On the Ontological Argument

Spurred to reading Spinoza's Ethica after Delany's use of it in Through the Valley of the Nest of Spiders, I've found myself thinking over the last few days of the ontological argument. Hence the previous entry, a short story as a sortie into it, a little skirmish with the irksome bootstrapping. I've tackled it before, returned to it a few times, I think, but as Bertrand Russell said, "the argument does not, to a modern mind, seem very convincing, but it is easier to feel convinced that it must be fallacious than it is to find out precisely where the fallacy lies." There is little more frustrating for someone like me, a philosophically-minded ex-programmer with a somewhat obsessive interest in religion, than the niggle of a defiant problem of mental chicanery so intuitively unsound and so gnarly one can't help but want to unravel it. So, in an attempt to deal with this bugbear once and for all, I thought I'd take to it concertedly, try and rip it apart as thoroughly and decisively as I could. It may not be of interest to many reading this blog, but so it goes. Maybe it'll exorcise that irk at last.

So, let's begin with an analysis, stripping away the archaicisms of Anselm and laying out the basics of the argument in an overview such that it might, I hope, be more transparent what is going on here. I will abstract a little for a start, for reasons that should become obvious:

1. Any quantifiable quality, X, can be used to define a hypothetical existential maximum, M, the most X thing in existence.
2. We can then define a hypothetical essential supremacy, S, which trumps all contenders, a thing so X we can't imagine anything more so.
3. We can then premise that the quantity of the quality depends on existence: a thing is less X if it does not exist.
4. But, we say, then we have countless things in existence which possess that quality X, any one of which we can imagine.
5. We already have, indeed, the hypothetical M, the most X thing in existence.
6. If S does not exist, M is more X than S, that thing so X we can't imagine anything more so.
7. Unless S exists, we say, we have a self-contradiction: M is greater than S which is greater than M.
8. So, we say, S must exist.

Problem 1: This applies to monstrosity as well as to magnificence. If it is held to work for magnificence, we can apply the same ontological argument to prove the existence of a thing so monstrous we can't imagine anything more so. If this is accepted as simply a proof of the Devil consistent with the metaphysics of the Deus, we can push further.

Problem 2: Echoing #3: if the monstrosity of S can be said to be dependent on existence, it can also be said to be dependent on potency; a thing is less monstrous if it is not omnipotent. Echoing #6: if S(1) is not omnipotent, we can imagine an S(2) which is omnipotent, which is clearly the more monstrous. Not only must the Devil exist by the ontological argument, but he must be omnipotent.

Result: We then have two omnipotent beings, utterly opposed in magnificence and monstrosity and each by definition simultaneously capable of overcoming the other to achieve their will and yet incapable of being overcome. This is a contradiction.

Response: Since a being with the capacity to empower has greater power than a being without, it must be included in omnipotence. A being limited to the degree to which it may empower another has less power than one with no such limits, so omnipotence can have no such limits. So, one may imagine a response that the omnipotence of one is invested in it as an extension of the omnipotence of the other, that the S1 so magnificent we can't imagine anything more so empowers as a subordinate the S2 so monstrous we can't imagine anything more so. A supremely magnificent being imagined without the power to empower the supremely monstrous being is less magnificent than one imagined with that power, so only the latter can fit the criteria of a thing so magnificent we can't imagine anything more so.

Problem 3: It is equally possible to argue the reverse however, that the S1 so monstrous we can't imagine anything more so empowers as a subordinate the S2 so magnificent we can't imagine anything more so. A supremely monstrous being imagined without power to empower the supremely magnificent being is less monstrous than one imagined with that power, so only the latter can fit the criteria of a thing so monstrous we can't imagine anything more so.

