But isn’t that what I just indicated by suggesting that the logic itself obtains in all possible worlds?
Yes. I think that’s a fair way of putting it, Eris.
For the OP’s information, not all ontological proofs are necessary valid. Some are even circulus in probando. (Those are valid but trivial.) But some are quite sophisticated, and that includes the modern modal arguments. They have been developed by some of the greatest thinkers of the 20th century from Godel to Plantinga.
I agree with those who say that the argument, even if valid and nontrivial, is not convincing. But I also agree with Plantinga who said that what a proper valid argument ought to convince anyone of is that those who hold it are reasonable people. Sentient Meat, for example, respects my views and I respect his. It is not reasonable that people who believe in God be treated as intellectual savages who hold to nothing but superstition.
And if I mean exactly what I said? What then?
Well, then I guess you’ll have to explain what you mean. There’s no formal meaning for the term “communication” that I know of in any system of K.
While accessibility relationships are another problem I have with the proof (namely,that they are not defined, the closest I can fathom would be if all universes are mutually accessible if they follow the rules of logic, in which case I have yet another issue with it…) my beef with “communication” is in the assumption of “greatness”.
Now, most proofs along these veins assign qualities to greatness other than mere size. But in the proof you use, “greatness” is determined by how many universes an entity appears in.
I, however, would not assign an entity this “greatness” even if it existed in all possible worlds. That is because the entities, while possessing the exact same properties, are not part of the same entity. For instance if g exists, and there are X worlds, there are X g’s, all possessing the same properties, but are not the same entity. The only way they could be the same entity is if information could be exchanged between worlds, thus my reference to communication.
To use another example, a human is not greater, even in breadth, than an orangutan simply because there are more humans.
Since it uses the S5 axioim, the accessibility relation is Euclidean: (wRv&wRu) -> vRu. That is, if v and u are modes onto w, then v is accessible to u and u is accessible to v.
Not exactly. A modality is a view, or frame of reference, onto a world. Greatness is not determined by cardinality but by perfection — that is to say, there are no frames of reference not accessible to the entity.
Perhaps you misunderstand. Yes, S5 uses that sort of accessibility relation, perhaps I used misleading terminology. I meant that the subconditions under which accessibility exists in the first place are not well defined.
I see no reason to limit the accessibility function we are using to the definition of “g”. There may be other worlds which I believe are accessible to ours which do not include “g”. Of course, if I assume that they are accessible, this means that “g” cannot exist per the assumptions of this MOPoG.
In what way is this perfect, considering that the set of frames of reference is arbitrary?
Are the axioms of modal and predicate logic the same in all worlds, or individual but the same? Is there communication between worlds if the fundamental theorems of the calculus are derived in them?
I’m not sure what you mean by “subcondition”, but I’ll take a stab at answering. The Euclidean relation posits that <>A -> <>A. In other words, if it is possible for A to be true in the actual world, then in every world it must be possible for A to be true. That is a postulate that most materialists would accept readily since it forms the basis of their worldview.
Well, that’s the point of the proof: to determine in what world(s), if any, “g” is accessible. It is not known until the penultimate inference that “g” is accessible in all worlds. And it is not known until the final inference that “g” is accessible in the actual world. We begin only with what we know — that “g” possibly is accessible in some world.
Perfect in the sense of complete. Noncontingent. That is, all frames — no matter how many and no matter any other consideration — are accessible.
Slight nitpick: the law of the excluded middle is well established in bivalent logic calculi, which are dominant but not the only logical calculi around (much like Euclidian geometry isn’t the only plausible geometry). Intuitionistic logic comes to mind as a logical calculus that specifically denies the law of the excluded middle.
In paraconsistent logic, not only does excluded middle fail, but so does noncontradiction.
Where all these arguments fall apart is in the unstated premise that the Universe is somehow compelled or constrained by our ability or lack of ability to comprehend. This is, of course, utter nonsense. But y’all keep it up. Y’all’re funnier than a yard full of headless chickens.
except for impossible worlds. Impossible worlds are those without NE (the only accessibility parameter I can find in the proof.)
So NE is contingent upon being within the S5 Euclidean “circle”, as it were, of worlds with NE. There are plenty of imaginable worlds that are not “possible” according to the parameters of the proof. For instance, as someone has said, what if the Prime World does not follow the rules of bivalent logic?
We are not talking about the universe. The universe is known epistemically. It is ontologically irrelevant.
Please, do pay attention if you wish to join in.
OK. For Universe substitute God. I didn’t want to use that word because it carries so much extraneous garbage with it, which is another probelm with the whole argument, it doesn’t really prove anything, it merely attaches some sort of sophistic pseudorelevance to a poorly defined word. If the ontological argument does prove anything it is not any God of the book religions, it is the Buddhist concept of Godhead.
Impossible worlds don’t exist. And you have the contingency backwards. S5 is contingent on there being NE. Saying that NE is contingent on S5 is like saying that gravity didn’t work until Newton wrote his equation. Finally, the bivalent system of S5 is the appropriate system for determining the modal status of “g” for the reasons already stated. If a triangle is proved to be a right triangle by Euclidean geometry, it doesn’t matter that it cannot be proved to be a right triangle by Peano arithmetic.
This counter-example is quite a convincing proof that there is a flaw in the method (even for one with no background in modal logic). You only have to determine whether or not the second premise is reasonable and you are on your way to debunking this proof. So far, no one has shown an acceptable reason to reject the second premise short of begging the question.
It fails because of the coherent definition of g as the greatest possible being. The assertion “<>~g” reads “it is possible that the greatest possible being does not exist”. If it is the greatest possible being, then it cannot be impossible. Therefore, <>~g (or ~g) is a contradiction. On the other hand, the assertion “<>g” reads “it is possible that the greatest possible being exists”, and that assertion is intuitively tenable. Therefore, whatever g might represent in the statement <>~g, it cannot represent God as defined.
I’m suddenly seeing this proof in a whole new light. Maybe it is the vicodin.
As a theist, it would be in my interest to prove god’s existence with this. To do so, one of the assumptions is that God is not impossible, where impossibility is symbolically ~G, that is, “necessary not”. So we’re saying god is not impossible, or it is not necessary that there is no god. ~~G, or <>G. Definitionally equivalent. What this actually means, though, is that there is at least one logical world where G is the case.
Suppose a strong atheist wants to use this proof. The counter proposition runs, ~G, or “God is not necessary.” What this says, in fact, is that there is at least one world where G is not the case. And so we come to the point where if g fails to obtain in one world, it fails to obtain in all of them.
The weak atheist, or agnostic, would have to counter the theist as such: either the other assumption (G->G) is not a logical quality god would have, or would have to hold onto strong atheism which, as ~G implies.
Interesting. This almost forces weak atheists to become agnostics or strong atheists, if I’m understanding my head properly (again: drugs).
Lib, I still strongly dislike the idea that G is defined into existence like that. The proof, however strong it is, seems just as strong without it, since the hypothesis <>G assumes existence anyway.
[sub]This is not meant to usurp my previous comments wrt the meaning we may actually assign these symbols, which still might only add up to “Necessary existence exists.” Also, it is a prescription from dental work, nothing illegal here folks.[/sub]
But, if using this method, you can’t even posit the possibility of g’s non-existence, how “credible” is the method? Talk about un-falsifiable.
(Feel free to educate me / expose me as an idiot. I really don’t get this part.)