I'm going to paste the criticism of the argument and I'll see if any of you guyts can respond. I have yet to study the argument so any help would be appreciated. I'm getting the Companion to Natural theology in about 2-3 weeks!

Anyway, here it is

This is going to crop up at several points in this analysis, so I'll mention it here at the outset:

Theorem 2 is a rewording of the S5 axiom: the axiom seeks to eliminate excessive operators and does so by treating the last as the only significant one:

- If possibly necessarily p, then necessarily p

Maydole's Theorem 2 says that:

- If it's possible that p is not possible, then p is not possible

And put another way, this reads:

- If it is possibly necessary that p is false, then it is necessary that p is false (which as you can see, is the S5 axiom).

Now onwards......

Step 1. Possibility: It's possible that a supreme being exists.

(P1) If it's not possible that a supreme being exists, every being has the property of not being supreme.

(P2) If every being has the property of not being supreme, not being supreme is a necessary condition.

(P3) If not being supreme is a necessary condition, not being supreme is a perfection. (from M2)

(P4) Not being supreme is not a perfection. (from M1 and M3)

(P5) It's possible that a supreme being exists. (from P1-P4)

P2 seems incomplete to me, and this fact seems to be what causes the error (P3) in this argument; M2 states that property A must be a

**perfection**, and that if property B is a necessary condition for that

**perfection** (property A), then property B is also a perfection. Now P2 identifies that if every being has the property of not being supreme then not being supreme is a necessary condition - but it does not specify what it is a necessary condition for. The answer, of course, is found in P1 - existence. If there are necessarily no existent beings which are supreme, then a necessary condition for being an "existent being" is the property of "not being supreme". So, let us keep in mind that according to M2, property B (in this case, "not being supreme") is only a perfection if it is a necessary condition for

**another perfection** - which, logically, would be the property of being "existent". The hidden premise in this argument, then, is that existence is a perfection - in order for P3 to follow from M2, we must make the assumption that existence is a perfection, and that since (according to P2) "not being supreme" is a necessary condition for the perfection "existing" (from M2), not being supreme is a perfection.

I, however, take issue with the assumption that existence is a perfection; in relation to Descartes' argument Kant points out to us that existence cannot be considered a perfection as it adds nothing to a concept - merely posits the subject and all of it's associated predicates in the actual world. If existence is not a perfection, then P3 does not follow from M2 and this argument collapses.

Step 2. Existence: A supreme being exists.

(E1) There exists an x so that it's possible that x is supreme. (from P5 and Theorem 3, the Barcan Formula)

(E2) There exists an x so that it's possible that {[it is not possible that (there exists a y such that y is Greater than x)] and [it is not possible that (there exists a y such that x is not y) and (x is not Greater than y)]}. (from E1, definition of "x is supreme")

(E3) There exists an x so that it's possible that [it is not possible that (there exists a y such that y is Greater than x)] and it's possible that [it is not possible that (there exists a y such that x is not y) and (x is not Greater than y)]. (from Theorem 1)

(E4) There exists an x so that {[it is not possible that (there exists a y such that y is Greater than x)] and [it is not possible that (there exists a y such that x is not y) and (x is not Greater than y)]}. (from Theorem 2)

(E5) There exists an x so that x is supreme. (from E4, definition of supreme)

As we have established that Maydole's method of demonstrating possibility has failed, we are already justified in rejecting (E1), but let us grant it for the sake of analyzing this argument, as I believe that analysis will show us WHY Maydole opted for a different approach to demonstrating possibility than, for example, Plantinga.

(E2) appears harmless, but if we look closely we can already see the setting up of the same type of argument as used by Plantinga; nested modal operators are already appearing in the definition of "x is supreme".

(E3) is simply a matter of distribution - no problems there.

(E4) is where S5 comes into play, and the nested modal operators are exposed (as well as Maydole's chosen modal system); in (E4) the sequence of operators:

"it's possible that [it is not possible that......"

