Thanks for the links, Eris. From the first one:
Emphasis mine.
That criticism has already been rebutted. Rejection of Axiom 1 is a substantive denial of a positive ontological proposition; and rejection of Axiom 2 is a refusal to accept the definition — which would be, well, bizarre.
Your second site, I have already seen. I have nothing much to criticize about it, as the writer is reasonably careful to refrain from stating any outright opinion.
I’m not sure how it was rebutted; many of us here have rejected the definition as it stands with respect to or in the context of either of the axioms.
Also, as a sidenote of how much this topic has been preying on my mind, it seems to revolve completely around the correspondence theory of truth; that is, that there is an isomorphic relationship between true propositions and existence. You can’t avoid the empistemological concern here, no matter how much we try to keep this ontological.
This discussion (along with other similar ones I have had over time with my friends) is, in fact, what prompted me to begin the “incomplete universe” thread.
Secondly, and this just occurred to me so please feel free to correct me as necessary, but it seems to me that existence as predicable can only apply to our world. There is no such thing as existence in a possible world, only an actual world. that is the whole point of ontology. So what’s the deal?
This is one of the dumber things I think I have ever posted, so please ignore it.
Damn.
It’s the first thing you have said in weeks that I have understood.
Sigh.
“You can tell whether a man is clever by his answers. You can tell whether a man is wise by his questions.” ~ Mahfouz Naguib ~
Rejecting a definition is so twighlightzonish that had I seen anyone do it, I would have ripped apart my shirt and screamed at the sky. The definition is given before any axiom. If we are to go about rejecting definitions, then why may I not define your words however I please, as in “rejected” means “embraced”, so that I put you saying that many of us here have embraced the definition? In fact, merely discussing this matter is distressing. Don’t forget how easy it is to make pigs fly.
I agree with you. I think valid epistemological concerns are important. Any of the theories of truth may be applied here.
I love that thread, though I do wish it dealt more with the broader issue of what the universe is. I’ll be revisiting it shortly in the hope that the discussion has moved a bit that way.
Good on you! The correspondence theories of truth were more interesting before Russel and Moore redefined existence to mean reality. That has mislead a whole generation of scientists into believing that reality is in their brains.
Look, I think the definition begs the question, that’s why I reject it. I feel you have essentially said, “God is the most perfect being that exists.” I don’t think that is a good definition. I’ve given what definition I would accept, and the proof falls apart and <>~G may be assumed (or whatever was assumed, I don’t recall the syntax now :)).
I don’t think so. The proof requires that existence has meaning for truth since it was stated that it would be a contradiction for a possible god to not exist in any possible world. Let me give you an example (and I am amazed how this thread and my thread are coming together!). It is possible that all the air in this room will suddenly fly out the window to not be replaced with anything, and I will die. Does this have to happen in a possible universe?
I’m not sure that’s the case. You want “possible universes” to be the completely enumerated set of true states of the universes (see the link?), but that doesn’t mean that possible states will ever happen. It just means that they are not forbidden. IOW, you want us to accept that, “Whatever is not forbidden is compulsory.” I reject that outright!
It is not a contradiction for a possible being to not exist in every possible world (and those two “possibles” aren’t the same; one means “not forbidden” and the other means “will happen”).
I’m sorry, it is not a contradiction for a possible being to not exist in any possible world.
But that’s absurd! Definitions don’t beg the question; assertions beg the question. Definitions aren’t premises.
This is amazing. Why are you paraphrasing a perfectly clear definition? God is defined as “the greatest possible being”. As Tisthammer observed, “it’s unclear why a rational person should be reluctant to call such a being God”. And so, I’m curious — why would a rational person be reluctant to call the greatest possible being God? What else would such a being be called?
“I couldn’t believe my ears!” — Lyndon Johnson
Well, gee. If you’re going to use a different definition, then I reckon the proof would fall apart! I can define God as ear wax, making any attempt to prove His necessary existence problematic.
But we, I mean, that is, Tisthammer and I, aren’t talking about a being that is merely possible, but one that is necessary (see the, I mean, that is, our, definition).