Result: The equal legitimacy is a problem in and of itself, again returning us to a contradiction. Moreover, the ontological argument now supports a scenario in which the Deus is subordinate to the Devil. Indeed, given that benevolence is a key aspect of magnificence, and malevolence a key aspect of monstrosity, the latter of the two scenarios is more compelling:

Problem 4: In the first scenario, where S1 is magnificent, we can imagine an S1(2) that does not empower a monstrous subordinate S2. Being clearly the more benevolent, S1(2) is clearly the more magnificent. If we are holding to the ontological argument, we must dismiss that scenario. In the second scenario however, where S1 is monstrous, we can imagine an S1(2) that does not empower a magnificent subordinate S2, but this does not render S1(2) more malevolent. On the contrary, if a supremely magnificent S2(2) simply does not exist, this is less monstrous than if a supremely magnificent S2 is in fact a subordinate of a supremely monstrous S1. Surely a Devil that has the Deus for servant is more monstrous than the Devil that does not. If we are holding to the ontological argument, we must sustain that scenario then.

Outcome: If we accept the legitimacy of the ontological argument for the quality of magnificence, we must do so also for the quality of monstrosity. This creates a contradiction which in itself should be sufficient to invalidate the ontological argument. If we appeal to omnipotence in order to resolve this contradiction, supposing the empowerment of one supreme being by another, we can do so for the monstrous as legitimately as for the magnificent. Indeed, if we apply the ontological argument again, we see we can only truly do this for the monstrous, and we are left with a Supremely Magnificent Being which is empowered on the whim of a Supremely Monstrous Being.

Response: We should assume a response then in which the ontological argument is held to be legitimate for magnificence but not so for monstrosity. Rather than being valid for any quantifiable quality, X, the ontological argument must be held valid only for those qualities which would serve to construct magnificence. To this end, Anselm constructs magnificence--or greatness, as he calls it--as a product of sundry perfections, perfectible properties such as knowledge, power and righteousness that make a being great.

Problem 5: Monstrosity can equally be constructed as a product of perfectible properties. Knowledge and power may be perfected to omniscience and omnipotence, and we need only replace perfect righteousness with perfect iniquity in order to turn the supremely magnificent into the supremely monstrous.

Response: We must imagine an argument that iniquity cannot be a negative perfection, that it is rather a state of imperfection. While righteousness is perfectible by cleaving perfectly to the righteous path of action, iniquity is defined as straying from the path; no matter how far we imagine straying from the path, we can always imagine a step that takes us further, so no matter how wicked we can imagine a being, we can therefore always imagine an action making the being more wicked.

Problem 6: For righteousness to be perfectible requires iniquity to be so too. If omniscience is knowing all things, and omnipotence is the power to do all things, perfect righteousness must be constructed as a state in which all things done are right. All things must thus be decidable as right or wrong, good or wicked, so perfect iniquity can be constructed as a state in which all things are done other than they would be done by the righteous. It does not matter if we say that there are multiple ways to do things wrong, some more wicked than others. This only means that some are less wicked, and therefore more good. This is only to set a sliding scale of moral judgement, a spectrum that runs from mandatory (acts we must do) through laudable (acts we should but may not do) through reprehensible (acts we may but should not do) to forbidden (acts we must not do.) That is to say, if straying from the righteous path means breaching the mandatory and the forbidden, greater wickedness can only be achievable via reprehensible acts if greater righteousness is achievable via laudable acts. Perfect righteousness would then be the state in which the least wicked option is always selected, while perfect iniquity would be the state in which the most wicked option is always selected.

Problem 7: Alternatively, if the perfectibility of iniquity is denied, we can as legitimately deny the perfectibility of righteousness. Where ethical perfection is cast as supremacy, supremacy as the achievement of a state so ethical we can't imagine anything more so, the ontological argument crumbles if we can always imagine a more ethical state, if there is always a further step that we can imagine being taken which would increase virtue. This is exactly the case. Perfect righteousness would entail not just cleaving to the mandatory and eschewing the forbidden, but doing every laudable act possible in every given context. If we consider benevolence as a linchpin of righteousness however, and acts of charity as laudable exercises of that principle, there is no intrinsic maximum to charity. Where Gaunilo seeks to show the ontological argument absurd by proving the existence of a perfect island, his argument is held to fail because the qualities that make an island magnificent are not perfectible; if we suggest an abundance of fruit as a perfection, for example, there is no inherent maximum for this, so it will always be possible to imagine a more magnificent island. In so far as we can map an island's production of fruit directly to an individual's provision of charitable gifts, the same problem holds for the argument here. In the form of charity, benevolence has no inherent maximum, so any ontological argument including this as a facet of magnificence is incoherent.

