Mort Furd
I suggest that you go find the man who lowered the dignity of Great Debates with a wild and renegade post that invoked retarded chimps and microcephalic mice. Find that man and scold him thoroughly on behalf of us all.
Hawthorne
How many implies cardinality. All that can be said is that, for possible worlds, there is at least one and that, for necessary worlds, there are as many as possible.
A possible world is a world with at least one true statement.
ObiWan mops his furrowed brow as he tries to keep up with the debate. 
Just a quick question really…
I’m not sure I am clear why The Greatest Possible Being (in Modal Logic) has to be the same as The Greatest Possible Being (in English)?
I agree with you that it is not unreasonable to define God to be that which is the greatest possible but isn’t the ‘possible’ used here the English one and not the Modal logic one?
I agree that you proved the existence of The Greatest Possible Being (in Modal Logic) but I just don’t see why that has to be the same as The Greatest Possible Being (in English). The latter is what people consider to be God, the former could just be human life or it could be God or it could be something else, we just don’t know which one. We just know which ever one it is, it exists. I am honestly not sure where we have proved that The Greatest Possible Being (in Modal Logic) is the same as the The Greatest Possible Being (in English).
So currently two of the things we can do are:
Apos
I didn’t read your post, but I just wanted to let you know that I disagree with you. Okay? 
Obi
[…tip o’ the hat…] You are spot on. And frankly, were what you said not correct, there would be no moral decision to make.
—I didn’t read your post, but I just wanted to let you know that I disagree with you. Okay?—
That’s not particularlly helpful, no. Frankly, it’s out of character for you: disagreeing with people, instead of arguements.
You read and respond to Scylla’s posts, yet he is downright abusive. And I certainly think that there’s something in what I’m saying that bears further examination, regardless of whether it even challenges the soundness of the arguement at all, even if it is to only clear up my confusion.
My suspicion is this: <>G is talking about a being (that exists in some possible world). But G is not a characteristic of a being IN a possible world at all.
Let’s say, for instance, that X demonstrably exists in the actual world. Is the fact that X exists in another possible world a characteristic of A in THIS world? I would say no. Existence is a binary characteristic of a being for the specific particular world we’re talking about.
So what if I said this: in no possible world can there meaningfuly said to exist a being who has the characteristic of “existing in all possible worlds” because the characteristic of existence only pertains to the world in question, not other worlds (existence in those worlds is a characteristic of THOSE worlds).
Further, I do not think you’ve fully addressed the contention that “greatest possible existence” is carefully defined (for the proof here) as reffering to necessary existence (the greatest number of possible existences: i.e. all). I do not see how this concept of “greatest” then extends to any other characteristic one might think up: that makes the term do double, triple, infinate duty, despite originally only claiming a single duty. Having the greatest number of existences is not the same concept as having the greatest power, or greatest knowledge.
Omniparticle, if it exists, is a singular particle that, by random pertubations in its spin, determines the nature of existences. If omniparticle exists, then it is incoherent to talk about existence without talking about it. If it isn’t incoherent, then we are not really talking about omniparticle: avoiding the implications of its definition. Now, I can’t think of any reason why it wouldn’t be possible that omniparticle exists, that it is indeed the ground of existence. So can’t the modal proof work just as well for omniparticle? If so, then so far the arguement is sort of trivial.
But what if we say that omniparticle has all knowledge.? In one sense, this is sort of sensible: because all knowledge (all acts of “knowing”) must be a result of the spin of the particle. But the particle itself doesn’t actually “know” anything (it indeed has no processes by which it would do so, being singular, not complex), and indeed, it’s spin is originally random: knowledge is a phenomenon that only arises in some beings as a result of occasional order, in the same way that nebula formation is a phenomenon that arises. The particle is responsible for nebula formation and knowledge, but it is not undergoing nebula formation, nor is it “knowing.” That would be the genetic fallacy or the fallacy of composition, depending on which way you argue for it. Omniparticle is the greatest being (in terms of existence), but it is not the greatest being in terms of being a knower or being a forming nebula.
I have studied formal logic. Let’s get one thing out of the way first: I am not familiar with modal logic specifically, but as far as I can tell, your proof that G exists, given your definition of G and your axiom, appear valid to me. Please stop pretending that we am attacking your proof on formal ground;
We are not.
