Holy Cyclops

In The 70th Philosophers’ Carnival appears The Barefoot Bum’s analysis, here, of what goes wrong with Alvin Plantinga’s “Victorious” ontological argument for the existence of God. Since it’s something I’ve been looking at, I thought I’d take my own shot.

Plantinga’s argument takes differing forms.  For technical reasons, he puts it in terms of the exemplification of properties in possible worlds, rather than in terms of the existence of entities in possible worlds, and in its more detailed form, he puts it in terms of properties that entail other properties.  None of that will really affect my objections to the argument.  I’m going to present the simpler of the forms Plantinga presents in The Nature of Necessity.

Let maximal excellence (ME) be the property of being omniscient, omnipotent, and morally perfect—i.e., Godlike.

Let unsurpassable greatness (UG) be the property of necessary maximal excellence—of being maximally excellent in every possible world—of being Godlike in every possible world. 

Notice that in the widely accepted modal logic S5, which Plantinga uses, any statement that is necessarily true in one possible world is necessarily true in each possible world.  This is because if we had Np in world W[1] but ~Np in world W[2], we would have both P(Np) and P(~Np) (because truth in some possible world is what possibility means, in possible-worlds semantics)—but in S5, P(Np) collapses to Np and P(~Np)=P(P~p)=P~p=~Np, so we wind up with Np and ~Np, a contradiction.  In S5, a necessary truth in one possible world is a necessary truth in all other possible worlds, too.

Let a universal property be one which is instantiated in every possible world or in no possible world.  Note that UG is a universal property.  If UG is instantiated in any possible world, then N(ME) is instantiated in that possible world, so that N(ME) is instantiated in every possible world (because what is necessary is necessary in every possible world), so that UG is instantiated in every possible world.  Hence, either UG is instantiated in every possible world or in none of them.

1)  There is a possible world in which unsurpassable greatness is exemplified.     (Premiss)
2)  The proposition a thing has unsurpassable greatness if and only if it has maximal excellence in every possible world is necessarily true.    (Definition of UG)
3)  The proposition whatever has maximal excellence is omnipotent, omniscient, and morally perfect is necessarily true.      (Definition of ME)
3a)  Unsurpassable greatness is a universal property.  (As noted above)
4)  Possesses unsurpassable greatness is instantiated in every possible world.    (1,3a)
5)  Possesses unsurpassable greatness is instantiated in the actual world.  (4, universal instantiation)

And any being possessing unsurpassable greatness in the actual world is clearly an actually existing God.  Q.E.D. 

What is wrong with the argument?  Well, perhaps nothing is really wrong with it; but it certainly doesn’t give any reason to believe in God.  When one defines UG=N(ME), and then uses the premiss P(UG), he is using the premiss P(N(ME)).  But if he is working in S5, in which P(N(ME))=N(ME), it’s hardly surprising that the assumption of the possibility of the exemplification of universal greatness gets him the existence of God.  Defining UG as N(ME) guarantees, as Plantinga well realizes, that UG is a universal property:  Either UG is exemplified in all possible worlds or in none of them.  P(UG) seems like a tempting premiss, because it’s easy to confuse logical or metaphysical possibility with epistemic possibility.  One might think, “Gee, all I have to assume is that UG’s exemplification is possible?  That’s not much to ask!”  But it is a lot to ask when UG is defined as N(ME).  If one instead assumed the possibility of UG’s non-exemplification, a “proof” of God’s nonexistence would follow:

1)  There is a possible world in which unsurpassable greatness is not exemplified.     (Premiss)
2)  The proposition a thing has unsurpassable greatness if and only if it has maximal excellence in every possible world is necessarily true.    (Definition of UG)
3)  The proposition whatever has maximal excellence is omnipotent, omniscient, and morally perfect is necessarily true.      (Definition of ME)
3a)  Unsurpassable greatness is a universal property.  (As noted above)
4)  Possesses unsurpassable greatness is instantiated in every possible world.    (1,3a)
5)  Possesses unsurpassable greatness is instantiated in the actual world.  (4, universal instantiation)

1.  P(~UG)      (Premiss)
2.  In some possible world, ~UG.   (Definition of possibility in possible-world semantics)
2a.  UG is a universal property.   (As noted above)
3.  In every possible world, ~UG.     (1,2a)
4.  N(~UG).      (Definition of necessity in possible-world semantics)

Therefore, an unsurpassably great being does not exist in any possible world, so there is no God.  (The conclusion that there is no God requires the ascription of unsurpassable greatness to God.  Without it, one simply has P(~N(ME))=P(P(~ME))=P(~ME), so that in some possible world there is no God, but might be one in the actual world.)