I agree that is what you are talking about. But when you say that god must exist in some world because he is, by definition, possible, then I have to reject that. Everything not forbidden is not compulsory.
I would reject that, too. Thankfully, no one (on this side of the debate) has said it.
Everything not forbidden is not compulsory.
We’ve said that he exists…but how do we know what form he takes? Or that he is even male?
Eris
“I dun tink dat word means what you tink it means.”
What Tisthammer has pointed out is the substantive denial of a positive ontological proposition. Note that ~G and ~G are not the same thing. Note also that <>~G is different from either of them. What is absurd is not that a possible being might not exist — that is not absurd at all; what is absurd is that the greatest possible being might not exist, i.e., a being that exists necessarily. That is the whole reason for Axiom 2.
Yes, you’ve said that. But everything that is necessary is.
Monica
Or that He takes a form at all? (Note that the deific pronoun is not intended to convey gender.)
Nope, no question-begging here. 
Between you and me, Lib, if I stated that G was what it was, and gave axiom one, and allowed the skeptical axiom 2 as “It is possible that God doesn’t exist”, that is, <>~G, I think that would be very sound if it could still lead to the same conclusion. In fact, that is how we approach the subject. We wonder if god has to exist, hypothesizing that if he did, he would do so necessarily (that is, be undeniable in all possible worlds).
And yet, though that is how we approach it, that is not how we frame it. We frame it as “if god exists in one possible world, he exists in all possible worlds”, then follow that up with the cincher that god must exist in one possible world (if there can be any other interpretation of ~~G I would love to hear it). The whole proof is superfluous when the question is thusly begged, and the definition forbids us from altering either axiom, which is why my problem is with the defintion.
The question is, does god exist? The answer is given in the axioms. This is fine if you want to accept God axiomatically; I will never argue with such a claim. But as a deductive proof I find it sketchy.
In speech and in thought about speech, the translation of <>G and <>~G should be equivalent. I’d hate to argue with logicians, and as an armchair philosopher my credentials are certainly lacking, but that’s just what “possible” means. If modal logic has no means of expressing that something that was possible didn’t have to exist in some possible world, then I must regard it with extreme skepticism when it tries to discuss existence of anything at all without complete induction.
It is possible that there is a world which has my conception of a perfect island. It is not necessary that such a world exists. Perhaps my beef is not with this proof but with modal logic in general. In fact, on rereading Wade’s page, he defines the possibility operator as such: p is true in at least some possible worlds. Then, indeed, my problem goes deeper than the definition of G.
Eris seems to be on the right track by wondering how you can use the idea of it being possible for something to exist, while rejecting the idea of it being possible for it to not exist. It seems to me that if you reject the latter, you are not really using the former, however much you say you are.
One of my main objections is that possible worlds are irrelevant to god, so that it is absurd to say that god exists in at least one possible world. In fact that axiom is so obviously wrong, that I had determined it must be intentionally blindingly wrong so as to ward off potential arguments. The only defense I have seen is that it is unavoidable, and again, if something is both wrong and unavoidable, then is it really wise to accept whatever makes it unavoidable? But now I see why it seems so wrong.
After reading Tisthammer’s page again I see that he and Lib are arguing entirely different points of view. Lib cannot defend an axiom that says god exists in at least one possible world, nor can he argue why we should accept that axiom and not an axiom saying that god does not exist in at least one possible world. This is because, as far as I can tell, Lib is speaking of a god who is not contingent on possible worlds. Possible worlds are completely irrelevant to Lib’s god, and as such, the axiom becomes simply “god exists.”
Tisthammer, on the other hand, DOES believe god is contingent:
Tisthammer is saying that god is contingent on possible worlds, and that it is counterintuitive to believe that god is not contingent, that he either exists in all possible worlds or none of them! Not only this, but god being contingent is the reason Tisthammer rejects the axiom that it is possible for god not to exist! Therefore, the proof relies on god being contingent. This is of course obvious, because possible worlds have no relevance to god if he is not contingent on them.
