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7. Plantinga's OntologicalArgument
The "victorious" modal ontological argument ofPlantinga (1974) goes roughly as follows: Say that an entity possesses"maximal excellence" iff it is omnipotent, omnscient, and morallyperfect. Say, further, that an entity possesses "maximal greatness"iff it possesses maximal excellence in every possible world that is, iff itis necessarily existent and necessarily maximally excellent. Then consider thefollowing argument:
There is a possible world in which there is an entity which possesses maximal greatness. (Hence) There is an entity which possesses maximal greatness.
Undersuitable assumptions about the nature of accessibility relations betweenpossible worlds, this argument is valid: from it is possible that it isnecessary that p, one can infer that it is necessary that p.Setting aside the possibility that one might challenge this widely acceptedmodal principle, it seems that opponents of the argument are bound to challengethe acceptability of the premise.
And,of course, they do. Let's just run the argument in reverse.
There is no entity which possesses maximal greatness. (Hence) There is no possible world in which there is an entity which possesses maximal greatness.
Plainlyenough, if you do not already accept the claim that there is an entity whichpossesses maximal greatness, then you won't agree that the first of thesearguments is more acceptable than the second. So, as a proof of the existenceof a being which posseses maximal greatness, Plantinga's argument seems to be anon-starter.
Perhapssomewhat surprisingly, Plantinga himself agrees: the "victorious"modal ontological argument is not a proof of the existence of a being whichpossesses maximal greatness. But how, then, is it "victorious"?Plantinga writes: "Our verdict on these reformulated versions of St.Anselm's argument must be as follows. They cannot, perhaps, be said to proveor establish their conclusion. But since it is rational to accept theircentral premise, they do show that it is rational to accept thatconclusion." (Plantinga (1974:221)).
It ispretty clear that Plantinga's argument does not show what he claims that itshows. Consider, again, the argument: "Either God exists, or 2+2=5. It isnot the case that 2+2=5. So God exists." It is just a mistake for a theistto say: "Since the premise is true (and the argument is valid),this argument shows that the conclusion of the argument is true".No-one thinks that that argument shows any such thing. Similarly, it isjust a mistake for a theist to say: "Since it is rational to acceptthe premise (and the argument is valid), this argument shows that it is rationalto accept the conclusion of the argument". Again, no one thinks that thatargument shows any such thing. But why don't these arguments showthe things in question? There is room for argument about this. But it is atleast plausible to claim that, in each case, any even minimally rational personwho has doubts about the claimed status of the conclusion of the argument willhave exactly the same doubts about the claimed status of the premise. If, forexample, I doubt that it is rational to accept the claim that God exists, thenyou can quite sure that I will doubt that it is rational to accept the claimthat either 2+2=5 or God exists. But, of course, the very same point can bemade about Plantinga's argument: anyone with even minimal rationality whounderstands the premise and the conclusion of the argument, and who has doubtsabout the claim that there is an entity which possesses maximal greatness, willhave exactly the same doubts about the claim that there is a possible world inwhich there is an entity which possesses maximal greatness.
Forfurther discussion of Plantinga's argument, see for example Adams (1988), Chandler (1993), Oppy (1995:70-78,248-259), Tooley (1981), and van Inwagen (1977)).
8. St. Anselm's OntologicalArgument
There is an enormous literature on the material in ProslogionII-III. Some commentators deny that St. Anselm tried to put forward anyproofs of the existence of God. Even among commentators who agree that St.Anselm intended to prove the existence of God, there is disagreement aboutwhere the proof is located. Some commentators claim that the main proof is in ProslogionII, and that the rest of the work draws out corollaries of that proof (see,e.g., Charlesworth (1965)). Other commentators claim that the main proof is in PrologionIII, and that the proof in Proslogion II is merely an inferior firstattempt (see, e.g., Malcolm (1960)). Yet other commentators claim that there isa single proof which spans at least Proslogion II-III see, e.g.,Campbell (1976) and, perhaps, the entire work see, e.g., La Croix (1972). Ishall ignore this aspect of the controversy about the Proslogion.Instead, I shall just focus on the question of the analysis of the material in ProslogionII on the assumption that there is an independent argument for theexistence of God which is given therein.
Hereis one translation of the crucial part of Proslogion II (due to WilliamMann (1972:260-1); alternative translations can be found in Barnes (1972),Campbell (1976), Charlesworth (1965), and elsewhere):
Thus even the fool is convinced that something than whichnothing greater can be conceived is in the understanding, since when he hearsthis, he understands it; and whatever is understood is in the understanding.And certainly that than which a greater cannot be conceived cannot be in theunderstanding alone. For if it is even in the understanding alone, it can beconceived to exist in reality also, which is greater. Thus ifthat than which a greater cannot be conceived is in the understanding alone,then that than which a greater cannot be conceived is itself that than which agreater can be conceived. But surely this cannot be. Thus without doubtsomething than which a greater cannot be conceived exists, both in theunderstanding and in reality.
Therehave been many ingenious attempts to find an argument which can be expressed inmodern logical formalism, which is logically valid, and which might plausiblybe claimed to be the argument which is expressed in this passage. Totake a few prime examples, Adams (1971), Barnes (1972) and Oppenheimer andZalta (1991) have all produced formally valid analyses of the argument in thispassage. We begin with a brief presentation of each of these analyses, precededby a presentation of the formulation of the argument given by Plantinga (1967),and including a presentation of some of the formulations of Lewis (1970). (Chambers (2000) works with the analysis of Adams (1971).)
Plantinga
1.
God exists in the understanding but not in reality.
(Assumption for reductio)
2.
Existence in reality is greater than existence in the understanding alone.
(Premise)
3.
A being having all of God's properties plus existence in reality can be conceived.
(Premise)
4.
A being having all of God's properties plus existence in reality is greater than God
(From (1) and (2).)
5.
A being greater than God can be conceived.
(From (3) and (4).)
6.
It is false that a being greater than God can be conceived.
(From definition of "God".)
7.
Hence, it is false that God exists in the understanding but not in reality.
(From (1), (5), (6).)
8.
God exists in the understanding.
(Premise, to which even the Fool agrees.)
9.
Hence God exists in reality.
(From (7), (8).)
Barnes
1.The Fool understands the expression "the being than which no greater can be conceived".
(Premise)
2.
If a person understands an expression "b", then b is in that person's understanding.
(Premise)
3.
If a thing is in a person's understanding, then the person can conceive of that thing's existing in reality.
(Premise)
4.
Each thing which exists in reality is greater than any thing which exists only in the understanding.
(Premise)
5.
If a person can conceive of something, and that thing entails something else, then the person can also conceive of that other thing.
(Premise)
