Night
What does “necessary nonexistence” mean? I’m not familiar with the term. (Careful if you say that it means that His existence is not possible in any possible world because you’ll find yourself negating nothing. Remember that a substantive denial of a positive ontological proposition is a contradiction.)
1, 2, 3 are axioms, 4 is the statement, 5( misnumbered 4) is the deduction. Sorry 'bout that!
—When I was an atheist, my biggest problem with God was that He wasn’t necessary.—
I’m not sure why one would have such a problem: many things that are, are not provably necessary. I exist: but I was not necessary in all possible worlds. Perhaps aliens exist: but I can think of no reason to believe that their existence is necessary. That doesn’t mean that they don’t, however. Perhaps a God exists, perhaps not.
—And necessity, of course, is a key component of William of Ockham’s famous Razor, a component seldom even intimated, I might add, in most pop-culture paraphrases of it. The one that irks me most is “All things being equal, the simplest solution is the best”. Ackkk! What the hell? Ockham wrote, “Entia non sunt multiplicanda praeter necessitatum.” Beyond necessity. He rightly in no way advocates that we discard necessary entities just because doing so might simplify matters.—
Quite so: but the problem applying the Razor to this situation is that Occam is talking about the necessity for the explanation of a particular phenomena, NOT trying to assert that entities THEMSELVES must be, by definition, or in all possible worlds, necessary, before their existence is acceptable and demonstrable. The Razor is only rightly used against a suggestion of God’s necessity, given some particular phenomenon we wish to explain, and the claim by some that it can best be explained by god. It has no useful bearing whatsoever on the direct question of god’s existence itself, or any posited entity.
—Thus, I suppose, it is normal that when I experienced God’s presence for myself (as it so happens while on a quest to prove the incompetence of biblical scholars) He became suddenly necessary in a very personal way. He is more real to me than the hand in front of my face.—
This is yet again another sort of necessity: a personal one. The problem comes in telling others that what you experienced was god’s prescence, when that is merely your interpretation of your experience: an experience not immediately avaliable to others so that they can examine it and interpret. You may feel that it is necessary for you to believe what you believe, but that can only ever tell us about you, not about objective reality.
—Frankly, I see Tisthammer’s argument more as uncontestable proof that a rational man can believe in God than as uncontestable proof that God exists, proof that can only be acquired subjectively because of our nature and the kind of beings we are.—
A rational man can be wrong. The fact that someone is rational, and can give a proof phrased in the symbology of logic, does not mean that the proof is both correct, meaningful and convincing, or even that, if it is not correct, meaningful, or convincing, that the person advocating it is not a rational person. The kind of beings we are is the kind prone to error and misjudgement: that, after all, is why we even NEED a system like logic to examine our claims in the first place.
It is quite easy for rational men to make rational arguments about gods, as everyone should agree. The only relevant question is whether they are convincing or not.
Newton Meter
A very quick question – we’ve been saying K means that “K exists in all possible worlds.” Wouldn’t a better “translation” (especially in the context of this discussion) be “K is a property of all possible worlds?”
** Maybe the mods can merge this thread into your “Up The Butt, Bob” thread. 
About what experience is that not true? That’s not anything exceptional to the theist. What experience of mine have you shared in the same way and with my consciousness?
I know of no rational argument about gods. Can you link me to one?
Now, that’s funny.
No… you see, your original postulate is that IF god exists, then he exists necessarily. The reason for this is that god is the greatest perfection, so because of symmetry he must exist in all possible worlds. The reasoning is NOT that his nonexistence is not possible in any possible world. In the same way, my postulate says that IF god is nonexistent, then he is nonexistent necessarily. Not because his existence is not possible in any possible world, but because he is the greatest perfection, and therefore because of symmetry he must be nonexistent in all possible worlds.
Libertarian:
Excellent post. My biggest problem with ontological arguments has always been that they failed both to convince and to explain. They don’t seem compelling enough to a non-believer, and they don’t explain the real reasons one believes in God. Perhaps I have to give up both of those prejudices in light of what you’ve just said.