Problem 8: Further, the very notion of righteousness as a quantifiable quality may be seen as incoherent. If we consider justice and mercy to be linchpins of righteousness, there is a clear incompatibility if we imagine these two as perfected: perfect justice would entail punishing every wrongdoer to the degree they merit, while perfect mercy would entail exercising leniency on every wrongdoer, punishing them less than they merit. That incompatibility points to a more fundamental problem with the notion of righteousness though, in so far as the two constitute competing imperatives on a judge, rendering his judgement subject to evaluation in both dimensions. That's to say, whether he is just or lenient, his action is both laudable and reprehensible--by different measures. With any number of other principles that might be applied, the righteousness of an act may well be ultimately irreducible to a singular measure. If we consider virtue in any but the crudest sense, by any ethical system other the most primitive one-dimensional moralism, we may well reject the notion of maximal righteousness entirely, holding that there is only the ethically optimal course of action.

Problem 9: We may question also whether omniscience could truly be maximal, or whether it too must be optimal. For omniscience to be maximal, the omniscient being must know completely what it's going to think next. If it does not, it doesn't know everything, so it is not omniscient. Since thoughts include intentions, decisions and actions of volitions, indeed, without complete foreknowledge of one's thoughts, one can have no foreknowledge of one's future deeds, only imperfect predictions. If the omniscient being's own future deeds are not perfectly predictable to itself, neither is the eventual outcome of those future deeds upon the world, in which case its knowledge of the world's future is also uncertain. Omniscience is meaningless without this last, so the omniscient being must know what it's going to think next. If this is the case however, then it is aware of the thought. Since entry into awareness is the action by which a thought becomes a thought, by which a being thinks that thought, the omniscient being aware of its future thoughts is thinking them in that instant. For omniscience to be maximal, all future thoughts must enter into awareness in the instant omniscience comes into being, and must remain so as long as omniscience persists. The omniscient being is therefore static, and therefore not thinking in any meaningful sense of the word. It is arguable that it is not even aware. The only possible solution to this is to posit optimal rather than maximal knowledge, the limitation of omniscience to that which is needful to know at any given moment.

Problem 10: We may question also whether omnipotence could truly be maximal, or whether it too must be optimal. For omnipotence to be maximal, the omnipotent being must be able to perform in the immediate instant all actions it might perform in any future instant. That is to say, it must be able to preempt its own future actions. If it cannot, it is not omnipotent but rather bound within its own performance. Again, this limitation propagates to the world: if the omniscient being cannot preempt its own future actions upon the world, all changes in the world resulting from those actions could not have been made preemptively. At any given moment, the omnipotent being is unable to change the world by any action that would be premature; thus it is not truly omnipotent. If it can preempt its own future actions, it must have foreknowledge of them, including its own thoughts. It can't not preempt its own thoughts. Since thoughts include intentions, decisions and actions of volitions, it can't not preempt its own actions, carrying them out at the moment of its own creation--and continuing to do so if it continues to experience every thought, every decision, every act of volition. If every act of volition and therefore every act occurs the instant this omniscient omnipotence comes into being, and continues as long as it persists, again this is not action in any meaningful sense of the word. The only possible solution to this is to posit optimal rather than maximal power, the limitation of omnipotence to that which is needful to do at any given moment.

