Wednesday, November 14, 2007

Philosophy of Religion 2 - Natural Theology 1: The Modal Ontological Argument

The Modal Ontological Argument
NOTE - Corresponding YouTube videos are up:












§I. Introduction

One of the most intriguing arguments in the history of the philosophy of religion has been the famous ontological argument for the existence of God. The argument gained its famous first proposal in the Proslogion by Saint Anselm of Canterbury.1 The argument was then revised over the centuries multiple times, such as René Descartes' continuation of Anselmian thought.2 The argument has also been subject to blistering criticisms, the most famous criticisms consisting of Ganuilo's parodies,3 Immanuel Kant's argument that existence is not a property,4 and David Hume's denial of necessary existence.5 Nonetheless, it has continued to capture the imagination of philosophers. As Alvin Plantinga has said,6

[Although the ontological argument] looks, at first sight, like a verbal sleight of hand or a piece of word magic, it has fascinated philosophers ever since St. Anselm had the good fortune to formulate it. Nearly every major philosopher from that time to this has had his say about it... [it seems that] the argument has about it an air of egregious unsoundness or perhaps even trumpery and deceit; yet it is profoundly difficult to say exactly where it goes wrong.
Indeed, there is much disagreement as to what precisely St. Anselm's argument was in the first place.7 Although most philosophers agree that St. Anselm's original argument is flawed in some respect, many disagree as what the exact flaws are. As Plantinga elaborates,8
[Many] of the most knotty and difficult problems in philosophy meet in [the ontological] argument: is existence a property? Are existential propositions ever necessarily true? Are existential propositions what they seem to be about? How are we to understand negative existentials? Are there, in any respectable sense of 'are', some objects that do not exist? If so, do they have any properties? Can they be compared with things that do exist? These issues and a score of others arise in connection with St. Anselm's argument.
However, in this paper, I shall not focus on either St. Anselm's ontological argument nor shall I devote my attention upon Descartes' ontological argument. Instead, I shall examine what I, as well as most modern philosophers, take to the most promising version of the ontological argument, namely, the modal ontological argument. As its name suggests, the modal ontological argument employs the powerful apparatus of modal logic and possible world semantics that is prevalent throughout most of modern analytic philosophy. Modal versions of the ontological argument were first suggested by Norman Malcolm, who argued that St. Anselm had offered two ontological arguments.9 Charles Hartshorne has given a formalized version of the argument as well.10 However, I shall not concern myself with either Malcolm's nor Hartshorne's version of the argument here. Instead, I shall devote my energies to what I, as well as most philosophers of religion, take to be the most influential and most powerful version of the argument, as developed by Alvin Plantinga.11 This paper shall assume a familiarity with the logical apparatus of modal logic, in particular, the system S5. Moreover, this paper shall assume a familiarity with possible world semantics.12 Without spending anymore space on introducing issues, I shall pursue the heart of the matter.

§II. A Brief Exposition of Plantinga's Argument

After discussing what he construes to be mistaken ontological arguments, Plantinga presents what he labels the 'victorious' modal version of the argument in a remarkably short space.13 The argument proceeds as thus
(1) Definition: Maximal greatness is exemplified if and only if maximal excellence is exemplified in every possible world.
(2) Definition: Maximal excellence is exemplified if and only if a being exemplifies omnipotence, omniscience, and moral perfection.
(3) Premise: Maximal greatness is exemplified in a possible world.
(4) S5 Axiom: If maximal greatness is exemplified in a possible world, then maximal excellence is exemplified in every possible world.
(5) Maximal excellence is exemplified in every possible world. [3, 4]
(6) S5 Axiom: If maximal excellence is exemplified in every possible world, then maximal excellence is exemplified in the actual world.
(7) Maximal excellence is exemplified in the actual world. [5, 6]
(8) Therefore, there is a maximally excellent being. [7]
And, hence, God (a maximally excellent being) exists. Some elaboration is required here, just to see how this argument proceeds. (1) and (2) consist of the two crucial definitions Plantinga employs in order to reach the conclusion. Maximal greatness being exemplified by definition exemplifies maximal excellence in every possible world. If there is a possible world in which maximal greatness is exemplified, then, it follows (per an S5 axiom as well as intuitively) that maximal excellence is exemplified in every possible world, since maximally greatness is exemplified. And if in every possible world, maximal excellence is exemplified, it follows (per an S5 axiom as well as intuitively) that since the actual world is a member of all possible worlds, then it follows that a maximally excellent being exists in the actual world, and hence, there is a maximally excellent being. God, who is by definition a maximally excellent being, therefore exists.

