Ontological Arguments: A Critique

Well this is it: my first serious blog post ever.

I'm almost as nervous as I was the first time I rode my bike without training wheels. I've tried to keep technical terminology to a minimum, and provide lots of useful examples and analogies, so my arguments should be relatively easy to follow. I still don't know how to insert links into the outline section so that readers can easily jump to the section they want (if anyone could tell me how to do this, I would greatly appreciate it). So if you want to jump to a certain section, I'd recommend just copying and pasting the section heading from the outline into the "Ctrl + F" menu. Only underlined headings appear in the body of the text. 

Given this post's length, feel free to use the shorter argument map to keep track of all the arguments or, if you're in a rush, as a substitute for the longer post itself.

Without further ado, let's tackle ontological arguments for God!

Ontological Arguments: A Critique

Have you forgotten? The sin given to me is “Pride.”

- Lucuha, Lucu Lucu (as translated from Japanese)

…there are many things to say about these objections…almost all of them require far more controversial assumptions than non-theists require in order to be able to reject ontological arguments with good conscience. Trying to support most of these claims merely in order to beat up on ontological arguments is like using a steamroller to crack a nut (in circumstances in which one is unsure that one can get the steamroller to move!).

- Graham Oppy, “Ontological Arguments” in the Stanford Encyclopedia of Philosophy

Steamrollers FTW!

- NoctambulantJoycean

OUTLINE

Introduction

I. Prelude

   I-A. Preliminaries

   I-B. An Introduction to Modality

      I-B-1.  Modality

      I-B-2.  Logical and Broadly Logical: Do not confuse them

   I-C. Modal Ontological Arguments; everything comes in pairs

II. The Collapse of the Metaphysical OA

   II-A. Question-begging and Invalidity

      II-A-1. Question-begging

         II-A-1-a. The Meaning of Modal Statements [“insulting two brilliant mangakas…like a boss”­­­]

         II-A-1-b. Uninformative Question-begging [“death-defying Socrates: enemy of the OA and feminism”­­­]

      II-A-2. The OA’s Structural Flaw [“‘logical obfuscation’ for 1000, Alex”]

      II-A-3. The OA’s Proper Role [“winning isn’t everything”]

   II-B. Gaunilo-type parodies and counterexamples

      II-B-1. Gaunilo-type Objections + the OA is Parasitic upon NE [“everything under the Sun”]

      II-B-2. Reply to Theistic Rejoinders [“apathy and tyranny”]

      II-B-3. Greatness Reconsidered

         II-B-3-a. Rebutting Plantinga’s “Intrinsic Maxima” Reply [“Mr. Maximum’s buxom babes”]

         II-B-3-b. God’s Missing GMPs [“loneliness, but with elbow room”]
         II-B-3-c. The Incoherence of the MGB ["easy come, easy go"]

      II-B-4. Full-Scale Gaunilo Assault

         II-B-4-a. Gaunilo's Initial Skirmishes

            II-B-4-a-i. A Flaw Common to All OAs [“she’s perfect…but I still prefer Fran”]

            II-B-4-a-ii. More Flaws in the MPA [“Hyper Cutter blocked 32-step logical proof’s Intimidate”]

         II-B-4-b. The Flaw Generalized [“anything you can do, I can do better”]

   II-C. PEOPLE NEW TO MODAL LOGIC: Get Here Soon

      II-C-1. A Helpful Modal Thought Experiment [“pandemic: the OA goes viral”]

      II-C-2. An Epistemological Error [“could I please switch to an a-religious epidemiologist?”]

   II-D. Unsupported Modal Intuitions [“…and the dualists rode in on pale horses…the OA trembled”]

III. The Fall of Logical OAs

   III-A. The Logical OA is Less Plausible than the Metaphysical OA [“logic gets picked on”]

   III-B. The Logical Version of Plantinga’s OA [“+/- ?”]

   III-C. Rebutting Theistic Replies [“logic leans right”]

   III-D. Malcolm’s Argument [“why bother?”]

IV. Why Theists Still Defend Ontological Arguments [“please have a seat on the couch”]

Works Cited

Introduction

This paper will critique two versions of the modal ontological argument (henceforth known as the modal OA): one version based on logical modality and another version based on metaphysical modality. In section II-A-2 I examine a flaw common to most, if not all, ontological arguments. In section II-B-4, I discuss another flaw apparent in most OAs and further examine two other OAs.

[I owe a debt of gratitude to the Youtube theist Mentat1231 for his/her critiques of my arguments and his/her patience with my often maddening methods. The same goes for Rayndeon’s and MistyGothis’s helpful suggestions and resources. Hope things go well for them.]

I. Prelude

I-A. Preliminaries

Pop quiz: do critics of Plantinga’s modal OA need to show the concept of God is incoherent/logically impossible in order to rebut Plantinga’s argument?

If you answered “no,” then you can probably skip to section I-C.

If you answered “yes” or “I don’t know,” then continue on with this section and please read section I-B.

In section I, I will explain the modalities relevant to the OA and present both Plantinga’s and Malcolm’s arguments. Readers familiar with modal logic can, if they wish, skip to section I-C. A number of novice proponents of modal OAs lack a basic understanding of modality (see my pop quiz); so I recommend that proponents of the modal OA read section I-B, even if that section simply serves as a useful modal review.

Readers unfamiliar with modal logic should first refer to an introductory text on the subject [or consult (in order of increasing technical jargon): Wikipedia’s entry on “Modal logic,” Alighieri, Garson], before continuing on with this paper. Alternatively, the reader could begin with section I-B-1 to get a general understanding of modality, and then read my presentation of Plantinga’s modal OA in section I-C before finally following along with the thought experiment in section II-C-1. This thought experiment should intuitively guide the reader through the reasoning involved in modal logic.

I have tried to provide useful illustrations (hence this paper’s length) and avoided unnecessary technical terminology + pages-long formal proofs; so even people new to modal logic should be able to understand my conclusions. Hopefully, OAs will never again baffle atheists nor mislead theists.

I-B-1.  Modality

[see Chalmers 1996, chapter 2, for further context on the issues discussed in this sub-section, along with criticism of how I characterize the distinction between logical modality and metaphysical modality]

Both philosophers and lay people talk about “possibilities.” This multiply ambiguous term admits of many readings. When lay people say “it is possible that OJ Simpson committed murder” or “it is possible that my husband cheated on me,” they may be making claims about their epistemic position. Epistemology relates to one's knowledge, how sure one is of one's beliefs, etc. So when people make the aforementioned claims, they express their doubts about OJ’s innocence or their husband’s fidelity. A person who was very sure that OJ was guilty would thus say, “it is impossible that OJ Simpson did not commit murder.” This is epistemic possibility, and the associated modality is epistemic modality.

When philosophers say “possible”, however, they normally do not refer to epistemic possibility. Instead, they intend to refer to different ways the world could have been. So when a philosopher says “it is possible that OJ Simpson committed murder,” they mean that the world could have been such that OJ Simpson committed murder. The notion of “possible worlds” should help elucidate this distinction. A possible world represents a way the world could have been, given certain specified restrictions (conceptual, metaphysical, and physical restrictions, as discussed below). So in one possible world Yuno presides as President, in another Sanakan reigns as queen, etc. A distinct possible world holds for each different way things could have been. This does not imply that multiple worlds actually exist (*cough* David Lewis *cough*). Instead philosophers use possible worlds as a mental tool for analyzing the notion of possibility. Furthermore, “world” in this context does not just refer to “Earth;” it instead refers to the total description of everything going on. So a proposition is possibly true iff [“iff”  =  “if and only if”, a.k.a.:  “↔”] it is true in at least one possible world, necessarily true iff it is true in every possible world, contingently true iff it is true in at least one possible world but not true in every possible world, impossible iff there is no possible world where it is true, and actually true if it is true in our world (i.e. the actual world). The same holds for a being’s existence or any other description in which a modal term such as “possible” appears. For instance, God is possibly existent iff there is a possible world where God exists (WARNING: do not read this as claiming another world actually exists and this world contains an existent God. We are not Lewis-ians; only one world actually exists and that is the world we currently inhabit. Instead, this should be read as saying: “we can describe another way the world could have been such that, if that description were actual, then God would actually exist.” The same holds for any other possible world statements.), necessarily existent iff God exists in every possible world,…

Philosophers further distinguish between logical possibility, metaphysical possibility (or broadly logical possibility), and physical possibility. Logical possibility (and logical modality in general) relates to conceptual truths. Conceptual truths are analytic truths or truths regarding meaning. Synthetic truths are non-analytic truths. For instance, in the conceptual system represented by the English language, the concept “bachelor” means the same thing as the concept “unmarried male” and thus “a bachelor is an unmarried male” is a conceptual truth of English. Logical inference rules (such as modus ponens in propositional logic) serve as the conceptual truths of each logical formalism [I will elaborate more on this in section II-A-1-a], while other conceptual systems have their own conceptual truths. The term “logic” can be thus used in a wide or narrow sense. In a wide sense, logic refers to logical modality, logically possible worlds, etc.; i.e. logic serves as a place holder for all conceptual truths. People refer to this wide usage of logic when they make claims such as “the notion of a married bachelor is logically contradictory.” "Bachelor" conceptually entails "not married", so the notion of a "married bachelor" is self-contradictory (i.e. it states "A and not-A"). Alternatively, logic in a narrow sense refers to particular logical formalisms such as propositional logic, S5 modal logic. etc. These formalisms represent just one genus in the family “conceptual systems.” Many philosophers also interpret mathematical truths as conceptual truths regarding different concepts such real numbers, natural numbers, etc. and thus mathematics also falls under the domain of logical modality. A logically possible world is thus a world where no conceptual truths are violated. So there are no logically possible worlds where 2 + 2 = 5, married bachelors and round squares exist, or “If A, then B” holds while “If not-B, then not-A” fails to hold.

Physical possibility (and physical modality in general) relates to the laws of physics (or laws of nature). So when I say “it is physically impossible for a human being with a certain bone structure to fly with wings of a certain structure”, I am saying that the laws of physics prevent this. A physically possible world is thus a world where none of the laws of physics are violated. So there are no physically possible worlds where something travels faster than the speed of light; even though faster than light travel is a coherent notion and thus holds in at least one logically possible world.

Finally, metaphysical/broadly logical possibility (and metaphysical modality in general) relates to ways the world could have been. The restriction here is not conceptual or physical. It instead simply relates to what could have been or what could have been actualized. This goes back to my discussion from three paragraphs ago on OJ’s innocence. To say that “there is a metaphysically possible world where OJ murdered” is to say we can describe a way the world could have been such that OJ murdered. Many novice proponents of the modal OA confuse logical possibility with metaphysical possibility. They therefore believe that if they prove the conceptual coherence of God, they have established the metaphysical possibility of God. But this deduction fails. Metaphysical possibility plausibly entails logical possibility, but the reverse entailment does not hold. Even most philosophers who run the modal OA accept this.

