A. The Modal Ontological Argument and Possible Worlds Semantics
B. The Anti-PMOA-Argument
C. Confirmation of the Anti-PMOA-Argument
D. The Nature of the Modality Operative in Possible Worlds Semantics
E. The Plausibility of Premise 1 of the PMOA: Is it Possible that a Maximally Great Being Exists?
In this paper I examine the modal ontological argument based upon possible worlds semantics expounded by Alvin Plantinga (PMOA) and further developed and defended by William Lane Craig. In section A I set forth the definitions and premises of the PMOA and its conclusions before disclosing its flawed underlying assumptions. In section B I expound and defend what I call the “anti – Plantinga modal ontological argument – argument” (or anti-PMOA-argument). There I rigorously show that, despite appearances, a maximally great being is not broadly logically possible. In section C I set forth why the anti-PMOA-argument is amply confirmed—namely, because the procedure used to construct the PMOA plausibly allows the construction of arguments relevantly similar to it, but inconsistent with it. Such rival arguments show the existence, in all possible worlds, of either (a) beings relevantly similar to, but different from, that of God conceived of as a maximally excellent being (as defined in the PMOA), or, more strikingly, (b) several conceivable maximally excellent beings that nevertheless constitutively or otherwise differ from each other in some important respects. Section D examines the nature of the modality involved in possible world semantics, in so doing explaining why the notion of what is broadly logically possible/necessary ought to be distinguished from the notion of what is metaphysically possible/necessary. Section E independently considers the plausibility of premise 1 of the PMOA (i.e., that it is possible that a maximally great being exists) according to the writings of other scholars.
A. The Modal Ontological Argument and Possible Worlds Semantics
1. William Lane Craig considers Alvin Plantinga’s version of the ontological argument as having “the best chance of being cogent” (WLC 2004, p. 125: WLC 2008, p. 183), because “the formulation and defense of the argument provided by Plantinga are the most sophisticated in the long history of the ontological argument, profiting from the missteps and oversights of his predecessors” (WLC 2008, p. 183). Hence Plantinga’s Modal Ontological Argument (PMOA) is often expounded and defended in Craig’s scholarly and popular writings (although rarely if ever in his many public debates about God’s existence).
2. The PMOA employs the concepts of possible world semantics. (PWS). Craig explains PWS as follows:
[PD1] “[B]y ‘a possible world’ one does not mean a planet or even a universe, but rather a maximal description of reality or a way reality might be.”
[PD2] “Only one of these descriptions will be composed of conjuncts all of which are true and so will be the way reality actually is, that is to say, the actual world.”
[PD3] “[T]he possible conjuncts which a possible world comprises must be capable of being true both individually and together.”
[PD4] “A possible world is a conjunction which comprises every proposition or its contradictory, so that it yields a maximal description of reality—nothing is left out of such a description.”
[PD5] “By negating different conjuncts in a maximal description … , we arrive at different possible worlds.”
(WLC 2004, p. 126)
3. The PMOA includes two essential definitions which can be stated as follows:
[PD6] A maximally excellent being is a being with such excellent-making properties as omnipotence, omniscience, and moral perfection.
[PD7] A maximally great being is a maximally excellent being that exists in every possible world.
4. The PMOA, as accurately reconstructed by Craig, consists of the following propositions (with bracketed matter added). (WLC 2004, p. 128):
[PA1] It is possible that a maximally great being exists.
[PA2] If it is possible that a maximally great being exists, then a maximally great being exists in some possible world. [Therefore, PA2.1: A maximally great being exists in some possible world.]
[PA3] If a maximally great being exists in some possible world, then it exists in every possible world. [Therefore, PA3.1: A maximally great being exists in every possible world.]
[PA4] If a maximally great being exists in every possible world, then it exists in the actual world. [Therefore, PA4.1: A maximally great being exists in the actual world.]
[PA5] If a maximally great being exists in the actual world, then a maximally great being exists.
[PA6] Therefore, a maximally great being exists.
And, I should add, that one may also deduce from these propositions: (a) If a maximally great being exists in the actual world, then a maximally excellent being exists in the actual world and all other possible worlds; (b) A maximally excellent being exists in the actual world and all other possible worlds.
5. It is generally agreed that the PMOA is formally valid. And I think that it is fairly obvious (assuming that a maximally great being is defined as a maximally excellent being that exists in every possible world) that if a maximally great being exists in some possible world, then that being exists in all possible worlds and therefore in the actual world. The critical question is whether premise PA1 (that it is possible that a maximally great being exists) is true or so warranted that its plausibility is greater than its negation. The stakes are rather high. As Craig points out: “[I]f God is conceived as a maximally great being, then his existence is either necessary or impossible, regardless of epistemic uncertainty” (WLC 2004, p. 128). But let us not be lead astray. If the PMOA is sound, then if premise PA1 is true (or more plausible than its negation), then it indeed follows that God conceived as the maximally great being (G-CMGB) exists. Hence one deduces that God conceived as a maximally excellent being (G-CMEB) exists in the actual world. However, one may not licitly conclude that G-CMEB does not exist in the actual world from the negation of premise PA1.
B. The Anti-PMOA-Argument
1. Right at the outset my chief complaint with PMOA is that it is a radically defective formulation since it omits some essential steps in PWS analysis. Moreover, it seems counterintuitively absurd that the PMOA results in a situation where the only possible worlds we are left with, once having accepted PA1, are those in which a G-CMEB exists—and all this as a result of purportedly engaging in PWS analysis. The PMOA, for that reason alone, suspiciously appears as a mighty finely-tuned argument for God’s existence. However, since it is thought persuasive by many able theist philosophers and theologians, it deserves our serious consideration on its merits.
2. So what follows is my formulation of not yet another version of an ontological argument for the existence of G-CMGB. Rather its conclusions are that G-CMGB does not possibly exist and that whether G-CMEB exists in the actual world is indeterminate based solely upon PWS considerations. The anti-PMOA-argument goes as follows:
AD1. A possible world is a maximal description of reality or a way reality might conceivably but not factually be. (Cf. PD1 above.)