I never doubted the rationality of belief in God. Lest that seem like a major concession, I also do believe in the existence of God. My concern is to avoid assuming too much (or at least, to identify when we do).
Well, surely that’s a postulate you have to make regarding God. Nothing generally prohibits <>P and <>~P (or do you mean <>P and ~<>P?)
But I’ll back off from rsa’s argument a tiny bit. It is ambiguous, and his clarification hasn’t helped matters for me. Let me try to help, rsa.
I think just one modality is all we need. If P is true in this world, we write “P”. If P is possible in this world, we write “<>P”. When you say “possible in some…worlds”, I think you might mean that there is some world where <>P is true, that is “<><>P”. When you say “…but not all worlds”, do you mean that ~P is possible in some worlds? That would be “<><>~P”, which just says that P is possibly not necessary: “<>~P”. Or do you mean that P is not possible in some worlds: “<>~<>P”, which would be “<>~P”, an entirely different thing (<>~P says that P might not be necessary, <>~P says that P might be impossible).
Your >< modality seems to be most properly written as (<><>P & <>~P). I think you might be iterating modality more than you intend (for instance, I think you might be using “possible” to simply mean a disjunct (one of the propostions in a disjunction (logical OR)). If accessibility is transitive, <><>P is equivalent to <>P and <>~P is equivalent to ~P. This seems to be what you are trying to say:
(<>P & ~P) = P is possible and P is not required
Which can be rewritten also as:
~(~<>P V P) = It is not the case that either P is impossible or required
or as
(<>P & <>~P) = it is possible that P is true and possible that P is not true
those are all the same thing. Do they sound like what you’re trying to say?
If you intended (<><>P & <>~P) instead, then you could get something else: (<>P & ~<>P), P is possible and P is impossible. I suspect this isn’t what you really want.
Your () modality, “possible in all worlds, but not just in some worlds”, might just be necessity. Or, it could just be possibility. If P is possible in this world, we write “<>P”. If P is possible in all worlds, then its possibility is necessary: “<>P”. In some logics, <>P is equivalent to <>P. Or perhaps you mean something else: that P is possibly necessary (rather than necessarily possible)? Do you mean
—The greatest possible being is that which is perfect in every possible world.—
Again, there is no neccessary ideal connected with the concept of “perfect.” Perfect in regards to what set of ideals, and why only that collection of ideals?
—Well, we aren’t using it by itself. It’s used with other words. (Look for the squiggly marks.)—
Which are, as I said, ultimately a list of lacks, not a being. How many times do we have to run through this before you address more than half of my response at a time, instead of the whole response? How is a being that lacks any characteristics different from no being at all? Once we’ve proven the existence of this entity, what are we left with: an entity which still cannot be distinguished from a non-entity.
—It proves that a being exists Who is greater than any other.—
In that it lacks any positive characteristics that would thereby provide grounds for a comparison with any other. So? One can do the same with any collection of lacks. Nothing ventured, nothing gained.
Further, it certainly in no shape or form establishes an entity that is a “Who.”
K? We’re not talking about K, we’re talking about G here.
The most faithful translation of K would be “in all possible worlds, K is true”, or “K holds in all possible worlds”. In this case, the proposition G is something like “God exists”, so we are saying “in all possible worlds, ‘God exists’ is true” or “‘God exists’ holds in all possible worlds”. Slipping between truth and existence is sloppy of us.
I’m not sure what the thrust of your question about properties is. We could define a property or a predicate on worlds. For instance, a world might have the God-property iff it is the case that ‘God exists’ is true in that world.
That would be legitimate, but it raises the question of what the decision procedure for the God-property would be.
I agree, that is funny.
I’m done for the (long) weekend. Let’s talk about something interesting when I get back. 
