Libertarian’s postings in this thread highlighted a form of argument I have not come across before.
I have very little in the way of education with respect to logic (just a few courses for the degree I’m doing now).
So how valid was Libertarian’s argument? Is it considered a sound argument at all (obviously, judging by the thread, not everyone thinks so)?
The argument is unsound, specifically because it indulges in the fallacy of begging the question. He “proves” that God exists by presuming that it is necessary for God to exist. However, he never actually proves that it is necessary for God to exist.
He puts forth a great deal of jibberjabber to mask the basic fallacy, and along the way commits a few more.
There is no “Law of Excluded Middle”. There is no “Law of Necessitation”.
He goes through a lot of meaningless symbolic manipulation for five steps–then he throws it completely away by stating, flatly and without proof, that it is necessary for God to exist. Of course, it is nearly a tautology to go from the necessity of an existence to a flat statement of existence.
The argument is perfectly valid with respect to the symbology, but seems specious with respect to the content (meaning) we would like to place in the symbols. As far as the meaning actually put in the symbols in the modal logic arguments, they seem almost completely without justification, and still hinges on Anslem’s idea that a being that only differs from another being by existing is “better” in terms of justifying G.
Note the assumption: **G->[]G: “If this perfect being exists in one world, it exists in all worlds.” The next assumption is: <>G: “The being exists in one world” (the perfect being is possible). When put into English the conclusion is obvious, and the logic is only there to try and solidify the process, but the process isn’t especially questionable. There is some hubbub about which version of modal logic to use, etc, but the core issue is whether or not the two assumptions are warranted.
Personally, I do believe that only an all-powerful god could have the “property” G->[]G. However, <>G is a bit more perplexing.
Another problem with respect to the meaning of the proof lies with the question of whether we can safely say that the symbol G applies to the same entity in all worlds, and if so, to what extent, and how this might impact our reading of the proof. For example, using the possible worlds semantics, we could say that in several worlds that an inventor of eyeglasses exists. But suppose we wanted to say that not only do these worlds contain an inventor of eyeglasses, but that they are the same person in each case (even though the worlds differ in other ways)…? The issue here is whether G is such that it differs from world to world in some way. We might be lead to read the proof simply as, “Necessary existence exists” which is really unsurprising and already assumed under S5 modal logic anyway.
It’s interesting, but trivial, and likely cannot contain the meaning Libertarian would like to put into it.
The law of the excluded middle is very well-established. It’s the tautology A v ~A, where A is any wff of propositional logic.
erislover’s final paragraph sums up my feelings on the proof perfectly.
The Ontological Argument defines God into existence.
Silly, really.
What Lib showed you there was the Modal Ontological Argument for the Proof of God’s Existence, or MOAPGE for short.
The logic you are studying now is most likely simple first order logic, eg.
Praying mantids are insects
Pat is a praying mantis
*Valid logic:*Therefore, Pat is an insect.
Praying mantids are insects
Pat is an insect
*Invalid logic:*Therefore, Pat is a praying mantis.
The MOAPGE uses more complicated Modal logic, eg.
Praying mantids are necessarily insects.
Pat is an insect.
Valid modal logic: Pat is possibly a praying mantis.
Invalid modal logic: Pat is possibly an insect.
Now, the second word in MOAPGE is ontological, and this is the key to the entire proof. Ontology deals with the nature of being and existence. However, it only relates to the existence of metaphysical entities. Metaphysics is, literally, after the physical, and so anything that can be known epistemically (ie. by our senses), such as a rock, atom or synaptic discharge is ontologically irrelevant: Ontology only deals with the transcendental - that which is solely intuitive.
Of course, it is at this point that one can say “Whoa! Stop right there. Only the physical exists. Metaphysics, and therefore ontology, is naught but a big bunch of hooey.” You would thus show yourself to be a physicalist.