For instance, James F. Sennett states that for Plantinga’s OA: “A proposition is possible in the broadly logical sense just in case its denial is not a necessary truth. Plantinga adopts the notion of broadly logical modality to allow for the necessity of propositions that are neither truths of logic nor mathematics, nor the denials of the truths of logic or mathematics (Plantinga, 23).” Plantinga employs broadly logical, not logical, modality in his modal OA (Plantinga, 53). William Lane Craig builds on this claim as follows: “Plantinga points out that broadly logical possibility cannot plausibly be defined in terms of a proposition's freedom from inconsistency in first-order logic…Broadly logical possibility/necessity is therefore frequently identified with metaphysical possibility/necessity. A state of affairs which is strictly logically possible may, in fact, be metaphysically impossible, incapable of being instantiated (Craig, “Graham Oppy on…”).”

{Of course Craig, unlike Plantinga, is not above being two-faced and disingenuous: “As for the atheist’s retort that it’s not self-contradictory to say, ‘God does not exist,’ this is irrelevant because the argument is framed in terms of broadly logical possibility/necessity, not narrowly or strictly logical possibility/necessity…The atheist has to maintain that the idea of maximal greatness is broadly logically incoherent, like the idea of a married bachelor. But the idea of maximal greatness seems perfectly coherent and therefore possible—which entails that maximal greatness is exemplified! (Craig, “Does the…?”).” But Dr. Craig, I thought the argument related to metaphysical modality, not coherence? And what is this monstrosity you call “broadly logically incoherent;” since when has metaphysical possibility had anything to do with coherence?! When has ANY philosopher argued for such a notion without reducing metaphysical possibility to logical possibility (as Chalmers 1996, chapter 2 suggests). For instance, David Chalmers (1999) writes that, "of course, I hold that conceptual possibility = logical possibility = metaphysical possibility (at the level of worlds). But when we are discussing a potential distinction between conceptual and metaphysical possibility, 'logical possibility' always goes with the former and not with the latter."

On this view, broad logical modality just is logical modality and conceptual possibility (i.e. coherence) suffices for broad logical possibility. But then, of course, the atheist easily rebuts the modal OA; denying God’s existence is not logically contradictory [Craig admits as much in the above quote] and so God is not logically necessary (see section III-B).  Thus if theists included broad logically necessary existence in their definition of God, God's existence would be broadly logically impossible . But if Craig instead chooses to distinguish broad logical modality from logical modality, then, as Chalmers argues, coherence goes with the latter, not the former. This is elementary modal metaphysics and Craig should know this. So Craig engages in pure double-speak: if a modally-informed atheist philosopher claims God can be denied without contradiction and is thus not logically necessary, Craig will cynically shift to broadly logical modality to avoid the charge. And when he wants to establish God’s possibility in front of a less philosophically-astute audience, he’ll shift right back to coherence/logical modality without batting an eye. Intellectual honesty be damned! I simply do not know why some atheists treat Craig as if he is an well-intentioned seeker of the truth.}

However, Plantinga, in his early writings from 1964, expresses hesitancy over how God’s necessity should be characterized in relation to synthetic necessary propositions; i.e. metaphysically necessary truths which fail to be logically necessary:

“It is in virtue of that difference, I suggest, that non-contradictory existential statements are all synthetic. It follows, then, that ‘God exists’ is not analytic…Is the assertion that God exists necessary in the way that such propositions are said to be? Surely not. For the distinguishing characteristic of synthetic necessary propositions [emphasis added], as explained by their defenders, is that their denials, while logically quite consistent, are nonetheless inconceivable. And the best evidence that ‘God exists’ does not enjoy this characteristic is just that reasonable and intelligent people do in fact conceive of its denial. This answer would be inappropriate to the suggestion that the proposition is analytic, for reasonable people do sometimes appear to hold beliefs revealed contradictory by subsequent investigation…Hence, the claim that ‘God exists’ is a synthetic necessary proposition is implausible (Plantinga, 219-220).”

Nevertheless, in his later work Plantinga argues that God is metaphysically necessary (see section I-C); though he still maintains that God is not logically necessary.

I-B-2.  Logical and Broadly Logical: Do not confuse them

So what convinced most philosophers that logical possibility (or coherence) fails to entail metaphysical possibility? Two words: Saul Kripke.

Saul Kripke, in Naming and Necessity, argued for non-conceptual, a posteriori, synthetic necessary truths (Kripke). We can first apply a Fregean sense/reference distinction to Kripke’s argument, where “sense” relates to a concept’s meaning while “reference” relates to what matches the concept’s description, both in this world and other possible worlds. For instance, one should distinguish between the meaning of the concept “cat” and the real-world entities to which the concept refers (i.e. my cat, your cat, the lion at the zoo, etc.). Kripke might disagree with such a distinction, but I am not Kripke. The “sense/referent” and “meaning/entity” distinctions parallel the “concept/property” distinction.

Prior to Kripke, and certainly since Frege, philosophers recognized that two concepts can refer to the same entity. For example: take the concepts “Superman” and “Clark Kent.” Both of these concepts refer to the same entity in the world. But this is not a conceptual truth. Contrast “Superman is Clark Kent” with “bachelors are unmarried males.” The latter is a conceptual truth while the former is not. So Lois Lane can believe “Superman can fly” without believing that “Clark Kent can fly,” while still competently understanding the concepts “Clark Kent” and “Superman.” Thus we can correctly use two different concepts to refer to the same thing. Kripke built on this claim in a novel way.

According to Kripke, certain defined concepts refer to the same thing in every possible world and thus rigidly designate (Kripke, 424). For example, we could use the term “water” to refer to “the substance flowing in our lakes and streams and taps, etc.” We then perform a posteriori, scientific investigations to determine this liquid is H₂O. In other possible worlds, the substance flowing in the lakes and streams and taps could have the chemical structure XYZ. But our term “water” does not refer to those liquids XYZ. It instead refers to the liquid H₂O in our world. In fact, in every possible world our term “water” refers to the liquid H₂O in our world; “water” rigidly designates in this way. So if, unknown to me, someone transported me to a physical duplicate of the Earth where the only difference was that the clear liquid in the lakes and streams and taps was XYZ, my term “water” would not refer to XYZ; “water” would still refer to the H₂O of our world (see Hilary Putnam’s “Twin Earth” thought experiment). Water and H₂O refer the same entity in every possible world and thus are identical entities/properties. This is not an analytic, conceptually determined truth since no conceptual truths link the concept “water” to the scientific concept “H₂O”. Thus people who employed the concept “water” before our discovery that water was H₂O were not conceptually confused. The concept “water” had a pre-scientific meaning that had nothing to do with the scientific concept “H₂O” (Pigden, 426). So the two concepts do not share the same sense. “Water = H₂O” is a truth about reference, not sense and we determined the identity relation via a posteriori, empirical means. Thus no metaphysically possible world exists such that the entity known as water is not the entity known as H₂O, even though “water is H₂O” fails to be a conceptual truth. Though the statement “water is not H₂O” is not self-contradictory and therefore is logically possible, it is metaphysically impossible given the way water rigidly designates.

Other philosophers have also offered examples of metaphysically necessary truths which are not logically necessary. For example: “Some philosophers hold that propositions expressing the incompatibility of certain colors, or the relational properties of certain tones, or certain spatial and temporal relations are necessary though not analytic. The proposition, ‘Nothing can be green and red all over at the same time,’ e.g. is something said to be both synthetic and necessary (Plantinga, 219-220).”

So logical possibility (or coherence) does not suffice for metaphysical possibility. Equivalently, one can show that a given concept C lacks a referent in any metaphysically possible world (and thus its instantiation is metaphysically impossible) without having to show that C is incoherent. Novice proponents of the modal OA often ignore this point and say atheists must show that God is incoherent in order to rebut the modal OA, even though Plantinga and Craig (both proponents of the modal OA) explicitly warn against placing this burden on the atheist (or at least Craig does when he is among other philosophers and thus cannot afford to engage in double-speak; see the end of section I-B-1). With this distinction out of the way, I will now describe two versions of the modal OA: one based on logical necessity and the other based on metaphysical necessity.

I-C. Modal Ontological Arguments; everything comes in pairs

Norman Malcolm advocates an OA based on logical necessity (henceforth known as the logical OA). Malcolm’s employs complex reasoning and provides detailed arguments to support his premises [for brief commentary, see the videos “Norman Malcolm's Ontological argument debunked” (Youtube, AgnosticAntiTheist)  and “Once more on the Ontological argument” (Youtube, migkillertwo); for a more detailed presentation, see Reitan or Maydole, 572-573]. However, the bare essentials of Malcolm’s argument are as follows:

p1   :   Either God’s existence is logically necessary or God’s existence is logically impossible.

p2   :   If it is not the case that X’s existence is self-contradictory, it is not the case that X’s existence is logically impossible.

(truism regarding self-contradiction and logical impossibility)

p3   :   It is not the case that God’s existence is self-contradictory.

c1   :   It is not the case that God’s existence is logically impossible.

(from p2 and p3)

c2   :   God’s existence is logically necessary.

(from p1 and c1)

p4   :   If X’s existence is logically necessary, then X’s existence is actual.

(theorem of logic involving logical modalities)

c3   :   God’s existence is actual (i.e. God exists).

(from c2 and p4)

While Malcolm offers an OA based on logical modality, Alvin Plantinga advocates a modal OA based on metaphysical modality (henceforth known as the metaphysical OA). The argument can be summarized as follows:

Definitions: A maximally excellent being (MEB) is omnipotent, omniscient, and morally perfect (i.e. omnibenevolent).

A maximally great being (MGB) is maximally excellent in every metaphysically possible world and exists in every metaphysically possible world (i.e. is a necessarily existent [NE] MEB) (Plantinga, 67).

P1   :   Maximal greatness (MG) is instantiated in a metaphysically possible world.

P2   :   If MG is instantiated in a metaphysically possible world, then MG is instantiated in every metaphysically possible world.

(theorem of S5 modal logic involving metaphysical modalities)

C1   :   MG is instantiated in every metaphysically possible world.

(from P1 and P2).

P3   :   If MG is instantiated in every metaphysically possible world, then MG is instantiated in the actual world.

(theorem of S5 modal logic involving metaphysical modalities).

C2   :   MG is instantiated in the actual world.

(from C1 and P3).

One can convert Plantinga’s argument into a logical OA by shifting all the metaphysical modalities (i.e. all mentions of “metaphysically possible”, the NE in the MG, etc.) into logical modalities; though, to my knowledge, Plantinga never advocates this logical version of the argument.