§III. Does Plantinga Beg the Question?

Plantinga's argument strikes one as disarmingly surprising, as it moves from seemingly modest premises to an interesting conclusion. However, I am of the opinion that Plantinga's premises are not as modest as it appears prima facie. This will be inordinately clear if we formalize the argument into a symbolic S5 modal apparatus. Let propositon G represent maximal excellence is exemplified. From this, we can formalize Plantinga's argument as thus
(9) ◊□G [Premise]
(10) ◊□p → □p [S5 axiom]
(11) □G [9, 10]
(12) □pp [S5 axiom]
(13) G [11, 12]
Or, in English
(9') It is possible that it is necessary that maximal excellence is exemplified (i.e. it is possible that maximal greatness is exemplified). [Premise]
(10') If a proposition p is possibly necessary, then proposition p is necessary. [S5 axiom]
(11') It is necessary that maximal excellence is exemplified (i.e. maximal greatness is exemplified ). [9', 10']
(12') If a proposition p is necessary, then proposition p is true. [S5 axiom]
(13') It is true that maximal excellence is exemplified. [11', 12']
The crucial premise is (9). Prima facie, it looks modest enough. Unfortunately, this is all appearance. As (10) explicates, it is true that under S5 and possible world semantics, possibly necessary propositions entail the necessity of that proposition. However, the entailment runs the other way as well. Under S5 and possible world semantics, the following holds
(14) □p → ◊□p [S5 theorem]
(14') If a proposition p is necessary, then it is possible that proposition p is necessary. [S5 theorem]
The reason this entailment holds is because
(15) p → ◊p [S5 axiom]
(15') If a proposition p is true, then proposition p is possible. [S5 axiom]
Hence, given (10) and (14), it follows that
(16) ◊□p ↔ □p [10, 14]
(16') It is possible that a proposition p is necessary if and only if proposition p is necessary. [10', 14']
And from (9), (11), and (16), it follows that
(17) ◊□G ↔ □G [9, 11, 16]
(17') It is possible that it is necessary that maximal excellence is exemplified if and only if it is necessary that maximal excellence is exemplified (i.e. It is possible that maximal greatness is exemplified if and only if maximal greatness is exemplified ). [9', 11', 16']
Therefore, (9) and (11) are simply logically equivalent, and different ways of expressing the same fact. Both express the necessity of the exemplification of maximal excellence. Plainly, if in a possible world there is a necessary state of affairs, then, obviously enough, there is actually a necessary state of affairs and vice versa. Or, more formally, if some proposition p entails q which entails r, then p entails r, by substitution. Hence, if p entails q and q entails p, then p entails p. Hence, we need only reduce the syllogism to the assertion of p. Hence, Plantinga can simply reduce his argument to
(11) □G [9, 10]
(12) □pp [S5 axiom]
(13) G [11, 12]
However, this carries little, if any, persuasive force. Plantinga must now show that it is necessary that maximal excellence is exemplified. And why should one grant that possibility? This simply begs the question against the atheist, who denies God's existence and, hence, maximal excellence necessarily being exemplified. One cannot simply posit maximal excellence is necessarily exemplified in order to prove that maximal excellence is exemplified : one must first show that maximal excellence being exemplified is indeed necessary. If maximal excellence being necessarily exemplified is actual, then it is obviously necessary. If maximal excellence necessarily being exemplified is necessary, then it is trivially actual. Assuming the necessity of maximal excellence being exemplified simply presumes that maximal excellence is exemplified . Moreover, necessity is not acquired by fiat, hence, Plantinga's crucial premise is a good deal more controversial than some may think. Modal necessities, especially the supposed necessity of an existential proposition about a concrete object, are not merely supposed. I shall elaborate more on this later. However, Plantinga has a ready reply for such objections. I shall quote the entire section on his reply to such objections,14

