Let me join others in welcoming you, Wade, to Straight Dope Great Debates.
Meaning. Is there anything more subjective? More packed with personal implications drawn from our own experiences? At one time in my life, “God exists” was not just false but frivolous. Therefore, an implication that began with “If God exists” was equivalent in meaning for me to an implication that began with “If Plo skaga”.
All language is symbols. An abstract thing represents a concrete thing; i.e., an analytic thing represents a synthetic thing. G is always true if it means nothing because it’s a tautology. G is either true or false if it means that God exists because now it’s a meaningful proposition.
Truth most certainly is not found either in the grammar of “If God exists, then He exists necessarily” nor in the rules of “G->G”. Meaning (if it was there in the first place) is not suddenly lost simply because we elect to express the exact same proposition one way over the other. To suggest otherwise would be tantamount to saying that something expressed in French may not be expressed in Chinese, lest it lose all meaning and validity.
You don’t have to be a Randista to appreciate the methods and purpose of logic any more than you have to be a Christian to appreciate the teachings of Jesus (see Atheists for Jesus). In fact, had Ayn Rand seen Wade’s proof, she would have leapt out of her skin, crying “Foul!” and grasping at every conceivable straw, not just to attack its soundness, but its validity as well. For her, logic meant, “That which I think.” but we don’t mean that when we talk about logic.
The truth in Wade’s proof is not in the symbols. If it were, there would be no need to attach meaning to them. In fact, there is no truth in any proposition, whether expressed as words constructed with letters and dots or words constructed with lines and boxes, unless a meaning is assigned to them. They aren’t even propositions.
The analytic composed as “->” means exactly the same thing as the analytic composed as “what comes next follows from what came previously”. There is nothing about the latter that trumps the former. In fact, they are identical.
Throwing out the baby (the symbology) with the bathwater (the argument’s conclusion) is a mistake. It smacks of a reckless phenomenological approach to truth. If we discard what we observe the symbols representing simply because we don’t like what they represent, or even because what they represent just doesn’t “ring true” with us, we find ourselves painted into a corner where reality exists only in our consciousness. I interpret; therefore it exists. Phenomenology is nothing but solipsism that’s ashamed of what it is.
Despite what Newton says (and I offer this with the utmost respect), there is no contingency that a truth in one world be expressable the same way in another. It is not the whole proof, but merely the conclusion and the individual implications that are applicable across worlds. The whole proof is analytic; the premises are synthetic. Thus, if I observe that people who don’t eat in the United States will starve to death, I don’t have to construct a separate observation for people in Afganistan. I don’t need an induction here because of the nature of biology. It is a universal attribute of people everywhere.
Wade’s proof scrupulously uses just such universal attributes. It speaks of the greatest possible existence — not this particular kind of GPE or that particular kind, but of GPE generally. Thus it is a convergence of existence. It isn’t saying that God can tie His shoes in every possible world, but that God can tie His shoes in every world where shoe tying is possible.
Newton reserves the right to say (and so he should) that “In every accessible world, if God exists (in that world) then God exists in every accessible world (to that world).” But nothing about that implies that God must be identically perceived in all those worlds. In fact, he goes out of his way to insist, rightly, that God is not contingent on our perceptions. Thus, God may be a shoe tier in one world, but not in another completely accessible world unless accessible means identical, and it doesn’t.
In fact, the existence that is addressed in Wade’s proof (a convergence of existence) does not even require direct accessibility from one world to another, but rather accessibility merely from the being that is synthesized from all the different worlds. God may be viewed metaphorically to bridge worlds that might otherwise not be mutually accessible at all. This is why I told Mignigma that it is a mistake to view God from this proof as a leg in your world; rather, you should view your own legs as though you are God because that is the perspective from which the proof is drawn.
For example, consider a world that is constructed of matter, and another that is constructed of antimatter. Nothing that is material could exist in the antimaterial world, and vice versa. Neither world is accessible to the other. But an immaterial being has no problem existing in both, unless you can show that there is some property of matter and antimatter that prohibits other forms of existence, including existence that takes on no form.
Therefore, it is manifestly NOT necessary that we “insist that ours is the sort of world where God exists”. There is no equivocation with respect to the modal diamond. ~<>(G AND <>~G) drops a diamond and jumps the gun. This should be ~<>(<>G AND <>~G). G is not realized until the conclusion of the argument, an argument that does not directly claim that God exists in this world, but merely in every possible world. The insistence that ours is the sort of world where God exists cannot be derived from the axioms, but only from the conclusion, and is self-evident therefrom. Clearly, our world is one of the possible ones.
Newton, your mixture of doxastic logic with tense logic when you spoke of what we might believe at points in time has recently (only a couple of years ago) been shown to reduce to action logic. (See A Reduction of Doxastic Logic to Action Logic from Heinrich Wansing of the Dresden University of Technology Institute of Philosophy.) Again, even while insisting on the objective nature of God as a being, you’re painting Him with perceptions of people who are temporal. Whether anyone believed that the speed of light was not constant at some point in time says nothing about the nature of the speed of light, but rather about the nature of belief and time.
Becker’s Postulate is not controversial in this case. The existence of the God in question is established before the axioms are even stated as existence that is necessary. Thus, a modality is established with respect to the nature of His existence, and is expressed in Axiom 1. At that point, it is already clear that the modal status of His existence is necessary because His greatness has already been synthesized.
If anything about the proof at all is a dirty trick, it isn’t the application of any necessary modal status, but rather the definition itself! You keep insisting that we may go directly from “it is necessary that God exists” to “God exists”. But we can’t just pull the proposition from the implication without risking an argumentum ad logicam. It would be like saying that we can reduce 16/64 to 1/4 by cancelling the sixes. We’d get the right results, but the method is dubious.
The argument never states propositionally that it is necessary that God exists. That necessity remains tied, until the very end of the argument, to whether He exists at all. The proposition made is not that it is necessary that God exists, but rather that IF He exists, then it is necessary that He exists. We can’t just cancel out the left side of the implication and leave ourselves with the right. Note that G is not established until statement (9) where it is found to contradict the excluded middle. Only then may we derive by modus ponens that God indeed exists.