At this point, some novice proponents of the modal OA might feel tempted to mix modalities. For instance, some theists will try to support P1 by showing that a metaphysically necessary God is coherent and thus logically possible. But such ad hoc modal mixing runs into an immediate problem: the argument becomes invalid. S5 modal logic deals with metaphysical, not logical, modality. The modal inference rules in P2 and P3 only work when one keeps the modal system constant without shifting from logical modality to metaphysical modality or vice versa. The theist might alternatively mix modalities by saying MG involves logically NE, while P1 involves metaphysical possibility. This move also runs into the same “modal system” flaw I just mentioned. Furthermore, the resulting argument just reduces to Plantinga’s metaphysical OA since logical necessity implies metaphysical necessity and thus MG involving logically NE entails MG involving metaphysically NE. The failure of the metaphysical OA would thus entail the failure of this modified argument. So modal OA proponents should not invalidly mix modalities and should instead pick either logical or metaphysical modality and stick to that choice throughout their argument.

In section II, I will provide a detailed rebuttal of Plantinga’s metaphysical OA and OAs in general before shifting, in section III, to a briefer rebuttal of Malcolm’s logical OA and the logical version of Plantinga’s OA.

II. The Collapse of the Metaphysical OA

II-A-1-a. The Meaning of Modal Statements, or “insulting two brilliant mangakas…like a boss”­­­

[Rayndeon, on his own, has argued for some of the conclusions I discuss in section I-A-1-a and I-A-1-b. However, we both arrived at our conclusions independently and thus any mistakes in these sub-sections should be attributed to me and not Rayndeon]

The meaning of modal term/statements in modal logic is given by possible world semantics, i.e. the truth values of modal statements/terms in different possible worlds. Truth value tables similarly provide the meaning of the logical operators used in propositional logic. For instance, the meaning of the logical operator “and” or “˄” is exhausted by the following claims:

“A ˄ B” is true if “A is true, B is true”

It is false if: “A is true, B is false” or “A is false, B is true” or “A is false, B is false”

Logicians make similar truth value tables to define the meaning of logical operators such as the material conditional (“If A then B”), the material bi-conditional (“If A then B, and if B then A” or, more simply, “A iff B”), etc. In section I-B-1, I explained how possible world semantics similarly provides the meaning for modal terms such as “possible,” “contingent,” etc. (and the concepts in which they appear such as “possibly existent,” “necessarily true,” etc.) by assigning truth values across possible worlds. Therefore, if two modal statements have the same truth values in every possible world, then, via possible world semantics, they mean the same thing [note that I said “modal statements”, not statements of any sort: modal logic provides the meaning for modal terms, not all terms, so no conflict exists between my claims here and the metaphysically necessary Kripkean truths I discussed in section I-B-2]. Furthermore, if two modal statements are logically equivalent under modal logic, then they have the same truth values in every possible world and thus mean the same thing. The logical inference rules of modal logic thus serve as modal logic’s conceptual truths. This might be easier to see with an example.

Suppose I try to convince Urasawa that Mohiro is an unmarried male, when Urasawa believes Mohiro is not an unmarried male. I use the following argument:

A1   :   Mohiro is a bachelor

A2   :   If Mohiro is a bachelor, then Mohiro is an unmarried male.

A3   :   Mohiro is an unmarried male

(from A1 and A2)

A2 follows from the meaning of the concept “bachelor” and is thus a conceptual truth. Conceptual truths divide into one-way truths or two-way truths. One-way conceptual truths link two non-equivalent concepts or statements. For example, “a bachelor is a male” is one-way conceptual truth since “bachelor” and “male” are not equivalent; the entailment only goes in one direction from “bachelor” to “male”, not from “male” to “bachelor.” Two-way conceptual truths link semantically equivalent concepts or statements. For example, the entailment between “bachelor” and “unmarried male” is two-way since one concept entails the other and vice versa. Similarly, the inference rules of a given logical system (ex: propositional logic, S5 modal logic, etc.) can be one-way or two-way. Logical conditionals (“If A then B”) serve as the one-way conceptual truths of a given logical system, while bi-conditionals (“A iff B”) serve as the two-way conceptual truths. A bi-conditional links modal statement A to modal statement B iff A can be logically derived from B and vice versa. If a modal bi-conditional links modal statements A and B, then A and B have precisely the same truth values across all possible worlds and thus mean the same thing in modal logic. This parallels the “Mohiro is an unmarried male” and “Mohiro is a bachelor” case: the statements mean the same thing due to the two-way conceptual truths linking them. In Plantinga’s argument, modal statements P1, C1, and C2 are logically equivalent (Alighieri; Rayndeon, section §III; readers unfamiliar with modal logic should follow along with the thought experiment in section II-C-1 to get the intuitive idea behind the formal proof for the equivalence of P1, C1, and C2) and thus, under the semantics of modal logic, mean the same thing. As in the “Mohiro is a bachelor” and “Mohiro is an unmarried male” example, P1, C1, and C2 are thus just different ways of saying the same thing.

At first glance, my argument appears to leave a loophole: the theist could reply that Kripkean truths rebut my account of synonymous modal statements. For example: “It is possible that X is water” and “It is possible that X is H₂O” are modal statements with the same truth values across all metaphysically possible worlds but which, by the arguments in section I-B-2, do not mean the same thing. I have at least three available responses. First, I could wade into the thorny issues over syntax/semantics, the sense/reference distinction, semantic internalism vs. externalism, etc. in order to develop a complete account of meaning such that logically equivalent statements mean the same thing. This would be a book-long project, so I will not delve into those matters here (thought I make a few suggestive points in section I-A of my paper on moral nihilism and moral arguments for God). Alternatively, I could opt for any one of the standard theories of meaning under which logically equivalent claims mean the same thing.

Second, I could say that meaning is determined by identical truth values across all logically, not just metaphysically, possible worlds. Since the two aforementioned Kripkean modal statements have the same truth values in every metaphysically possible world but not every logically possible world, they do not mean the same thing and thus do not serve as counterexamples to my analysis. Third, I could note that the Kripkean counterexample does not parallel P1, C1, and C2 of the metaphysical OA and therefore does not serve as a defense of the OA. The counterexample involves a shift from the concept “water” to the concept “H₂O”, which explains the loss of logical necessity while metaphysical necessity is kept intact. However, the modal OA sticks with the concept “MG” in P1, C1, and C2, and thus has no such conceptual shift by which P1, C1, and C2 could be said to have identical truth values in every metaphysically possible world, but not every logically possible world. So the Kripkean counterexamples do nothing to defend the modal OA from the charge that P1, C1, and C2 mean the same thing.

When I say P1, C1, and C2 are equivalent under modal logic, I mean those three modal statements are equivalent in the same way that P → Q (“If P then Q”) and ~Q → ~P (“If not-Q then not-P”) are equivalent under propositional logic. To put this into the symbolism of S5 modal logic, for any X (regardless of whether X is a chipmunk, my brother Tenzen Yakushiji, or the MEB), the following three modal claims are logically equivalent (Alighieri) and therefore mean the same thing [  ◊  :  possible,    □  :  necessary; note:  if X = MEB,  then  □X = MGB]:­

◊□X   [P1 of the OA]

□□X   [C1 of the OA]

actual□X   [C2 of the OA]

And if the OA proponent wishes to throw in an unnecessary de re / de dicto distinction (see section II-A-2; Craig, “Does the…?”), then the following modal statements are logically equivalent and thus mean the same thing [the same equivalence holds if MG is replaced with any description which includes NE]:

◊MG   [P1 of the OA]

□MG   [C1 of the OA]

actual MG   [C2 of the OA]

Note that I am not saying “NE” and “MG” are equivalent or mean the same thing; for some reason, numerous Youtube defenders of the modal OA fall into this misunderstanding. In fact, I will explicitly deny this equivalence in section II-B-2. Instead I claim that the premise and conclusion of the modal OA mean the same thing, just as the premise and conclusion of my Mohiro argument mean the same thing, since the premise and conclusion are linked by a two-way conceptual truth. To reiterate: two statements have the same meaning iff a two-way conceptual truth links the statements. Two concepts mean the same thing iff a two-way conceptual truth links the concepts.

II-A-1-b. Uninformative Question-begging, or “death-defying Socrates: enemy of the OA and feminism”­­­

Furthermore, two logically equivalent statements presuppose the truth of one another in the following way:

proposition U presupposes V iff W is a conceptual truth where W is: “U is true only if V is true” 
[this is logically equivalent to both: “if V is false, then U is false” or “if U is true, then V is true”]

Given that premises P2 and P3 are just truths of S5 modal logic, they can be vacuously/tautologously deduced from any modal claim made in S5 modal logic (Pigden, 424) and are therefore presupposed by P1, C1, and C2. Moreover, given the logical equivalence of P1, C1, and C2, all three propositions presuppose one another. Positive atheists, by definition, deny C2 while negative atheists think that belief in C2 is unjustified.

{Sidenote: Positive atheists believe that God does not exist. Negative atheists have heard about God, but they lack belief in God. Normally, negative atheists think that God's existence lacks sufficient evidence, but they do not actively believe that God does not exist; otherwise they would be positive atheists. A real-world analogy might help:

Suppose the Governing Authority tells me that Killy cannot die. Based on my past experience with human and machine life, I could actively disbelieve this claim; i.e. I could believe that Killy can die. This is analogous to positive atheism. Conversely, I could ask the Governing Authority provide evidence for its claim. I could then critique the Authority's evidence and thus show we lack sufficient evidence for believing that Killy cannot die. This, however, would not imply that I actually believe Killy can die. I simply analyzed the evidence, found it wanting, and thus did not believe in Killy's immortality. This often occurs in daily life. We encounter people making strange, novel claims and ask them for their evidence. If they provide insufficient evidence, we do not accept their claim as true though we need not believe their claim is false.

Many theists claim that atheists invented the "positive/negative atheism" distinction in order to avoid providing evidence for their position. So if someone is an atheist, they must be a positive atheist and thus believe that God does not exist. Of course, these theists are incorrect. The "positive/negative atheism" is just one example of a commonly-accepted distinction between "disbelief" and "informed lack of belief."}

Since the non-logically-necessary premises P1 and C1 presuppose the truth of the conclusion C2, both P1 and C1 presuppose the necessary truth of theism. Thus the metaphysical OA begs the question against the atheist. One need not explicitly infer one’s premises from one’s conclusion in order to beg the question; that would be the different, but related, fallacy of circular reasoning. As long as at least one of your premises, on its own, presupposes the falsity of your opponent’s position or the truth of your conclusion, you begged the question. Moreover, one can beg the question in other ways besides having a premise semantically equivalent to one’s conclusion. For instance, if an atheist assumed (without a supporting argument) that the Bible is an evil fairy tale when debating a Christian over whether the Christian God exists, the atheist begged the question even though their assumption was not logically equivalent to saying God does not exist. The atheist begged the question since they asserted (without a supporting argument) something that only people who rejected Christianity would accept. So employing premises which logically presuppose your conclusion is just one of many ways to beg the question. Again, this might be easier to see with our Mohiro example.

My argument for convincing Urasawa that Mohiro is an unmarried male was as follows:

A1   :   Mohiro is a bachelor

A2   :   If Mohiro is a bachelor, then Mohiro is an unmarried male.

A3   :   Mohiro is an unmarried male.