.....has become:

{[it is not possible that

In other words, translating this into the language of S5:

1) It is possibly necessarily the case that ~p

has become

2) It is necessarily the case that ~p

(notice that the listed derivation of E4 is theorem 2, which I identified in the beginning as being a rewording of the S5 axiom)

To highlight why the failure of the possibility is so significant, I would like to reword Theorem 3 in a way that does not alter it's logical structure, for the sake of argument:

Theorem 3: If it's possible that there exists no x that is an F, then there exists no x so that it's possible that x is an F.

(this converse version will henceforth be denoted Theorem 3*, and our counterexample to P5 will be denoted CP5)

Now, having demonstrated why the possibility argument fails, I am going to construct a new argument that will prove the NON existence of a supreme being using precisely the same structure as Maydole, the only difference being our use of the converse version of Theorem 3, and our counterexample to P5 that it is NOT possible that a supreme being exists:

(E1) There does not exist an x so that it’s possible that x is supreme (from CP5 and Theorem 3*, the Barcan Formula)

(E2) There does not exist an x so that it’s possible that {[it is not possible that (there exists a y such that y is Greater than x)] and [it is not possible that (there exists a y such that x is not y) and (x is not Greater than y)]}. (from E1, definition of "x is supreme")

(E3) There does not exist an x so that it’s possible that [it is not possible that (there exists a y such that y is Greater than x)] and it's possible that [it is not possible that (there exists a y such that x is not y) and (x is not Greater than y)]. (from Theorem 1)

(E4) There does not exist an x so that {[it is not possible that (there exists a y such that y is Greater than x)] and [it is not possible that (there exists a y such that x is not y) and (x is not Greater than y)]}. (from Theorem 2)

(E5) There does not exist an x so that x is supreme. (from E4, definition of supreme)

So what has gone wrong? In his possibility argument, Maydole took a different route to Plantinga; Plantinga attempted to demonstrate the possibility of the maximally great being on the grounds that did not appear to be self contradictory, however he ran into problems when his use of the world indexed property (maximal greatness) combined with the S5 axiom (which entails that what is necessary or impossible does not vary from possible world to possible world - thereby allowing for collapsing of modal operators) appeared to allow contradictory statements to be proven true (namely, "maximal greatness" and "no maximality" - as discussed in my post "Ontological Arguments".).

After analysis of Plantinga's argument it becomes clear that he must either allow for NON collapsing modalities (so the statement "possibly necessarily p" would not collapse to "necessarily p"), or he must alter his possible

world system to accommodate the view that we cannot argue from non contradiction to a possible world.

To highlight this simply and briefly: if Plantinga fails to do the above, then "possibly necessarily p" and "possibly necessarily ~p" become "necessarily p" and "necessarily ~p".....which is clearly unacceptable.

Getting back to Maydole then: realizing this problem (perhaps...), Maydole attempts to demonstrate possibility by a different route. By smuggling in the hidden premise that existence is a perfection (an antiquated notion that has it's origin in Descartes' ontological argument and has been convincingly objected to) Maydole tries to demonstrate that the NON-possibility of a supreme being results in contradiction.

To return to my earlier demonstration: his stated derivation of P3 is M2, which states:

"If a property A

**IS A PERFECTION** and the property B is a necessary condition for A, then B is a perfection"

So the fact that "B is a perfection" does not follow only from the fact that B is a necessary condition for A - it is also required that A is a perfection.

Ergo as stated before, P2 should read:

(P2*) If every existing being has the property of not being supreme, not being supreme is a necessary condition of being an existing being.

(P3) would then only follow from M2 if is was assumed that "being an existing being" was a perfection.

SO TO WRAP THIS UP............

Maydole's alternative route to the demonstration of a supreme being's possible existence fails as Plantinga's did - we still appear to have no reason to assert the possible necessity of p rather than the possible necessity of ~p. Given equal justification for assuming the possibility of both, we are in default of any other reason to adopt Maydole's P5. Turning to Occam's Razor then, we may accuse him of multiplying entities beyond what is necessary (since the being's necessity only follows if it is both possibly necessary that a supreme being exists, and S5 is the correct modal system to employ, allowing him to collapse modal operators).

This certainly does not demonstrate the impossibility of the existence of a supreme being, but provides us with a rational reason for adopting "possibly necessarily ~p" rather than "possibly necessarily p", on the grounds of Occam's Razor (and in default of any other reason to choose one over the other).