Vorlon, you seem to be forgetting that our world is one of the “possible worlds”, so existence in all possible worlds (necessary existence) implies existence in reality, i.e. our world.
[blank stare]
Um, no, Libertarian, that’s the premise, which takes for granted that necessary existence is possible. It doesn’t say that it must exist in all conceivable sets of possible universes.
Why don’t you go look up the definition of ‘be’ again?
FriendRob: Your statement is correct, but I’m not sure what point you’re trying to make.
We don’t know what the limits of possibility are (or even if there are any). If necessary existence exists in the ‘real’ set of all possible worlds (whatever that means), then it exists in reality. But the fact that we can imagine it existing in a hypothetical set of possible worlds doesn’t indicate anything about what’s really possible.
I can imagine a set of possible worlds in which it is impossible for there to be any being named ‘Rob’, for example. Clearly, that’s not the case in this reality (and our reality is not contained in that set).
Some possible worlds that we can imagine are mutually exclusive, so we have to consider every possible way that possibility might be limited. The argument doesn’t show that necessary existence must exist in all conceivable sets of possible universes.
If you meant something other than this, I’m sorry about the lecture. Would you explain further what you had intended to communicate in your last post, please? 
Friend
Frankly, after reading your post, I like “meta-world” better, using meta in its sense of “at a higher state of development” (e.g., metazoan). I think that nicely describes necessary existence, an existence that is at a higher state of development than mere possible existence. And I have used “convergence” as a synonym for necesssary existence.
You, and others like you, make this discussion thoroughly interesting and of great value. Thank you, Friend.
Vorlon
I reprint this for your convenience. It is proof that necessary existence exists:
Call necessary existence [symbol][/symbol]. Select any arbitrary interpretation, I, and show that the open modal formula, [][symbol][/symbol][sub]y[/sub](y = x) is T[sub]I[/sub] at W[sub]0[/sub], where y and x are things that exist, T is truth (and so, true at I), and W is an actual world. If the proposition represented by the formula is true, then it will have to be true for every assignment function, F, meaning that [symbol]"[/symbol]x[symbol][/symbol][sub]y[/sub](y = x) will be true. That requires showing that [][symbol][/symbol][sub]y[/sub](y = x) is T[sub]I[/sub] for every possible world.
Select an arbitrary world, say W[sub]a[/sub]. Now, show that [symbol][/symbol][sub]y[/sub](y = x) is T[sub]I[/sub] at W[sub]a[/sub] such that any and all assignments of variables to F, in T[sub]I,F[/sub], are true in W[sub]a[/sub] for [][symbol][/symbol][sub]y[/sub](y = x). Select an arbitrary assignment for F, say F[sub]a[/sub]. If the proposition is true, then [symbol]$[/symbol][sub]y[/sub](y = x) is true for T[sub]I,F[sub]a[/sub][/sub] at W[sub]a[/sub].
Call the individual that F[sub]a[/sub] assigns to X, D[sub]a[/sub], representing a nonempty domain. Now, show that there is some assignment function, F’, that differs from F[sub]a[/sub] at most in what it assigns to y, and such that y = x is true (specifically T[sub]I,F’[/sub]) at W[sub]a[/sub]. This will show that [symbol]$[/symbol][sub]y[/sub](y = x) is T[sub]I,F[sub]a[/sub][/sub] at W[sub]a[/sub]. In other words, it is true of any arbitrary assignment for any arbitrary world.
Now call upon the definition of an assignment function, and consider the assignment F’[sub]a[/sub]. It is just like F’, except that it assigns D[sub]a[/sub] to y. Since F’[sub]a/sub = F’[sub]a/sub (implying that d[sub]D,F1[sub]a[/sub][/sub] at x = d[sub]D,F1[sub]a[/sub][/sub] at y), y = x is T[sub]I,F[sub]a[/sub][/sub] at W[sub]a[/sub].
Tisthammer’s proof (and indeed modal logic itself) accepts as given, due to this proof, that necessary existence exists.
Friend
A bit more. Please indulge me:
Emphasis in the original.
Yes. In all.
The point is your perception of the being.
That’s not what the definition says! It doesn’t say that the GPB is the same in all the worlds; it says that the GPB exists in all the worlds. Merely because the nature of the worlds (not the nature of the GPB) cause various manifestations of perception, that absolutely does not mean that the being is not the same being. Remember, the exact same paint that looks blue in this world would not look blue in a world with no blue light. But it is the same paint nonetheless.
As a One Point Worlder, you merely can perceive the GPB as a point in One Point world. That has nothing to do with the nature of the GPB’s existence, but of yours.