Problem 11: As well as being individually incoherent, these qualities are mutually incompatible in all combinations. If the perfectly righteous being cannot perform any wicked action and remain perfectly righteous, then it cannot therefore be omnipotent. If the omnipotent being can perform any wicked action and remain perfectly righteous, then righteousness is infinitely mutable and therefore cannot be perfected. If the perfectly righteous being cannot know completely what it is to enjoy a wicked action because one does not know that it is wicked, then it cannot be omniscient. If the omniscient being can know completely what it is to enjoy a wicked action because one does not know that it is wicked, then it cannot be perfectly righteous. If the omnipotent being can create a being with the free will to perform an action that is not predestined, it cannot know whether the being will perform that action or not, and is thus not omniscient. If the omniscient being knows every action that a being will perform as a predestined outcome, then it cannot invest that being with free will, and is thus not omnipotent. The notion of maximal magnificence as a totality of these three maximal qualities is therefore incoherent.

Problem 12: The notion of maximal magnificence is also incompatible with that of a being in so far as it extends to defining the being as unlimited. While maximal magnificence is often decomposed simply to these three qualities, omnipotence entails the power to do anything anywhen, and precludes external causes of creation and destruction beyond the omnipotent being's control. Thus, the omnipotent being must be eternal and indestructible, removing all limits (except perhaps logic,) and we find ourselves at Norman Malcolm's simplification of the notion as that of an absolutely unlimited being. But the use of the determiner, a, requires that the being so determined is determined as distinct from any other being or thing. If it is determined as distinct from any other being or thing, it is by definition limited: it is not any of those other beings or things. Malcolm's notion of an unlimited being is hence logically impossible, a non-starter.

Response: One might respond that this holds for all but the totality of all things. We can say that a being determined as distinct from its constituent things--e.g. as a person is distinct from their hand--is an exception, as the constituent things are included within the limits of the being rather than excluded as beyond them: the being is that constituent thing in combination with all others; the constituent thing, in combination with all others, is the being. If all things are constituents of one totality, then all things are within the limits of that totality, and that encompassing totality may be considered to have no limits in and of itself. Here we approach Spinoza, since there can be no distinction then between that being and the entirety of Nature. Indeed, if we admit of a multiverse beyond the scope of even the universe, that being must be considered, to coin a term, holocosmic.

Problem 13: A being is, however, a subclass of thing which is limited in a singular and profoundly distinctive aspect: a being must have agency or it is not a being, merely a thing. Or at least, where we may strictly speaking include as beings the most basic orders of creatures, those too primitive to respond with more than a taxis or suchlike, the agency that emerges, as creatures scale up in complexity, as the animating system of each individual being is an absolutely fundamental attribute of the type of being (being-as-agent) that the term is being used to refer to here. The crux of the issues with omnipotence, omniscience and perfect righteousness is, as much as anything, the degree to which each of these attributes individually and as a whole specifies criteria for the conceit of a being-as-agent that become entirely incompatible with the very definition of a being-as-agent even before we follow the ramifications through to their ultimate end-point in the holocosmic. Spinoza nails this to the wall in his Ethica, sweeping away all anthropomorphic projection, down to the very idea of (intellect and) will as he parses it--i.e. agency. Spinoza speaks with forked tongue, his use of the term "God" a patent feint for a stance that is actually radically antitheist, but given a modern context with no threat of heresy accusations hanging over us, let us dispense with that weakest of sops to propriety:

• Agency is an existential phenomenon, the definitive feature of a sentient being with the capacity to react autonomously to changes in its environment. Note: not sapient, but sentient: there is nothing in the world to substantiate a specious exceptionalism conflating sapience and sentience, ratiocination and basic (self-)awareness, in order to sustain a conceit of agency as an exclusively human phenomenon; until such time as that sort of haughty claim is proven, a simple principle must be applied: Where sensation is, there agency am. What we can rule out as capable of agency is any conceit of a thing that can struggle with neither the world nor itself. Agency is a matter not just of aims and objectives manifest on whim, but of the formation of such in response to disruptions exterior or interior, a matter not just of the achievement of goals by willing it so, but of active engagement with the obstacles that thwart achievement until agency is applied (and applied right.) For agency, there can be no decision without dilemma. A little hyperbolic perhaps, but the core point is simple:

• By the term agency what I mean is the animating system emerging in and of a sentience as it parses sensations of self and world into stances of one toward the other, these stances (boulomaic, deontic, epistemic or alethic) being always already ephemera of a dynamics driven by the absence of power, knowledge and/or aesthetic equilibrium. At its most basic level, I mean, we can perhaps situate the very birth of agency in the breach of aesthetic equilibrium we call hunger, in the sentience of this absence of power in its most immediately and intuitively measurable form: the fuel we call food. One might say that the conceit of a thing woven by the ontological argument can never know hunger, but this is not a matter of knowledge, but rather of the dynamics of agency which is the very thing abolished with the abolition of limitation.

Result: All the omniscience in the world will not help the ontological argument, since agency is not to know hunger but to be driven by it to a decision the consequences whereof we do not know.

Response: We must imagine a response which ignores all these problems, obliviates all criticism and retreats to entrench within the logical gambit at the heart of the ontological argument. Yet, it insists, there is a notion defined here of a being of maximal magnificence, and without the property of existence such a being is a contradiction in terms. Perhaps, if we set maximal magnificence as maximal for a being with agency, if we appeal to the mystery of a transcendent agency to excuse aspects that appear incoherent in the idea, is it not still so that this being would be less magnificent if it did not exist and therefore, to be what it is defined as, must exist?

Problem 14: A thing is not less X if it does not exist. If it does not exist, a thing has no state. None of its quantifiable properties are actually set, as we can tell if we simply imagine a ten ton bus. Rather than an object property, ten tons is a specification made upon a class. That is to say, "ten ton bus" functions as a template such that an object fitting that template is and can only be a ten ton bus. Such an object having a state, it has weight as an alterable property, and we can change this without changing the object into another object. Changing the weight specification of the class to five tons gives us a different class, "five ton bus." If we imagine a "ten ton lorry," indeed, we can change the vehicle specification to bus and reconstruct the original class in our imagination. The fact that we can do so tells us that neither class has an alterable state such that properties can be increased or decreased. Rather any constituent dimensions--e.g. "weight: ten tons"; "vehicle type: bus"--are criteria, specifications that an object with state must meet in order to be of that class. Where Hume says that existence is not a quality, we can say that this is because it is a state, the state of instantiation that only an object can have; and because to treat it as an attribute and specify a class with such is, as with any attribute, simply to set a criteria that an object must meet to be an object of that class. The same is true for Kant's rejection of existence as a predicate. If we imagine existence as something that an object of a class does, as a procedure of that class, any procedure is simply another type of criteria, a specification of requisite performance that an object must match to be an object of that class. So we can construct a class "ten ton lorry driving down the road," where "driving down the road" is a procedural criteria. But it is still a criteria, a specification that an object with state must meet in order to be of that class. We do not make a class more magnificent by ascribing existence to it. Applied to a class, existence is a criteria.

Problem 15: The ontological argument obfuscates this simply by sleight of hand. If we construct a class of a "being so X we can't imagine anything greater" this has no state and therefore no alterable property of greatness. Where we inspect existential beings for their relationship to this class, we're not matching property with property but rather criteria with property, which makes that action inherently a confirmation of existence rather than a comparison of quantities. The class in question is however constructed wholly in relation to other classes. It is--and you must forgive the convolution--a class of being with the criteria (of greatness specified such) that no other class of being can be specified with the criteria of greatness specified higher. If the convolution obfuscates what's going on here, let me spell it out. The sole criteria of the class is not actually specifying the class's own greatness at all; it's specifying the limitation of all other classes. We can remove the bracketed text to clarify: It is a class of being specified with the criteria that no class of being can be specified with the criteria of greatness specified higher. It may become clearer still if we restructure: It is a class of being specified with the criteria that a criteria (of greatness specified higher) cannot be specified in any other class. Again, we can remove the brackets to draw out what is going on: It is a class of being specified with the criteria that a criteria cannot be specified in any other class. Boil it down to this and we find the notion is empty. It sets no matchable criteria, only performs an operation on how a certain criteria can be specified.

