Sorry, I missed that, yes I was using 1 as a subset of mathematics.
But then if God is defined as that which necessarily exists in all possible universes.
And mathematics necessarily exists in all possible universes. Then Mathematics is a possible answer to “What is God?”
Or does something that exists in all possible universes not mean that it necessarily exists in all possible universes?
To be fair to him, all the confusion about what the characteristics of God are come from various brands of theists who disagree.
This is exactly what I was getting at. You are a gentleman, sir.
That’s not quite what I was getting at, which is psychological more than logical. I think you can prove, through contradiction (and you either implied this or stated it outright - I’ve been to a conference today and my brain is muddled) accept the premise that god is not necessary - in other words a world exists without god, is contradictory to the premise that god is possible. So from this innocuous premise come major inferences. I have admitted that god is possible, but I was not referring to your definition.
BTW, I am not proving, demonstrating or asserting that your premise is not true. I am withholding judgement on it from lack of evidence. I believe you started this to test Scott’s assertion that a proof would change his mind. I won’t talk from him, but I think one can argue that agreeing that if you accept the premise of possibility you buy existence is less convincing than proving existence from more generally accepted premises.
BTW, it seems that we are closing on agreement of where we disagree much faster these days. That’s progress!
If A is necessary, then in every possible world, A is true.
Now, let’s talk about Wittgenstein. He crystalized the rather self-evident notion that a label’s meaning and the thing the label represents are not the same. In other words, the meaning of the word is not the object that it names. To help clear this up, we can use a Kripke style nomenclature. (Kripke was a big fan of Wittgenstein.) Consider the word “APPLE”. And consider the object that the word names. We can map the word “APPLE” to the object, apple. But that’s all it is — a mapping. The object, apple, is made of atoms. The name, “APPLE”, is made of letters. They are not the same entity. We can also call the object, apple, “POMME”. (Which is what they do in France.) Both labels, “APPLE” and “POMME” map to the same object. It doesn’t really matter how complex the label is, or how many words it has. Thus, we can also map “TUNDA LA KIZUNGU” to the object, apple. (Which is what people who speak Swahili do.)
But there is no rule that requires us to stick with cultural languages. We can map anything we can scribble. We can map “X” to the object, apple. Or “[symbol]§[/symbol]”. Not only that, but we can, if we wish, map to the object, apple, some word that does not ordinarily mean apple. We can call the object, apple, “PEAR”, or “WOODEN DESK WITH LAMINATED SURFACE”.
Or, we can call it “MATHEMATICS”.
As long as we make clear up front to what object we are mapping, we may use any term we like. Now, most people will protest mightily if the term is too confusing, which likely would be the case if we map “MATHEMATICS” to the object, apple. After many years of using the word, it is an onerous task to think of it differently upon seeing or hearing it. In speech or writing, it would require quite some effort to get used to a person saying something like, “Let’s make a mathematics pie.”
So what we naturally try to do is use or borrow terms that, at the very least, closely resemble and are normally associated with the common meaning that is usually mapped to a given object.
Now, let’s take what we’ve learned from Wittgenstein and Kripke and apply it to the ontological argument. To do so, let’s first consider what exactly it is we’re talking about when we make an ontological argument. Certainly, what we are talking about existence. That’s what ontology means: “The branch of metaphysics that deals with the nature of being”. (American Heritage). Already, we know that we are not going to discuss what kind of hair, or what kind of color, or what kind of knowledge, or what kind of power — we are going to discuss what kind of existence. We are going to discuss the nature of being. Existence and being are, in fact, “synonyms: existence, actuality, being”. (American Heritage).
Therefore, we are going to talk about a being. Now, if we want to talk about something else, fine, let’s do so. But if we DO want to talk about a being, why don’t we, well, call it a being?
Now, we know that we’re going to discuss a being (an object that is in existence or has the quality of being). We could discuss the existence of coffee, tulips, or mathematics. We could talk about a mathematical being. If so, we would be concerned about the existential properties of mathematics. Things like cardinality and ordinality. Or, we could talk about a supreme being. If so, we would be concerned about the existential properties of supremeness. Things like “Of the highest order, quality, or degree; surpassing or superior to all others”. (American Heritage).
If we map the label “MATHEMATICS” to the object, supreme being, we face the same difficulty that we face when we have to talk about baking a mathematics pie. It jerks at our cognizance, and makes discussion unnecessarily difficult and laborious. We are not interested in properties like square root. We are interested in properties like highest quality. Still, nothing stops us from doing so other than convention, so yes, we could call the object of the proof “MATHEMATICS”.
But that would mean that we are not talking about mathematics as it is commonly understood. In fact, it is so far removed as to be ridiculous. We would be talking about something altogether different — an object that is ordinarilly mapped to other terms. We would have to remind ourselves constantly that when we use the label, “MATHEMATICS”, we mean supreme being. Although it is something a person could do, why it would be something that a person would want to do is a mystery, unless it is for the sake of sheer novelty or, at worst, deliberate obfuscation. Why go there at all? Let’s don’t.