—I know of no rational argument about gods. Can you link me to one?—
Come on, I wasn’t being facetious. I meant different conceptual gods (such as necessary vs. contingent ones), not several actual gods (like the Greeks). Of course, we might not have covered the objection that there could be an infinate number of “maximally perfect” beings (whatever THAT means), none of which is inferior to any other being, have we? If the argument is good once, why not twenty times over?
—About what experience is that not true? That’s not anything exceptional to the theist. What experience of mine have you shared in the same way and with my consciousness?—
I didn’t argue that it WAS exceptional: I pointed out that it was a different sense of “necessary.” Strangely, it echoed D.Z. Phillips: “God is a necessary reality in the hearts of believers.” About what strong, passionate belief is THAT not true, regardless of whether the object of belief exists or not?
Night
But I’m asking you to define necessary nonexistence. I don’t know what it means. I’ve never seen the term used.
Newton
Yes, the latter. As stated, Rsa’s axioms declare at once that God may possibly exist in all worlds AND that He may not-possibly (there is no possibility that He) exists in any world. Both can’t be true, and if either-or is true, then it’s a tautology: “Well, either He exists or He doesn’t”, which is always true.
Apos
Perfect in the sense of maximal. Ideals that are synthetic a priori. Only those are allowed because otherwise, the descriptions would be analytic.
Your saying it doesn’t make it so. Synthetic attributes that are also a priori may be (and are) given to Him. He can know all that can be known. He can do all that can be done. He is eternal (infinite temporality). He is as good as good can be (maximal positivity). And in general, any such attributes that have maximal positive perfections may be assigned to Him.
Grounds? […shrug…] I don’t know why you would have any problem comparing Him with other beings anymore than you would have a problem comparing infinity with, say, 42.
Inasmuch as He is, in essence, quite like you, only perfect, I think He deserves a “Who” as much as you do.
Once you’ve changed the definitions for an argument, you must start over with new postulates and premises.
Necessary simply means truth in every possible world. At least for the topic under discussion, it does.
I have a hard time believing that you do not know the meanings of the two words, or that you are incapable of putting them together.
Necessary:
Nonexistence:
So I guess necessary nonexistence means that the condition of not existing is logically inevitable.
For the proof, the first postulate could just as easily say that the condition of not existing is logically inevitable, as it could say that the condition of existing is logically inevitable. Because the definition only means that whatever state of existence god has is logically inevitable - no particular state of existence follows from the definition, because no particular state of existence is greater or more perfect than another. Only the logical inevitability could follow from perfection, and even that is a stretch because you have to base greatness on symmetry, which as you are aware is hardly what most people base greatness on, and therefore the god you define is hardly the god most people conceive of.
As it is, even if I fully accepted the proof it does not prove what kind of existence god has. Even if the proof is valid, god could just as easily exist only as a concept (and as I have argued, this is more likely because concepts are more perfect than real things). Since the proof can tell us nothing about god’s existence it is rather worthless. So the concept of god exists; so what.
Still, even proving the concept of god exists is a bit much for this proof. The fact is, it is only the contrived logical system used for this proof that allows it to work as well as it does. If this logical system is incapable of expressing logical ideas such as the idea that it is logically inevitable that something must not exist, then I would have to say that the logical system is very flawed. It intentionally leaves out certain valid logical ideas that would be bad for its purpose. It is only the flawed nature of this logical system that allows a postulate such as “god is not impossible.” Of course we don’t know if god is impossible; but because of this logical system we can say that he isn’t. As far as I can tell, it is a flawed logical system created for the sole purpose of having loopholes that will allow for a rather meaningless proof of god existing as either a real thing or a concept or some other kind of existence, most of which have no impact on us.
Obviously, Night, I do know what the two words mean. But we aren’t Beavis and Butthead having a casual conversation here. We can’t just pull terms out of a hat without defining them, especially when they’ve never been used before in the context of an ontological argument. There can be no such thing as “necessary nonexistence” the way you use the term. Such a thing, an a priori X, where ~<>X in every possible world, cannot be conceived or defined, let alone said not to exist.
