Nope, Kit. You’re not dragging me back into this. The record is what the record is. If you care to look for what I’ve said, have at it. Starting tomorrow, I have a five-figure contract that I’m going to work on until I get it done. I might drop in occasionally, but I have the discipline to know my limits. God already exists. That money won’t exist until I finish my work. 
Oh pleeeaase? C’mon. Y’know you want to really!
Nah, that’s fine with me. I just noticed that you’d kept posting after saying you’d stop, so figured you might find the call of the debate irresistable and keep posting. Good luck with the contract.
Thanks. But I didn’t say I’d stop posting. I said I was throwing in the towel and that I couldn’t keep up with the barrage of posts. Do you understand the difference? A post like this takes, what, two minutes to compose. As you can see by the time stamps, I spent sometimes all day on the others. That’s what I’m stopping.
(And you’re right, I do want to continue. But hey, the proof is there. The inferences follow from one another. The axiom is reasonable. And the definition is coherent. I think it holds just fine on its own.)
—But hey, the proof is there. The inferences follow from one another. The axiom is reasonable. And the definition is coherent. I think it holds just fine on its own.—
Let’s not drag what you think into this again! It already seems as if you’ve become more important to the threads than the proof itself, which is what got you into this mess in the first place. 
So, potential questions, for anyone…
-
If we include Lib’s concept of exercised vs. unexecised capacity, couldn’t this being could be consistent with any logically possible being (except only that it is “capable” of being maximally more).
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Is the proof’s use of the axiom illicit? It seems to treat necessary existence as a characteristic of a being in a possible world: more than the modal sense of “possible” can legitimately grant to any being.
Wouldn’t the axiom (A=A) work as ‘god’?
A=A exists in this possible world, so it is necessary (exists in every possible world), including the possible world that is composed of nothing but A=A (if I understood correctly that a possible world is one that contains at least one true statement, namely A=A).
Am I correct in thinking that anything else wouldn’t work as god because it would not exist in the possible world composed solely of A=A?
The problem is that A=A proves nothing interesting to distinguish any A from any other A, certainly not to distinguish a god “A” from the various other possible beings. The proof here at least has the merit of trying to establish the existence of a Supreme Being.
—A=A exists in this possible world, so it is necessary (exists in every possible world),—
It is my understanding that actual existence does not in the least imply necessary existence. I actually exist: but there are plenty of possible worlds that can be formulated without me in them. I am not a necessary being (unless actualism is true).
A=A might well be a necessary truth: but not BECAUSE it is simply a possible or actual one.
Apos writes:
“So, potential questions, for anyone…”
Hey, yeah, I think it would be nice to discuss this without Libertarian. So I’m gonna jump back in.
(Hey, Libertarian. I am not going to discuss anything with you.)
“1) If we include Lib’s concept of exercised vs. unexecised capacity, couldn’t this being could be consistent with any logically possible being (except only that it is “capable” of being maximally more).”
By one definition of exercised capacity, yes. I don’t think this is worth discussing though, as I believe the “proof” is fatally flawed in the first place.
“2) Is the proof’s use of the axiom illicit? It seems to treat necessary existence as a characteristic of a being in a possible world: more than the modal sense of “possible” can legitimately grant to any being.”
This is the same point I have been making (I think). I object to any statement of the form “In a possible world a modal statement holds.” (Where a modal statement is one about necessity or possibility.) I think you are specifically objecting to saying <>G since Libertarian’s G=G would give <>G, which means “In at least one possible world, it is true that in each of the possible worlds G is true.” Which does not make since, since the possible worlds do not live in individual possible worlds.
Kitarak raised a good point that G=G is not a legitimate definition, and seems to prefer Dougherty’s “G is a being with the property G=>G” definition.
Well, Dougherty’s proof uses Brouer’s theorem: (p=>p)=>(<>p=>p). And the only proof I have seen of it
http://www.angelfire.com/mn2/tisthammerw/rlgn&phil/ontological.html
uses Becker’s postulate, which introduces a statement of the form “In a possible world a modal statement holds.” (Specifically, ~G.) And in that case, the objection I think Apos shares with me applies.
I guess the issue remains: can you prove Brouer’s theorem without making the type of problem statments I am talking about in this reply?
That is, without saying that in a possible world a modal statement must hold?
Well, in Trent Dougherty’s presentation of the proof of God’s existence:
http://www.abarnett.demon.co.uk/atheism/ontol.html
he says that:
“One of the most used systems of modal logic is called S5. There is an interesting theorem in S5 called Brouer’s Theorem.”
According to this Stanford link:
http://plato.stanford.edu/entries/logic-modal/
S5 allows this sort of problem statment. Although Dougherty notes “This theorem [Brouer’s Theorem] is derivable in weaker systems as well.” Perhaps he means S4? Well, then according to the Stanford link, S4 also allows such problem statements. (Unfortunately, Dougherty doesn’t present a proof of Brouer’s theorem.)
As I see it, any worthwhile discussion must address these points:
- Can you prove Brouer’s theorem without requiring a modal statement to hold IN a possible world?
- And then can you use Brouer’s theorem to complete the argument without using such a statement?
Because as I (and I think Apos) argue, modal statements cannot be true or false IN a possible world.
(This isn’t to say systems like S4 and S5 might be useful in other applications, where such statements make sense in terms of what they are being applied to. Just that using the sound interpretation of possible worlds and necessity and possibility, it does not make sense in this application.)