(from A1 and A2)

This argument is question-begging because premise A1 presupposes the truth of the conclusion A3:  if A3 is false, then A1 is false. This is because just as A2 is a conceptual truth, the following is also a conceptual truth:

A2’   :   If it is not the case that Mohiro is an unmarried male, then it is not the case that Mohiro is a bachelor. 

The negation of A3, in conjunction with A2’, implies that A1 is false. So the premise A1 is acceptable only if the conclusion A3 is acceptable. Thus if Urasawa already understood the meaning of “bachelor” and “unmarried male”, he would immediately object that the argument begs the question. However, that does not make the argument uninformative. Conceptual/purely logical arguments often beg the question even when they reveal something interesting. For example, Urasawa might have already believed A1 without knowing A2 and thus failed to believe A3. After all, Urasawa may not know English’s conceptual truths very well and thus may not be English-competent. Moreover, many conceptual truths are unobvious (Joyce 2006, 149; Pigden, 427; Plantinga, 220), especially those in mathematics. Thus the Mohiro argument, even though it begs the question, could have revealed something new to Urasawa and provided him with an argument for A3. If, however, Urasawa already knew that A2 and A2’ were conceptual truths, then it would be both question-begging and uninformative to use A1 in an argument against him. As a rational person, if Urasawa knew A3 conceptually entailed A1 and denied A3, then he would deny A1 as well. A1 of my Mohiro argument would then just be uninformatively presupposing that Urasawa’s position was false (analogous to positive atheism) or assuming a premise he thinks is unjustified (analogous to negative atheism).

Similarly, just as theists would not be interested in an argument against God’s existence if one of the premises presupposed God’s non-existence, atheists would not be interested in an argument for God if one of the premises presupposed God’s existence. But Plantinga’s OA begs the question in precisely this way: P1 and C1 are true only if the MGB actually exists (i.e. only if C2 is true), P2 and P3 are just theorems of modal logic (analogous to A2 and A2’), and C2 entails the truth of both P1 and C1 (just as A3 entails A1). In fact, P1 of the OA not only presupposes the truth of theism (i.e. an MEB actually exists) but presupposes something much stronger: that theism is necessarily true; i.e. the MEB necessarily exists, so theism is correct in every metaphysically possible world. Or if God is defined as the MGB: that the MGB exists in every metaphysically possible world. No rational, modally-competent atheist who understands modal logic/what modal terms mean, while denying C2, is going to accept an argument for C2 when the argument’s core premises are logically equivalent to C2 (Oppy 2011, subsection 3 of section 4). So Plantinga’s metaphysical OA begs the question against the atheist and remains uninformative to the modally-competent atheist.

Unfortunately, most people fail to grasp modal logic; their expertise lies elsewhere. However, most educated people intuitively grasp the basic rules propositional logic and are thus propositionally-competent. So for most people, the following argument would be obviously question-begging and uninformative [thanks to the Youtuber MistyGothis for this example; Plantinga provides a similar example on page 71 of The Analytic Theist to address a similar point]:

P4   :   It is not the case that it is not the case that God exists. (~~G)

P5   :   If it is not the case that it is not the case that God exists, then God exists. (~~G → G)

C5   :   God exists. (G)

[from P4 and P5]

Almost no propositionally-competent person would be persuaded by this argument, unless they already accepted C5. This argument is not “logical proof” of God’s existence. P5 is just a rule of propositional logic which the arguer uses to deduce a conclusion from a premise which presupposes theism. Similarly, if P4 had been rephrased into saying “~~(God does not exist),” this would not be logical proof of atheism; the revised version of P4 would have then begged the question against theism. But once an atheist becomes modally-competent, they will view Plantinga’s modal OA in exactly the same way: as a question-begging logical deduction from a premise which presupposes theism. In fact, Plantinga’s argument is worse than the above argument, since P4 presupposes only the truth of theism, while Plantinga’s P1 presupposes the necessary truth of theism. I eagerly await the day when enough people learn the rules of modal logic so that modal OAs engender polite dismissal, as opposed to confusion, in people.

Contrast Plantinga’s argument with a standard example of a valid, non-question-begging argument:

E1   :   All men are mortal.

E2   :   Socrates is a man.

E3   :   Socrates is mortal.

[from E1 and E2]

This argument fails to beg the question since neither premise presupposes the truth of the conclusion: the conclusion could be false without conceptually entailing the falsity of either premise. In order for premise E1 to presuppose the conclusion, L1 would need to be a conceptual truth where:

L1   :    if it is not the case that Socrates is mortal, then it is not the case that all men are mortal.

And for premise E2 to presuppose the conclusion, L2 would need to be a conceptual truth where:

L2   :   if it is not the case that Socrates is mortal, then it is not the case that Socrates is a man.

For L1, a logically possible world exists where Socrates was an immortal alien (or immortal woman) feigning humanity (or feigning being a man [no feminists, that’s not what I meant!]), so it is logically possible for L1 to be false. For L2, a logically possible world holds where Socrates is an immortal man. Mortality results from physical facts concerning from physical laws, not logical laws; therefore there is nothing conceptually incoherent about a man who is born and never dies. Christian proponents of Genesis should know this. So it is logically possible that Socrates was an immortal man; his death may have been an illusion. Therefore, it is logically possible for L2 to be false. Since it is logically possible for L1 and L2 to be false, neither are conceptual truths. So as with all valid, non-question-begging arguments, the premises of the Socrates argument do not presuppose the conclusion. Plantinga’s argument fails this presupposition test and therefore begs the question.

Also notice that we can restate the Socrates argument as follows:

E1   :   All men are mortal.

E2   :   Socrates is a man.

E’   :   If all Bs are D and X is a B, then X is D

E3   :   Socrates is mortal.

[from E1 and E2]

We can thus explicitly state the logical rules involved in our syllogisms, giving us two non-logically-necessary premises and one conceptual premise. As I previously noted, statements such as E’ represent the conceptual truths of logic or the statements which give the logical operators their meaning. E’ is a thus conceptual truth of Aristotlean logic or predicate logic. We normally leave out premises such as E’ and simply assume them implicitly. However, Plantinga’s metaphysical OA does not follow this standard, informal rule of reasoning. Instead Plantinga explicitly states his logical truths (P2 and P3) as premises, leaving P1 as his only non-logically-necessary premise (P1 is logically equivalent to C1 and C1 is explicitly derived from P1, so C1 does not count as an additional independent premise). This gives the argument a false veneer of support since, at first glance, it appears to be employing multiple interesting premises. Unfortunately, this illusion needs to be stripped away. In the Socrates case, as with all non-question-begging arguments, when we strip away the conceptual inference rules known by and already accepted by the arguer's audience, an informative argument remains. But what happens when we strip away the inference rules from Plantinga’s argument? What remains is:

P1   :   MG is instantiated in a metaphysically possible world

(a rephrasing of C1 and C2).

C1   :   MG is instantiated in every metaphysically possible world

(a rephrasing of P1 and C2; explicitly derived from P1).

C2   :   MG is instantiated in the actual world.

(a rephrasing of P1 and C1; explicitly derived from C1)

Look upon Plantinga’s metaphysical OA in all its glory: three statements which mean the same thing! If a rational atheist knows the rules of modal logic and thus knows that P1, C1, and C2 mean the same thing (to reiterate: the meaning of modal terms is encapsulated by their truth values in different possible worlds and the inference rules which serve as the conceptual truths of the modal system), then the atheist will treat the metaphysical OA as uninformative and question-begging; if Urasawa already knew what “bachelor” meant, he would give a similar reply to my Mohiro argument. Thus, once one strips the veneer from the metaphysical OA, Plantinga’s argument is both question-begging and uninformative.

II-A-2. The OA’s Structural Flaw, or “‘logical obfuscation’ for 1000, Alex”

[This section was inspired by discussions with MistyGothis on Youtube]

Most, if not all, OAs have the following form:

P   :   Non-logically necessary premise(s)

L   :   Reasoning involving conceptual truths (usually those of a particular logical system)

C   :   Conclusion

This argument has at least four forms, depending on whether P contains conceptual claims or existence claims and on whether C is a conceptual or existence claim. A conceptual claim discusses concepts and says nothing about what exists (see the latter half of section III-C for the distinction). For example: “the concept ‘cat’ is coherent.” An existence claim discusses what exists. For instance: “cats actually exist.” OA proponents want to conclude that God actually exists, so in their OA, C will be an existence claim, while P will be a conceptual or existence claim. But now the core problem emerges: many modal OA proponents misidentify what counts as an existence claim. Take MistyGothis’s argument from section II-A-1-b:

P4   :   It is not the case that it is not the case that God exists.

L4   :   If it is not the case that it is not the case that God exists, then God exists.

C5   :   God exists.

Does P4 count as a conceptual claim simply because it does not explicitly state God exists? No. P4 is an existence claim, not a conceptual claim. And since P4 is an existence claim, P4 presupposes the existence of God (see section II-A-1-b) and thus the argument begs the question. This reflects a general philosophical principle: one does not use logical/conceptual deduction to non-tautologously derive existence claims solely from conceptual claims. I block theistic attempts at such deductions in the latter half of section III-C and in my discussion of logical possibility’s (or conceptual coherence’s) failure to entail metaphysical possibility (sections I-B-2 and I-C). This results in a dilemma for modal OAs: if P merely contains conceptual claims, the theist cannot employ logical deduction alone to infer that God exists. Conversely, if P contains an existence claim, P presupposes the truth of theism and thus begs the question. So OAs that employ only logic to derive existence claims from a non-logically-necessary premise either beg the question or are formally invalid.

If one can non-vacuously derive an existence claim from premise P using logic alone, then P is an existence claim. A given person will have more difficulty recognizing P as an existence claim if: a) L’s logic or P’s phrasing is especially arcane and/or, b) the person lacks the logical competence to adequately analyze P or L. For instance, propositionally-competent people (see section II-A-1-b) will immediately recognize P4 of MistyGothis’s argument as an existence claim; L4’s logic and P4’s phrasing is not complex enough to hide this fact. So the modal OA proponent shifts to S5 modal logic to increase the complexity of L and modify P1 such that P1 is not instantly recognized as an existence claim. But then modally-competent atheists recognize P1 is an existence claim and thus note the argument begs the question.

So some modal OA proponents then include even more arcane logic in order to prevent modally-competent atheists from recognizing P as an existence claim and thus realizing the OA is question-begging. For instance, some modal OA proponents throw in the second-order logic of Gödel (Oppy 2011, section 6; Maydole 2009), Barcan’s Formula [see section II-B-4-a-i], a de re / de dicto distinction (Craig, “Does the…?”), etc. The de re / de dicto distinction deserves special mention  since it artificially modifies the metaphysical OA in a way Plantinga never attended, solely in an attempt to further disguise the question-begging nature of P1. So the de re / de dicto distinction is an unnecessary addition to the modal OA (Alighieri). Ironically, many people who use this distinction to defend Plantinga’s OA against the charge of question-begging simultaneously accept Barcan’s Formula, even though the formula negates the de re / de dicto defense.