So, let’s look at the existential properties that we ARE interested in, and see whether we can find a label that is a better match. What does it mean to have the highest order of existence? Or to have an existence that is superior to all others? Clearly, it means an existence which must manifest in every possible circumstance. In other words, the highest possible order of existence would be existence that would never NOT exist so long as existence were possible. There can be no bounds of existence that surpasses all-possible-existence.
Now, here is where someone who is unscrupulous might try to slip in a parlor trick. He might say, “Well, what about existence that is NOT possible? Shouldn’t the supreme being have that kind of existence as well?” (Believe it or not, I’ve seen it tried.) Well, okay, let’s give for the sake of argument that we mean both all existence that is possible and all existence that is not. Let’s call all possible existence “A”. Then all existence that is not possible would be “~A”. (Not A). That means we would be discussing (A And ~A). But (A And ~A) is the definition of contradiction. Both A and ~A cannot be true. Only one of them. Therefore, we must select one and only one to discuss. Now, which one seems to be a higher order of existence to you — no existence at all, or existence in every possible world? You’d be surprised to know that some people might argue for no existence at all, but for some people, believe it or not, the emotional attachment to their preconceptions is so strong that they will stop at nothing to weasel out of a conclusion that they don’t like. That’s the wonderful thing about logic. It catches parlor tricks. Although people might try to misuse logic, the eye that knows its rules will always spot the trick.
What does it mean, then, to exist in all possible worlds? First, it would be helpful to know what we mean by “possible”. A good definition might be: “Capable of happening, existing, or being true without contradicting proven facts, laws, or circumstances”. (American Heritage). We might say that if something is capable of being true, then it is not necessarily false. All we need now are symbols for necessity and negation. Let’s use “” for necessity. (Just because of convention.) And for negation, let’s use “~”. (For the same reason.) Now, if A is true, then ~A is false. (By the Law of Noncontradiction that we discussed just above.) We can now easily write the statement, “A is not necessarily false”: ~~A.
Extracting necessity back out is as simple as constructing possibility. Simply remove all the negations: A. Or, A is necessarily true. Therefore, to exist in all possible worlds, without negation, is to exist necessarily. We can reasonably map supremeness to necessity, and being to existence. Thus, our proof is about Necessary Existence. Or Supreme Being. Necessary -> Supreme. Being -> Existence. Protests against this mapping smack of disingenuousness and unreasonableness to me.
So, here we are. We have decided to construct an ontological argument. Because of this, we know that we are discussing existence. Not power. Not knowledge. Not morality. Not judgment. Not whether the being is as depicted on the Sistine Chapel. We are discussing the bounds of existence. We know also that there is no greater bounds than the greatest possible bounds, because we know that that which is not possible contradicts that which is. And we know that the maximum possibility is necessity — possibility without negation, realization in every possible world. And we know that if it surpasses all others (from American Heritage), there is only one. (Otherwise, it would surpass only *most * others, not *all * others.) We are discussing the Supreme Being.
If anywhere in what I’ve said, you spot a logical flaw, or a hyperjump, or a parlor trick — you tell me where it is. Otherwise, I must ask you — which label more reasonably maps to Supreme Being, God or mathematics? But either way, by whatever label, the object itself does not change. It is simply a matter of convention and reasonableness to call the Supreme Being God.
It is, and I appreciate it. I suppose where we disagree is two-fold: (1) whether God is defined coherently, and (2) whether acceptance of ~~G compels the conclusion, G.
As to (1), I believe I’ve made a good case in my remarks to Bippy for the coherence of the definition. I extend to you the same invitation that I extended to him to examine my reasoning for error. As to (2), the conclusion cannot be discarded without discarding the rules of inference that produced it.
Once you’ve accepted ~~G, there simply is no turning back. It isn’t the case that you could do it all differently from there and draw some different conclusion. And thank goodness. Were that the case, logic would be inherently contradictory and supremely unreliable.
-a quick one for now, as I will need time to really consider that excellent and well appreciated post of yours Liberal -
Have you not just added a new term to the ontological argument, that God is the supreme being. I thought the only definition put on God in the o.a. is that God is necessarily existant? I certainly don’t make any claim for Mathematics being the supreme being, just that within the o.a. it could be substituted for the word God without breaking any part of the arguments logic.
That’s actually covered pretty thoroughly beginning with “So, let’s look at the existential properties that we ARE interested in, and see whether we can find a label that is a better match”.
I covered that as well. In fact, the whole post was about that. You can use the word “Samxthanax” if you want, just so we both know that it’s mapped to supreme being. But what’s the point? The word “God” has been mapped to supreme being for, well, for a long long time. Why NOT use it? Because of certain extraneous baggage? Well, if “God” has baggage, then “Mathematics” has the whole airline.
