Friday, December 18, 2009

If g is possible, g exists...

[Just trying out some ideas from James Ross's Philosophical Theology....]

Let's define "g" as "a necessary or necessarily existing being" and "(Ex)(gx)" as "a necessary being exists." Is g possible? It seems so, for g is not logically inconsistent. There is nothing intrinsically incoherent in coupling "necessary" and "existing." If there were, the assertion A of the impossibility of "necessary + existing" would have to be true in every possible case, and would therefore be a necessary truth-- which is to say the assertion A that "necessary existence is impossible" would necessarily exist. If A is possible, it is impossible. If A is impossible, then g is at least possible. So g is at least possible.

Now, if g is possible, the conditions of its existence entail that nothing can bring about or prevent (Ex)(gx). For if anything could bring it about that (Ex)(gx), then g is contingent, not necessary, which violates g itself. Alternatively, if anything could prevent (Ex)(gx) then g is, once more, contingent, not necessary, which violates g itself. The very possibility of g entails that no other possible state of affairs (P(~g)) could bring about or prevent (Ex)(gx). If anything P could bring about or prevent (Ex)(gx)-- producing (~g)-- then g as such would not be possible. For if (P(~g)) could bring about ~g, then g would be a contingent being, not a necessary being. The alleged possiblity of (P(~g)) entails the impossibility of g, but g is possible, so (P(~g)) is not possible. Nothing can bring about or prevent g. The possibility parameters of g exclude the possibility of its non-possibility.

So, if g is possible, there must be some explanation for its being. Define "g accounts for itself" as (gEg), and "something besides g accounts for g" as (qEg). If qEg, then q is an essential factor in g. As such, if qEg is possible, it is just as necessary as g. If, by contrast, gEg, then g exists as necessarily as any a priori truth of the form "m accounts for m insofar as m accounts for m." Hence, whatever account is given of (Ex)(gx), if g is possible, then g is necessary. If g is necessary, g is actual. Therefore, if g is possible, g is actual, and necessarily so.

If we define "G" as "God exists" and "(Eg)(Gg)" as "God exists and is a necessary being," then, if G is possible, G is actual, and necessarily so. G would have to be an omnipotent being, to which all possible effects are causally accessible, for if any effect E or set of effects (E(E)) were causally inaccessible to G, then E or (E(E)) could bring it about that G does not exist. But G not existing is impossible by definition. Therefore, G exists necessarily and omnipotently.


UnBeguiled said...


I wonder what is the purpose of such arguments.

The Codgitator said...

Where you been? Why'd you shut down yer blog? Did you still want to get back to me about finality?

The Codgitator said...


I also wanted to ask you: are you familiar with Zeno's motion/change paradoxes? If so, what do you think of them as refutations of motion/change?