It is clear now that the proof is based on a god who is contingent on possible worlds. Which brings us to an obvious argument. Wouldn’t a god who was NOT contingent on possible worlds be greater than a god who is? I certainly believe this to be true, and I think Lib would agree. The only way to get out of this would be to say that not being contingent on possible worlds is impossible, and god only needs to do what is possible. I personally do not believe it is counterintuitive to believe that god need not be contingent on possible worlds, and if I am to accept that god must be contingent on possible worlds I will certainly need to see a better argument than merely stating that all other positions are counterintuitive.
The crux of your post, Eris, is this:
No it isn’t.
Even if you say it a hundred times, it ain’t so.
Axiom 1. It is possible — possible, possible, possible — that God exists.
Axiom 2. If — if, if, if — God exists, then — then, then, then — He exists necessarily.
Well, you’ve got them flipped, but whatever. I must have repeated myself a million times in this debate (and you, too! lol). Either the definition or one of the axioms have to give. This is becoming so obvious to me that I find it troubling.
<>~G should not be a contradiction in any sense at all. If it is a contradiction, then we have certainly asserted God’s existence in either the axioms or the definition. Just because we beg the question in three steps instead of one makes the argument no less circular.
We assert that if god existed he would exist necessarily.
We assert that it is not impossible for god not to exist.
Under no circumstances should this prove that anything exists at all, unless we somehow demand that God exists in one possible world. So the proof would have to prove that G is true in one possible world. Yet it never does this. Instead, it takes for granted that <>G implies thatG is true in at least one possible world. :smack: I’ll come to this smacker again at the end.
We are equating “necessity” with “exists in all worlds”. Fine, I can’t think of a better definition of necessary existence. But ~p then means it exists in no world. In the case where p is substituted by ~G, then we should be saying ~~G means “It is impossible for god to not exist” or “There is no world where God doesn’t exist”. This is not the same as <>~G, which should only contradict the statement G. How convenient that we cannot get to G when we substitute Axiom 2 as it stands with <>~G!
The proof given suggests that ~~G is equivalent semantically to <>G. This being the case, it seems we reach a contradiction if we assume the opposite; that is, if we assume <>~G, which, in terms of necessity, would be ~G. So let’s do it and see what happens. (I’ve replaced the "u"s with “implies” arrows in case it doesn’t display correctly for someone…) (on preview some of the symbols somehow got messed up, but I’ve rechecked this and it should be correct)
No problem by my eye. Again, Wade says, “Put another way, []~G can be translated to mean, ‘The greatest possible being cannot possibly exist,’ which is absurd because of its self-contradictory nature given the coherent, meaningful definition of God.” It can only be self contradictory if we have asserted the existence of God. Which is fine, as I said in one of my previous posts n pages back, earlier above, and in this very post, but if we are going to go around asserting the existence of God in some possible world, why mess around? Just assert its existence in this one and be done with it.
And, finally, for the record, if ~G doesn’t make sense because of the definition (obvious contradiction), then 8 was contradictory even when Axiom 2 was ~~G.
Am I honestly the only one of the two of us, Lib, that see that in every interpretation we make of the symbols we run into an explicit or implicit assumption that God exists in the first place?
God: n, An entirely perfect being.
Universe: n, The set of all things.
Exist: v, being a member of that set of things which are real, and are part of the Universe.
It is possible that God exists.
It is possible that God does not exist.
If God does not exist, all real beings are less than perfect.
Therefore, the most perfect being that exists might not be God.
I think Tristhammer’s definition subsumes the identity of closest approximation and actual perfection. This argument assumes that perfection is essential for the definition, but is not necessarily real.
I am not very good at this logic stuff.
Oh, by the way, God happens to be real. That changes things.
A lot has been written since my last post, but I’ll try to cover some comments made.
Erislover mentions:
>*This entire proof is done without concern for *
>meaning. The “flaw” in the proof will never be
>found (assuming there is a flaw anywhere to be found)
>because logic is strict symbol manipulation according
>to explicit rules, and the rules were followed. Instead
>we must turn to the assignment of meaning to propositions.
>
>And where do we turn to for such a thing? Not logic.
>That’s like looking solely to grammar in order to
>understand a sentence.