[Technical sidenote: If Craig's uses the de re / dicto distinction to defend against the charge that P1, C1, and C2 mean the same thing, then Craig may be stuck advocating at least one of two implausible positions: semantic infallibilism and the denial of synonymity. On the former view, it is not possible to make mistakes regarding meaning. For instance, if Urasawa denied that the concept "bachelor" meant the same thing as the concept "unmarried male," then Urasawa would not and could not be wrong. On the latter view, synonymity never obtains: no two concepts ever mean the same thing. This may also imply that no one-way conceptual truths hold between concepts. However, I will not fully argue for this conclusion until Craig explains how the de re / de dicto distinction shows the P1, C1, and C2 may be logically equivalent without being semantically equivalent. Unlike Craig, I do not pretend my opposition needs to adhere to an erected strawman (ex: all atheists being committed evolutionary naturalists, being committed to life lacking meaning since the universe will end in either a Big Crunch or heat death, etc.) (7/29/12)]

The OA proponent’s additional layers of logical artifice do not change the fact that if P [non-vacuously or non-tautologously; Pigden, 424] logically entails an existence claim, P is an existence claim. It just means that one has to become more logically-competent in order to automatically recognize P as an existence claim. Thus atheists with sufficient logical-competence will view OA’s with arcane logic as uninformative, in much the same way that most people would view MistyGothis’s argument as uninformative.  Similarly, if the revised version of P still presupposes the (necessary) truth of theism (see section II-A-1-b), then the resulting OA begs the question, regardless of the amount of arcane logic employed.

II-A-3. The OA’s Proper Role, or “winning isn’t everything”

So I have explained how modally-competent atheists will respond to Plantinga’s OA. What about modally-uninformed people? Modal logic is, in a deep sense, almost like another language (see sections I-B-1, II-A-1-a and II-A-2). And as with any other language, most people take awhile to grasp its nuances. Just as one learns that “unmarried male” means the same thing as “bachelor” in English, people new to S5 modal logic soon learn that “possibly necessary X” means the same thing as “necessary X”, “necessary necessary X”, and “actual necessary X” (Alighieri). If the modal OA proponent includes more arcane logic (ex: an unnecessary de re / de dicto distinction), the atheist simply needs to learn more logic until they recognize that premise of the revised OA means the same thing as the conclusion.

If someone did not understand modal logic well enough to know that P1, C1, and C2 meant the same thing, then theists should not be using the modal OA on that person until they explained S5 modal logic to them. The theist should not simply tell the person what an MGB means, while leaving out what modal necessity means and leaving out how any metaphysically possible description that includes modal metaphysical necessity would either be metaphysically necessary or metaphysically impossible or how the entire argument turns solely on NE (as discussed in section II-B-1). To do otherwise would be deceptive, since the addressee would lack the knowledge necessary to engage in an informed analysis of the argument. Hence my advice in section I-A to people new to modal logic.

{Of course, William Lane Craig is a master at deception and obfuscation (see: section I-B-1, section II-A-2, section II-D, and Youtube: TheoreticalBullshit’s “William Lane Craig is Not Doing Himself Any Favors,” ProfMTH’s “William Lane Craig Is Not a Constitutional Scholar,” SisyphusRedeemed’s “William Lane Craig is not the Lucasian Chair of Mathematics,” etc.). But that’s neither here nor there.}

For instance, imagine an atheist argued that the Bible is immoral with a Christian who was, due to their social context, illiterate. Before presenting their argument, a responsible atheist would first need to teach the Christian to read or find some way to get them easy access to the Bible’s contents. Then the atheist would need to make sure the Christian understood the Bible’s contents and had time to reflect on it. After all that, then the atheist could present their argument. The same principle holds for advocates of the OA: theists should not use the argument on people who do not understand modal logic. As TheoreticalBullshit discusses in the context of the transcendental argument for God (Youtube, “The Matt/Matt Debate - Part 1: Introduction”), the OA confuses [but rarely persuades] people who do not understand it. But once atheists understand modal logic and thus the meaning of the modal terms within the argument, I doubt they will find the argument convincing or informative. Theists should not find the argument convincing either, unless they prefer arguments that involve presupposing that theism is necessarily true.

So if the OA begs the question and fails to inform, how should we interpret its role in the atheist/theism debate? Well, once we note that P1 just rephrases the conclusion “the MGB necessarily exists,” we can then see that the OA has no real argumentative force. The metaphysical OA thus pales in comparison to the following atheistic “argument”:

Definition: “God” is the creator of this universe

G1   :   If God exists, then God is evil.

G2   :   If X is evil, then X is not good

G3   :   If God exists, then God is not good

(from G1 and G2)

The conclusion denies the theistic claim that God is omnibenevolent. Thus we have an argument against theism. However, the real debate took place in the argument for the G1. Atheists (well, responsible atheists; by which I mean atheists who are not presuppositionalists) should not treat the argument from “God is evil” to “God is not good” as some additional argument against theism. The argument simply performs a semantic deduction after all the real argumentative work has already been done. Similarly, the metaphysical OA just engages in irrelevant logical wordplay. The real question is whether we have any reason to accept P1. In fact, the “God is evil” argument does more argumentative work than the OA since G3 is not logically equivalent to the argument’s only non-logically-necessary premise G1: it is not a conceptual truth that “if God is not good, then God is evil.” This is because it is logically possible for a being to be amoral via lacking moral responsibility or agency, engaging in only morally neutral thoughts or actions such as breathing, or some other means; see section II-B-3-b. God could be amoral and thus be neither good nor evil, which would make G3 true and G1 false. So G3 does not entail G1, which means G3 is not logically equivalent to G1. Contrast this with the metaphysical OA, where the conclusion C2 is logically equivalent to the both non-logically-necessary premises P1 and C1.

Some theists try to offer arguments in favor of P1 in the hopes of using the modal OA in a cumulative case for God. For example, see the last ninety seconds of “Ontological argument” (Youtube) where telemantros defends P1 via Craig’s Kalam cosmological argument. But these theists: 1) do not actually provide arguments for P1 since they usually provide arguments for the MEB’s actual existence, not the MGB’s actual existence [see section II-D] and, 2) miss the point: once one has an argument for P1, the OA is irrelevant wordplay. It is analogous to arguing that “Mohiro is bachelor” when you have already shown that is “Mohiro is an unmarried male” and your opponent is fluent in English. And as I already mentioned, P1 not only presupposes the truth of theism, but presupposes the necessary truth of theism. So why would any atheist take seriously an argument which includes P1 as premise?

The OA does not provide an additional piece of evidence for God’s existence. It instead just deduces God’s existence from an uninformative premise which already presupposes the strongest possible form of theism. So theists might as well just use Kalam or some other argument to directly demonstrate the MEB’s existence rather than tack the OA to the end while thinking they have provided an additional argument for God. I doubt theists will take my advice for reasons I discuss in section IV.

II-B-1. Gaunilo-type Objections + the OA is Parasitic upon NE, or “everything under the Sun”

The metaphysical OA only requires necessary existence and nothing else. Furthermore, NE is solely sufficient for the OA to work (if the OA actually works). The metaphysical OA takes the claim that an NEX (i.e. a being X that is metaphysically NE) is metaphysically possible and derives two conceptually equivalent conclusions, C1 and C2. The other properties of X are irrelevant, as long as those properties do not make the NEX metaphysically impossible. One can thus replace MG with any property or description one wants, as long as that description includes NE. For example, replace MG with maximally dangerous (MD). A MD being (MDB) is omnipotent, omniscient, omnimalevolent, and exists in every metaphysically possible world [note: Please do not get too attached to labels here. One can call the MDB whatever one wants as your description includes the features I listed]. Platonists supply another example of an NE entity: the number 7. Or take an NE unicorn (Rayndeon, section §IV). If theists wish to arbitrarily include necessary existence in their account of God, they should not complain if other people make the same move for their proposed being.

The OA proponent seems to include NE in the definition of God for no other reason then running an OA. I certainly do not see why NE is a great-making property, especially given how intentionally vague most OA proponents are about "greatness" or "perfection" or whatever other concept they use as a substitute for God's nature (see section II-B-3-a for more on this). Furthermore, as Rayndeon notes, "necessity is not imagined into existence or granted by fiat (section §IV)." You cannot just decide to include metaphysical NE in your account of being B and expect other people to take B seriously or believe the concept "NE B" has a referent in reality; you need an reason for including NE. 

{Most rational people only claim a thing T has a given property once they have evidence that T has that property, though some theists have not caught on to this trend. Since many theists lack evidence for God's traits, they use religious tradition and dogma to grant God properties by fiat (see section IV).}

Anyway, normally the the explanation for why B is metaphysically NE is either that B's non-existence is inconceivable (see Plantinga's quote in section I-B-1) or an absurdity results from denying B's existence (Rayndeon, section §III). Plantinga himself provides an example of a logically possible, but metaphysically impossible absurdity: being red and green all over at the same time (219-220). TheoreticalBullshit provides another way to show B is necessary: show that B is required for something else which we already know to be necessary (Youtube, "Random...Necessarily"). For example, one might argue that if abstracts objects are logically necessary and God is required for abstracts objects to exist, God must be logically necessary as well (see section III-C for more on this). However, if one does not provide evidence or an argument for including NE in one's description of B, one cannot just assert "by definition, B is metaphysically necessary" and expect to be taken seriously. Necessity is not granted by fiat (Rayndeon, section §IV).

Unfortunately, most novice OA proponents do not bother giving an explanation for why they included NE in their account of God; NE just magically became apart of the description of God once theists stumbled across  the idea of an OA. However, when OA proponents do attempt to justify their inclusion of NE in God's description, one of two things occurs: 1) their justification fails, and/or 2) their justification would work just as well for any number of beings. For 1, God's non-existence is conceivable (Plantinga admits as much in the quote from section I-B-1; I make a similar claim in section II-D), fails to result in any metaphysical absurdities, and for many possible worlds W, if W were actualized, God would not be required for anything in W. So inconceivability, entailed absurdities, and requirement do not serve as explanations for why God should be thought of as metaphysically NE. If OA proponents wish to claim otherwise, I expect an argument for that conclusion. What absurdity results from denying God's existence? Why can't there be possible worlds which, if actualized, would not contain anything which requires a God? Some OA proponents might argue that NE is a great-making property and thus can only be apart of the description of the maximally great being. I argue against this conclusion in the latter part of section II-B-2. In section II-B-4-b, I also show "God cannot come into or out of existence" and "God's description is coherent" cannot avoid 2.