However, many people have trouble with the idea that ideas don’t exist (or at least, that an idea exists only as a physical entity, like a snowflake or a supernova). And so, ignoring the slight nick they receive from Ockham’s Razor, they hold that both physical and metaphysical things exist, and so a subject relating to the existence of metaphysical things (ie. ontology) is OK. (Incidentally, I believe Lib keeps his skin flawless by denying the physical and holding that “atoms are not real”; perfectly logically consistent, but quite a big bullet to bite!)
Now, if one accepts the existence of the metaphysical, one must accept the axiom that Necessary Existence is true. That is: there is something metaphysical which exists in every possible world. Something with Necessary Existence (hereafter “NE”) cannot not exist.
Now, here’s the thing. Lib, and indeed the rest of us, can conceive of a supreme being. The ontologically perfect entity. The highest, bestest metaphysical thing there is. And he proposes this:
The supreme being has necessary existence.
One may ask “Why so?”. Answer:
The two are synonymous. Being is synonymous with existence. Supreme existence is Necessary Existence. Supreme Being = Necessary Existence.
Now, one can be forgiven for seeing this as a cute parlour trick. Suddenly, the Supreme Being cannot not exist! However, as long as one is still simply saying “Necessary Existence is true”, there need be no problem. The problems come when further characteristics, not of Necessary Existence (NE), but of Supreme Being (SB), are posited (“goodness”, “intelligence”, “omnipotence” and the like.)
This all stems from these rather odd words: Perfect. Supreme. Highest. Best. In what sense is a metaphysical entity which exists better, superior to or more perfect than one which doesn’t? Furthermore, what the heck does existence have to do with goodness, intelligence, power or the rest of it? How is a benevolent entity more supreme than an Evil one?
The only truth in every possible world is NE. Lib chooses to call this “God”. However, following the principle of Modal Logic, there would be possible worlds in which God was omnipotent but not omniscient (the “powerful idiot”, say), others in which God was an omniscient weakling, and others in which God wasn’t very clever or powerful at all. There would be possible worlds in which God was Evil incarnate. And there would be possible worlds in which God’s only characteristic was Necessary Existence.
And so, even if I were not the physicalist I avowedly am, I would still find the MOAPGE unconvincing. But the only reason I studied the subject at all was, when I arrived here some time ago, I found some guy proposing a Proof of God. Expecting a fool or a crackpot, I engaged him and asked him to explain his proof.
Never had I encountered a more articulate, kind and good mentor in a subject I had little experience of but which I immediately found fascinating. Libertarian is the best advertisement for philosophy I have ever seen. The MOAPGE is merely his flashy pop-up.
You must admit, it’s a damned effective at attracting new customers!
I’ve been puzzling over Lib’s ‘proof’ for a while, and before my brain explodes, I must blurt out my layman’s take.
Lib isn’t saying God exists, necessarily (pardon the pun).
He’s saying that, if you allow the existence of anything metaphysical, then God exists, since the existence of the metaphysical leads to a higher ‘power’ via his ontology, which I just can’t parse.
But he’s also saying that, only if you deny the existence of anything metaphysical, God does not exist. He then goes on to extrapolate that this is inconsistent with anyone but a strong ‘even-deny-proof’ ‘hand-stabbing’ atheist.
If I’m right, which I’m prepared to admit I’m not, not being a logician nor philosopher, then I see this as a tricky argument of excluded middle, and while it might have some internal logical consistency, begins from a premise that has nothing to do with real-world thought - that accepting even the slightest possibility of something’s existence (subject to proof) means that it exists, which just doesn’t make sense to me.
You call it God, I call it ‘an idea’.
I think that calling NE god is making one unholy hell of an assumption about the universe. If we live in you basic physical-only universe, than that which exists necessarily is the universe. So, you’ve proven that if it exists, it exists. If you’re of a soliptistic bent, you’ve proven that you exist, as you are necessary for the rest of everything to exist. Congratulations. As far as I can tell, claiming that that which exists necessarily is God, when most people have a definition of God that would exclude themselves and/or everything physical, is rather intellectually dishonest.