Erislover is right when it comes to the symbolic logic. The formal proof demonstrates that the structure of the argument is valid (i.e. the conclusion is true if the premises are true). What symbolic logic can’t do is determine whether or not the premises are correct.
>Now, when we look at Tisthammer’s rejection of the
>"<>~G" as a substitute for (II) we see that it leads
>to a contradiction: the greatest possible being must
>be possible, by definition! But if that is the case, and
>we know that we can only be discussing worlds
>sufficiently like our own, then we have simply defined
>God into existence! The most assured case of question
>begging I’ve seen.
Suppose that God existing naturally flows from His essence. So what? That would be confirming the ontological argument, not criticizing it. An example: the law of noncontradiction is true by definition: its existence naturally flows from its essence (i.e. its definition). Now it is true that one cannot define Santa Claus this way: “A fat jolly existing guy in a red suit,” and then claim he exists by definition, because the property of existence has been artificially added in its definition. But there is nothing inherent in the statement of “the greatest possible being” that begs the question of that being’s existence. The evidential justification for the first premise may be based on the definition, but that is contingent on the predicate of existence (something that I’m not entirely sure on). Similarly, the possibility of God may be true based on the definition of God, but that is contingent on the coherent meaning of that definition of God (though that’s something I’m fairly confident on). Furthermore, possible worlds need not be similar to our own.
>I reject the notion that “possible” in the definition of
>god means <> in the symbolic proof. They are not the
>same kind of possible (unless we simply want to assert
>that god exists in one world, period, which sort of makes
>the idea of proving anything superfluous when we can
>simply assert that god is possible in our world and leave
>it at that).
Ah, but it does! Recall that God is defined as, “the greatest possible being.” Let’s focus on the aspects of the being that are perfect to a particular extent, which happens to be the greatest possible extent. A being with such traits would in fact exist in at least one possible world, since a possible world is a world where reality could have been like. After all, if there were no way reality could have been like to possess a being with such traits, then this would not be the greatest possible being (since that extent would not be possible).
Furthermore, it is not clear that the idea of proving anything would be superfluous since the mere possibility of God does not imply His existence. If it did, the first and third premises of the ontological argument would be superfluous. But as it stands, one cannot construct a proof of God merely from <>G.
>We are equating “necessity” with “exists in all worlds”.
>Fine, I can’t think of a better definition of necessary
>existence. But ~p then means it exists in no world.
>In the case where p is substituted by ~G, then we
>should be saying ~~G means “It is impossible for
>god to not exist” or “There is no world where God
>doesn’t exist”. This is not the same as <>~G, which
>should only contradict the statement G.
Contrary to what was claimed here, ~p does not mean that p is true (or “exists”) in no worlds.
Rather, ~p means that, “It is not the case that p is true in all worlds,” or in other words, “p is not necessarily true.” Thus, it is equivalent to <>~p. Furthermore, ~~G means, “It is not the case that ~G is true in all possible worlds,” or in other words, “~G is not necessarily true.” Thus, it is equivalent to <>G. Erislover, I advise you to go to my website on the ontological argument (it’s at http://www.angelfire.com/mn2/tisthammerw/rlgn&phil/ontological.html and has been revised considerably since it was first mentioned on this message board) since it explains symbolic logic such as this.
>Again, Wade says, “*Put another way, ~G can be *
>translated to mean, 'The greatest possible being
>cannot possibly exist,’ which is absurd because of
>its self-contradictory nature given the coherent,
>meaningful definition of God.” **It can only be self **
>contradictory if we have asserted the existence
>of God.
That is simply not true. The self contradiction arises from what was defined as God, namely the greatest possible being. Suppose (what I think is in fact true) that omnipotence as the ability to do literally everything is not possible (e.g. one cannot create a round square). Thus, by the definition of God as described earlier, the Deity is only omnipotent to the greatest possible extent. Given the coherent meaning of God, it is logically impossible for God to have impossible traits (the traits can only exist to the greatest extent possible), and it is impossible for the greatest possible being to not be possible.