Bippy, if you’re in a hurry, for the SB - NE thing, you can go straight to:
“Thus, our proof is about Necessary Existence. Or Supreme Being. Necessary -> Supreme. Being -> Existence. Protests against this mapping smack of disingenuousness and unreasonableness to me.”
That’s in the third paragraph from the end. But please read the supporting commentary as well. It might answer a lot of your questions. I know it’s a long post, but all I’m doing now is repeating parts of it. I tried to be as thorough as possible. I don’t believe that there is much left unanswered.
Necessary doesn’t map at all to “supreme” to me, either in common usage or in modal logic usage. Nor does “being” map to “existence.” Gravity has existence, but gravity is not a being in the sense that the word is most commonly used.
The mapping feels kinda ghoti to me. While in some cases “necessary” may be synonymous with “supreme,” those cases are rare–and divorced from those cases, “supreme” means something different. Same thing with “being” and “existence.” And when you put them together, you’ve got the gh from laugh, the o from women, and the ti from nation: while you might pronounce the result as “fish,” most people will disagree that you’re justified in doing so.
I do not believe that’s either disingenuous or unreasonable.
Daniel
I disagree that we disagree about these.
I think your definition is coherent but not useful. In fact yours is the only coherent definition of God I have seen. It is inconsistent with common definitions, but that does not mean it is not coherent. The closest thing to another concise definition I can imagine is that God is as defined in the Bible, but this is not very good since there are contradictions, so there is interpretation needed.
Now, why do I say it is not useful? Because it is not remotely testable, from either side. Clearly you can never demonstrate that a God is existent in all possible worlds. But you can’t even disprove it, since even if you have strong, even Biblical, evidence for a supreme type being, if one whispers in your ear and parts the Red Sea, it does not show that this entity meets your definition of God.
As for the second part, if ~~G implies G, the ~ ~~G implies ~G. But we do not know the truth value of either G or ~~G, so while this is an interesting exercise it doesn’t say much about the topic in which we are interested.
With respect to existence (the topic and context of the proof), what would you say is superior to existence in all possible worlds? Also, rather than merely disagreeing with the conclusion I reached, would you mind pointing out a specific flaw in the argument that I built to reach it?
Okay. 
Testable? Since when is a definition — any definition — testable? How do you test that gravity means “Solemnity or dignity of manner”?
I think you meant ~~~G, since ~~~G is contradictory prima-facie. But that’s what I’ve said all along. You may deny “it is possible that God exists” by asserting “it is possible that God does not exist”. But if you do, you have the onus of defending the untenable position that there might not be existence in all possible worlds. If they are possible, why don’t they exist?
Oops, I meant to address this, Voyager:
Inasmuch as I spent an hour or two explaining why it is in fact consistent with common defintions, would you mind showing me specifically from my text where I went wrong in your view?
Here is a non-serious answer:
Take a random sampling of people, and ask them what the word “gravity” means.
If one of them answers “That thing that is like a brownie, but made without coco”, then we know that there is something wrong with our understanding.
How do you know they don’t?
Thanks again Liberal I will read and cogitate on your reply when I get home from work.
If you ask a random sampling of people the meaning of supreme being, will not a sizable number respond, “God”?
Well, if they do, then the statement that they possibly don’t is false.
You’re welcome. Take your time. 
I might not even get to respond any tomorrow. Looking to be a busy day.
Yes, that is quite true. However, some will say, “The invisible pink unicorn”, and resist any attemp to shoe-horn her into being called a mere “god”, some will say “Hank?” other will say “Do you mean the invisble gravity elves?”, and other would say the concept is meaningless.
I must be missing something here.
Regarding the notion that necessary existence is not mapped to supreme being, I would be interested in citations and lines of reasoning from philosophers who hold the view — because I can’t find any.
Even Immanuel Kant, who, to his own embarassment later, argued against even the possibility of necessary existence, begrudgingly acknowledged that it is reasonable to say that a being that exists necessarily is the supreme being. Kant wrote:
Descartes wrote:
Even opponents of the ontological argument concede that the mapping of supreme being and necessary existence is reasonable. Caterus wrote:
Leibniz wrote:
Finally, to those who maintain that necessary existence is somehow foreign, new, or untraditional with respect to mainstream Christianity and how it commonly views God’s ontological nature, I offer this written by Calvanist, Kelly James Clark:
You said to test the definition by asking people what the word means. I posit that a significant number of people would say that supreme being means God. Including these people.
Well, let me review for you.
I said, " But if you do, you have the onus of defending the untenable position that there might not be existence in all possible worlds. If they are possible, why don’t they exist?".
You said, “How do you know they don’t?”.
I said, “Well, if they do, then the statement that they possibly don’t is false.”.
Put another way, how can it be possible that the possible is possibly not possible?
You got me. I should have said orthogonal to common definitions.