AD2. Only one of these descriptions will be composed of conjuncts all of which are true and so will be the way reality actually is, that is to say, the actual world. (Cf. PD2 above.)
AD3. The possible conjuncts which a possible world W comprises must be capable of being true in W both individually and together. (Cf. PD3 above.)
AD4. A possible world is a conjunction which comprises every proposition or its contradictory, so that it yields a maximal description of reality such that nothing is left out of such a description. (Cf. PD4 above.)
AD5. Different possible worlds are formed by negating different conjuncts in a maximal description. (Cf. PD5 above. The proposition is to be understood as meaning that any candidate maximum description is composed of conjuncts capable of being true both individually and together since there will be cases in which a negation of a proposition in W entails the negation of other propositions in W.)
AD6. A maximally excellent being is a being with such excellent-making properties as omnipotence, omniscience, and moral perfection. (Cf. PD6 above.)
AD7. A maximally great being is a maximally excellent being that exists in every possible world. (Cf. PD7 above. This proposition should be understood as meaning that if a particular entity is a maximally excellent being in any one possible world then it is also maximally excellent in all possible worlds In which it exists.)
AP1. A maximally excellent being exists in some possible world.
AP2. A possible world can be formed by the negation of different conjuncts in maximal description.
AP3. If a maximally excellent being exists in some possible world and since possible worlds can be formed by the negation of different conjuncts in a maximal description, then a maximally excellent being does not exist in some (other) possible world.
AP4. A maximally excellent being does not exist in some possible world. (AP1, AD5.)
AP5. If a maximally excellent being does not exist in some possible world, then a maximally excellent being does not exist in all possible worlds. (AD5, AP1, AP2)
AP6. A maximally excellent being does not exist in all possible worlds.
AP7. If a maximally excellent being does not exist in all possible worlds, then a maximally great being does not exist in the actual world.
AP8. A maximally great being does not exist in the actual world. (This proposition contradicts PA6.)
However, it is indeterminate (based solely upon PWS considerations) whether a maximally excellent being exists in the actual world.
3. The critical steps in the argument are AP2-AP4 since AP2 involves a negation of the relevant conjunct of the possible world mentioned in AP1. The proposition in the PMOA that it is possible that a maximally great being exists (i.e., PA1) presupposes the proposition that a maximally excellent being exists in some possible world. Indeed, the notion of a maximally great being is defined in terms pertaining to the notion of a maximally excellent being. Thus the negation in AP2 of the conjunct of the possible world mentioned in AP1 is analytically prior to determining whether the notion of a maximally great being is admissible based on PWS conditions. The anti-PMOA-argument confirms the widely held view that there is something rather piscatorial about the PMOA in that it fails to explicitly include in the argument relevant equivalents of AD1-AD5. My conclusion is that PA1, although perhaps prima facie coherent, turns out nevertheless to be radically defective because it is not a well-formed statement in terms of PWS. Despite appearances, a maximally great being is not really possible after all—it is not really coherent after all.
C. Confirmation of the Anti-PMOA-Argument
1. The conclusion of the anti-PMOA-argument is amply confirmed because the procedure followed in the construction of the PMOA also allows the construction of beings of numerous kinds relevantly similar to that of a G-CGEB and where each being can be also plausibly claimed to exist in all possible worlds—assuming that the PMOA is plausible.
2. One such world, discussed by Craig, is the quasimaximally great being, i.e., a being which allegedly differs from a maximally great being only in that it is not omniscient in that it does not know truths about future contingents (i.e., particularly the future free acts of humans and angels). Craig rightly points out that if maximal greatness is possibly exemplified then quasimaximal greatness is impossible. He acknowledges that “[p]erhaps the greatest challenge to the appeal to intuition to warrant the premise that maximal greatness is possible is that it seems intuitively coherent in the same way to conceive of a quasi-maximally great being [as defined above]” (WLC 2004, p. 130). His efforts, however, to obviate the possibility of a quasimaximally great being are pathetically weak ploys. In one essay, his tepid response is as follows (WLC 2004, p. 131):
[O]ur intuition that a maximally great being is possible is not undermined by the claim that a quasi-maximally great being is also intuitively possible for we see that the latter intuition depends on the assumption that a maximally great being cannot possibly exist, which begs the question.
3. To which the advocate of quasimaximally greatness can readily respond that the intuition that a maximally great being is possible depends on the assumption that a quasimaximally great being cannot possibly exist, which begs the question. But Craig’s lame response should not surprise us because, earlier in the essay, he candidly declares that the PMOA “assumes that the concept ‘God’ or ‘greatest conceivable being’ is a coherent concept, or employing the semantics of possible worlds, then there is a possible world in which God [i.e., maximally great being] exists” (WLC 2004, p. 125).
4. In another effort to answer the advocate of quasimaximal greatness Craig argued (WLC 2008 #51):
My answer here is that there’s an asymmetry between our intuitions about the possibility of such beings [i.e., maximally great and quasimaximally great beings, respectively]. Any intuition for thinking that a quasi-maximally great being to be possible also warrants belief in the possibility of a maximally great being; indeed, the way we came to form the idea of the former was by diminution of the idea of the latter. But our intuition of the possibility of a maximally great being, once we understood its implications, tends to undermine our intuition of the possibility of a quasi-maximally great being, we begin to suspect that despite appearances, it is not really possible after all.
5. To which the advocate of quasimaximal greatness can reply almost verbatim mutatis mutandis (with necessary changes having been made) and by asserting that the way we come to form the idea of maximal greatness is by augmentation of the idea of quasimaximal greatness. In his Reasonable Faith: Christian Truth and Apologetics (2008), responding to objections “that we have no way of knowing a priori whether maximal greatness or quasi-maximal greatness is possibly exemplified [since] [i]t cannot be both, but we have no idea if either is possible,” Craig wrote (WLC 2008, p. 187):
We might plausibly reply to this objection that the intuition that a maximally great being possibly exist has priority over any intuition that a quasi-maximally great being possibly exists. The latter intuition seems to depend on the former, and yet upon reflection we come to lose the latter intuition through the realization that if a maximally great being is possible then a quasi-maximally great being is not. Thus, our prima facie warrant for premise [PA1 above] remains.
