rationalskepticism.org

Thommo wrote:

Mick wrote:One thing which caught my attention is this idea that his claiming that 'possibly god exists' is just to claim that god exists. I think that's unfair. Firstly, Plantinga doesn't refer to god as a proper name or otherwise. He talks about a being- a general term.

He also tells us he's defending the rationality of theistic belief, and indeed has spent his whole life doing so. Does the relabelling to what we all agree he's talking about make anything less clear? Personally (I can't speak for Paul) I find it makes things more clear.

Mick wrote:Secondly, while the possibility is logically equivalent to the conclusion, it is not synonymous with the conclusion.

It is. You can prove that you can transpose any occurence of "possibly god exists" with "god exists" within the formalism under discussion, making them perfect synonyms. They aren't synonyms in English language, nor does the proof hold in English language.

Mick wrote:Neither is it obvious that it is logically equivalent to the conclusion.

It is obvious to anyone who understands the formalism, though why we would be concerned about what's obvious eludes me.

Mick wrote:Keep in mind that the possibility premise is not given as <>[](Ex)Gx; it is simply offered as <>(Ex)Gx.

Your second Gx there is not the same Gx, it's clearer if understood that he's giving it as:

<>∃x([]G(x)) ⇔ <>∃x(F(x)) where F(x) is defined to be []G(x), i.e. F is Maximal greatness and G is Maximal excellence.

Since he's chosen the rules so that he can pull the quantifier out (in fact I'm not sure if the formalism uses quantifiers there or not even) it really doesn't matter where the quantifier appears, they are the same statement.

ETA: I have switched to a conventional notation which only uses brackets as parenthesis, because I find the use of them in place of quantifiers in addition to parenthetical usage ugly and ambiguous.