So even if a theist can construct some ad hoc justification for including NE in their definition of God, that same justification could be used to include NE in the description of a multitude of other beings. And as long as the resulting being’s description includes metaphysically NE and is metaphysically possible, then Plantinga’s argument shows that the being in question actually exists. This is known as a Gaunilo-type objection and dates back to at least St. Anselm’s OA. Gaunilo argued that if the OA worked, it would prove the existence of things we know do not exist, such as perfect islands (Youtube, khanpadawan’s “21b Anselm's ontological arguments - objections to the Proslogion 2 argument”). Therefore the OA must be fallacious. I am updating Gaunilo’s objection and applying it to Plantinga’s metaphysical OA.

II-B-2. Reply to Theistic Rejoinders, or “apathy and tyranny”

In response to Gaunilo-type counterexamples (the MDB, the NE unicorn, etc.), some theists reply that the proposed beings lack the “credentials” of God: we lack sufficient reasons for thinking those beings exist, while we have reason for thinking that God exists. This is one variation on the idea I mentioned at the end of section II-A-3: some theists think they have evidence for P1 over other alternatives. But that response fails for the reasons I discussed in that section and further discuss in section II-D. Furthermore, many Gaunilo-type examples have better credentials than the MGB. Controversy persists over the actual existence of the MEB and thus the existence of the MGB. No such intense controversy persists over the existence of the universe, horses, some non-physical minds, etc. Some Platonists could even argue that there is less controversy over the existence of abstract objects than over the existence of the MEB. So if we have strong evidence for thinking abstract objects, horses, the universe, etc. actually exist while our evidence for the MEB’s existence is weaker and more controversial, then we are more sure of the metaphysically possibility of the former over the latter. So the credentials of the NE versions of these beings are at least as well supported, if not better supported, than the existence of the NE version of the MEB (i.e. the MGB).

This response becomes even more persuasive once we compare the MGB to other proposed creator minds. Suppose Kalam and the teleological argument both work (which they do not) and an omnipotent, omniscient, creator of the universe exists. The problem of evil and the problem of suffering immediately kick in: why would an omnibenevolent creator allow for the sorts of suffering and evil we observe? This can be coupled with the problem of non-belief [Youtube, DasAmericanAtheist’s “Nonbelief 2.0”; Youtube, TheoreticalBullshit’s “Nonbelief & Peek-A-Boo...” and “Nonbelief Revisited: The Ghost of Veritas48”]: why would an omnibenevolent creator who wanted a relationship with humanity provide such limited evidence of its existence? Theists have their standard replies, but most of those replies fail to make any sense. However, the problems of evil/suffering/non-belief evaporate once we deny that the creator is omnibenevolent. For instance, suppose a deistic God (call this creator deity Kengo Hanazawa, or “Kengo,” for short) created the universe and remains unconcerned with human suffering or the suffering of sentient life in general; though it remains fully aware of suffering due to its omniscience. Or suppose a creator (call it “Fran Madaraki” or “Fran,” for short) exists who plays favorites: the creator enjoys the company of a certain group of humans and destroys, confuses, hardens the hearts of, etc. any sentient or non-sentient entities that fight with those humans, even if the attacker’s response was justified. 

Both Fran and Kengo, plausibly, fail to be omnibenevolent. But both Kengo and Fran avoid the problems of evil/suffering/non-belief since we do not need to invent wildly implausible, ad hoc explanations for why these creators allow for such things while still having perfectly good plans nor do we need to resort to the time-honored theistic dodge of “the Lord works in mysterious ways.” Kengo allows for suffering/evil because Kengo does not care about sentient life; it has other, more pressing concerns. Kengo does not provide obvious evidence of its existence because it has no interest in a relationship with humans. Any supposed encounters with Kengo can be explained via the abundant evidence provided by religious psychology [Youtube, AntiCitizenX’s “Psychology of Belief” series; Youtube, KnownNoMore’s “Against Religious Experience (Why Religious Apologists Cannot Possibly Win - part 3)”; any basic textbook on religious psychology or anthropological studies of religion]. Fran, on the other hand, causes many of the good things that happen to people. It speaks with certain individuals, answers some prayers, inspired a holy book, etc. But Fran also has no interest in preventing evil from occurring to those it dislikes. In fact, Fran not only allows for suffering and evil, but causes some of it. And Fran only has an interest in interacting with some people. It arbitrarily chooses who to present evidence of its existence to: its choice has nothing to do with the moral character of the person chosen, how desperate that person’s situation is, how open that person is to the evidence, etc. So the nature of Fran and Kengo easily explains the suffering/evil/non-belief we observe in the world without recourse to the standard, ad hoc, and implausible explanations offered by most proponents of the MEB/MGB. So even if some of the standard arguments of natural theology work, there are creator deities whose existence is more likely than that of the MEB.

So why do most theists argue for a tri-omni God such as the MEB, but not Fran or Kengo? The answer should be obvious; but the full explanation lies beyond the scope of this paper. All I want to note here is that both Kengo and Fran avoid at least three plausible arguments against the existence of the MEB. Suppose we now include metaphysical NE in the descriptions of Fran and Kengo via whatever justification OA proponents use for including NE in the description of the MGB. We now have two further Gaunilo-type counterexamples to the metaphysical OA, both of which take advantage of some of the standard theistic arguments for God and are more likely to exist than the MGB. So these omnipotent beings have better credentials than the MGB. Similar Gaunilo-type counters to the MGB can be made by simply modifying other proposed features of the MGB to avoid persuasive atheistic arguments.

This leads to a further serious problem for the metaphysical OA: given the plausible assumption that only one omnipotent being can exist per possible world and an MDB (or NE Kengo or NE Fran or…) is not the same as an MGB, the OA implies a contradiction if it works equally well for proving the existence of both MGBs and MDBs (or NE Kengos or NE Frans or…). So Gaunilo-type examples show, via a reductio ad absurdum, that the metaphysical OA must be fallacious.

Finally, some theists may be disingenuous when they employ the “credentials” reply. In my encounters with novice proponents of the modal OA, I noticed that some of them believed P1 presents a very modest claim (I discuss this further at the end of section II-C-2 and paragraph 2 section IV). After all, P1 simply states that a metaphysically necessary God is coherent, right? Though I addressed this mistake in sections I-B-2 and at the end of I-C, set aside my rebuttal for a moment. If these theists think P1 is so modest, why do they suddenly increase their standards of proof when examining P1’s where one replaces the MGB with the MDB, NE unicorns, NE Kengo, etc.? Where is the obvious incoherence in the definition of these beings? So some apologists seem to think P1 is modest only when it makes reference to their God. When P1 includes another being the apologist is not committed to arguing for, then the test of adequacy for P1 subtly shifts from “coherence” to “credentials/need evidence that it actually exists.” So some apologists exhibit textbook special pleading when employing the “credentials” objection. This is not surprising, given the theistic manipulation of the concept of “maximal greatness” I discuss in section II-B-3-a. However, this is all beside the point: the theist’s “credentials” reply is largely irrelevant since, as I will argue in sections II-D and II-B-3-c, the MGB is metaphysically impossible + logically impossible and thus lacks credentials.

Some theists offer another reply to Gaunilo-type examples: none of the beings (the MDB, 7, etc.) embody maximal greatness, while God does. Therefore the OA works for God but not the other beings. However, this objection fails. First, it misses the point. The OA derives its conclusion solely from its modal wordplay involving NE, not because of maximal greatness. The other features of MG are irrelevant and just along for the ride. Furthermore, the theist may be confused about what MG means in the context of the metaphysical OA. MG is not some evaluative claim about how awesome/marvelous/normatively outstanding/unsurpassable something is; MG does not mean “great” in the colloquial sense, where this roughly means a being of the highest objective value [or whatever ad hoc definition of "greatness" OA proponents employ to avoid Gaunilo-type objections; different theists employ different, non-equivalent definitions, depending on the specific Gaunilo-type counterexample that needs to be rebutted and personal convenience (see section II-B-3-a)]. Instead, MG just is ME + NE, where ME refers to a being with the properties mentioned in section I-C. And MG, so defined, lacks any special privilege in the context of the OA since, like any other concept, it works in the OA iff it includes NE and it works solely because it includes NE. So pointing out that God embodies maximal colloquial greatness while other beings fail to does nothing to rebut my argument.

Some theists may disagree with my claims in the previous paragraph. They will argue that ME is evaluative, so MG must be evaluative as well. They might therefore think that greatness in the colloquial sense entails MG and thus implies NE. But this is where the second problem kicks in: even if NE is a great-making property or GMP in the colloquial sense, the theist still needs to explain why if a being X has one GMP (namely: NE), then X must have all the other GMPs (supposedly: the properties of the MEB; though I argue against this in section II-B-3-b). If theists could show this, then even if I am right and the metaphysical OA required only NE, the theist could argue NE brings all the other properties of the MGB along with it. But why think this is so? Why think that because NE has a feature K (ex: K = “being a GMP”), a being X with NE must have all other properties that have feature K?

The OA proponent could opt for a trivial answer: if NE is a great-making property, then NE is a property a maximally great being would have. How uninteresting. It's just an instance of: "If V is Y-like (i.e. apart of Y's description), then V is a property Y would have. So you need to privilege Y over other descriptions that include V." No one would take such an argument seriously unless they were already committed to believing in Y. To see this substitute in any random you thing you want for V and Y. Examples: V is NE and Y is an entity with all the modal properties; V is NE and Y is NE Fran; V is NE and Y is the evil mind you cannot possibly escape; etc. Nelson Goodman would have a field-day! Theists certainly do not grapple night and day over the necessity of the impossible to escape evil mind or NE Kengo, even though the latter entity is more likely to exist than the MGB. So why should anyone care when OA proponents plug in MGB for Y when V is NE? Saying the MGB is coherent is certainly no defense since: a) the MGB is not more likely to be coherent than NE Kengo, the evil mind you cannot possibly escape, etc., b) coherence is not enough to establish metaphysical possibility, and c) I will argue in section II-B-3-c that the MGB is incoherent. So enough with the OA proponent's unjustified special pleading in favor of their preferred Y over all the other Ys. They're just engaging in modal wordplay involving NE and then acting as if that wordplay can only be done with their preferred Y.

Given these issues, the OA proponent could opt for an blatantly unsound argument: since the MGB's description includes NE this implies: 1) an NE being must have all the other properties of the MGB and 2) that no other description (other than that of the MGB) which includes NE can be instantiated; thus the MGB should be preferred over other descriptions that include NE. I trust the the reader recognizes why such an argument is unsound. For instance, we certainly do not think that simply because NE is a modal property, a being with NE must possess all the modal properties. Nor is the following argument sound: “I have property D. Property D has objective value. Property E has objective value. Therefore I have property E.” The argument fails because having a property with objective value such as kindness, power, etc. does not entail having all the properties with objective value. Similarly: “Being K has NE. NE is a GMP. Omnipotence is a GMP. Therefore K is omnipotent,” is a fallacious argument. Moreover, the following argument is unsound as well: “Description Z includes all the valuable properties. Feature F is valuable. So Z includes F. Thus description W lacks F.” If this argument were sound, it would imply that since God’s description includes kindness, no other being can be kind. That is absurd. So just because the description “MGB” includes NE does not somehow privilege it over other descriptions which include NE.