6. To which the advocate of quasimaximal greatness may reply in like manner, mutatis mutandum. However, I should point out that the intuition that a maximally excellent being does not exist in some possible world has analytic priority over any intuition that either a maximally great or quasimaximally great being exists in some possible world. This is the case because the notions of a maximally great and a quasimaximally great being, respectively, are necessarily defined and understood in terms of the relatively primitive notions of maximal excellence and quasimaximal excellence.
7. Craig acknowledges that his foregoing responses to the advocate of quasimaximal greatness rest “solely on the basis of appeal to modal intuitions alone (i.e., our intuitions about what is possible or necessary)” (WLC 2008 #51; see WLC 2008, p. 187). For this reason, he has advanced “a posteriori considerations that it is possible that a maximally great being exist [such as] other theistic arguments like Leibniz’s cosmological argument, the moral argument, and conceptualist arguments for God as a ground of abstract objects or necessary truths that may lead us to think that it is plausible that a maximally great being exists” (WLC 2008, p. 187). This all amounts to an implicit admission that the PMOA is a very weak stand-alone argument for God’s existence. But an appeal to other theistic arguments to prove that a maximally great being possibly exists and therefore exists in the actual world presupposes that the notion of a maximally great being is really coherent (i.e., broadly logically possible) within the context of PWS. But, as it now appears, a maximally great being, despite appearances, is really impossible and hence incoherent—based upon PWS considerations.
8. Alleged quasimaximal greatness may involve different kinds of qualified cognitive powers other than, or in addition to, that pertaining to the issue of knowledge of future free contingents. However, the properties of an alleged quasimaximally great being could also pertain to different kinds of qualified causal powers of an allegedly maximally great being.
9. For example, an interesting issue considered by some theologically conservative Christian philosophers and theologians has pertained to the question whether a power to create something (but not everything) out of nothing (subject, however, to divine control) is the exclusive prerogative of God—although it was generally agreed, and indeed was the doctrine of the Roman Catholic and Eastern Orthodox Churches, that God alone creates or has created ex nihilo in this actual world. Let us stipulate, for purposes of argument, that a maximally great being cannot endow a creature with a power to create ex nihilo. And let us further stipulate as a plausible hypothesis that an otherwise maximally great being can endow a creature with a limited power to create ex nihilo. On the one hand, each scenario is prima facie coherent based solely on PWS considerations. But (to paraphrase Craig) maximal greatness is logically incompatible with quasimaximal greatness since a maximally great being by definition lacks the power to communicate the power to create ex nihilo to a creature. Hence, there cannot be possible worlds in which a maximally great being exists together with a creature that has the power to create ex nihilo. Thus we have another analog of PA1: i.e., It is possible that an otherwise maximally great being can endow a creature with a power to create ex nihilo. The reader can readily see that it would not be difficult to construct many equally coherent scenarios with respect to beings similar to but differing from a maximally great being in some particulars except with respect to the property of existing in all possible worlds.
10. Other rival candidate premises would be those in which the relevant differences pertain to constitutive matters with respect to G-CMEB. Thus, for example, one such candidate would be a G-CMEB described as one unipersonal spiritual being within the context of historical Unitarianism and Arianism. The complementary, or rather competing, candidate would be a G-CMEB described as tripersonal, unisubstantial spiritual being. The standard Christian doctrine of the Trinity is that officially professed by the Roman Catholic, Eastern Orthodox, and historical and mainline Protestant Churches. According to this doctrine, there are three persons in Godhead, i.e., the Father, the Son, and the Holy Spirit. Each person is really distinct from the other two yet consubstantial (i.e., the three persons having the numerically one divine essence, substance, or nature. Thus the Father is God; the Son is God; and the Holy Spirit is God; but there are not three God’s but one God. Thus we have two additional analogs to PA1: (1) It is possible that the Unipersonal G-CMGB exists and (2) It is possible that the tripersonal G-CMGB exists. In which case, it ultimately follows that both the Unipersonal G-CMGB and the tripersonal G-CMGB actually exist—which conjunction involves a manifest contradiction in excelsis (in the highest degree).
11. Matters get a bit more complicated. They relate to time, broadly considered. The first issue pertains to nature of the eternity predicated of the maximally great being. Is G-CMGB, everlasting or timeless—or something else vis-à-vis time? Here, for argument’s sake at least, I presume the A-(i.e., tensed dynamic) theory of time. Let us moreover suppose we are considering this issue sans creation. According to one view, G-CMGB is everlasting (i.e., omnitemporal); in other words, it exists without beginning or end, with an inner life consisting of [an] infinite temporal series of moments or events of infinite duration. According to another view, G-CMGB is timeless if it exists atemporally or if it exists without beginning or end, without succession in a single, undifferentiated moment. For argument’s sake, I shall assume an infinite temporal series of infinite duration is not metaphysically impossible based upon transfinite arithmetical considerations. For our purposes, we need not consider alternative hypotheses concerning God and time. So we have several rival candidate mutually inconsistent premises similar to PA1: (1) It is possible that the tripersonal G-CMGB everlastingly exists; (2) It is possible that the tripersonal G-CMGB sans creation timelessly exists; (3) It is possible that the Unipersonal G-CMGB sans creation timelessly exists; and (4) It is possible the Unipersonal G-CMGB everlastingly exists.
12. There are more. These candidate premises pertain to whether the divine power to create a spiritual and/or material world ex nihilo necessarily entails that such creation must have occurred a finite time ago.
13. Were the reader to consult theologically conservative Christian standard treatises in systematic or dogmatic theology, it would be a relatively easy but rather tedious matter to construct a multitude of various but contradictory hypotheses about the constitutional and other properties of G-CMGB (in addition to those already considered) which collectively constitute a kind of a reductio ad absurdum of the PMOA.