It is your interpretation of G that is problematic. You define God as that which must exist if it exists in some possible world. I don’t see how this is a definition of God. Then you throw around the term “greatest” without defining it. What does “greatest” mean? Greatest capacity for love/hate? Greatest mass/volume? What exactly? Then, out of the blue, you assume that G is a being – That is not in your definition or axiom.
You do not assume G formally. But by any reasonable interpretation of your definition and axiom, G must exist. Your proof just verifies this trivial fact. We all saw you put a rabbit into your hat. We are not astonished when you pull a rabbit out of the same hat.
That is just what I was thinking.
[Moderator Hat ON]
Only one person, however, alluded to a group of posters he did not belong to as being analogous to microcephalic mice and retarded chimps. “Go talk to idiots” and “we idiots” is not a direct insult to a poster; “you idiots” is.
[Moderator Hat OFF]
Great jumping Jehosephat!!! Libertarian has just gone and admitted to exactly what everyone has been trying to tell him, to wit:
His “proof” that “God” exists is irrelevant. He hasn’t proven that God (presumably the Judeo Christian one, but then one never knows) exists, he has proven that “God” exists in some artificially constructed system of logic that has no bearing on the real world.
It is not an argument that can convert non-believers to believers because you must still make the leap of faith that “God” and God are the same. :rolleyes:
BTW:
Libertarian, you conveniently missed the rest of my first post (you remember, mice and chimps, etc.) in this thread in which I tried to point out the irrelevance of your “proof.” This is (I think) what has irritated Scylla (and others, myself included.) You have obstinately refused to admit that your argument is irrelevant, and ignored statements that disagreed with you.
Mort
Demonstrably false. I might have missed Phoenix’s earlier post, but ask him now whether I’ve ignored him. What I’m doing (or rather ought to do) is ignore posters who are deliberately disrespectful and have nothing of substance to contribute except the same old, tired foot-stomping breath-holding nonsense.
Now that you have both a moderator and an administrator on your side, I respectfully submit that you’ve drawn sufficient blood to suit any rational bully. Why don’t you argue with reason rather than inciting enmity?
That proves conclusively that you aren’t reading anything, or else are trolling. How could you have missed this:
That directly contradicts your assertion, proving it to be false. Of course, I don’t expect you or your cohorts to give any credence to proof.
Gaudere
Very well, then.
Dr Matrix
I have addressed this to a fare-the-well forty ways from Sunday. I’ll make it short, and if you care to read my other posts, feel free. Is there some reason that you ignored my request to reprint my proof here other than that you didn’t see it?
Supreme (necessary, greatest possible) Being (existence).
Supreme: “Greatest in power, authority, or rank; paramount or dominant.” (American Heritage)
Being: “Something, such as an object, an idea, or a symbol, that exists, is thought to exist, or is represented as existing.” (American Heritage)
Apos
I’m sorry for being flippant with you. It appeared to me that you had not read what you quoted from me, so I responded with a rather bad joke. I apologize. I ask that you allow me to respond to you in the morning (assuming that I am still allowed to post).
Jab
That’s quite funny, thanks. 
You did a good job. I enjoyed it and have responded to you there.
As is usually the case with debates that relate to religion, which foot you get off on seriously affects where the debate leans. Anyone who has ever suffered through an abortion debate (please, please, please no one turn this into one just because I said that word–I’m sure there’s another message board elsewhere if someone feels the need) knows that if you start out with a discussion of whether a fetus is a “person” or not, the debate leans toward the pro-lifers, whereas if you start out with a discussion of the kinds of actions the law normally requires of one person who has the ability to save the life of another, the debate leans toward pro-choicers.
Similarly, this debate seems to me to be leaning toward the religious side (intellectually although perhaps not democratically). But I believe the source of this is a home court advantage of sorts.
First, let me thank Libertarian for his post timestamped 07-31-2002 11:11 AM. I only wish he’d started the argument with it instead of waiting until today.