Newton meter:
>You claim that this is a consequence of God’s perfection
>and what perfect existence would be. I claim that it says
>something that you haven’t said explicitly about the
>kinds of possible worlds you are talking about. Are you
>talking about any conceivable world? Certainly not. If
>you were, then the ability of any atheist to conceive
>of a world without God would be damning to his existence.
That is not exactly my claim on the consequence of God’s perfection, it is the argument’s (remember, I don’t claim to know whether or not the ontological argument is sound). Simply because something is conceivable to some people does not necessarily mean that it is actually possible. Nevertheless, the fact that God not existing is conceivable to some apparently rational people is something well worth noting. God not existing is conceivable to me as well, and at least on some intuitive level the nonexistence of God seems possible. That is perhaps the main reason why I do not currently accept the ontological argument. Part of my intuition that disagrees with the notion of maximal perfection (God) not existing contingently, whereas the ontological argument states otherwise. Unfortunately, mere intuition of this sort is not hard evidence (in my view), so I don’t see it as a very solid reason for rejecting the argument. I’ve found some ones that I think might work, but I’m uncertain whether they do or not (see my disputable point sections in my web page).
>It seems to me that you are only talking about
>worlds that have a structure of reality similar
>to our own; similar enough to agree on God’s
>existence.
No, I was referring to all possible worlds, regardless of how dissimilar some of those worlds may be. However, I do believe that all possible worlds, however dissimilar, follow the basic rules of logic.
On Becker’s Postulate
>Finally, Becker’s postulate. It is still controversial.
>There are some logics where it is valid, and some
>where it isn’t. Can you build a strong case why
>we should accept that the “possibility” you are
>talking about above is the sort that is necessarily
>possible wherever it occurs?
I’ll make a note to provide some sort of justification in my web page. Basically, this application of Becker’s Postulate says this (remember that G = “God exists”): If G does not hold true in all possible world (i.e. ~G), then ~G (“G is not true in all possible worlds”) is true in all possible worlds. To me this makes perfect sense. If G is not true in every possible world, then ~G is true (by definition). Thus, in all possible worlds, ~G is true because it is in fact the case that G is not true in all possible worlds.
I believe Becker’s postulate to be valid in all circumstances in the sense that I believe the law of noncontradiction to be valid in all cases. Two criteria must be satisfied though. First, Becker’s postulate must be in the way that I mean it (as I described in the web page, symbols and all). Second, the statement constant (proposition) must mean the exact same thing in the entire line of the application of Becker’s postulate. Only if those two criteria are satisfied will it be valid in the sense that I mean it. That goes for both of the above rules. Since those criteria are satisfied in the ontological proof in my use of Becker’s Postulate, the third premise is in fact true. Examining your examples:
>Consider historical necessity (tense logic). A-><>A
>means that if something is true now, then it was always
>the case that that thing was true at some time in the
>past. But if “John F. Kennedy is dead” is true now,
>has it always been the case that that was true sometime
>in the past? No.
This is not what I mean when I use Becker’s postulate because the proposition changes from “Kennedy is dead at this particular point in time (i.e. the present)” to “Kennedy was dead at another point in time in the past.” The boxes and diamonds would have different meaning (referring to points in time in a certain way, not veracity in “possible” and “necessary” as I defined it), and so this is a misapplication of Becker’s postulate and it did not satisfy the two criteria.
>Consider moral necessity (deontic logic). A-><>A
>means that if we perform some action, then it ought
>to be permissable to perform that action. I don’t think
>we can say that that is the case. I could call you a
>nasty name in Great Debates (I won’t try it), but that
>doesn’t meant that it is a matter of moral necessity
>that I be allowed to do so.
The boxes and triangles would then mean different things than its original definitions (i.e. different from “possible” and “necessary” as I defined in my web page), unacceptably warping Becker’s postulate in the way that I meant it. Failing the first criterion, this is a misapplication.
>Consider belief (doxastic logic). A-><>A means
>that if something is true, then we believe that it is
>believable. That is, if something is true, then we
>believe that we don’t believe it to be false (whew!).