Now, some philosophers do not take kindly to the Ontological Argument; the claim that it or some version of it is sound is often met with puzzled outrage or even baffled rage. One objection I have heard is that the formulation of the last section (call it Argument A) may be valid, but it is clearly circular or question-begging. Sometimes this caveat has no more substance than the recognition that the argument is indeed valid and that its premiss could not be true unless its conclusion were—which, of course, does not come to much as an objection. But suppose we briefly look into this complaint. What is it for an argument to be circular? In the paradigm case, one argues for a proposition A1 on the basis of A2, for A2 on the basis of A3,..., for An-1, on the basis of An, and for An on the basis of A1. Whatever the merits of such a procedure Argument A is clearly not an example of it; to conform to this pattern one who offered Argument A would be obliged to produce in turn an argument for its main premiss—an argument that involved as premiss the conclusion of A or some other proposition such that A's conclusion was proximately or ultimately offered as evidence for it.
So, the argument is not obviously circular. Is it question-begging? Although surely some arguments are question-begging, it is by no means easy to say what this fault consists in or is related to circularity. But perhaps we can get at the objector's dissatisfaction by means of an example. Consider Argument B:
(46) Either 7 + 5 = 13 or God exists.

(47) 7 + 5 ≠ 13.

Therefore

(48) God exists.

This argument is valid. Since I accept its conclusion and therefore its first premiss, I believe to be sound as well. Still, I could scarcely claim much for it as a piece of Natural Theology. Probably it will never rank with Aquinas' Third Way , or even his much less impressive Fourth Way. And the reason is that indeed this argument is in some way question begging or dialectically deficient. For presumably a person would not come to believe (46) unless he already believed (48). Not the alternative is impossible—it could happen, I suppose, that someone inexplicably finds himself with the belief that (46) (and (47)) is true, then go on to conclude that the same holds for (48). But certainly that would not be the general case. Most people who believe (46) do so only because they already believe (48) and infer the former from the latter. But how do these considerations apply to Argument A? It is by no means obvious that anyone who accepts its main premise does so only because he infers it from the conclusion. If anyone did do that, then for him the argument is dialectically deficient in the way that B is; but surely Argument A need not thus be dialectically deficient for one who accepts it. [Emphasis in original]

However, the problem with what Plantinga labels Argument A is the fact that it is question-begging. First of all, it can be demonstrated that Plantinga simply begs the question since he assumes that maximal excellence being exemplified is necessary, from which he trivially obtains the conclusion that maximal excellence being exemplified is actual. Furthermore, it is worth noting that, as Plantinga points out, the conclusion of an argument tends to be stronger than the premises. And yet, in Plantinga's argument, his premise is stronger than the conclusion, indeed, infinitely so, since his argument not only assumes that maximal excellence is exemplified, but the necessity thereof. Hence, Plantinga's argument is wholly question-begging.
Secondly, let us examine whether or not Argument A and B are closely related in their argumentative structure. Unfortunately, they are. While (46) and (47) entails (48), it also true that (48) entails (46) and (47). The reason is because in propositional logic
(18) ppq [Theorem in propositional logic]
(18') If a proposition p is true, then either proposition p is true or proposition q is true. [Theorem in proposition logic]
This is because a disjunction is true if and only if at least one of the disjuncts is true. If a propositon is true, then any disjunction involving it is true. Therefore, (48) entails (46) [which is a disjunction], and (46) in conjunction with (47) entails (48). Furthermore, in propositional logic,
(19) ¬(q ∧ ¬q) [Axiom in propositional logic]
(19') It is false that a proposition q is both true and false. [Axiom in propositional logic]
This is a tautology of propositional logic. Given the definition of a material conditional, any proposition entails a tautology (a material conditional is true if and only if the consequent is true or if both the antecedent and the consequent are false, and, of course, all tautologies are true),
(20) p → ¬(q ∧ ¬q) [Definition of material conditional]
(20') If a proposition p is true, then it is false that a proposition q is both true and false. [Definition of material conditional]
Hence, (48) also entails (47), since (47) is a theorem of Peano arithmetic; its falsity entails a contradiction in the Peano arithmetic by use of the successor function. In other words, (47) is a necessary tautology, and given the definition of a material conditional, since all necessary propositions are true, any material conditional with (47) as the consequent is true. Hence, (48) entails (47). Given (18), (19), and (20), it follows that (48) also entails (47) and (48). So, Argument B can simply be reduced to
(48) God exists
(48) God exists
Needless to say, Argument B isn't exactly persuasive. The only reason (46) is true is because (48) is true; hence, (48) simply justifies itself, resulting in a question-begging argument. And, Argument A does not differ in this respect. This can be demonstrated easily. I have already demonstrated similar entailments in Argument A. Furthermore, in modal logic, a proposition is necessary if and only if its negation entails a contradiction or metaphysical absurdity; in this case, entailed by a tautology.