Second, while that post contains an interesting inference, I believe it suffers from some of the classic problems of the ontological argument. The line (G -> G) is justified from the definition. The “justification” of <>G is that it follows from the definition. However, in logic it is invalid to derive anything from a definition except something of the form:
thingBeingDefined -> definitionOfThing
So while (G -> G) is acceptable, <>G is just an unproven assumption. Which is fine, except all the argument really shows is that God exists if He possibly exists.
How, Libertarian asks, can something which has necessary existence (or the greatest possible existence or whatever) not have possible existence? The answer is it does, but only if it exists at all. Until you prove G exists, you cannot use the fact that (G -> <>G) to show that <>G is true.
So this simple version of the argument which we have been debating over is most assuredly invalid. It suffers from the same problem as all the pre-modal versions of the ontological argument, namely, it assumes that just because it defines something as having necessary existence that thing must actually exist.
Third, Libertarian, however, has given us another (more complicated) version of the deduction which he swears up and down that all the experts call valid. I’m definitely not a modal logic expert, but I’ve had training in several modal systems (including: K, M, B, S4, S5, and a couple modal variants that deal with the logic of obligations) so I certainly know my ass from a hole in the ground.
The complicated proof is given here:
I don’t see how you infer from 2 to 3. Without that inference, the rest is in trouble. So I’d appreciate a line-by-line explanation of this proof.
Nonetheless, I’m willing to assume for the time being that this argument is valid. Hell, I’ll call it sound for the time being. At this point I’d like to ask what exactly has been proven? The existence of G, where G is something that necessarily exists and has “the greatest possible existence”.
It is my belief, however, that this proof is fully compatible with materialism. Let me return to another post where Libertarian argues what properties he claims that he has and has not shown are true of this variable “G” whose existence is proven.
I will agree here that the panentheistic interpretation seems arbitrary. However, I believe that Libertarian’s assertation that “the pantheistic interpretation seems weak” is itself arbitrary. Or, the assumption that being weak is a problem is arbitrary and unjustified. I believe that the view that pantheism’s weakness is a problem comes from an unjustified emotional association with the word “God”. Let me go into a little more depth about the pantheistic interpretation, using the neutral variable “G”.
We have shown that G (an entity such that it has the greatest possible existence) exists. While Spinoza did have a somewhat theistic view of God, I will take the stance that the entity “G” is simply identical with the materialist universe. I will grant that my position is weaker than Libertarian’s theistic view of G in the sense that he postulates something over and above the physical while I do not. We can refer to these two conflicting views of what G is as the “weak view” which is mine, and the “strong view” which is Libertarian’s. At this point we have not shown which of the two views is correct. (It is also important to note that “weak” and “strong” refer to how ambitious the claims are, NOT how much logical support they have.)
At this point, both the weak and strong views have identical support. G is an entity such that it has the greatest possible existence. To a materialist the universe itself has more existence than anything in it and to a theist the theistic God does. So far, so good.
Libertarian went on to say
Let me take these arguments point-by-point
Fair enough. What is knowledge? To a theist/non-materialist, it is probably some spiritual thing; so to a theist/non-materialist, G has spiritual knowledge. To a materialist, knowledge is just having information encoded in it. In a strict materialist view, a computer can have knowledge. So we have shown that somewhere in G, information of some sort is encoded, more than is encoded in any one human being.
The parallel here runs the same. Any star puts out more power than a human can ever possibly put out and it exerts more force and sway over the universe than the whole of the human race has ever achieved.
I’ll come back to this after (4).
My answer to this is simply that on a theist (or compatibalist) view we have a will. But a materialist (like me) who is willing to bite the bullet here will flatly assert that we do not have any more will than a rock or a star. So the argument is compelling to a theist but not to a materialist.
My response to (3) is essentially the same. We cannot discern morality in any grandiose sense. We simply have visceral reactions which cause us to approve or disapprove of various actions. But I have never once seen a way to judge between two conflicting moral systems which does not assume either one of them or assume another equally uncertain moral system.
At this point people start babbling about consciousness or the like. I am not an eliminativist about consciousness, I believe consciousness is a material phenomenon. So does the variable G have consciousness? On the materialist view it does in the sense that conscious beings are contained in it.