The use of unsurpassable greatness, defined as necessary maximal excellence, is a trick.  One might use it to “prove” the existence of unicorns.  Let maximal unicornness (MU) be the property of being one-horned, white, equine, and so on; let unsurpassable unicornness (UU) be the property of necessary maximal unicornness (UU=N(MU)).  Notice that UU, just like UG, is a universal property.  Then

1)  There is a possible world in which unsurpassable unicornness is exemplified.     (Premiss)
2)  The proposition a thing has unsurpassable unicornness if and only if it has maximal unicornness in every possible world is necessarily true.    (Definition of UU)
3)  The proposition whatever has maximal unicornness is one-horned, white, equine (and so on) is necessarily true.      (Definition of MU)
3a)  Unsurpassable unicornness is a universal property.  (As noted above)
4)  Possesses unsurpassable unicornness is instantiated in every possible world.    (1,3a)
5)  Possesses unsurpassable unicornness is instantiated in the actual world.  (4, universal instantiation)

And, therefore, unicorns exist. 

Well, obviously not.  The point is that one must have some reason, in Plantinga’s “proof,” to prefer P(UG) to P(~UG).  The two are jointly inconsistent, so you can’t have both.  But one cannot give any reason to prefer P(UG) that is independent of the conclusion that God exists.   So, even if the argument is valid—and the making of St. Anselm’s argument into a valid one is the reason for Plantinga’s labeling it “victorious”—we have no reason to think it is sound.  But more than that, we have no reason to accept its crucial premiss:  P(UG).  Plantinga seems to think that it is rational to accept that premiss, and therefore rational to accept the conclusion that God exists.  But since P(UG)<—>N(UG), it is precisely as rational to accept P(UG) as it is to accept N(UG); how rational can it be to accept N(UG) without reason?  I am not claiming that it is more rational to accept P(~UG); only that I can see no rational reason for accepting either P(UG) or P(~UG).

Saturday, I played in the West Chester Chess Club’s First Saturday of the Month Quads.  Normally, we have around thirty-two to thirty-six players, but we only had twenty-two players this time.  Maybe people were staying home so that they could watch the Kentucky Derby, which the pre-race favorite Big Brown won.  But sacrificing a whole day’s worth of chess for two minutes of horse racing seems unlikely.  Whatever the reason, turnout was down, and I, with my low Class A rating, played in the second quad.

For those who are unfamiliar with how quads are run, and perhaps even with chess, I’ll note that when someone plays in a USCF-sanctioned tournament (”USCF”=”United States Chess Federation”), he gets a rating—a measure of playing strength—based on his results and on the strengths of his opponents.  The more rated games one plays, the more accurate his rating becomes.  In quads, the four highest-rated players are grouped together, and the four highest-rated players below them are grouped together, and so on, and each player plays one game against each of the other three players in his quad.  (If the number of players isn’t even, the tournament director plays, making it even; and if the number of players still isn’t a multiple of four, the bottom group is a six-person section in which each person still plays three games but in which the pairings are handled by something called the “Swiss system,” a well-established system for pairing players, round after round, in a tournament.)  My rating (1815, but now probably up to about 1830) is in the top fourth or fifth of tournament players; I had the seventh-highest rating among the twenty-two players.  USCF classes include Senior Master (2400+), National Master (2200-2399), Expert (2000-2199), Class A (1800-1999), Class B (1600-1799), Class C (1400-1599), Class D (1200-1399),  and Class E (1000-1199); few adults are lower-rated than 1000, although many kids are.  (The local chess club only has one master and one expert.) 

I had a strange quad.  I won my first game, when I should have lost—I got into a very inferior position straight out of the opening, struggled to come up with active play, and held on, only to reach a middlegame position in which I was sure I was lost.  But my opponent didn’t make the moves I thought he’d make, and I wound up trading down into a favorable endgame, which I then won.  In the second round, I played a very drawish game, only to stumble into a lost ending!  <Sigh>  Then, in the third round, my opponent handed me an Exchange (a rook for either knight or bishop—in this case, a knight) by letting me fork his queen and rook with my knight, and after many more moves, I forced his resignation.  So, it wasn’t a bad quad, measured by results—I scored 2-1—but it wasn’t a quad in which I played the way I want to.