>Is that the case? The velocity of light is a constant,
>but does that mean that everyone always believed
>that it was not believed to be non-constant? No, in
>fact, right now I believe that at some time some
>person did believe it was non-constant.
Again, the boxes and triangles would then mean different things, unacceptably warping Becker’s postulate in the way that I meant it. Failing the first criterion, this is another misapplication.
>Consider physical necessity. A-><>A means that
>if something occurs, then it is required by physical
>law to be allowed by physical law. The mass of the
>Earth is about 5.96 x 1024 kg. This particular mass
>for our planet is clearly permitted by physical law,
>but is that fact itself (that it’s permitted) required
>by any physical law?
To be fair, this more closely approximates what I meant when I used the term “Becker’s postulate” than the above two. The first translation strikes me as accurate (if I am understanding you correctly). But the meanings are still different (about laws of physics, somewhat similar to but still different from “possibility” and “necessity” as I defined it), thus failing the first criterion. A -> <>A means that if A happens, then the laws of physics require that physical laws permit it. The answer to your question depends on how one defines “physical laws.” If one is simply talking about the sum total of all the rules of nature, then the answer is yes. If A happens, then as a rule (the laws of physics require that) the physical laws permit it. Otherwise A wouldn’t have happened in the first place. If one is not referring to all the rules of nature, but only the first order or tier (mere empirical regularities) then the answer is no, because even though as a rule the physical laws permit something if it happens, that rule would not be a physical law. In such a case though, we have a noticeably different meaning of Becker’s postulate than I originally defined it.
However, since both criteria are satisfied in my application of Becker’s postulate, the third premise stands as true. I challenge you to find any counterexample to disprove the two criteria I mentioned.
>My objection is (still, and has been since the beginning)
>that the sort of box that means “necessary” in “box
>(God exists implies box God exists)” is not the same
>box that means “necessary” in “not box not God exists”.
>And the only possible avenue to insist that it is requires
>you to relinquish “not box anything therefore box not
>box anything”.
Newton meter, this is a good example (for me) why symbols are sometimes necessary. Looking at the paragraph for the first time, I don’t have a clue what you just said. Therefore, I’ll put it in symbols (please correct me if I have misinterpreted you).
Your objection is that the sort of that means “necessary” in (G -> G) is not the same that means “necessary” in ~~G. And the only possible avenue to insist that it is, requires me to relinquish ~p -> ~p (where p is a general placeholder for statements).
To me this is an extraordinary claim. I have no idea how your claim follows (or could follow) in any logical way. From what I’ve read, means “true in all possible worlds” regardless of the statement constant (compound or otherwise) it’s being connected to. If the in (G -> G) does not mean “true in all possible worlds,” then what the heck does it mean? If it means something else, I would like to know the justification for that meaning. I think it’s safe to say that there might exist some sort of proof or argument (e.g. a reductio ad absurdum) that shows how the negation of your claim leads to the denial of ~p -> ~p. If there is I would like to see it. Otherwise I am forced to remain skeptical.
One thing is certain: the proof is valid (if the premises are true, then the conclusion must be true also) as me and others have proved. What is not certain is whether the proof is sound (i.e. whether all the premises are correct). You seem to be attacking Becker’s postulate. Is this correct? If true, then your approach is a very interesting one to me. Rather than attacking what I perceive as being the weakest premise, you attack one of the (if not the) strongest ones.
>Let’s cast it in terms of possibility: ~<>(G & <>~G)
>it is impossible for God to actually exist and possibly
>not exist. (That’s your “God’s existence cannot be
>contingent”.)
>
>You claim that this is a consequence of God’s
>perfection and what perfect existence would be.
Correction: I don’t exactly claim that, though the ontological argument might (this includes both the consequence of God’s perfection and God’s contingency). I think this is a good time to reiterate that I’m not sure if the ontological argument is sound or not. In the future, I would appreciate it if you would replace “You claim” with “the argument implies” or something to that effect. It is a pet peeve of mine that people falsely attribute beliefs to me and then attack that belief as irrational, illogical, unreasonable, etc.