That ‘proof’ is rather hotly debated, Libertarian. Aren’t you completely ignoring the other forms of modal logic which don’t have those statements as theorems?
The proof also suggests that everything exists necessarily.
Huzzah! Everything is God! Well, that clears up a lot, doesn’t it?
Additionally:
We don’t know what it really means to say that something is possible. It’s a useful way of looking at things, but we have no way to know whether or not the universe could actually be anything other than what it is.
The argument you’ve presented is valid with the bounds of modal logic, but many philosophers use that result to argue that the original form of modal logic doesn’t work.
Also, you should really phrase your arguments in English instead of symbolic logic. It’s easier to understand, if somewhat harder to construct proofs in.
Lib:
Nobody said anything about “one property of existence over another.” I am saying (and Tisthammer is admitting) that perhaps it does not make sense to say that existence itself makes a being “greater”. Not a property of existence. Existence itself.
Still, this flaw is nothing compared to the fact that the proof also says that existence in imaginary worlds makes a being greater! Just the fact that you are arguing that god exists in your fictional “one point” land should tell you something about how sound your argument is.
Person: I am imagining a world containing only one point… and god is there!
God: YES! My greatness is complete!
“lesser existence in fewer than all possible worlds”? Possible worlds are a human concept. A logical device. Do you really think god is forced to comply with your imagination of him?
Tisthammer:
Since you would not explain how you were using the word possible, I checked on how Tisthammer was using it. As you can see, he is using possible to mean other ways OUR reality COULD have been like. Then he says that god is at least possible. In other words, even if god doesn’t exist, he COULD have existed. He exists “in some possible set of circumstances.” He “might have existed in the real world.”
How? Do you not see that this is absurd? God by definition cannot be dependant on “some possible set of circumstances” for his existence! It makes no sense to call god at least possible, in the way I have finally discovered you are using the word, because to do so makes god dependant on circumstances.
God either exists, or doesn’t exist. A premise that says god is “at least possible” just doesn’t work. But since you have already disagreed with Tisthammer so often, I suppose you will now defend the proof by telling us what premise he should have used instead. You may as well make up a completely new proof.
Vorlon
Inasmuch as modal logic is defined as “the logic of possibility and necessity”, I’m not aware of any form of modal logic that does not posit necessity.
Factually incorrect. The proof says [symbol]"[/symbol]x[symbol]$[/symbol][sub]y[/sub](y = x), not [symbol]"[/symbol]x[sub]y[/sub](y = x), will be T[sub]I[/sub] for every possible world.
Sure we do. It means true in at least one world. I thought you said you had reviewed the thread.
But then I might end up rambling about irrelevancies. And there’s enough of that already.
Night
The being is not the greatest possible because it exists; it is the greatest possible because it exists in every possible world. How much greater can existence (being) get?
If Tisthammer has been distracted by that red herring, that’s unfortunate. See, for example, this from his site: “To use another example, is the existence of Stalin, the Devil, Hitler, and maniacal mass murderers (say that three times fast) greater than their failure to exist?”
The proof doesn’t address that issue at all. It merely suggests that a Stalin who exists in all possible worlds is greater than a Stalin who doesn’t. Once again, “greater” is not used metaphorically; it is used in its strict sense as a mathematical and logical operator: [symbol][/symbol]X > [symbol][/symbol]Y where X exists in more worlds than Y.
I consider a flaw to be a fallacy. I don’t know about you, but I measure the soundness of an argument by two things: (1) is it a valid argument (i.e., does its conclusion follow from its premises)? and (2) do I accept its axioms as true?
I don’t judge arguments based on whether I find it hard to imagine their implications. If I did, I would likely throw out all of quantum physics as so much hocus-pocus. I trust that you have done exactly that since surely you are consistent in how you evaluate soundness. Right?
Night, don’t do that. That sort of dishonesty is beneath you. I have explained many times — again and again — that possible means true in at least one world. That is how I use the term. That is how Tisthammer uses the term. That is what the term means in modal logic.
Let’s disregard the lie about how I’m using the word “possible”. The definition of God in the proof is the exact opposite of what you state. God’s existence is the greatest possible (i.e., existence in every possible world). That is why Axiom 1 derives from the definition. His existence is necessary, and therefore contingent on nothing.
Nonsense. Failure to present such a premise would constitute a substantive denial of a positive ontological propostion, and would render the proof invalid.
You suppose wrongly. As I stated above, the premise is unavoidable.
Lib:
You are being confused by the fact that “possible” is used in many different ways in the proof. I am talking about the use of the word possible when it comes to “possible worlds.”