Think of it this way: I have consciousness. When I sit at the computer does the entity: The-computer-plus-me have consciousness? Yes it does. Does the computer by itself? Not in any sense we’d recognize.
So there is no way to judge between the weak and strong views of G based on the proof itself or the definition of G.
We can look at this another way: We know that G has the greatest possible existence. But what has any existence? Do I have existence? Do my shoes have existence? What has “more” existence: me by myself or me wearing my shoes? To a theist perhaps I by myself do in some spiritual way, but to a good old staunch materialist the shoes add at least a little big of existence. Maybe G is just someone with a whole lot of shoes.
This post is titled “Are theism and logic incompatible?” The answer to that question is most assuredly “NO!”, just as the answer to Libertarian’s original question “Are materialism and logic incompatible?” is also most assuredly “NO!” If you start from a theist point of view, you will end up proving God exists, if you start from a materialist point of view, you will end up proving the universe exists. And neither the proof given nor the definition of G can judge between those.
If any one was hoping to find the answers to age-old questions in logic, I’m sorry but you’ll have to look elsewhere. Logic is made up of simple inferences and it’s only when you read more into the inferences than they allow you to that you think you find answers which you simply put there.
I hope I’ve shown that there is simply no way to judge between the conflicting views of theism and materialism by logic alone, just as there is no way to judge between conflicting moral systems by logic alone (anyone who wants more on that, read a book by Richard Rorty). As far as logic is concerned, the two are in a dead heat. You’ll have to look to faith or experience or some other place to decide which is right.
I really have to wonder though: the way it smells in the bathroom after I take a dump, what in the universe does G’s shit smell like?
Xargque writes:
“First, let me thank Libertarian for his post timestamped 07-31-2002 11:11 AM. I only wish he’d started the argument with it instead of waiting until today.”
Yes I agree that the argument given at the start of this thread is not the same as the argument Xargque refers to. A good discussion of it can be found here:
http://www.angelfire.com/mn2/tisthammerw/rlgn&phil/ontological.html
Xargque writes:
“I don’t see how you infer from 2 to 3. Without that inference, the rest is in trouble. So I’d appreciate a line-by-line explanation of this proof.”
I too have a problem with line 3. Line 3 is basically just stating an instance of Becker’s postulate (see the above link for Becker’s postulate). I raised an objection to it, and Libertarian wrote:
“No, I don’t intend to get into definding Becker’s Postulate here. I already did that in the other thread…”
Well I read that thread, and I had an objection not previously discussed. Here is a link to the page of that thread, where I detail my objection:
http://boards.straightdope.com/sdmb/showthread.php?s=&postid=2321714#post2321714
Line 3 is: ~N(g) -> N(~N(g))
Basically, I argue that N(~N(g)) is nonsense. It requires that IN each possible world, “~N(g)” is true. But “~N(g)” is not a valid statement IN a given possible world. It is only valid in the hypothetical meta-world containing all possible worlds. For a more verbose explanation of my objection, see the last link I gave above.
Thus the proof is not valid. And even if it were, as many people point out here, the proof is not sound. I wonder why so many so-called luminaries take it so seriously, as Libertarian maintains.
Grrr… Computer crashed and ate my post when I was over halfway through replying, so I’m going to cut it short and summarize a bit instead of going through point-by-point.
Lib, your definition of god is flawed in that it insists things that are unproven and without evidence. There is no evidence that god is the “greatest possible existance”. There is also no evidence that the “greatest possible existance” is necessary existance. In fact, it seems like were it to follow your logic thoroughly, it would only have to exist in a single world, instead of all of them, and there still is nothing to support that there is a “greatest possible existance,” instead of just “existance.” Or that the “greatest possible existance” can do and know everything; Such a “great” existance might not be possible, while a “lesser” “greatest possible existance” might be possible.
In addition, it is flawed because the definition you use implies god exists. If he is defined as “god is a supreme being,” then it is explicitly implying that he exists; It couldn’t be said that god is the supreme being if he doesn’t exist, because you can’t be something if you don’t exist. Your whole argument simply throws up more smoke and mirrors infront of this flawed definition.