Problem 16: In fact, an operation like this is inherently metalinguistic (for notional classes considered as a language.) Setting a limit on the specification of criteria for classes is a system-wide procedure. Any class with a sole criteria like that includes an implicit "henceforth," because it is in fact executing a procedure to redefine class construction: It is a class of being specified with the criteria that henceforth no other class can have a criteria specified in a now proscribed manner. What Anselm's ontological argument is really saying is that he can perform an act of imagination by which, henceforth, no being he imagines can be specified as greater than the supreme being he is already imagining. Any attempt to do so will simply result in whatever specification that would consist of being applied to the supreme being he imagines. This is all very well as a description of how faith sustains itself by shifting the goalposts, but it should now be clear that all he is doing when he specifies existence as a criteria is just that: specifying existence as a criteria that must be met. The preceding convoluted mechanics is irrelevant, not a logical premise but a description of his diversionary mechanisms of imagination. He is left with a class of "existing supreme being" which is in the exact same situation as a class of "existing ten ton lorry"--a class with certain criteria specified that must be matched to an object for confirmation that it exists. The criteria of "existing" is of course wholly redundant in a class; any object that meets all other criteria is an object and therefore, by definition, exists.

Response: The last refuge of the ontological argument is that proposed in Anselm's restatement and adopted by more contemporary philosophers like Plantinga: necessity. Here a criteria of "necessarily" is added to the criteria of "existing" such that the class proposed is that of "necessarily existing supreme being." Given that a contingent "existing supreme being" still must be matched to an object for confirmation that it exists, it is less magnificent than one which does not require matching because to deny it would be a contradiction in terms. The quality of supremacy requires necessity, so by definition it would be a contradiction in terms to deny a "necessarily existing supreme being."

Problem 17: The necessarily supreme being inherits all of Problems #1-#13, and is patently echoing the gambit unpacked in Problems #14-#16: apply a criteria to a class as a way to establish there's an object matching it. If a "contingently existing supreme being" is a contradiction in terms due to the utter incoherence of omnipotence, omniscience and perfect righteousness, individually, together, and in combination with being, we hardly really need to address a "necessarily existing supreme being." We already have a "necessarily not-existing supreme being." But let's set aside the incoherence in order to unpack this last gambit in and of itself, lest any shred of faith remain in the capacity of the ontological argument to define anything into existence. We'll take our cue from Plantinga and reproduce his argument, with a variation following to draw out the problem.

Argument 1:

Premise A: A being is maximally excellent in a given world if and only if it is omnipotent, omniscient, and morally perfect in that world.
Premise B: A being is maximally great in a given world if and only if it is maximally excellent in every possible world.

1. The notion of a maximally great being is self-consistent, so it is not logically impossible.
2. Therefore, there is at least one logically possible world in which a maximally great being exists.
3. By Premise B, if a maximally great being exists in one logically possible world, it exists in every logically possible world.
4. Therefore, a maximally great being exists in every logically possible world.

Argument 2:

Premise A: A thing is quite relevant in a given world if and only if it is applicable, comprehensible and all about dogs in that world.
Premise B: A thing is brilliantly relevant in a given world if and only if it is relevant in every possible world.

1. The notion of a brilliantly relevant thing is self-consistent, so it is not logically impossible.
2. Therefore, there is at least one logically possible world in which a brilliantly relevant thing exists.
3. By Premise B, if a brilliantly relevant thing exists in one logically possible world, it exists in every logically possible world.
4. Therefore, a brilliantly relevant thing exists in every logically possible world.