Possible worlds: Worlds that are true in at least one world?
I think we can safely say that your definition does not hold. Then what does possible mean when it comes to possible worlds?
Possible means other ways our reality could have been like. Possible worlds are our concepts of the way our reality could have been, under different circumstances. This makes intuitive sense, because if possible worlds were simply any world you could imagine, then you would only have to imagine a world without god to disprove him, and that is obviously not the case.
The implications of possible worlds being other ways our reality could have been should be obvious. They can not apply to the creator of said worlds! Clearly there are no circumstances under which the creator of a world would no longer have created it. And equally clear is the fact that there are no circumstances under which a world which was not created by god could suddenly find itself created by god. God is the one thing that is particularly unable to be thought of in terms of possible worlds, because if he is there at all he was there before the worlds, and therefore there are no possible circumstances that could have a bearing on his existence. Note that this inability to work with the concept of possible worlds is unique to god. Other things which we deem necessary can at least be conceived to be changed by altered circumstances. But god alone existed before any of the possible worlds, and therefore is out of their scope.
The premise that god is at least possible is absurd, because there are no circumstances in a world that could be altered in order to change the existence of something that existed before the world. It makes no sense to speak of god in terms of possible worlds at all. In fact, all the possible or imaginary worlds you can think of have absolutely no relevance to god’s existence! He came first. He either exists, or does not exist. No amount of talking about possible worlds can ever have any relevance.
You are assuming that god can be part of this kind of proof at all, which he certainly can not. Now we have reached the part of the proof where your definition of possible comes into play. God must exist in at least one world. But god existed before any of the worlds, and therefore this premise doesn’t work. God can not be spoken of as existing in terms of worlds that are completely irrelevent to him, except by people wishing to prove his existence at the expense of logic and reason. You might as well say god must exist in at least one orange, or at least one shoe. Oranges, shoes, and worlds are irrelevent to god’s existence because he came before all of them.
The premise may be unavoidable if you are trying to prove god’s existence by using concepts that have absolutely no relevance whatsoever to his existence. But that is hardly a reason to accept it.
Night
There are many good online introductions (including the one Newton gave very early in the thread) to modal logic. They have these definitions. Restating them here over and over is becoming tedious. And yet, if I abandon restating them, I will, as has been demonstrated, become victim to the unscrupulous tactic of assigning to me statements about them that I haven’t made.
A possible world is a world that contains at least one true proposition.
Speaking of out of scope, I suppose that by now, since it has been settled that the argument is valid, I might as well join you in leaving the topic of ontology and musing about much broader metaphysical matters. God IS the necessary world, the world in which all propositions are true. His existence and His world are identities, the convergence of all truth. Thus, [symbol]$[/symbol][sub]G[/sub] = W[sub]G[/sub]. His holiness and His truth are the same. His name is “I AM”.
He spawns worlds by His will, fiat ex nihilo. He is why worlds without truth are not possible. Atheists are fond of quoting Francois Voltaire, “Si Dieu n’existait pas, il faudrait l’inventer”. (If God did not exist, it would be necessary to invent Him). They believe, ignorantly, that Voltaire was denying the existence of God. But see Epître à l’auteur du livre des Trois imposteurs for yourself, and see that he meant quite the opposite. A sufficiently good English translation is given with it.
If God did not exist (as the convergence of all truth), then neither would any world, including ours. God is just as much God in One Point world as He is in Infinite Points world, because He is not contained by either of them. The single true proposition in the former is equally as significant as each of the uncountably true propositions in the latter.
Tisthammer’s proof has nothing to do with any of that other than as a basis, from its conclusion, to draw speculations. God’s existence (the necessary world) predicating other (possible) worlds is testimony that He is fully truth. (And that statement can be proved; i.e., it can be proved that a world with at least one false proposition can spawn a world with nothing but (a) false proposition(s), leading to a contradiction that the impossible can exist, thereby demonstrating that worlds must be spawned by the perfect being).
An orange is not a world until a proposition is stated about the orange. A shoe is not a world until a proposition is stated about the shoe. They then become relevant to God because God is truth.
But I beg of you, in the name of all that is decent and with all the passion that I can muster, whether or not you ever decide to study modal logic, do not dismiss the argument simply because you mistakenly believe that it limits God. It does, in fact, do the opposite. It removes from Him all limitiations other than any that He might, in His wisdom, impose upon Himself. It states both implicity and explicitly that His existence is contingent on nothing exterior to Him.