So, necessary propositions p in Plantinga's example are such that
(21) ¬(q ∧ ¬q) → p
(21') If it is false that a proposition q is both true and false, then a proposition p is true.
This is logically equivalent with
(22) ¬p → (q ∧ ¬q)
(22') If a proposition p is false, then a proposition q is both true and false.
Recall, furthermore, (20). Given (20) and (21), we have
(23) p ↔ ¬(q ∧ ¬q)
(23') A proposition p is true if and only if it is false that a proposition q is both true and false.
In Argument A, it is the case
(24) G ↔ ¬(q ∧ ¬q)
(24') Maximal excellence is exemplified if and only if it is false that a proposition q is both true and false.
Hence, unless Plantinga can provide good reason for accepting (24) [as I shall discuss later], such an argument is purely-question begging and can simply be reduced to the assertion of the question, maximal excellence is exemplified. This becomes clearer if we examine the situation as thus. It is also true that, in propositional logic,
(25) (pq) ↔ (¬pq) [Theorem in propositional logic]
(25') A proposition p implies a proposition q if and only if either proposition p is false or proposition q is true. [Theorem in propositional logic]
Therefore, given this logical equivalence, Argument A can simply be expressed as thus
(26) G ∨ (q ∧ ¬q) [Premise ]
(27) ¬(q ∧ ¬q) [Axiom in propositional logic]
(28) G [27, 28]
(26') Either Maximal excellence is exemplified or a proposition q is both true and false. [Premise]
(27') It is false that a proposition q is both true and false. [Axiom in propositional logic]
(28') Maximal excellence is exemplified. [27', 28']
Certainly, (26) and (27) entail (28). But, (28) entails (26) as well as (27), in the precise same manner that Argument B does. Hence, we can simply reduce Argument A to
(28) G
(28) G
(28') Maximal excellence is exemplified.
(28') Maximal excellence is exemplified.
And like Argument B, Argument A hardly carries any persuasive force at all. It is only true because (28) is taken to be true, hence, (28) justifies itself and, hence, Argument A constitutes a question-begging argument. So, we must ask why anyone should accept (9), (11), or (26) at all. We have merely attached a contradiction onto the conclusion, and then reasoned to the conclusion. Both the conclusion and the premises entail the other. Hence, the argument simply reduces to an assertion of its conclusion. Interestingly, Plantinga somewhat agrees with this sort of criticism.15

But here we must be careful; we must ask whether this argument is a successful piece of natural theology, whether it proves the existence of God. And the answer must be, I think, that it does not. An argument for God's existence may be sound, after all, without in any useful sense proving God's existence. Since I believe in God, I think the following argument is sound:

Either God exists or 7 + 5 = 14

It is false that 7 + 5 = 14

Therefore God exists.

But obviously this isn't a proof; no one who didn't already accept the conclusion, would accept the first premise. The ontological argument we've been examining isn't just like this one, of course, but it must be conceded that not everyone who understands and reflects on its central premise -- that the existence of a maximally great being is possible -- will accept it. Still, it is evident, I think, that there is nothing contrary to reason or irrational in accepting this premise. What I claim for this argument, therefore, is that it establishes, not the truth of theism, but its rational acceptability. And hence it accomplishes at least one of the aims of the tradition of natural theology.

Plantinga's remarks here are somewhat baffling. Like Argument B, one wonders how Argument A fares any better at all. Necessity is not simply granted by fiat. And, in fact, the sort of reasoning Plantinga seems to engage in here would show the rational 'acceptability' of a literal infinity of objects, merely that we posit that such objects are in fact necessary. And hence, I turn to my second line of criticism.

§IV. Why Accept Maximal Greatness?