The analogy I used to explain modal logic was a computer called OmniSim that simulated every possible way reality could have been like, i.e. possible worlds. (Confer my web page for a further description.) Do you believe I have interpreted the concept of modal logic incorrectly? The application of Becker’s postulate states ~G -> ~G, which can be translated to read that, “If G is not true in all possible worlds, then ~G is true in all possible worlds.” To me, this makes perfect sense. After all, if G is not true in all possible worlds, then in each possible world the statement “G is not true in all possible worlds,” would in fact hold true.
>Now, when you claim <>G, you are saying that there
>is an object that serves as the subject of G=“God exists”
>and has the property that G->G in every accessible
>possible world. Just saying that we can conceive of such
>a thing isn’t enough, because we’ve already agreed to
>only consider worlds with a structure of reality similar to
>our own.
Correction: You agreed to that. I agreed to no such thing. I will however grant you that all possible worlds are similar in one respect: that they all share the same basic rules of logic (e.g. the law of noncontradiction). So that if a statement (call it p) is necessarily it true will be true in all other possible worlds as well (this follows from the definition of necessarily true). Of course, since p would be true in all possible worlds if it were necessarily true, p would hold true in each of those worlds also.
Again, if all possible worlds share the same basic rules of logic, then if a statement (such as the law of noncontradiction) were necessarily true for some logical reason in one possible world (such as our own) then it would be true in all others as well, because each possible world shares the same rules of logic.
Now it may be that just saying we can conceive of <>G isn’t enough, but I provided an evidential argument one might use to back that claim up.
>To get one to accept <>G (after accepting your
>first axiom), you must insist that ours is the sort of world
>where God exists. But that’s the question! You are begging
>that we accept it!
I’m not sure how the argument begs the question. No single premise assumes G. Let’s ignore Becker’s postulate for the moment, and assume (which I think may be in fact true) that if G were true in at least one possible world, then G would be true all of them (and thus this one). In such an instance, one can construct a valid argument for G from those two premises. This is not begging the question, but the construction of a valid argument to arrive at G. No single premise can accomplish the conclusion. The fact that both (albeit only when they’re together) imply G is quite unproblematic as to the validity of the argument (indeed, it is quite the opposite).
If you think that G -> G somehow presupposes G, I’d like to know why. The notion that G -> G seems to misconstrue the nature of conditionals. After all, G is only true if G is true. Can you arrive at the conclusion of G simply from G -> G? If you can provide such proof, I’d be happy to see it. But until some sort of adequate justification is made, it seems highly doubtful to me that G-> G somehow presupposes G.
>And still, that’s the problem. The very first axiom
>is , which we know is equivalent to the
>contrapositive: . “If it is possible
>that God does not exist, then God does not exist”.
>Wade says that examining this made him conclude
>that he should immediately reject the possibility
>that God does not exist (based presumably on the
>offensiveness of accepting that God does not actually
>exist).
I did not say any such thing.
Nighttime:
>Basically, the proof uses two different meanings
>of the word possible. It first uses the word
>possible to mean that god is possible, therefore
>a conclusion that he is not contradicts the definition.
>It is possible that god exists.
>
>It then uses the word possible to mean what we
>can imagine. God is the greatest possible being;
>the greatest being we can conceive of.
>
>Only one of these uses can be justified in the
>same proof
Maybe, maybe not. But in either case that is irrelevant. I did not use “possible” to be perfectly synonymous with the word “conceivable.” The word “possible” means the same thing in both instances that I used it. God is defined as “the greatest possible being” in the sense that the being is as great as the being can be.
Libiterian has said:
>Precisely. You can throw out the premise, <>~G,
>not because it contradicts some
>conclusion, but because it contradicts itself.
And Nighttime responded:
>That is not what Tisthammer said. He said he
>rejected the premise “it is possible for god not to
>exist” because the conclusion he got from using
>that premise contradicts not itself, but because it
>contradicts the definition! (greatest POSSIBLE being)
Which one is right on what I said? Well, both. Note that <>~G obviously includes what G means (and therefore its definition). So if <>~G is self-contradictory it will have contradicted its definition, which is what self-contradictions of statements are often all about.