Dismiss the argument, if you are hell bent on doing so, for nothing more than one of the following reasons: (1) you believe that if God exists, He does not exist necessarily; or (2) you believe that it is not possible that God exists; or (3) you believe that if God doesn’t exist, then it is not necessary that He doesn’t exist. Any other objection you raise to the argument is irrelevant.
Perhaps you should have been more complete in your web-surfings: Prior’s Modal Logic
Strange, that such a clearly intelligent and well-educated person has never heard of the many alternate forms of modal logic. How peculiar.
Check out this site, which is related to the earlier link. Not only does it provide the proof of necessary existence you showed earlier, but several simpler derivations as well. It also shows why modal logic cannot discuss the existence of contingent beings, in addition to showing that necessary existence can be derived from any logically necessary property of a system in modal logic.
**
But we don’t know that there is more than one world. Perhaps everything that is must be that way, and could never be any other way. Standard modal logic cannot discuss true possibilties, only ‘actuality’. I thought you said you knew what you were talking about.
I quite agree. You’ve contributed far too much to this thread already. :wally
Numbers are an abstraction created by human beings to enable us to make sense of the world we live in. There can be no empirical evidence for an abstract concept. (This applies to words, as well.)
You, however, are stating that it’s possible, through logic alone, to prove that God actually exists in some sort of concrete form (“concrete” in the sense that he affects the world in which we live, even though he is spirit and not flesh), that empirical evidence is totally unnecessary.
I submit, sir, that that is absurd.
Vorlon
Interesting site. I like Stanford. In fact, you’ll find on that site a proof much like the one I gave you that necessary existence exists.
Well, I’m familiar enough with them, I think, including Prior. And as you know, having provided the cite, central to Prior’s modal logic is the idea of necessary statability.
You made the same mistake that people make who quote Voltaire as a proponent of a ficticious God: you didn’t read all of the page. When Prior said that SQML is “haunted by the myth that whatever exists exists necessarily”, he didn’t mean what you might think he meant. He meant that there is a contingent existence that is apart from necessary existence but that is not possibly false, e.g. A = A, which is not statable in worlds without A, but is not possibly false in any other world.
Tisthammer’s proof does not imply that whatever exists exists necessarily. It merely states that God’s existence (in Axiom 1) is necessary since God is defined as the greatest possible being, and the greatest possible existence (or being) is necessary existence. Do you understand?
Tisthammer does not posit God’s existence as contingent.
I’ve never said any such thing. I leave to the reader to decide whether I know what I’m talking about.
Let’s not take you into territory where you’re not comfortable. If you find the idea of more than one world (where world is defined merely as a set of propositions), then let’s deal with one and only one. Any one. One that you select. Let’s call your selection Vorlon’s World.
Now, please note that if Vorlon’s World is the only world (or set of propositions), then what I said still holds: a proposition that is true in Vorlon’s World is true in at least one world, now isn’t it?
I think it’s clear enough that you enjoy engaging me, Vorlon. After all, you posted your magnum opus, drawing cheers from the inimitable Jab, and then promised us that you were done here, and, well — here you are! :eek:
Jab
Oh, okay. Well, is gravity an abstract concept? Prove to me empirically that an apple will never fall up.
Concrete form? What madness is this? Show me my reference to His “concrete form”.
Stop staring at me! Eat your checkers. 
[sigh]
No, that is the greatest conceivable existence. It’s not at all clear that it is real.
That site does indeed demonstrate that one of the consequences of SQML is necessary existence – of everything that can exist. That’s why it’s not useful.
Are you sure that you actually read that entire page?
[The Wrath of the Swarm]: “You might as well stop, Aide. There’s no point in arguing with this waste of protein.”
Well said, Wrath.
Lib, you know (or you should know) that it’s impossible to provide empirical evidence for future events. So, no, I cannot provide empirical evidence that apples will NEVER fall up. Your question is meaningless.
If God does not exist in some concrete form, then he does not exist.
Checkers are delicious when they are made of chocolate.
Vorlon
Actualism, though young, is an active philosophy already, with disputant branches. But one thing none of them disputes is that a necessary proposition is a proposition that is true in every possible world.
You will recall that your original assertion was “Aren’t you completely ignoring the other forms of modal logic which don’t have those statements as theorems?”. I answered then, and I answer now, that I know of no school of modal logic that does not posit necessity.
Incidentally, calling me a waste of protein does nothing to advance your side of the debate. We generally do not resort to ad hominem assaults on this board.
Jab
Interesting use of the word “meaningless”. I’ll have to add that one to my repertoire. “Sir,” I’ll say in the future, “your question has shown the error in my assertion and is therefore meaningless.”