D. The Nature of the Modality Operative in Possible Worlds Semantics
1. As Craig notes, “the modality operative in possible worlds semantics is not strict logical necessity/possibility, but broad logical necessity/possibility” (JPM & WLC 2003, p. 503). The former notion pertains to freedom from contradiction in the sense of conforming to the truths of logic, i.e., truths of propositional logic and first order quantification theory. Broad logical necessity/probability, Craig observes, is a notion that Plantinga “leaves undefined but merely illustrated” (JPM & WLC 2003, p. 50).
2. As Plantinga himself explains the matter as follows:
The first and rough answer [to the question as to what sort of thing a possible world is] is that it is a way things could have been; it is a possible state of affairs of some that obtain, or are actual, and some that do not obtain. So, for example, Kareem Abdul-Jabbar’s being more than seven feet tall is a state of affairs, as is Spiro Agnew’s being President of Yale University. Although each of these is a state of affairs, the former but not the latter obtains, or is actual. And although the latter is not actual, it is a possible state of affairs; in this regard it differs from David’s having travelled faster than the speed of light and Paul’s having squared the circle. The former of these last two items is causally or naturally impossible; the latter is impossible in that broadly logical sense.
A possible world, then, is a possible state of affairs—one that is possible in the broadly logical sense. But not every possible state of affairs is a possible world. To claim that honour, a state of affairs must be maximal or complete…. [A] state of affairs S is complete or maximal if for every state of affairs S’, S includes S’ or S precludes S’. Of course, the actual world is one of the possible worlds; it is the maximal possible state of affairs that is actual, that has the distinction of actually obtaining. (Plantinga 1974, pp. 44-45)
Objects or individuals exist in possible worlds, some like Socrates existence in only some but not all possible worlds, and others, like the number seven, exist in every world. To say that an object x exists in a world W is to say that if W had been actual, x would have existed; more exactly, x exists in W if it is impossible that W obtain and x fail to exist. (Plantinga 1974, p. 46)
3. For theists (who hold that God is omnipotent, omniscient, and morally perfect) it is important in the Plantinga version of PWS that states of affairs that are causally or naturally impossible in this actual world may nevertheless be broadly logically possible. This is the case because such theists typically maintain that God’s omnipotence extends to the actualizability of all broadly logical states of affairs compatible with God’s existence and attributes. Thus for these theists there are some factually possible worlds each with a natural law contrary to each other and to that which obtains in our actual world. Thus for example, God has the power to actualize a broadly possible world in which some but not all physical entities could naturally travel faster than the speed of light. Moreover, God being omnipotent could supernaturally cause David to travel faster than the speed of light even in this actual world. Some metaphysical naturalists (myself included) maintain that states of affairs that are causally or naturally impossible in this actual world (or some other possible worlds) may nevertheless be broadly logically possible.
4. On the other hand, some metaphysical naturalists (myself included) hold that a particular natural law (i.e., not a theoretical construct) that obtains in this actual world is metaphysically necessary in the sense that no broadly possible world would be actualizable were there a different law governing the domain in question. For example, if it is factually impossible for physical entities to travel faster than the speed of light in this actual world because it is metaphysically necessary that nothing travels faster than the speed of light, then no broadly possible world could be actualized where faster-than-light travel is permitted by a natural law. Those theists faithful to the intuitions underlying the legitimate analysis of PWS who hold that omnipotent God exists in the actual world would not hold that there are no broadly possible worlds in which G-CMEB does not exist. Similar considerations apply to naturalists mutatis mutandum—such naturalists would not maintain that having concluded that G-CMEB does not exist in the actual world (and hence in any actualizable world) it follows that there are no broadly possible world in which he exists. Such naturalists might very well also readily concede that if God (conceived as that one supernatural person with at least great power and knowledge, and with the requisite power to have created this our universe supposing him to exist) is indeed maximally excellent in this actual world, he (i.e., the numerically identical entity) is also maximally excellent in what other broadly possible world in which he exists. On the other hand, such naturalists will hold that G-CMEB does not exist in all possible worlds if he does not exist in this actual world.
5. However, theists and naturalists faithful to the intuitions underlying the legitimate analysis of PWS would sharply differ as to what broadly possible worlds are metaphysically possible or necessary. The theists in question would likely hold that virtually any broadly possible world in which G-CMEB exists is metaphysically possible; whereas the naturalists in question would hold that any broadly possible world in which such a God exists is metaphysically impossible. Quite clearly, it is necessary to distinguish between broadly possible/necessary worlds and those that are metaphysically possible/necessary since existence in a broadly possible world does not entail its existence in the actual world or any actualizable world. Thus, one must distinguish between broadly logically possible worlds and metaphysically possible worlds. Similarly, one must distinguish between broadly logically necessary worlds and metaphysically necessary worlds. In this connection, it behooves us to keep in mind that there are conditional metaphysically necessary worlds given that certain states of affairs actually obtain. Thus, if G-CMEB exists in the actual world there then are possible worlds in which he exists that are radically different from that which actually obtains by reason of his omnipotence; e.g., God could have actualized a possible world in which only created spiritual beings exist; or he could have actualized a world in which only physical beings exist—besides himself. Moreover, by virtue of his moral perfection certain broadly possible worlds would be factually impossible were G-CMEB to exist in the actual world.
6. To be sure, the existence of G-CMEB in the actual world or some particular broadly possible world precludes the coexistence in that world of particular states of affairs that are incompatible with his existence and his standing properties. But it does not follow that an otherwise broadly possible world with properties incompatible with the standing properties of G-CMEB is not broadly logically possible simply because it is assumed that he exists in the actual world.