[QUOTE=erislover]
But suppose we wanted to say that not only do these worlds contain an inventor of eyeglasses, but that they are the same person in each case (even though the worlds differ in other ways)…? The issue here is whether G is such that it differs from world to world in some way.
[QUOTE]
I think the issue is even more fundamental than that. There may be possible worlds where the inventor of eyeglasses exists and has the exact same properties as the inventor of eyeglasses in the actual world. Now, in terms of ontological “greatness”, does this inventor actually exist in both worlds? IMO, no. Since there is no communication between worlds, the entities are, although possessing all the same qualities, nonetheless completely separate. So, since they are separate entities, I do no consider ontological breadth to impart “greatness”.
Well, no, the inventor wouldn’t actually exist, Ludovic. The semantics involved in understanding possible worlds runs like this:
P: “P is the case in every world.” aka necessity
P: “P is the case in this world.” aka actuality
<>P: “P is the case in some world (at least one world).” aka possibility
We also have the identity: <>P <-> ~~P
What can throw us is suggesting that <>P, often called “P is possible” or “possibly P”, has a very direct correspondence to the English word “possible” when this isn’t the case.
The lack of communication between worlds isn’t a sticking point; it only deals with worlds where the logic under consideration applies. No communication is necessary. Seen in this light, it is almost like we are asking, “What is compulsory, what is not forbidden, etc”. We could readjust our interpretation of the content of the symbols like:
P: “All worlds compell P.”
P: “P obtains in this world.”
<>P: “P is not forbidden.”
It is almost like you are making a list, enumerating every permutation possible given the laws of logic we are insisting be the case (predicate logic, modal logic, etc). Every “world” on the list is <>P (possible), the one that applies to us is P (actual). Propositions which are always the case in every permutation are P (necessary). There’s no requorement for interaction.
I am not arguing the definitions of the modal system.
But the only way I would concede that “greatness” is implied by ontological breadth is if the entities in question not only have the exact same qualities, they are part of the very same entity, which exists across worlds. And to do that, you need communication. That’s what I was trying to get across.
Well, the logic is the same across all worlds. Does that mean you reject modal logic? (not that I’d have a problem with that, of course)
erislover I think what Ludovic is saying is that it isn’t impressive to merely say that god exists in all worlds and in all worlds has the same properties. What would be impressive is being the exact same entity, including input from all the worlds. Basically god can’t be somehow transported to another logically possible world and meet god there and be like, “Hey, how’re you doing?” God has to be in both logically possible worlds simultaneously.
Thus communication between worlds becomes important. If logically possible words are truly and forever seperate then the gods in them are seperate beings, even if they have the same properties.
It’s leger de main, smoke-and-mirrors made of clouds of necessity. The presupposition of necessitation leads inevitably to tautology. There’s no way around it. The position is firmly established, within the confines of the rules of the argument (neccessity), and then there is nothing left to prove except that the argument is consitent with the presupposition. It’s the logical equivalent of a dog sniffing its arse.
Well…it’s true. This is B.S. of the rarest quality. It’s the kind of fallacious position one must do hard mind-altering drugs (so as to torture a good intellect sufficiently) to even conceive of, if you ask me, because it turned my brain into a knot for about five minutes. But when you get the basic fucking inanity of the thing, the smoke vanishes.
It’s not even that original. Godel had a similar idea, I think. Necessity is not a valid presupposition. It forces you to accept that if God can exist somehow, He must exist anyhow. If you simply deny necessity, there’s nothing left to talk about. And there’s nothing stoping you from doing that. All you’re left with is somebody who believes in God, and someone who doesn’t, same as before. An empty exercise.
They are the same axioms and theorems in all worlds. With god, all things are possible, no? 
He knows everything that can happen/be, must happen/be, and is happening/existing. Suppose this creature existed in all worlds. Suppose we wish to address whether or not it is one being or many beings: how would we go about finding out? Suppose we could know everything and communicate across worlds while doing so, could it possibly change our answer? Why or why not?