These unsound arguments reveal two important points: a) even if the MGB’s description includes NE, this fails to show that the MGB is more likely to actually exist or more likely to be metaphysically possible than other being's whose description also includes NE and, b) the theist needs to show why having one GMP implies having them all. Otherwise, the OA proponent fails to show that descriptions such as NE unicorn, NE Kengo, etc. which include NE along with other non-GMPs are less plausible than the description of a being with all the GMPs, i.e. the MGB. If the theist runs the logical OA, the implication needs to be logically necessary. If the theist runs the metaphysical OA, this needs to be a metaphysically necessary implication. I doubt that OA proponents can provide evidence for these implications since: 1) there is nothing incoherent about a being having only one or some GMPs, 2) my Gaunilo-type examples [the MDB, the number 7, etc.] provide instances of beings that have at least one GMP (namely: NE), while lacking the others, and 3) I will argue in section II-B-3-b, via the examples of “all-existence” and “maximal freedom”, that the theist’s God lacks GMPs and thus serves as an example of a description which includes some, but not all, GMPs.

II-B-3-a. Rebutting Plantinga’s “Intrinsic Maxima” Reply, or “Mr. Maximum’s buxom babes”

Plantinga’s reply to Gaunilo also trades on colloquial greatness. Plantinga responds to the idea of a maximally (colloquially) great island by saying, “the qualities that make for greatness in islands – number of palm trees, amount and quality of coconuts, for example – most of these qualities have no intrinsic maximum. That is, there is no degree of productivity or number of palm trees (or of dancing girls) such that it is impossible that an island display more of the quality (Plantinga, 54).” So if we follow Plantinga’s reasoning, this is not true of God’s “omni-” traits, so the OA could work for God and not the other beings I mentioned. Plantinga’s reply fails for a number of reasons.

First, Plantinga’s makes the errors I noted in section II-B-2: he trades on colloquial greatness when this is not the sense of greatness relevant to the OA; and even one grants that colloquial greatness implies ME and vice versa, the argument fails to show that NE is a GMP and that a being who is NE must have all the other GMPs. But if Plantinga fails to show this, then he has not explained why one should prefer the MGB over some other description that includes NE. There are plenty of counterexamples where an NE entity lacks the other GMPs or fails to reach the intrinsic maxima for a given property. For example, Platonists could say that the number 7 is NE even though it fails to maximize the property of “quantity” or the property of “being the largest natural number less than 9” [if you think this is a weird property, look-up the controversy over whether “existence” is a property]. Furthermore, even if one accepts Plantinga’s claim that only traits with intrinsic maxima can be GMPs, this fails to address the MDB. If benevolence plausibly has an intrinsic maximum (thus allowing the MGB to reach the maximum for this state), then malevolence plausibly has an intrinsic maximum (thus allowing the MDB to reach the maximum for this state). And since the MGB and an MDB differ only in benevolence vs. malevolence, Plantinga’s “intrinsic maximum” reply fails to show that the OA works for the MGB but not the MDB.

Second, Plantinga does not provide a non-ad-hoc reason for adding the “intrinsic maximum” clause to his account of GMPs. For example, take the mathematical concept “quantity.”  This concept admits of degrees. Suppose I have the concept of a “number of the greatest quantity.” Someone could respond that, “there is no intrinsic maximum for the concept ‘quantity.’” To which I reply “of course. That just means that there is no ‘number of greatest quantity,’ i.e. the concept lacks a referent in this world or any possible world (see section I-B-2 for the sense/reference distinction). Please do not try to massage the concept of ‘greatest quantity’ just to insure that a number of the greatest quantity exists.” Yet this is exactly what Plantinga does for the concept of a “maximally great being”: in order to insure that the concept “MGB” has a referent in reality, he massages the concept by including conditions such as the GMPs must have an intrinsic maximum.

Proponents of OAs generally employ this tactic. They remain vague about what “greatness/perfection/better than” mean (ex: Maydole 2003, 299): the terms almost serve as a placeholder for whatever properties the theist thinks the God of their religion possesses. But if this is how theists define greatness, then the OA’s question-begging nature becomes even more obvious. As with most religious apologists, the OA proponent already knows what conclusion they want (“the God of my religion exists”), and then they work backwards, crafting an ad hoc account GMPs (or “greatness” or “perfection” [see section II-B-4-a-i] or whatever else their argument involves) to insure that the argument leads to their preferred deity or at least a description compatible with their preferred deity (Youtube, TheoreticalBullshit’s “Onto-ollogical” from 5:54 to 6:34). Anyone familiar with the philosophy of William Lane Craig has seen this method in action. That ends now. So my third criticism of Plantinga’s reply involves actually considering “greatness” in a way unmotivated by a concern to prove God’s existence.

II-B-3-b. God’s Missing GMPs, or “loneliness, but with elbow room”

Third, even the theist’s God (i.e. the being theists actually believes exist) fails to maximize certain intrinsically maximizable GMPs and is thus not the MGB. For example, God lacks “all-existence,” where this means:

X is all-existent in world W iff in every metaphysically possible world, X is solely-existent.

Y is solely-existent in world W iff Y is the only thing that exists in W.

All-existent has an intrinsic maximum and is, plausibly, a GMP. How great must a being be to not only be all that exists, but all that ever has, ever will, and ever could possibly exist! But the theist’s God is not all-existent since it chose to create the universe as an entity distinct from itself. So the theist’s God is not maximally great in the colloquial sense or in the sense of maximizing traits with intrinsic maxima. If Plantinga’s reply to Gaunilo worked, and the MGB possesses all the GMPs, then the MGB would need to be all-existent and thus could not be the theist’s God. And the MGB could actually exist only if we, along with everything else, are part of the MGB. This fits well with the conclusion of some mereological OAs offered by pantheists (pantheists believe the sum total of existence, usually described as the universe or the multiverse, is God; Oppy 2011, subsection 6 of section 4). This also parallels a move made by some theists: they do not want abstract objects to exist independently of God, so they make abstract objects a reflection of God’s nature [for discussion, but not advocacy, of this view, see chapter 9 of The Analytic Theist, particularly page 226]. If it seems implausible that humans could exist within a being, then this just shows the MGB’s existence remains implausible. One should not be tempted to manipulate the concept of “maximal greatness” or “MGB” to insure it has a referent in reality (see section II-B-3-a).  But I know OA proponents will do so anyway; I expect them to generate an ad hoc account of “greatness” or “objective value” to insure that all-existence fails to be a GMP. I expect the same in response to my following “maximal freedom” example.

[NOTE: “All-existence” is not the same thing as “existence,” so Kant’s objection that “existence” is not a property may not apply. Furthermore, if Kant’s objection works against all-existence, it also works against NE, thus sinking the modal OA. Finally, I can defend all-existence by employing Plantinga’s rebuttal of Kant’s objection (Plantinga, 54-60).]

The concept of “maximal freedom” further rebuts Plantinga’s argument since the Christian God fails to exemplify this maximizable GMP. Suppose we list all actions performable in a given situation S (appeasing Slaking, consuming planets, trolling, praising Ratchet, thinking about manga, etc.) and call this set of actions M1. We then look at the set of options available to respective agents in that situation. So my set would be N1, Kotonoha’s set would be K1, the theistic God’s set would be G1, etc. A maximally free being would be able to do anything in M1. To put it more formally:

a being X is maximally free in S iff X’s set in S is M1

Maximal freedom certainly has an intrinsic maximum. Furthermore, maximal freedom is a GMP; how could a maximally great being be limited in its options? But the theistic God, on many interpretations, lacks maximally freedom. The problem arises because some theists accept an implausible account of free will [one which I deny, though my compatibilism does not entail my denial; the view I give here may be Plantinga’s view on free will in chapter 2 of The Analytic Theist] where:

a being X is free with respect to an action A in situation S only if there are metaphysically possible worlds W1 and W2 such that:

W1 and W2 have the same causal laws and antecedent conditions up until X’s choice in situation S

in W1, X chooses to do A

in W2, X chooses to do not-A

Many theists assume God is necessarily omnibenevolent and thus no possible world exists where God is not caring, empathetic, loving, etc. So it is metaphysically impossible for God to not have those traits. But under the proposed partial definition of freedom, God had no choice about whether to be empathetic, loving, etc. Since moral agency, plausibly, requires freedom, God is thus neither morally responsible nor morally good with respect to being empathetic, loving, etc. Furthermore, God’s omnibenevolence in every possible world entails the following conclusion: God could only do the morally best actions, not just the non-evil actions or the actions that were extremely good, but not the morally best. So God’s set G1 in S includes only the morally best actions and is thus limited. This means that G1 is much smaller than M1 and therefore God lacks maximal freedom in S. This conclusion can be generalized to any proposed situation S, implying that the theist’s God always lacks maximal freedom. So maximal freedom represents another GMP the theist’s God fails to possess and Plantinga’s reply to Gaunilo does nothing to address this example.

[NOTE: Some theists might reply to my maximal freedom example by mentioning God’s omnipotence in relation to pseudo-acts and acts which contradict its nature, and try using that to defend against my example. I do not think this strategy will work, though I will not go into a complete explanation of why this response fails. For the curious reader, a good place to start would be the following Youtube videos: KnownNoMore’s “God's meaningless attributes - Part 1 - Omnipotence” and TheoreticalBullshit’s “Omni VERSUS Omni!” and "The Matt/Matt Debate - Part 2: Borrowing Worldviews."]

Contrast the theist’s God with NE Fran or NE Kengo (see section II-B-2). Since many theists hold that God is necessarily omnibenevolent, God’s set G1 falls short of M1. However, neither NE Fran nor NE Kengo are defined as necessarily good, bad, or uncaring. There is no pre-existing orthodox, theological baggage placed upon proponents of Fran and Kengo. So there could be possible worlds where a caring Kengo chooses to interact with humans or worlds where an omnimalevolent Fran punishes most sentient life. Since both Fran and Kengo are omnipotent, this shows one reason why the “omnipotence/pseudo-act” response to maximal freedom fails: non-omnibenevolent acts (evil, uncaring, good but not the morally best, etc.) are not logically contradictory nor are they pseudo-acts. After all, humans perform them all the time. The only reason theists think God cannot do them is because they claim that God is essentially omnibenevolent. Once this claim is dropped, God’s freedom, according to the above account of freedom, is uninhibited. Kengo and Fran therefore have more freedom than the theist’s God. So Kengo’s set O1 and Fran’s set R1 could be the same as M1. Fran and Kengo possess a GMP (maximal freedom) lacked by God and therefore may be greater than the theist’s God.