7. Craig’s approach is to synonymously use the terms broadly logically possible and metaphysically possible, and such that both expressions are to be construed in terms of actualizability. He distinguishes between what he calls metaphysical possibility, “that lies somewhere in between the strict logical modality that characterizes the laws of logic and the broader physical modality that characterizes what is permitted by nature’s laws and boundary conditions” (WLC 2009 #118). Thus, for example, “it is metaphysically possible that [he, Craig] might have had an alligator body, even though such a thing is not physically possible” (WLC 2009 #118). He (and J. P. Moreland) point out that “[t]he situation [i.e., determining the meaning of broadly logically possible] is further complicated by the hypothesis of theism, for if God’s existence is necessary then some worlds which seem intuitively to be broadly logically possible, but it may not be actualizable after all because God, necessarily, would not actualize them … [since, in some cases for example, he] is essentially too good to actualize [them]” (JPM & WLC 2003, p. 50). “Such problems,” they acknowledge, have led “some thinkers to differentiate between broadly logical possibility and metaphysical possibility, or actualizability” (JPM & WLC 2003, p. 50)—which, as the reader is now aware, is my position.
8. Craig’s failure to distinguish between what are broadly possible worlds and metaphysically possible worlds respectively leads him to so widely construe actualizability so as to stack the deck in favor of the PMOA. In the first place a determination as to what is actualizable depends upon what fundamental propositions are true. Consider the tantalizing and astonishing claim by Craig that it is metaphysically but not physically possible that he might have had an alligator body. I am not aware of any place where Craig has explained this astounding state of affairs. Probably, he is familiar with Plantinga’s discussion of the question: “Could Socrates have been an alligator?” (Plantinga 1974, pp. 65-69), Plantinga’s conclusion was that a human person “is an immaterial object and, and, indeed is an object in every world in which he exists…. [and] that human persons are essentially immaterial”—nevertheless, “Socrates … could have been an alligator only if it is possible to be both an alligator and immaterial” (Plantinga 1974, pp. 68-69).
9. Craig believes that he could have been an alligator because he thinks that it was actualizable. And it would appear that Craig holds that this hypothetical state of affairs is actualizable because he believes most firmly that: (1) G-CMEB actually exists and had created by virtue of his omnipotence this physical universe but could have created a radically different universe—provided that such a universe, otherwise broadly logically possible, has properties consistent with those of a G-CMEB. (2) In this actual world, Craig is essentially an immortal, rational, and immaterial substance that animates his human body. (3) In this actual world, it is naturally necessary that Craig requires an appropriately configured human body in order for him to effectively think and function rationally; and (4) G-CMEB by virtue of his omnipotence could have created a world in which Craig’s spiritual soul animates an alligator body (complete with an alligator brain). We suppose that in this possible world God designed the natural world such that despite Craig having an alligator body he would nevertheless be so endowed as to effectively think and function rationally despite having an alligator brain. Craig having an alligator body would not be actualizable unless the substance of each of the foregoing propositions is true.
10. Now I for one not believe propositions (1), (2), and (4). Moreover, I believe that God, even if conceived as having at least great power and intelligence, does not exist. But even were God so conceived to exist, I surely do not think that it is metaphysically possible that Craig might, in some possible world, have had an alligator body (complete with alligator brain). But I would not hold that the scenario envisioned in the two preceding paragraphs is broadly logically impossible just because it is, in my view, metaphysically impossible for a putative alligator to be a rational being without having something equivalent to a human rather than an alligator brain. But Craig, were he to conclude that the scenario in question is not actualizable, would necessarily conclude that it is not broadly logically possible.
11. Craig confuses matters because he reduces any putative broadly possible world in which God does not exist to being a merely epistemically possible world—once it is determined that God exists in the actual world. However, in determining whether God exists in all possible worlds the question as to what all possible worlds means should not be answered using some sort of légerdeparole (i.e., what Plantinga might call a “verbal sleight of hand” [légerdemain] (Plantinga 1974, p. 196)). Actualizability should not be considered the legitimate determining factor in deciding what supposed state of affairs constitutes a broadly logically possible world. Rather, the legitimate determining factor in question is logical and semantical coherence.
E. The Plausibility of Premise 1 of the PMOA: Is it Possible that a Maximally Great Being Exists?
1. In this section I discuss the plausibility of premise 1 of the PMOA independently of the anti-PMOA-argument formulated above in paragraph B2 based upon the contributions of other scholars.
2. Interestingly, Plantinga after first professing that he thought premise P1 to be true and that his “version of the Ontological Argument is sound” (Plantinga 1974, pp. 216-217), considered various scenarios involving “properties that are non-compossible with maximal greatness; that is, their possibility is incompatible with that of the latter” (Plantinga 1974, p. 218)—such as that of near-maximality (i.e., a property “enjoyed by a being if and only if it does not exist in every possible world but has a degree of greatness not exceeded by that of any being in any world” (Plantinga 1974, p. 218), and that of no-maximality (i.e., “the property of being such that there is no maximally great being” (Plantinga 1974, p. 218).
3. Plantinga handsomely acknowledges that if either near- or no-maximality is possibly exemplified (i.e., exists in some possible world), then maximal greatness is not. Plantinga’s original position was that PMOA “is not a successful piece of natural theology” (Plantinga 1974, p. 218). Premise P1 is not something that “draws its premises from the stock of propositions accepted by nearly every sane man, or perhaps nearly every rational man” (Plantinga 1974, p. 218). He conceded that “a sane and rational man who thought it through and understood it might none the less reject it, remaining agnostic or even accepting instead the possibility of no-maximality” (Plantinga 1974, pp. 219-220). On the other hand, although the PMOA “cannot, perhaps, be said to prove or establish their conclusion…. It is rational to accept that conclusion” (Plantinga 1974, p. 221).
4. Subsequently, Plantinga changed his position. He confessed that he had “employed a traditional but wholly improper standard”—namely, that “arguments [in natural theology] are successful only if they start from propositions that compel assent from every honest and intelligent person and proceed majestically to their conclusion by ways of argument that can be rejected only on pain of insincerity or irrationality” (Plantinga 2003, p. 69). But Plantinga then came to profess his belief that “the ontological argument provides as good grounds for the existence of God as does any serious philosophical argument for any important philosophical conclusion” (WLC 2004, p. 128, 128n5). But I think that to say that the PMOA “provides as good grounds for the existence of God as does any serious philosophical argument [etc.]” does not say much for the probative value of other serious philosophical arguments for God’s existence.