Summary: Plantinga founds his argument in the notion of all possible worlds because this is the measure of positive and negative logical possibility and necessity. A contradiction in terms is logically impossible, which means in all possible worlds it's false: there are no square circles. If to deny something is a contradiction in terms, that thing is logically necessary, which means in all possible worlds it's true: all circles are round. If neither of these is the case then, with a self-consistent proposition like "all dogs are friendly," the set of all possible worlds must contain at least one world where this is true. So, Plantinga constructs a premise he holds to be self-consistent, and hence not logically impossible. If we accept that the premise is not logically impossible, we have to accept that there's one logically possible world in which it's true. That premise is so constructed, however, that if it's true in one world, it's true in them all. So his maximally great being must exist in all possible worlds, making it logically necessary.

Problem 18: If there is nothing to render Plantinga's premises a contradiction in terms, there is nothing to render ours a contradiction in terms. Indeed, where the incoherence of a maximally magnificent being is detailed above, our set of characteristics are demonstrably self-consistent: we can point to any decent book on man's best friend as proof of something "quite relevant" in this world. But following the argument through, we are led by the ontological argument to the conclusion that such a thing exists in every possible world. Unless dogs are logically necessary, there is at least one world where they do not exist, and we're left with the absurd notion of something "applicable, comprehensible and all about dogs" in a world without dogs. This absurdity in and of itself surely renders Plantinga's argument fatally flawed.

Problem 19: What is being overlooked here is the flip-side of contingency. If the negation of a proposition like "all dogs are friendly" is also a self-consistent proposition ("not all dogs are friendly,") the set of all possible worlds must contain at least one world where this negation is true. If a proposition is contingent, it must also be false in at least one possible world; otherwise it is logically necessary and not contingent. If we are to take the self-consistency of "all dogs are friendly" as proof that it is not logically impossible, then unless we are assuming necessity, we must consider whether the negation is self-consistent; if so "all dogs are friendly" is also not logically necessary.

• What then if we consider: "A thing is not brilliantly relevant in a given world if and only if it is relevant in every possible world"? What if we consider: "A being is not maximally great in a given world if and only if it is maximally excellent in every possible world"? There is no contradiction in terms evident in either of these. In either, we could simply say that there are other additional properties required to render a thing "brilliantly relevant" or "maximally great" in any given world. In such a case, we have an equally legitimate alternative #1: The negation of a maximally great being is self-consistent, so it is not logically necessary. Further, this generates a new #2: Therefore, there is at least one logically possible world in which a maximally great being does not exist. If we apply Premise B in #3 now, we get the exact opposite result: Therefore, a maximally great being exists in no logically possible world.

Result: The argument is wholly unsound, crumbling at the very first hurdle. Why? Because Premise B is only a definition of a metalinguistic operation: the confirmation of the logical necessity of a class and the subsequent renaming of it. It can be rephrased thus: A class is to be branched into a subclass as ["Necessarily" + (X)] in a given world if and only if it is [(X)] in every possible world. For any value of X one cares to enter into that, for any possible renaming operation that one might replace ["Necessarily" + (X)] with, all that premise does is take an existing class and create a new subclass inheriting from it, predefined as logically necessary. What follows is simply a contorted reiteration of the relationships that pertain between: any actually logically necessary thing, self-consistency, logical impossibility, all possible worlds, one possible world, and existence. There is no substance here, not a shred. This last refuge of the ontological argument is a flourish of intricate but empty gestures, making a grand show of elegant reasoning involuted to disguise what is not remotely the breathtaking bootstrapping maneuver it purports to be, but rather a concerted effort to tie one's laces together such that at the very first step one stumbles face-forward, crashes tumbling down the stairs, head over heels and face-planking every step of the way, to lie in a crumpled heap of nonsense at the bottom and, in the oblivious delusion that one has actually performed a feat, throw one's arms up in the air with a drunken, "Tada!"

In short: The ontological argument is dead. Let the scraps of its shredded corpse be trebucheted from the city walls, to splatter the rocks of the wilds beyond, food for the feral dogs and carrion crows.