If you’re going to define anything solidly, you will need to supply some sort of evidence for it. This applies to gods just as much as anything else. So untill you can provide evidence for your definition, your whole train of logic is irrelavant. And if you had anything to support the definition, we wouldn’t need your modal logic to show god’s existance, would we? And the further and further I read through your posts, the further you get from your original solid definiton, and closer you get to “god may be the supreme being,” which doesn’t say anything. According to your logic, if he is the supreme being, he exists, while if he isn’t, he doesn’t. You need to show that god is the supreme being before you can figure out if he exists or not with your logic (And again, makes your entire logical statement irrelavant).
As for you “assuming god must exist in one world,” it’s right there in your axiom; “god is possible.” There is nothing to support your axiom, any more than there would be to support “god is not possible.”
Next; If “worlds” simply means statements, then the most you can prove is that god exists in your statements. In all honesty, BFD. Pretty much anything can exist in statements. How does that relate to the real world?
Your example of the biologist having to define every single word also falls through. If I were that biologist, I would reply with “go read the fucking dictionary and piss off.” For the record, mine does not directly imply god to exist, and instead talks about conceptions and beliefs. I don’t find the definition to be vague and capable of multiple meanings, I find the definition to be completely unsupported. If someone were to “define” an atom of oxygen as weight 63.4 pounds, then their definition is wrong; It isn’t a quibble over the definition, it’s a statement that the definition is wrong. If they defined oxygen atoms as being neon pink, their definition is flawed by lack of support (Unless they really can show that they are neon pink). The definition you are using is similarly flawed, unless you can show support for it. You say “God is God because He can know all that can be known.” Well, prove it!
As for your “proof of greatest possible existance”, it would help a lot if you put that in english.
Your annalogy of the moon does not work, either (And I thought you were saying annalogies aren’t appropriate to logic?). We have evidence for what the moon is. It would be irresponsible to define the moon without knowing what it is. I could ask you to describe me, and you wouldn’t be able to do a complete description, because you don’t know me completely. You can define me by some of the traits you do know, because you have solid evidence of my actions here at this keyboard (At least on the SDMB). But I doubt you could define my hair color. That doesn’t mean that my hair doesn’t have color, just that you don’t know what it is. If someone told you that my hair was red, but had nothing to support that (Doesn’t know me, never saw me, etc), then would it be reasonable to accept that as “true,” instead of “might be true?”
I think proving the first step first might be a good idea. So, to start with, prove that god is “possible” in that he exists in at least “one world.”
Apos
Your suspicion about <>G is correct, but your assertion about G (I assume that’s what you meant by G) is off track. Not only must G be in a possible world, it must be in every possible world including (what I suspect you’re reaching toward) its own “metaworld” which basically would be the world that consists of all possible true statements.
For that Being, Pi is possibly a ratio of circles AND Pi is possibly not a ratio of circles. Why is that not a contradiction? Because what contradicts <>Pi is not <>~Pi but ~<>Pi. The Being is in both worlds. Their accessibility is defined solely by Him. Pardon the paraphrase, but no one comes to otherwise inaccessible worlds except by Him.
I’m not sure I understand what that means. What does “A” represent?
You’re looking at it from the point of view of contingency, and that’s a mistake. What you’re talking about is really accessibility.
Given two Worlds, W[sub]a[/sub] and W[sub]b[/sub], say that there exists a truth in W[sub]a[/sub], T[sub]a[/sub], that does not exist in W[sub]b[/sub]. Say also that there exists a truth in W[sub]b[/sub], T[sub]b[/sub], that does not exist in W[sub]a[/sub]. What you’re saying, if I understand you correctly, is that T[sub]a[/sub] is not accessible to W[sub]b[/sub], and T[sub]b[/sub] is not accessible to W[sub]a[/sub]. And you’re correct.
However, what is not correct is to say that either W[sub]a[/sub] exists while W[sub]b[/sub] doesn’t or vice-versa. But worlds exist because both worlds contain statements that are possible. So what makes them accessible to one another? The fact that there are universal truths that must exist in both worlds. Say that T[sub]u[/sub] is a universal truth (e.g., A = A). T[sub]u[/sub] is true in both W[sub]a[/sub] and W[sub]b[/sub].