As I explicated in §III, the crucial premise of Plantinga's argument is either (9) or (11) (it doesn't matter which, they are logically equivalent to each other and are different ways of expressing the same fact). Now, a number of questions arise. Namely, why accept that maximal greatness is exemplified?
Plantinga has continually remarked that there is no evidence against the possibility of maximal greatness being exemplified (in other words, the necessity of maximal excellence being exemplified). Apparently, he is under the modus operandi with respect to modality that modal claims are "innocent until proven guilty." However, one honestly wonders how such an approach would consistently apply to necessity. Recall that a proposition is necessary if and only if its negation is impossible, that is, its negation entails a contradiction or some metaphysical absurdity. If one were indeed to consistently apply the maxim "modal propositions are innocent until proven guilty," one ought to inquire, with respect to a purportedly necessary proposition if the negation of a proposition is really impossible. It seems that one is ruling the negation as "guilty" and as impossible. Clearly, one is not consistently applying the maxim if one applies it onto the claim that some concrete object is impossible, but, then that one fails to similarly apply the maxim for necessity.
And, clearly, it is a tall order for Plantinga to show that maximal excellence not being exemplified is impossible. Otherwise, one could hold to the following sorts of arguments as being rationally 'acceptable': It is necessary that matter exists, hence, matter exists. It is necessary that dualism is false, hence, dualism is false. It is necessary that unicorns exists, hence, unicorns exist; and so on and so forth. So, there is hardly any room for rational 'acceptability' to be ventured here. Necessity is not simply imagined into existence or granted by fiat. Instead, a contradiction or absurdity must follow from the negation of a proposition. One should be careful before concluding that apparent conceivability entails logical possibility, with respect to logical necessity. It seems, in some manner, that one can imagine that a certain extravagant mathematical equation has some value (which is, in fact, wrong); but plainly, that the equation has a specific value is necessary per the axioms of the mathematical system in question, since mathematical propositions are analytic and tautologies. For example, many people strongly conceive of 0.999 ≠ 1 or that in the example of the Monty Hall case, switching to another door has only a probability of 1/2 of getting the car. Hence, we must distinguish between epistemic possibility and modal possibility. And, I think we should rightly hesitate to label certain things necessary unless it can be rigorously shown that a proposition's negation entails a contradiction or it becomes plainly clear that it leads to a metaphysical absurdity. Now, what of the present case? Unfortunately, no such contradiction or absurdity is entailed by maximal excellence not being exemplified. Therefore,
(29) ¬□G [Premise]
(29') It is not necessary that maximal excellence is exemplified. [Premise]
And, from that, no ontological argument to God's actual existence can be made via Plantinga's reasoning, since that maximal excellence is necessarily exemplified is the crucial premise of this species of ontological arugment. Moreover, since modal propositions under S5 and possible world semantics are necessary, it is intrinisically part of the concept of maximal excellence being exemplified as being contingent; hence, the notion of it being necessary that maximal excellence is exemplified expresses that the proposition is both non-necessary and necessary: a contradiction. Hence, that maximal excellence is necessarily exemplified is incoherent. However, I can see three traditional responses by the defender of the modal ontological argument might offer.

Perhaps our interlocutor will argue that it is part of the definition of a necessary God to exist, hence, God exists. In other words, a necessary God is necessarily existent; a necessarily existent being is existent; hence, there is a necessary God. However, as Peter van Inwagen points,16 this sort of argument confuses two lines of argument. The argument a necessary God is necessarily existent; a necessarily existent being is existent simply does not entail that there is a necessary God. However, it does entail that If there were a necessary God, then there would be a necessary God. This is clearly true, but it is true by definition, and would be true even if there were not a necessary God. For instance all unicorns have one horn is true even though there are no unicorns. The same applies for that all necessary unicorns are necessarily existent is true, even though there are no necessarily existent unicorns. The only way the argument can succeed is by pointing out that there is a necessary God, hence, there is a necessary God. But, like Arguments A and B, this hardly carries any persuasive force. We are back where we started: why suppose that there is a necessary God? Or, perhaps under a more metaphysical slant, pointing out the concept or the definition of something does not entail that there is an exemplification of the concept or something that satisfies the definition. A round square, by definition, is both round and square, but nothing exemplifies or satisfies the definition as such. This is because such concepts represent concepts of impossible entities. A necessary unicorn, for instance, is impossible since, as I explained earlier, it is an intrinsic modal property and part of the concept of exemplifing a unicorn to be non-necessary; hence, a necessary unicorn is both necessary and non-necessary.