5. Critics of the PMOA have advanced sometimes the same and at times other grounds for their rejection of P1. Some do so by relying on so-called parodies of the argument (e.g., Martin 1990, pp. 94-95; Tooley 1981); or by urging that the purported notions of maximally excellent and maximally great beings are both actually incoherent (e.g., Martin 1990, p. 94). Some urge that since both P1 and its negation provide equally rational options, agnosticism is the appropriate stance (e.g., Smith 1997, p. 134); whereas others hold that the default position is to reject P1. Some scholars have presented persuasive grounds for rejecting P1 but without clearly adverting to whether the notion of maximal greatness is incoherent.
6. Thus, for example, as J. L. Mackie argued:
[I]f we are to choose between the premises [i.e., those that respectively assert that maximal greatness is possibly exemplified or that non-maximal greatness is possibly exemplified], in default of any other reason, we must ask which is more modest and which is the more extravagant, which can be accused of multiplying entities beyond what is necessary. And surely the more extravagant is that which asserts that maximal greatness is realized in some possible world. For this one carries with it the requirement that a maximally excellent being—and, indeed, a maximally great one—should exist in every possible world, whereas the rival premiss that no-maximality is realized in some possible world, still allows maximal excellence to be realized in some possible world though not in others. The latter, then, is less restrictive, less extravagant, and so on very general grounds the more acceptable. (Mackie 1982, p. 61)
Mackie also wisely observed that the PMOA is “insidiously attractive.” This is so because “[t]he premiss that it is just possible that there should be something unsurpassably great looks innocent” (Mackie 1982, p. 61). Who, I might ask, would be so illiberal as to claim that God’s existence is not logically possible, especially if he has not read the fine print to the effect that God is here conceived as maximally great? As Mackie remarked: “But unsurpassable greatness … is a Trojan horse, not an innocent little possibility.” Moreover, he cautioned, “[i]t is a gift of a sort that we should be very wary of accepting” (Mackie 1982, 61-62).
7. Richard M. Gale in rather colorful and, for some, censurable language adopted the same approach as Mackie. Gale wrote (Gale 2007, p. 89):
The problem is that whereas the fool rightly was willing to grant that it Is possible that the concept of a maximally excellent being be instantiated, he would have to be not just a fool but a complete schmuck to grant that it is possible that the concept that there is an unsurpassably great being be instantiated. For in granting that it is possible that there is an unsurpassably great being, he is granting that it is possible that it is necessary that there is a maximally excellent being. But if his consent to the latter is to be an informed one, he must know that the nested moral operator, “It is possibly that it is necessary,” is to be subject to the axiom of the S5 system of modal logic, according to which whatever is possibly necessary is necessary.
8. But what about the coherence of the notion of maximal greatness? Michael Tooley has showed how the notion of a maximally great being is incoherent even if that of maximal excellence is not (Tooley 1981, pp. 426-427). According to Tooley (1981, p. 427; emphasis in original):
[T]he statement ‘There is no maximally excellent being’ is a nonmodal sentence, so unless it can be shown to entail a contradiction, one is justified in concluding that there is a possible world in which it is true. And it will then follow that the property of maximal greatness is not capable of being exemplified.
Tooley provided the following explanation of his position:
How does one determine what properties can be exemplified? A natural line of thought is this. The concept of a possible world is introduced to provide a semantical account of the truth conditions of modal sentences. Whether or not a given modal sentence is true in particular world may depend upon what is true in other possible worlds. However possible worlds involve both modal and nonmodal propositions. Are we then saying that whether a modal sentence is true in a given world depends upon what propositions, both modal and nonmodal, are true in other worlds? In some cases, yes, but that does not mean that the resulting account is circular and unilluminating. For if we characterize a modal sentence as of order n if it has embedded modal operators of depth n, and of not greater depth, then whether a modal sentence of order n is true in a given world depends upon what sentences of modal order less than n are true in other possible worlds.
But there is a further requirement that must be satisfied if circularity is to be avoided, namely, that what sets of modal sentences of order less than n are logically consistent must not be dependent upon the truth values of sentences of modal order equal to or greater than n.
Setting n equal to one gives the requirement that what sets of sentences of modal order less than one are logically consistent must not be dependent upon the truth values of sentences greater than or equal to one. Since modal sentences of order less than one are just nonmodal sentences, we have the requirement that what sets of nonmodal sentences are true in some world cannot be dependent upon the truth values of modal sentences. (Tooley 1981, pp. 426-427)
For the above reasons, Tooley concluded that “Plantinga’s version of the ontological argument is unacceptable … [because] the crucial premise in the argument [i.e., “[t]here is a possible world in which the property of possessing maximal greatness is exemplified” (Tooley 1981, p. 422)] can be seen to be necessarily false, given an adequate account of the truth conditions of modal sentences” (Tooley 1981, p. 427).
9. Anthony O’Hear astutely and cogently described the radical deficiencies of the POMA as follows (O’Hear 1984, p. 180):
In addition to appearing to settle contingent existential questions by definitional means, Plantinga’s introduction of properties like maximal greatness, non-maximality and near-maximality actually subverts the intuition underlying the analysis of logical and logical possibility in terms of actual worlds. For in this analysis, any non-contradictory concept or logical possibility is said to obtain in some possible world. Thus, if the existence of God is possible, then there is a possible world in which there is a God, while if the non-existence of God is possible, there is a possible world in which there is no God. But the second of these possible worlds is excluded by the possibility of maximal greatness; that is, if there is a possible world in which there is a maximally great being, then there is no possible world in which there is no God. On the other hand, if there is a possible world in which there is a non-maximal being, then there is no possible world in which there is a maximally great being. So what appear, on the face of it to be genuine logical possibilities (God’s non-existence, maximal greatness, non-maximality) are ruled out once other logical possibilities are admitted.