That makes God, Who is E[sub]u[/sub] (or E) a Being in both worlds. God therefore has accessibility to the truths in both of them. In our example, the set of what He can know is {T[sub]u[/sub], T[sub]a[/sub], T[sub]b[/sub]}.
I understand what you’re saying, and I can understand why you would think that.
But things that exist have attributes, and that’s how you can tell one thing from another. You know that a refrigerator is not a planet, and that a rock is not alive. If I told you that I have a planet in my kitchen, or that I am married to a rock, you would be understandably nonplussed. If we speak of a being that exists in a very narrow sense, like a refrigerator, it is easy to see that the “coolingness” attribute of a refrigerator will extend to whatever you put inside it: it will cool any arbitrary thing that can be cooled.
It requires a bit more concentration to conceive of a being whose existence is more broadly defined, but such conception is not beyond your capability if you are sufficiently inclined to think it through. A Being Who exists as a necessary Being is assignable any and all attributes that are true. If a thing can be cooled, then the Being can cool it. If a thing can be known, then the Being can know it. And generally, if a thing can be done, then the Being can do it.
It is the nature of necessary existence that it takes on all possible attributes that are possibly attributable. That’s why I said that God is equally capable of the greatest possible good and the greatest possible evil. Which of those He might choose over the other is outside the scope of modal logic (and in fact is in the scope of deontic logic, but believe me, none of us wants to go there).
I’m not sure I follow you, but the nature of existence is determined by truth. Omniparticle, depending on how it is defined, is subject to that same determination. If you define Omniparticle as O, then all you have done is defined God using some other word.
It must then be understood that when you refer to Omniparticle, you are referring to a thing that exists in every possible world and that has every possible capability and attribute of existence. It’s just to-may-to and to-mah-to. This particular modal proof works for any entity that is defined as E.
Then you’ve settled your own controversy. Omniparticle is not E.
Xargque
Welcome to Straight Dope Great Debates.
You’re welcome.
There is a rule on this board that prohibits so-called “cross posting”, that is, the posting of a message in more than one thread or board. Unfortunately, I had already posted the proof in another thread about what contains the universe when I took up a challenge there to show a mathematical proof for the existence of God. Considering math and logic to be twin sisters, I presented Dougherty’s proof (restructured by me somewhat for clarirty).
In that thread, the person who asked for the proof reacted with great indignation and said that he wanted physical proof as well. The ensuing subdiscussion between us eventually resulted in my being asked to take the discussion elsewhere. (I sometimes jokingly think that “hijack” here is defined as “that which Lib posts”.) And so, as a courtesy to those who preferred to discuss the universe in the context of narrow materialistic mysticism, I opened this thread.
Neither a hint nor a direct appeal that I be allowed to repost the proof here was answered. Therefore, I took it upon myself simply to write the whole thing over in as substantially different a format as I could, praying that I would not be charged with a cross post. Luckily I haven’t (yet) been.
But this is not the first modal tableau of the ontological argument to be posted at SDGD. The Tisthammer proof (itself a modification of the famous Suber proof) has already been discussed in great detail. Tisthammer himself, in fact, visited the thread upon my invitation and, as a result of discussions there, modified his argument by moving Becker’s Postulate from his set of inferences to his set of axioms. I thought that that modification weakened his argument, but that’s another story.
Dougherty’s argument is much less controversial, eliminating Becker’s Postulate altogether and avoiding the whole mess of arguing by the excluded middle. So his was the argument that I selected for these renewed discussions.
I think the axiom, <>G, is acceptable since any other modal statement about G (those that I listed for Phoenix) would contradict the definition.
Consider how the Converse Barcan Formula applies in this case:
[symbol]"[/symbol]zPz -> [symbol]"[/symbol]zPz
which we can write equivalently (to apply to Barcan objects) as:
<>[symbol][/symbol]*z*P*z* -> [symbol][/symbol]z<>Pz
In plain English, that means that if it is possible that something exemplifies P, then something possibly exemplifies P. It follows from the T Axiom of modal logic ([symbol]f[/symbol] -> [symbol]f[/symbol]) and the 5 Axiom (<>[symbol]f[/symbol] -> <>[symbol]f[/symbol]) that because G is exemplified by G, meaning that something possibly exemplifies G, then whatever is encoded by G must be possible. So, while not a direct inference, it seems reasonable to believe that <>G.
