, it would have to be the universe (Something can either exist or not exist in this universe, not multiple examples of each). So how many worlds are there? This is another reason I don’t think modal logic works properly here. We don’t have any other defined worlds, so untill we can see other worlds (Universes), we are effectively working in a one-world system. Modal-logic possible therefor would be impossible; Something either exists or not, and if something does exist in this one and only “world” in our logic system, then it is either true or false. While this would seem quite appealing at first for your argument, since it seems to connect the earlier half of your argument to being completely true, it also destroys the earlier half of your argument at the same time. There can only be true or false in this single-world system, not possible. Since modal-logic possible means to be true in one world but not all (Since that would be simply “true”… Or whatever the term was you used… Necessary?), then it would be impossible to have a ‘possible’ condition. The first half of your argument would have to show god to be a true value, which isn’t accomplished untill after assuming it to be true. Again, I can do the same thing with a ‘great dragon’ or just about anything else I want, and the logic would hold up the same.
And finally, if you do manage to work up to the point of showing that god does exist in one world/universe, that doesn’t mean he exists in our world/universe, or that he doesn’t exist in a fictional world/universe that only exists in this “equation” of yours. And if he doesn’t exist in our universe… What was the point?
To put it basically, you’ve got a LOT of wide-ranging variables and definitions that you need to pin down first (And, in fact, some of which you need to prove are true to begin with, such as if there even can be a “greatest possible existance” instead of just “existance”). With your current argument, you presume to define most of these without any evidence to support appart from circular logic that relies on them necessarily being at a certain value. At the very least, you would have to supply firm evidence for defining “greatest possible existance” (After showing it can exist at all), and “god” (Which I imagine will be pretty tricky, seeing as you’re trying to prove he exists at all, and if you could show evidence for a definition of god, this whole modal-logic argument is pointless anyway). Your argument is weak because just about anything can be put in the place of “god” in your example, and still follow through just as “logically.” And as much as I would love something that would prove (To use the example one last time) that some great dragon exists and is the most powerfull being in the universe, the fact that it can be applied to individual rocks, every single other god, or even an antrhopomorphic mosquito, it results in so many “true” outputs that it is meaningless.
And now my head hurts. I hope it was worth it, at least…
Accepting the concept of necessary existence as something mystical seems about the same to me.
How on earth am I supposed to react when someone says, “your premise assumes your conclusion” when the premise is G → G and the conclusion is G? Formal study is not required to see that they are not the same. One is “if God exists, then He exists necessarily” and the other is “God exists”. Or when someone mentions a “second axiom” when there is only one. […sigh…] I honestly don’t know how to respond to such protests other than to repeat the rules of elementary first order logic. I feel obligated to do so if for no other reason than to place on record that the rule was explained.