10. The above-quoted remarks by Tooley and O’Hear amply disclose in somewhat different ways why the PMOA is fatally flawed because of the radical incoherence of the notion of a maximally great being. Quite clearly, these writers have anticipated grounds ultimately underlying the anti-PMOA-argument. However, I submit that my formulation of the anti-PMOA explicitly articulates what these two writers had implicitly in mind; and, moreover, the anti-PMOA-argument is I believe heuristically useful in showing why a maximally great being is broadly logically impossible and, hopefully, thus adds something significantly new to the literature. It is remarkable that neither Plantinga nor Craig have, as far as I am aware, yet addressed the issues raised by Tooley and O’Hear concerning the incoherence of P1 because it is necessarily false given the underlying assumptions and structure of possible worlds semantics.
1. I have argued that the PMOA fails because it is radically defective, as my exposition and defense of the anti-PMOA-argument explicitly shows. Moreover, the anti-PMOA-argument is confirmed by showing how (given the procedural assumptions of the PMOA) there are a multitude of entities that are plausibly maximally great beings, yet are different with respect to their constitutive and other properties. The failure of Plantinga and his school to clearly distinguish between broadly possible/necessary worlds and those which are metaphysically possible/necessary should lead perfect being theists and their sympathizers to reexamine whether they have been barking up the wrong tree. In his introduction to his examination of his “Victorious Model Version,” Plantinga approvingly noted J. N. Findley’s remarks about how “[i]t would be quite unsatisfactory from the religious standpoint, if an object merely happened to be wise, powerful, and so forth, even to a superlative degree” (Findley 1948, p. 108). I have also approvingly rehearsed the reasons advanced by other writers (namely, Tooley and O’Hear) against the PMOA, which constitute grounds upon which the anti-PMOA-argument is ultimately based.
2. Craig valiantly argues that the PMOA is a sound stand-alone argument for God’s existence. But, without abandoning that stance, he also marshals a posteriori grounds for buttressing his case that premise P1 is more plausible than its negation. However, I shall not criticize these alleged grounds because, as I have independently concluded, the PMOA cannot possibly hold given the incoherence of the notion of a maximally great being. So a maximally great being is not only metaphysically impossible; to paraphrase Craig, “despite appearances, [a maximally great being] is not really [broadly logically] possible after all” (WLC 2008 #51).
 I am grateful to Michael Tooley (professor of philosophy, University of Colorado — Boulder) for his valuable comments in his review of the penultimate and final drafts of this paper. He graciously opined that “you make some excellent points [in the paper] that to my knowledge have not been made before, and do so in a very clear and effective fashion.” My thanks also to Keith Augustine, scholarly paper editor for the Secular Web, for his careful editing of my paper, which is greatly appreciated.
 Craig presented the PMOA in a recorded “Does God Exist?” debate with physicist Victor J. Stenger at Oregon State University on March 1, 2010, which can be viewed on YouTube at https://www.youtube.com/watch?v=EjOs62PJciI.
 WLC 2004, p. 127. Craig’s exposition of the argument is faithful to its substance as stated by Plantinga: “The property has maximal greatness entails the property has maximal excellence in every possible world…. Maximal excellence entails omnipotence, omniscience, and moral perfection” (Plantinga 1974, p. 214). This paper accepts, and asks nontheist readers to do so at least for the sake of argument, that robust notions of omnipotence, omniscience, and moral perfection are coherent. Among able explications of these notions, see for example Joshua Hoffman & Gary S. Rosenkrantz, The Divine Attributes (Oxford, UK: Blackwell Publishers, 2002), pp. 111-178. Unless otherwise indicated, bracketed matter indicates matter supplied to or omitted from that in the original.
 Plantinga formulates the equivalent of PA1 as “[p]ossesses unsurpassable greatness is instantiated in every world—with “unsurpassable greatness [as] equivalent to maximal excellence in every possible world” (Plantinga 1974, p. 216). “Then…. [t]here is a possible world in which unsurpassable greatness is exemplified…. The proposition a thing has unsurpassable greatness if and only if it has maximal excellence in every possible world is necessarily true…. The proposition whatever has maximal excellence is omnipotent, omniscient, and morally perfect is necessarily true” (Plantinga 1974, p. 216).
 Technically, in the modal logic system S5, if a proposition is possibly necessary, then it is necessary. I ask the reader to waive any objections pertaining to S5, used in the context of the modal ontological argument, if only for the sake of argument.
 So a word to the wise is in order whenever it is asserted that nontheists necessarily deny the logical possibility of God’s existence should they reject premise P1 of PMOA. What the commonsensible nontheist (the target of the assertion) should do is insist that he is not by virtue of the denial of premise PA1 denying that the existence of G-CMEB is broadly logically possible, or that its existence does not obtain in the actual world as a matter of fact. What the nontheist in question must point out is that the denial of premise PA1 (i.e., that G-CMGB exists in all possible worlds) does not itself imply that G-CMEB does not exist in the actual world.
 On this point Tooley wrote, in his review of the penultimate draft of this paper: “Yes, I think this is right, and very important. My own way of putting this point—or, rather, for providing underpinning for it—would be that if one adopts an account of possible worlds in terms of sets of propositions, then a possible world is a consistent set of nonmodal atomic propositions and negations of atomic propositions. Alternatively, one can view a possible world as a single consistent conjunction of such nonmodal propositions. The key point is that if one proceeds to give truth conditions for modal propositions in terms of possible world semantics, one must, on pain of circularity, not define possible worlds in a way that itself brings in any modal propositions.”
 Here I assume that a tripersonal, unisubstantial maximally excellent being is broadly logically possible. Recall that the standard opinion among theologically conservative, Trinitarian Christians is that we can only know, or reasonably believe, that God is unisubstantial and tripersonal by virtue of the deliverances of supernatural (i.e., special) revelation.
 Craig holds that, necessarily, the created world began to exist (i.e., has a temporally finite past); and that God (assuming his atemporality sans creation) became temporal when the created world began to exist, and remains so until the created world ceases to exist.
 For my refutation of Craig’s doctrine that infinite temporal series of infinite duration are metaphysically impossible, see Secular Web essays “The Kalam Cosmological Argument: The Question of the Metaphysical Possibility of an Infinite Set of Real Entities” (2002, updated May 23, 2014) and “The Kalam Cosmological Argument Yet Again: The Question of the Metaphysical Possibility of an Infinite Temporal Series” (2003, revised June 9, 2014); both papers are also accessible at http://independent.academia.edu/ArnoldGuminski.