Perhaps our interlocutor is impressed by Leibniz's version of the ontological argument, a version that is echoed in Kurt Gödel's version of the ontological argument.17 Leibniz, a very powerful modal reasoner, realized that any successful ontological argument must include a proof of the coherence of a necessary God. Leibniz had an abstract metaphysical argument, namely, that all positive properties are compatible with each other. For instance, the property red is compatible with the property round. Necessary existence is a positive property, hence, it is possible that God possesses necessary existence, and hence, God exists. Much can be said about Leibniz's argument. I shall restrict myself to only a few objections that seem to have some force. First of all, as Peter van Inwagen points out,18 it is unclear whether or not properties are intrinsically positive or negative. Consider the property of not having parts. Leibniz considers this to be a positive property, simplicity. And yet, to not have parts seem to be a negative property. Moreover, the negation of not having parts would seem to be having parts, which does indeed strike one as a positive property. And yet, if simplicity is a positive property, then non-simplicity is a negative property. Hence, positivity and negativity do not appear to be intrinsic to properties, and hence, Leibniz's argument (which crucially depends on the intrinsic nature of positivity) does not work. Moreover, necessity is not any ordinary sort of property, it is a modal property, and more particularly, a transworld property: an object is necessary if and only if it exists in all possible worlds, and it can only exist in all possible worlds if and only if its nonexistence entails a contradiction. Therefore, it cannot simply do to point out that a maximally excellent being is coherent. Instead, as Plantinga realizes, one must show that maximally greatness being exemplified (maximally excellent necessarily being exemplified) is possible. The possibility operator is not simply scoped over the exemplification of maximal excellence, but the exemplification of necessary maximal excellence (i.e. maximal greatness). And there is no reason to suppose that it is impossible that maximal excellence fail to be exemplified, rendering maximal greatness incoherent.

Also, perhaps our interlocutor will finally rely upon the notion that God is by definition perfect and a perfect entity could not possibly be non-necessary. This reply is puzzling and deficient in various respects. On one hand, what does "perfect" even mean in this context? I am not being obtuse, but, I suppose one can only point out that "perfect" is typically defined with respect to some standard i.e. the notion of a perfect score. What could it possibly mean for an entity to be "really" perfect, that is, to have perfection without reference to any sort of standard? Hence, one is struck by the obscurity of such a claim. Furthermore, why suppose that perfection entails necessity? For instance, recall that necessity is a transworld property. Given actualism, only one world is actual. A contingent God does not differ in any real respects than a necessary God in the actual world. It is difficult to see, in any meaningful sense, why "perfection" should entail necessity. At least, such a claim cannot be merely asserted by our interlocutor. Some defense is clearly required; one cannot simply handwave one's way through philosophical argumentation. Moreover, even accepting that God is by definition perfect and that perfection entails necessity, this does not prove that God exists. For recall the former two objections made by our interlocutor and why they failed. Showing that a particular definition is as thus does not entail that the definition is ever satisfied or that the concept is ever exemplified, and moreover, the interlocutor is still left with the problem of showing there to be a necessary God. Pointing out the coherence of maximal excellence is deficient; he must show that maximal excellence is necessarily exemplified. Here, perhaps our interlocutor will retort that maximal excellence entails perfection and perfection entails necessity. The above same objections will reply, as well as the fact since maximal excellence being necessarily exemplified means that maximal excellence could not possibly fail to be exemplified, the objector to the modal ontological argument could simply point out that maximal excellence is possibly not exemplified; therefore, necessary maximal excellence is not exemplified. So, one is left puzzled by this deficient line of argument. It is clear that none of these lines of argument take to task the incoherence of maximal excellence being necessarily exemplified. The entailment proposed by such the an objector would be necessarily false, since an entailment is true if and only if that at all worlds that where the antecedent obtains, the consequent obtains. If the antecedent is true and the consequent is false, then the entailment is false. Since the consequent here, namely that maximal excellence is necessarily exemplified, is false and not only that, but necessarily false, and the antecedent, that maximal excellence is possibly exemplified, is true (barring, of course, the incoherence of omniscience, omnipotence, or moral perfection), therefore, the supposed entailment is false. The defender of the modal ontological argument simply does not meet the challenge.