Well, here goes:
The question, as you should realize, Lib, is not whether the greatest possible existence can be impossible, but whether it can be possibly not.
In other words, is it possible that there is no “greatest possible existence”?
Is is possible that there is no “greatest integer”? Yes. It is even true.
Suppose we have an infinite sequence of worlds, such that the greatest existence in world N is greater than the greatest existence in world N-1. Then there is no “greatest possible existence” since there is always a world with a greater existence than the one you’re thinking of.
Oops. I seem to have missed several pages of the discussion. Please disregard my previous post.
“Greatest possible existence” refers to existence between worlds, not within, FriendRob. Nevertheless, your ideas are correct (just substitute an infinite number of beings for your infinite number of worlds and the argument holds).
The problem is that Libertarian doesn’t only want to demonstrate that the greatest possible existence exists (which it does, if you’re willing to accept an infinite existence), but that necessary existence exists.
I was under the impression that A=A is a necessary truth, since a possible world without A=A could not exist (you would only be able to make false statements).
What’s wrong with only being able to make false statements?
Why can’t false worlds be considered to be possible?
—I was under the impression that A=A is a necessary truth, since a possible world without A=A could not exist (you would only be able to make false statements).—
A=A IS a necessary truth. But proving that requires more than simply noting that it is a possible truth, or even that it is true in the actual world. Your original post simply said that it was neccesary because it was true “in this possible world.” And actually, you even said it exists. This in itself is a little mislead: A=A is a logical truth. It doesn’t “exist”: it is, rather, a true statement (necessarily so).
Because in such a world, <>W is itself false.
Libertarian:
If you’ve already explained this, maybe I missed it, or it just went over my head, but other people have alluded to it, and I haven’t seen it explained in such a way that it made sense to me. So please explain in layman’s terms:
G is the greatest possible existence, granted. In my mind, I interpret this as follows: If you could somehow take each entity in this world, and quantify it with value X, and then take each of these quantities and order them, G would be that entity for which X is the greatest. This would mean that G had the greatest sum total of traits, but why does that require that he have the greatest value in each trait? For instance, say in the group of Bob, Ed and me, Bob is the best violinist, and I am a close second. Ed is the best mathematician, and I am a close second. If you quantify us based on those two traits, I am the greatest of these beings, without being the greatest at any single trait. How does the designation of “greatest possible being” guarantee having the greatest quantifiable value of all possible traits? And if this proof is somehow geared towards individual traits (say, it is proof that there is being with the Greatest Possible Wisdom, and a being with a Greatest Possible Bowling Score, and whatnot), how does it guarantee that all of these are the same being? Is it logically possible to infer from this proof that there are, say, a pantheon of gods, each one personifying a specific trait? Or does the proof preclude that?
Sorry if you’ve explained this and I missed it, but logic theory isn’t my forte, and while the proof makes a superficial sort of sense, I couldn’t explain it to someone else to save my life. I’m trying to change that bit. Thanks for your patience,
Jeff
btw, this is a damn interesting thread.
—This would mean that G had the greatest sum total of traits, but why does that require that he have the greatest value in each trait?—
As I understand it, this is simply straight from the initial definition of supreme being/greatest possible. For arguement’s sake, let’s say you construct a world in which there is a being which is the greatest possible violin player (greater than any other player could possibly be). It is still logically possible to construct a world, however, where it is both the best violin player AND the mathematician, and so on. The definition insists that we are talking about the latter possible being, not the former.
Jeff
Well since you ask nicely, I’ll give you a necessarily brief response. (It has already been covered, and I won’t be able to address fourteen rehashed protests.)
Apos has it essentially right. It’s not a matter of quantifiable value, but of qualifiable value: the relation is ordinal, not cardinal. Think of the Being’s accessibility among worlds as analogous to having legs. Though it might have only one leg in world A (where only one leg is possible), it might have a bazillion legs in world B (where a bazillion legs are possible). Remember that the Being exists in all possible worlds. In whatever world there is attribute X, the Being manifests the greatest possible X. Worlds where the Being cannot have at least one leg do not exist. So, it isn’t a matter of having a given number, but of having the most possible. What number the most possible is is irrelevant, since contingency inheres to the worlds and not to the Being.
It doesn’t matter whether a violin, due to contingencies on the worlds, can be played better in world A than in world B. In world A, the Being plays the violin the best it can possibly be played there; likewise in world B. Like Apos alluded to, noncontingency must hold. (That’s the nature of necessary existence, the Being’s definition.) Therefore, the contingency of world A cannot constrain the Being because, if violin playing is possible at all in any world, it can be shown (and I leave that as an exercise for anyone interested) that there exists a world in which voilin playing can be the greatest possible of all worlds. The Being plays violin also in that world.
If it helps, you can think of the Being as a metaworld of its own, since it is the convergence of all truth.
Even if you accept the argument, the God whose existence is concluded is not the God of the Bible, as evidenced by this statement contained in the Bible:
2 Thessalonians 1:8-9 reads:
“Blazing fire, inflicting punishment on those who do not acknowledge God and on those who do not obey the gospel of our Lord Jesus. These will pay the penalty of eternal ruin, separated from the presence of the Lord and from the glory of his power…”
Here hell is described as a world without the presence of the biblical God. Since hell is a possible world, this means that the biblical God’s existence is not necessary.
NICE!!!
Indeed. There are those who worship God, and there are those who worship the Bible.