Lib’s argument is flawed. As I pointed out to him in a previous thread, one can use a virtually identical proof to demonstrate that God doesn’t exist. Here it is, for the curious:
1. G -> []G – “If God exists he exists in all possible worlds.”
This is Libertarian’s definition of God.
2. ~[]G – “It’s possible that God doesn’t exist.”
A reasonable premise, since we have no evidence for God’s existence. And it’s easy to imagine a possible universe that contains nothing, not even God.
(This premise is slightly different from Libertarian’s. He chooses “It’s possible that God does exist” as his second step.)
The rest of the proof mirrors Libertarian’s proof exactly:
3. []~G -> ~G
4. []G v ~[]G
5. ~[]G -> []~[]G
6. []G v []~[]G
7. []~[]G -> []~G
8. []G v []~G
9. []~G
10. ~G
Look, I’ve proven that God doesn’t exist!
Unless you can demonstrate why Libertarian’s proof is valid and mine is not, you’re forced to conclude that modal logic is an inadequate tool for the task at hand … .
Ontological arguments, even if valid, even if sound, generally fail to be convincing. They aren’t convincing to atheists, and they aren’t convincing even to many people who already do believe in the existence of some deity, because they prove the existence of a God with few properties other than…existence. Oh yeah, and maybe “greatness”, whatever that means. Even if you believe in such a “God” in a rational sense, it doesn’t necessarily inspire faith or religious sentiment. It’s not the God of any major world religion, and it’s certainly not the Judeo-Christian God. Given the history and common use of the word, I think it’s misleading to call such a thing “God” at all.
Spinoza managed to work out a logical proof for the existence of a God so unlike what any normal religious person thought of as “God” that he was branded an atheist. To me, Spinoza’s God sounds suspiciously like a description of what we might today simply call “the universe”, and I don’t think there are many atheists who deny that the universe exists. When atheists say “I don’t believe in God” they have something more specific in mind. They’re usually thinking of a Creator God. A God that performs miracles and answers prayers. A God that rewards the righteous and punishes the wicked. A God that requires a certain kind of worship. Something like that. You know, a God that does more than just exist.
Ontological arguments reduce the idea of “God” down to the point where an atheist can no longer argue against its existence, but also to the point where an atheist no longer needs to. If you prove the existence of something that doesn’t match the idea of the “God” that an atheist doesn’t believe in, you aren’t going to convince the atheist of anything new. Nor are you going to strengthen the faith of a true believer. Just sticking the “God” label on something that you can prove to exist isn’t enough to change anyone’s mind; if it were, I could just get a dog, name it “God”, and say that atheism is illogical because God clearly does exist and I have the pictures to prove it.
There’s no good way to do this, as this is metaphysics, but even so, I see no good reason to assume they are one being, and my default assumption is that they are not.
It would change our answer in that it would no longer be multiple worlds 
If a Supreme Being could do that as well, it would also no longer be multiple worlds. Even if the supreme being is omniscient, it would only be omniscient to the extent of knowing what is happening on other worlds, not actually communicating.
Sort of like if we were a perfect chess player, and knew all possible moves in chess, we cannot say we are communicating with our other selves, merely that we know what we would do in that situation.
Granted, in the case of a Supreme Being, it is impossible to tell the difference, but cross-world communication is unnecessary since it can be explained by omniscience.
I don’t see why it matters if it is one being or not. Does the argument require one being? If one being is not logically possible, why do you feel the proof demands it, which you then rebuke?
I still don’t understand why you brought up the communication in the first place. Did Lib somewhere and I just don’t know it? The proof surely doesn’t demand it, nor does modal logic.
I think that by “communication”, Ludovic means accessibility. It is indeed necessary that there be an accessibility relation among the worlds in which G exists. But that relation is satisfied by the modal axiom, <>G -> <>G, which takes a Euclidean frame and invokes the modal rule of necessitation — that is to say, necessity obtains.