Furthermore, there seem to be powerful arguments against God's necessity, let alone His actual existence. For example, I believe that there are good logical and evidential problems of evil.19 And, of course, there are multiple other arguments to be had, which are just versions of asserting (correctly) that God's nonexistence is possible i.e. if God is necessarily existent, gratuitous evil is impossible; gratuitous evil is possible, hence, God is not necessarily existent. Moreover, as I shall elaborate in my next paper, God's necessity either lends itself to the failure of theism as a hypothesis or the absurdity that the actual world is the only possible world.20 Hence, one wonders why one should even accept God's necessity at all. There are plenty of compelling reasons to reject it.

§V. What Does Plantinga's Argument Show?

Finally, I wish to discuss what Plantinga's argument shows in the first place. Some take it as showing that there is a necessary God. I myself am skeptical of that conclusion. Recall that if Plantinga's argument is successful, it establishes that maximal excellence is necessarily exemplified. However, what is remarkably absent is that a specific individual entity is necessary. Plantinga's argument instead shows that there must be a entity that exemplifies maximal excellence, not any particular entity that exemplifies maximal excellence. For instance, as I shall argue in my second paper, an entity that takes some course of action in some particular situation and an entity that takes some other course of action in that identical situation are not and cannot be the same entity.21 Hence, the fact an entity with that specific set of conditional propositions of freedom exemplifies maximal excellence would be wholly contingent, and hence, that entity is itself contingent. The possible differences in entities that exemplify maximal excellence are multitudinous. Perhaps the entity essentially incarnates as a human, perhaps they do not; perhaps that entity essentially favors a particular group of humans, perhaps they do not. So, Plantinga's argument, to be successful, must not only establish that a being necessarily exemplifies maximal excellence, but that a specific individual exemplifies maximal excellence, else, that individual is in fact contingent. And clearly, this conflicts with Anselmian thought. So, even granting Plantinga's argument (and hence theism), one would not arrive at the conclusion of Anselmian theism at all.

§VI. Conclusion

Plantinga's ontological argument represents the pinnacle of all ontological arguments. In it, we find the necessary advances a defender of the ontological argument must make, namely, the supposition that there necessarily being a God is possible i.e. in other words, that there necessarily is a God. Unfortunately, even this argument fails to be persuasive insofar as it is question-begging and moreover that there is good reason to believe that there is not a necessary God. Finally, Plantinga's argument at best establishes that there necessarily is a God, but not any particular individual. Any such individual would be contingent, since the fact that that individual exemplifies maximal excellence is contingent, hence, Plantinga's argument does not establish Anselmian theism, let alone theism nor its rational acceptability.
 