But I’m surprised to see that materialists are now reduced to assailing their own epistemic bastion, reason. Unable to find technical fault in Tisthammer’s argument, you’re now engaging in rhetorical arm flailing: “Oh! He’s not talking about a thing; he’s talking about a concept! You see? Everything is a concept except for things that I say, like chemicals and planets and such.”
I’m not even going to address baseless complaints that modal arguments are valid only when their conclusions suit us, as when a computer spits out a result, or when a physicist shows that black holes must exist. Frankly, I’m disappointed. At the very least, you could say, “I don’t like the argument, and I find this or that questionable, but I must say that, while I do not think it proves God’s existence, it clearly demonstrates the intrinsic fault of hard atheism, namely that denial of God’s existence a priori constitutes a contradiction, a substantive denial of a positive ontological proposition.” Which, by the way, is exactly what “necessary nonexistence” does.
Yes, I am prejudiced. But I take great care not to allow my prejudice to blind me to clear and compelling reason. I expect others to do the same. Even materialists. And even when conclusions don’t suit them.
I am not assailing reason; I am saying that the system of logic used in this proof is not reasonable. It is a contrived system that allows us to make postulates that we can in no way verify.
Now, you have a reasonable argument to say that it is wrong to accept this flawed logical system when the results suit us, but not when they don’t. But the thing is, when we use this type of logic we ARE always talking about concepts, not hard facts. Some people might believe that black holes, for instance, are a hard fact. But most would admit that they are a concept which is useful in explaining hard facts. And that is the flaw in this proof. It seeks to use a system of logic that can only be used to create useful concepts and theories, in order to prove a hard fact.
There are many scientific theories that we use, that we know are not really true. In fact there are theories that contradict each other, and yet we still use them! We use them simply because they are useful. We do not have to believe them to be facts. Tisthammer’s proof is also not the kind of thing anyone should take as a fact. The difference is, that it is not useful, and therefore has no reason to exist.
The system of logic used in this argument is the cornerstone of modern model checking in every discipline from chemistry to physics to computer simulations and games. You won’t find anyone willing to accept shrugging it off as “not reasonable” other than those who don’t know what it is.
The notion of a “hard fact” is itself a concept if you want to play that game. People who cherry pick reason for their own comfort remind me of Lucy and Ethyl in the candy factory. It isn’t long before their mouths are full, their pouches are overflowing, and globs of chocolate lie in puddles all over the floor.
Wow. If God is Objective Reality, I guess I’m almost a converted theist 
I have to admit, though, I don’t do to much of my Quran reading. No, seriously. This is very encouraging because it demonstrates how most atheists and theist share a common conviction in some Absolute that imposes on us a way of being. But, I guess from there onwards the paths split pretty decisively.
I think it’s relevant to address this topic here because, after all, we are talking about if God can be rooted in reason. I can see why many forget logic to be meaningful and get lost in the rule’s game. All these placeholders floating around like P and G and ~b. And then symbols like V and => and and <>. Then we are told this is how they behave, basta. Like it or not. However, the formal symbols in logic are assigned a strict meaning derived from a priori realizations about the nature of thought. The debate about the validity of formal logical systems is an epistemic discussion.
For example, regarding modal logic, Quine writes:
It’s all about meaning. We may replace statements with variables. But the operations we perform on such in-an-of-themselves meaningless entities must make perfect sense. The rule of the excluded middle isn’t an optional “let’s add some spice to the game”. We can question it in the context of fuzzy sets. Nonetheless, the reason why fuzzy theory remains controversial is that the excluded middle seems to intuitively to follow from our deep conviction that a thing is or is not.
Ethic, an excellent post with exemplary analysis and commentary. Thanks for that important contribution to the thread.
Eris
Good question. Probably not. I think I’ll do that.
Okay, it’s done. I hope that Tisthammer will honor us with his presence.
Me, too… that would be interesting.