But it is interesting to note that, to me at least, G->G is certainly a property I would ascribe to God. This is why my focus in both of these was on the semantics of “possible”, and whether that was a sensable axiom.
Which is to say, I see nowhere else to attack it but on sematics or on an “axiom of choice” level where it seems to be an axiom that should be proved, if it can be, and if it can’t, then I feel comfortable rejecting it (or, as the case may be, accepting it).
The last statement you make would have REALLY served me well back in the other thread where I tried to put across that the definition+axioms begged the question of the conclusion. Your economy of phrasing there should have struck me earlier, but it didn’t and it did strike you and so credit is where credit’s due. 
Thanks, I’m always willing to take credit for stating the obvious (or in this case, mis-stating. The word I meant to type was assert, not assume. A subtle difference, but my fingers have a mind of their own. [sub]They also hate the word “the”[/sub].
Again, there is nothing wrong with the axiom. It is a fine means for identifying an S5-compatible “God space”. I simply have no reason to prefer that axiom over its alternatives as a description of the world I perceive. I certainly see no intellectual necessity to do so.
Erislover writes:
“Which is to say, I see nowhere else to attack it but on sematics or on an “axiom of choice” level where it seems to be an axiom that should be proved, if it can be, and if it can’t, then I feel comfortable rejecting it (or, as the case may be, accepting it).”
I think the objection I (and I think Apos) raise as to various sentences in the proof being out of the scope of the possible worlds is not an attack on the semantics. This objection accepts the semantics of possible worlds given by those making the argument, and shows that S5 is not appropriate.
This is a validity issue (not a soundness issue). The proof, valid in S5, is not valid for the given semantics of possible worlds.