Notes
  1. Anselm, Saint. Proslogion, Ch. 2-4. An online rendition of the text in its original Latin script can be found at the Latin Library. Jasper Hopkins and Herbert Richardson have an excellent English translation of the Proslogion, available at Hopkins website. [Back]
  2. Descartes, René. Meditations on First Philosophy, Meditation V. An online rendition of the text in its original Latin script can be found at the Wright State University website as well as the Latin Library. A corresponding English translation by John Veitch can also be found at the Wright State University website. [Back]
  3. Gaunilo. In Behalf of the Fool. An English translation of Gaunilo's response and Anselm's answer can be found at the Medieval Sourcebook. [Back]
  4. Kant, Immaneul. The Critique of Pure Reason. An English translation by Norman Kemp Smith of the relevant section can be found at the Chinese University of Hong Kong. [Back]
  5. Hume, David. Dialogues Concerning Natural Religion, IX. An online text is available at David Banach's webpage. [Back]
  6. Plantinga, Alvin. The Nature of Necessity. Oxford: Clarendon Press, 1979. 196. [Back]
  7. For various interpretations of the Anselmian argument, see Plantinga, Alvin. The Nature of Necessity. Oxford: Clarendon Press, 1982. 197-212. See also Oppenheimer, Paul and Edward Zalta. "On the Logic of the Ontological Argument." Philosophical Perspectives 5 (1991): 509-529. Online versions of the paper can be found at Paul Oppenheimer's website as well as at Edward Zalta's website. [Back]
  8. Plantinga, Alvin. The Nature of Necessity. Oxford: Clarendon Press, 1979. 196. [Back]
  9. Malcolm, Norman, "Anselm's Ontological Argument." Philosophical Review 69 (1960): 41-62. The paper without the footnotes is reprinted in Malcolm, Norman. "Anselm's Two Ontological Arguments." Philosophy of Religion: An Anthology. 4th ed. Ed. Louis P. Pojman. USA: Wadsworth, 2003. 76-86. [Back]
  10. Hartshorne, Charles. The Logic of Perfection. LaSalle, IL: Open Court, 1962. 51. An online version of the argument in S5 modal logic can be found at Peter Suber's website. [Back]
  11. Plantinga, Alvin. The Nature of Necessity. Oxford: Clarendon Press, 1979. 196-221. See also Plantinga, Alvin. God, Freedom, and Evil. MI: Wm. B. Eerdmans, 1977. The chapter on the ontological argument in Plantinga's God, Freedom, and Evil is reprinted in Plantinga, Alvin. "A Contemporary Modal Version of the Ontological Argument." Philosophy of Religion: Selected Readings. 2nd ed. Ed. Michael Peterson, et al. Oxford: Oxford University Press, 2001. 170-183. [Back]
  12. An excellent online introduction to modal logic can be found at James Garsons' entry in the online Stanford Encyclopedia of Philosophy. [Back]
  13. Plantinga, Alvin. The Nature of Necessity. Oxford: Clarendon Press, 1979. 213-217. See also Plantinga, Alvin. "A Contemporary Modal Version of the Ontological Argument." Philosophy of Religion: Selected Readings. 2nd ed. Ed. Michael Peterson, et al. Oxford: Oxford University Press, 2001. 179-183. [Back]
  14. Plantinga, Alvin. The Nature of Necessity. Oxford: Clarendon Press, 1979. 217-218. [Back]
  15. Plantinga, Alvin. "A Contemporary Modal Version of the Ontological Argument." Philosophy of Religion: Selected Readings. 2nd ed. Ed. Michael Peterson, et al. Oxford: Oxford University Press, 2001. 182-183. [Back]
  16. van Inwagen, Peter. Metaphysics. 2nd ed. USA: Westview, 2002. 94-97. [Back]
  17. Leibniz, Gottfried. New Essays Concerning Human Understanding. For an excellent online introduction to Gödel's ontological argument, see Christopher Small's website. [Back]
  18. van Inwagen, Peter. Metaphysics. 2nd ed. USA: Westview, 2002. 109. [Back]
  19. I shall not discuss the logical problem of evil until my seventh paper in this series. Hence, my papers form a sort of interconnected "web" of ideas, rather than simply proceeding linearly. [Back]
  20. See my upcoming second paper in this series, devoted to the modal cosmological argument. [Back]
  21. See my upcoming second paper in this series, devoted to the modal cosmological argument. [Back]

6 comments:

exapologist said...

This is a very nice blog, Rayndeon! I look forward to your future posts.

Best wishes,

exapologist

Timmo said...

Nice work, Rayndeon. I'll be reading!

Just a tip, though! Blogs tend to do better when they have shorter, more digestible posts. You can always break a protracted discussion down into a series of posts.

Timmo said...

I read an interesting, non-modal formulation of Anselm's ontological argument by Zalta and Oppenheimer. Their paper is available online here. They have a second paper where they evaluate the argument. That one is available here.

If I remember right, their version of the argument hangs heavily on the logic of encoding predication and a theory of definite descriptions. Thought you might find it interesting, if you weren't already aware of it!

Phaedrus said...

Wow! Someone who can write an actual argument by contemporary analytic standards! It's like trying to find a needle in a hay stack on the web. ;)

I hope you keep posting in the future Rayndeon. I have added your blog to my links. Peace

Touchstone said...

Rayndeon,

I am thoroughly impressed. I've been round and round on Plantinga's Ontological Argument a number of times now, and there are several points here that are both new insights for me, and very clearly articulated, at that. I've just been through it once, but have it bookmarked and will be digesting it more in the coming weeks.

This blog goes on my "regular reading" list! Good on ya!

-Touchstone

Rick Taylor said...

This is very impressive, the most complete account of this sort I'd seen. The only comment I'd make is regarding, "Plantinga's ontological argument represents the pinnacle of all ontological arguments." I like Anselm's argument best because it's written in plain language, and doesn't resort to complicated formal systems, and the flaw is more subtle to catch.