I agree completely, and that’s why <>G is presented as axiomatic rather than as an inference, and why I’ve said repeatedly that disagreement with that axiom is an acceptable protest against the proof.
However, as I’ve also stated, you MUST accept either <>G or ~<>G. And it seems to me, unless you can show otherwise, that there are profound logical obstacles to accepting ~<>G, not the least of which is that it is a substantive denial of a positive ontological proposition. In saying that it is not possible that God exists, you aren’t merely saying that it is possible that God does not exist; you are saying that the possibility itself does not exist.
The axiom <>G seems at least as reasonable to me as arithmetic’s Induction Axiom, which is solely derived by induction, while this axiom is derived by attempting to find a modal status that will not contradict the definition of its encoded element.
What you have shown is that the axiom cannot be proved true. And for that, you’ll get no quarrel from me.
I reckon you meant to say, not that it is invalid, but that it is unsound. You have not shown that the argument is ad logicam, but merely that you disagree with its initial postulate.
Moreover, I know of no “pre-modal” ontological argument, from Anselm to Godel, that presumes any “necessary existence” inasmuch as necessary existence is a modal state.
That particular argument was discussed in excruciating detail in the Tisthammer thread, and I welcome you to visit it. But I cannot imagine what sort of problem you might have with arguing from the excluded middle. It is a routine logical device that dates from antiquity: “Let’s just suppose that A is not true…” and is an excellent technique for showing that an eventual contradiction would imply that A is indeed true.
Well, that’s gracious of you, but I’d rather that you believe it to be sound only if you believe that it is inferentially valid and that its axioms are true.
I think that I explained in quite some detail to Phoenix, and then copied and pasted it again for the benefit of someone who asked, flummoxed, what G means. But because you are addressing the formalities of the argument (which, by the way, I so greatfully appreciate) I’ll state it for you here (albeit briefly).
G means that God actually exists. Not possibly. Not necessarily. But in actual fact. That’s what disturbed Dougherty so deeply. Heck, if the conclusion of the argument was <>G, I quite imagine that he or any materialist would just shrug and grin it all away.
So, to answer your question directly, what has been proved (in each of the many variants of the modal tableau) is that God exists.
Oh, no problem. I can accept that. I believe that I qualified what I said at the time — and repeatedly before and since — by the reminder that, in giving my solicited opinion on the metaphysical implications of the argument, I am stepping away from the strict limitations of ontology generally and giving my opinion on the basis of my own world view, that of a Libertrian Objectivist Christian. I don’t mind your calling my opinion arbitrary.
The rest of your post does much the same thing, broadening considerably into a much more general discussion of metaphysics, so I’m going to cut this off here and address that separately.
Xargque
I’m sorry, but I don’t think that’s a fair statement. G has all possible knowledge. Though I have not met, nor have I heard of, any human who has all possible knowledge, I do not hold that it is impossible that some human somewhere at some time might have all possible knowledge. Of course, if we go there, we’ll need to invoke Doxastic logic as well, and frankly, I’d sooner use a bed of nails as a trampoline.
Suffice it to say that the All-Possible-Knowledge human, if he exists, is without question a scoundrel. He could save the world’s scientists quite a lot of time and trouble. From the point of view of Temporal Logic, I’m not sure whether the status of the APK human is P, F, H, or G, although I suspect it must be both G and H because he must exist eternally (else his modal necessity will vanish).
Same protest. G is capable of all possible power.
You’re being very imprecises. G has the greatest possible moral discernment.
Okay, but a minor nit. G has the greatest possible will.
Well, that doesn’t make the argument any less compelling to either of them. Quantification of will is irrelevant. Whatever is the greatest possible will is the will that God has. If it is not possible to have greater will than a rock or a star (in any and all worlds) then God has only as much will as is possible.
I would say that there are as many moral systems as there are people. I have seen, on this board especially, quite eloquent and highly developed systems of morality from materialists. Likewise, I have seen systems of morality advanced by theists that have caused me to recoil in horror.