 Craig asserts that “a maximal state of affairs [described in a putative possible world] must be actualizable or capable of being actual…. [and that] Plantinga prefers to construe actualizability in terms of broad logical possibility” (JPM & WLC 2003, p. 50). I am not aware that Plantinga has in fact stated or implied such a preference.
 These philosophers include Quentin Smith (see Smith 2001) and Brian Ellis (see Ellis 2002, pp. 14-19, 38, 59, 88, 92, 100-102, 109-111, 121-122, 138).
 Cf. Thomas V. Morris (an adherent of perfect being theology), who put the matter this way:
For the Anselmian holds that in addition to existing in all possible worlds, God exemplifies necessarily the properties of omnipotence, omniscience, and goodness. Because of this, God has the unique ontological role of being a delimiter of possibility. To put it simply, some maximal groupings of propositions which, if per impossible, God did not exist would constitute possible worlds, do not count as genuinely possible worlds due to the constraints placed on possibility by the nature of the creator. Certain worlds can be described with full consistency in first order logic but are such that, for example, their moral qualities preclude their even possibly being actualized or allowed by an Anselmian God. (Morris 1987, p. 184)
 For example: “[B]road logical possibility is usually construed in terms of actualizability and is therefore often understood as metaphysical possibility” (JPM & WLC 2003, p. 503); “It is crucial to keep in mind [when evaluating the PMOA] the difference between metaphysical possibility (roughly understood as actualizability) and mere epistemic possibility (that is, imaginability)” (JPM & WLC 2003, p. 497). See also: “It is crucial that we keep clear on the difference between metaphysical and merely epistemic possibility” (WLC 2004, p. 128); “[T]he epistemic entertainability of the ontological argument’s key premise (or its denial) does not guarantee its metaphysical possibility” (WLC 2004, p. 128). Notwithstanding Craig’s distinction between strict logical possibility and broadly logical possibility (he ordinarily treats the latter as synonymous with metaphysical possibility), elsewhere he appears to distinguish between broadly logical and metaphysical possibility: “Insofar as by broadly logical possibility one means merely strict logical possibility augmented by the meaning of terms in the sentence within the scope of the modal operator, such a conception is still too narrow for the purposes of the present argument [the kalam cosmological argument]” (WLC & JDS 2009, p. 105). And again: “Propositions that are not strictly logically contradictory may nevertheless be metaphysically impossible—for example Socrates could have been a hippopotamus” (JPM & WLC 2003, p. 503).
 In his comments on the penultimate draft of this paper, on this matter Tooley states: “Plantinga says that there are two different ways in which one might use the term ‘alligator’. According to the first—given on page 65—an alligator is a composite of a body and a (rather dull) mind. According to the other, mentioned at the top of page 66, an alligator is a purely material object. Used in the first way, Socrates could have been an alligator, while if used in the second way, Socrates could not, Plantinga contends, have been an alligator.” I need not here resolve any differences of opinion with Tooley as to the proper interpretation of Plantinga’s discussion of the matter in question.
 In developing and formulating the anti-PMOA-argument I first interacted, as it were, with the writings of Plantinga and Craig. It was after I had done so that then I undertook a review of the writing of some other philosophers who might have considered the issue of the coherence of maximal greatness assuming (for the sake of argument at least) the coherence of the notion of maximal excellence. Because of the extensive literature on the PMOA, I do not pretend that my review is exhaustive.
 WLC 2004 quotes from a transcript of Plantinga’s “Reason and Belief in God.”
 Mackie has other objections to the PMOA grounded upon his concerns about world-indexed properties, and the applicability of the modal logic system S5 (Mackie 1982, pp. 55-57). But I do not find it useful to discuss these matters in this paper.
 The fool referred to by Gale is Gaunilo. Plantinga wrote the following fair account concerning him:
Gaunilo, a contemporary of St. Anselm, was a monk of Marmoutier, and accordingly a believer, like St. Anselm…. He did not reject St. Anselm’s conclusion that God exists, for of this he was already entirely convinced, but he protested against what seemed to him a specious argument for that conclusion. It appeared to Gaunilo, as it has to many since, that St. Anselm was merely defining God into existence, that by similar reasoning one could ‘prove’ the existence of anything he pleased. St. Anselm had maintained that only a fool, or someone who could form no clear conception of God, could really doubt His existence. Gaunilo, accordingly entitled his reply to St. Anselm, In Behalf of the Fool, and endeavored to show how such a man, though foolish, might nevertheless be right. (Plantinga 1965, pp. 6-7)
Anselm demonstrated that he was not only a saint, but a gentleman, since in his reply to Gaunilo, he wrote: “It was a fool against whom the argument of my Proslogium was directed. Seeing, however, that the author of these objections is by no means a fool, and is a Catholic, speaking on behalf of the fool, I think it is sufficient that I answer the Catholic” (Plantinga 1965, p. 13). Anselm concluded his reply: “I thank you for your kindness both in your blame and in your praise of my book. For since you have commended so generously those parts of it which seem to you worthy of acceptance, it is quite evident that you have criticized in no unkind spirit those parts of it which seem to you weak” (Plantinga 1965, p. 27).
 Indeed, in his review of the penultimate draft of my paper, Tooley wrote: “And so I claimed [referring to his 1981 essay] that the notion [of maximal greatness] is incoherent. I also went on to say something to the effect that a demonstration of this would require an account of the truth conditions of modal propositions. (An account in which the truth conditions of modal propositions is to be given in terms of possible worlds, where the latter are defined in terms of consistent combinations of nonmodal propositions, will do the job.)”
 O’Hear commendably points out that “before satisfying ourselves that maximal greatness, as defined by Plantinga, is possible, we will have to ensure, among other things, that there is an omnipotent, omniscient, morally perfect being in this world” (O’Hear 1984, p. 180).
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