But again, none of this is any limitation on God. His morality (like His knowledge and His power) are not contingent on ours (remain mindful of the definition of God); rather, it is the other way around. Whatever is the greatest possible moral discernment, that is what His discernment is.
Whoosh. That went way over my head. I’m not sure why you stop at the computer. What about the chair? Why not then your whole house along with you? Why not an Uberconsciousness comprised of You + All else?
Of course, eventually, you run into including me. And quite frankly, I would take issue with your inclusion of my consciousness with yours. I am unaware of yours, except for what my senses tell me of it. Yet somehow, intuitively, I believe that the entity typing these words is not you.
Agreed, and as you must know, I stated that myself early on.
What has any existence? Truth, and only truth. Nothing else exists.
Well, I’ll grant you that.
As I’ve explained already, the title of this thread was spawned ultimately by the incredible circumstance of providing a solicited deductive proof only to have it discarded summarily in favor of a new demand for an inductive one on the basis that the induction would somehow be superior to the deduction. The title is a bit tongue in cheek because I know from experience that logic is not incompatible with some materialists, and I know from experience that logic is indeed incompatible with some theists.
My purpose was to open a dialog and find out, not so much whether the argument is sound or valid (I am convinced that it is sound), but how materialists who, like Dr. Dougherty, concede its soundness interpret it. I wanted (and still do want) to hear such formations as you’re making here, about “what this all means”. When I hear that it means nothing it doesn’t bother me, unless by that protest the person intends that it mean nothing to everybody — in other words, that the argument is intrinsically meaningless and that G is an imaginary and arbitrary result. That interpretation I cannot abide.
Well, that’s random. I mean, it goes without saying that you should read the inferences and not the interstices. In my opinion, a person should read exactly what is there — no more, no less. Therefore, G means that God exists in actuality. But it does not mean that God exists only as a pantheistic universe. Nor does it mean that God exists as the one Christians call Jehovah. Either of those requires a leap of faith.
Only the so-called “hard atheist” (who insists on ~<>G) is exempt from the conclusion of this proof. And in my opinion, he takes the greatest leap of faith of all.
I pretty much agree with you there, too. The other modal logics are frighteningly weird.
It is the greatest possible smell.
Preguntas
For the reasons that I’ve explained. Put simply, the inferences follow from one another. That is the definition of a valid argument.
Phoenix
Huh?
Is the definition of unicorn flawed? Of irrational number? Materialism? I certainly regret wasting so much of your time in covering all this with you already.
Fair enough. I hope you agree that it’s fair for you as well:
Frankly, I don’t think that it would.
Axiom (see definition number 3)
It seems to me Libertarian, that you are saying that the universe or the set of all things must exist because all true statements that can be said about it hold true for it. You are substituting the word god for the word universe or the set of all things. But god implies sentience. The set of all things contains sentient creatures but why would the set of all things have an over all sentience and will, much less morals and feelings? The set of all things contains all knowledge (information) but why would there be an all percieving entity for this knowlege? The set of all things contains all power, but why would all of that power necissarily be controled by a single entity? I don’t see how your proof leads to these conclusions. I fully admit that this is over my head, but even in my limited understanding, I can see that you have failed to adress many counter points from the first three pages. Also the appeal to authority is not cool (pit thread and hinted above). Saying that leading philosophers agree with you and that you will take their word over posters here leads me to wonder why you would discuss this here at all. I think at the least you are in stalemate by agreeing with Xargque. Your whole argument becomes moot when you concede that “there is no way to judge between the weak and strong views.”
Libertarian, I don’t know if you are really ignoring me because I say that “the greatest possible being isn’t possible” or not, but I’m going to keep posting anyway and at least hope you read it.
I do agree that the greatest possible being is possible. I do not agree that <>G is a reasonable axiom because of the ontological implications involved in modal logic.
I do agree that it can be an axiom anyway. I reject it, however, without demonstration.
(G->G)-><>G is not the case, so it must be a seperate statement.
Because (G->[]G)-><>G is not the case we are allowed to say things like, “G might not be possible”. Think about that, will you please? If the definition demanded posibility then you should be able to easily demonstrate <>G. But I haven’t seen you do that except by semantic hand-waving. This is why I say the greatest possible being might not be posible.
Hail Eris,
erl