II-B-3-c. The Incoherence of the MGB, or "easy come, easy go"

If my arguments in the previous section were correct and "maximal greatness" entails both "maximal freedom" and "necessary omnibenevolence", two concepts which contradict one another, then "maximal greatness" is incoherent. Again, one should not be tempted to revise a concept in an ad hoc manner simply to insure the concept is coherent or has a referent. Also remember that a critic need not show the concept of a "MGB" is incoherent to rebut the metaphysical OA. However if they do manage to show the concept is incoherent, then of course the MGB is metaphysically impossible as well, since logical impossibility entails metaphysical impossibility. So metaphysical OA critics can rebut the OA by showing the MGB is incoherent, though they need not take this route. I have already provided one argument for the incoherence of the MGB; namely: the conflict between "maximal freedom" and "necessary omnibenevolence". Metaphysical OA critics can use other arguments as well, as I will now show (the method I am about to outline directly parallels my argument in the first half of section III-B, so the reader may want to skip to that section for further context; though this is not absolutely necessary).

MG  =  metaphysically NE + ME. Furthermore, saying X's existence is "metaphysically necessary" means that denying X's existence results in a metaphysical absurdity or some uninstantiable situation (i.e. something that could not have been; see sections I-B-1 and II-B-1), while saying X's existence is "metaphysically impossible" means that "X exists" entails a metaphysical absurdity or some uninstantiable situation. These are conceptual truths which help define metaphysically NE. But metaphysical OA proponents normally don't bother to show that denying the MEB's existence entails a metaphysical absurdity or some uninstantiable situation (section II-B-1), while atheists can argue that denying the MEB's existence results in no absurdities or uninstantiable situations (section II-D). So the MEB conflicts with a conceptual truth regarding metaphysically NE and thus the notion of an MGB (i.e. a metaphysically NE MEB) is incoherent. Furthermore, atheists could also argue that saying "the MEB exists" results in an uninstantiable situation: the uninstantiable property "all-existence" would be instantiated. Therefore, the MEB is metaphysically impossibile and therefore cannot be metaphysically NE. This provides another line of argument showing that the concept "MGB" is incoherent, even if the concept "MGB" only makes reference to metaphysically NE and not logically NE. So Gaunilo-type parodies and a thorough examination of great-making properties shows that the the concept "MGB" is incoherent.

II-B-4-a-i. A Flaw Common to All OAs, or “she’s perfect…but I still prefer Fran”

Gaunilo-type objections not only rebut Plantinga’s OA, but reveal the central flaw of most, if not all, OAs: the arguments could prove the existence of almost anything. Many OA proponents point out some feature F which they think can mediate the link between definitional coherence (or modal possibility or perfection or…) and actual existence. But then the proponents make their fatal error: they fail to provide a justification for the other properties of God they place around F. For example, Robert Maydole presents an OA in the form of a modal perfection argument (Maydole 2003; Maydole 2009, 580-581; thanks to Rayndeon for providing these sources, along with Maydole 2005, Landini, and Oppy 2004). Maydole presents the following definitions and argument:

“Think of a perfection (P₂) as a property that it is necessarily better to have than not; and define the property of being supreme (S₁) as the property that a thing has if and only if it is impossible for something to be greater and impossible for there to be something else than which it is not

greater…The conclusion of MPA [modal perfection argument] is that exactly one supreme being exists, and the premises are the following:

M1    A property is a perfection only if its negation is not a perfection.

M2    Perfections entail only perfections.

M3    The property of being supreme is a perfection.

We can show that MPA is valid by first showing that M1, M2, and M3 jointly imply that it is possible that a supreme being exists...We can then prove that the possibility of a supreme being implies the existence of a supreme being (580).”

Given Maydole’s thread-bare account of supremacy and perfection (Maydole 2003, 299), I could argue that maximal freedom and all-existence are perfections (see section II-B-3-b) and therefore the supreme being must be all-existent and maximally free. Since the theist’s God is neither all-existent nor maximally free, Maydole’s argument fails to show the theist’s God exists. Moreover, we can construct Gaunilo-type counterexamples to rebut Maydole’s argument. The crucial premise in Maydole’s inference from the possibility of the supreme being to the actual existence of the supreme being is as follows [  ◊  :  “possible (or ‘possibly’),”   S₁x  :  “x is the supreme being; x instantiates supremacy,” ∃x  :  “(the existential quantifier), there exists an X such that”   {NOTE: Maydole is not flagrantly begging the question in his use of the existential quantifier since, as I discussed in section I-B-1, this operator can be taken to mean that x holds in a possible world that is not the actual world; the question-begging results from what comes after that, as discussed in Landini, 126-128}  ]:

◊(∃x)S₁x → (∃x)◊S₁x

[where this is an instance of what Maydole calls “the controversial Barcan Formula (580),” as developed by Ruth Barcan Marcus]

We can then construct a feature F2 to represent the inference embodied by the Barcan Formula:

for any being V, the Barcan Formula applies to V iff V possesses F2.

However, Maydole still falls on the second horn of my dilemma from section II-A-2: he begs the question (Landini, 126-128) since his conclusion entails the truth of his premise and if his conclusion is false, his premise is false. Landini presents formal evidence that Maydole begs the question; however, given my intended audience, I will avoid Landini’s technical jargon. Instead, I will employ my intuitive Gaunilo counterexamples from section II-B-2 to show the reader the trivial nature of Maydole’s argument.

First, remember that Maydole needs to address my central questions from section II-B-2: A) why think the supreme being is possible while other, arguably more plausible, beings possessing F2 [such as F2 Kengo and F2 Fran] are not and, B) why think V’s possession of one perfection [namely: F2] entails V’s possession of all the perfections, thus entailing that V is the supreme being? Failure to address question A leads to the problems I already noted: Maydole’s OA would prove the existence of beings we know do not exist [F2 Kengo, F2 MDB, F2 unicorn, etc.] and Maydole’s argument, if it worked equally well for multiple omnipotent beings, would lead to the contradictory conclusion that multiple omnipotent beings existed. Failure to address B suggests that the modal OA proponent is working backwards in an ad hoc manner, attempting to argue for the being they wish existed or are theologically-committed to arguing for (i.e. the being with all the perfections) as opposed to other being’s whose existence could be just as, if not more, plausible even though they possess only some of the perfections.

Maydole attempts to address this sort of objection by providing an argument that shows the supreme being is possible, but which would fail to show that the other proposed beings (F2 Kengo, etc.) were possible. Since Maydole’s argument is stated under S5 modal logic, he deals with metaphysical possibility. So Maydole needs to show that a supreme being is metaphysically possible. An atheist could freely concede that the concept “supreme being” is coherent and thus logically possible, without conceding that a supreme being is metaphysically possible (see section I-B-2). To put this in the language of sections I-B-2, Maydole needs to rebut the following atheist position: the concept of a great being is coherent but lacks a referent in any metaphysically possible world, including the actual world. To do this, Maydole assumes the atheist’s position is true (i.e. the supreme being is metaphysically impossible) and attempts to show this conflicts with the supposedly plausible statements M1-M3 (Maydole 2003, 301). Here is Pumbelo’s presentation of Maydole’s argument, with Pumbelo’s re-phrasing of M1-M3 and my re-labeling to avoid confusion with P1-P3 of Plantinga’s argument:

“(M1) If a property is a perfection its negation is not a perfection.

(M2) If a property A is a perfection and the property B is a necessary condition for A, then B is a perfection.

(M3) Being supreme is a perfection

…

(K1) If it's not possible that a supreme being exists, every being has the property of not being supreme.

(K2) If every being has the property of not being supreme, not being supreme is a necessary condition.

(K3) If not being supreme is a necessary condition, not being supreme is a perfection. (from M2)

(K4) Not being supreme is not a perfection. (from M1 and M3)

(K5) It's possible that a supreme being exists. (from K1-K4)”

This is the intuitive idea behind Maydole’s formal proof in Maydole 2003 (301). Gaunilo-type counterexamples refute this argument. As Rayndeon argues (personal communication), the MPA proves too much: it would show that the maximum or minimum of any given ordered class exists. For instance, suppose F2 Fran and F2 Kengo’s descriptions are coherent. Given my arguments in section II-B-2, I can make this assumption unless theists present an argument for thinking these descriptions entail a contradiction while the description of the supreme being fails to. Maydole does not provide such an argument, since he only intends to show that the supreme being is metaphysically possible, not that other descriptions which include F2 are incoherent. So just as I grant Maydole the premise that “being supreme” is coherent since I will not provide an argument showing this notion is incoherent (“being supreme” does not include logically NE, so my argument from section III-C does not apply here; though see section II-B-4-a-ii for possible arguments for the conclusion that "being supreme" is logically incoherent), I expect modal OA proponents to operate by the same principle with respect to my descriptions F2 Fran and F2 Kengo. So until I am provided with an argument otherwise, I assume “F2 Fran” to be a coherent concept.

We can then list all the features of F2 Fran in a given logically possible world W1 and call this set of features “being Fran.” This parallels Maydole’s being supreme. In W1, F2 Fran’s description includes playing favorites, inspiring Holy Books, etc. Call these features “Fran-like;” they parallel Maydole’s perfections. So we can then revise M1-M3 as follows (I include the modifications to Pumbelo’s version of these premises as well):

M1’   :   A property is Fran-like only if its negation is not Fran-like.

M2’   :   Fran-like features entail only Fran-like features.

M3’   :   The property of being Fran is Fran-like.

(M1’)   :   If a property is Fran-like its negation is not Fran-like.

(M2’)   :   If a property A is Fran-like and the property B is a necessary condition for A, then B is Fran-like.

(M3’)   :   Being Fran is Fran-like

M1’-M3’ seem at least as plausible as M1-M3; we can simply parallel Maydole’s defense of M1-M3 in our defense of M1’-M3’ (Maydole 2003, 302-303). For M1’, if Fran’s description contains a feature A, her description cannot also contain not-A; that would be incoherent and F2 Fran’s nature is coherent. If OA proponents wish to deny this, I would direct them to section II-B-4-a-ii. There I show that atheists can, if they choose to, make the parallel move of denying that the “being supreme” is coherent and thus dismiss Maydole’s argument as well. For M2’, the entailment is meant to be logical entailment, as shown by Maydole's response to the following criticism: "being supreme" trivially (or tautologically) entails "being supreme or being a pedophile" via the logical rule of disjunctive addition ["T" entails "T or S"]. So by M2, "being supreme or being a pedophile" is a perfection. Since pedophiles meet the second-half of the disjunct, pedophiles exhibit a perfection. This absurd result serves to rebut M2. Oppy (2004, 205; Landini, 127) advances a criticism of this sort. Similarly, perfections could entail impossible to metaphysically impossible or logically impossible properties. So "being supreme" would trivially entail the perfections "being supreme or being black and red all over" (a metaphysically impossible, logically possible property; see the end of section I-B-1) and "being supreme and not being supreme" (an logically impossible set of properties). So M2 and M3 would together entail that possessing all the perfections (i.e. being supreme) is logically impossible.

Maydole, in his subsequent work (2009, 581), attempts to avoid this objection by limiting M2's entailment to non-tautological entailment [of course, this is reminiscent of Plantinga's ad hoc attempt to redefine "greatness" so as to allow it to be metaphysically possible (see section II-B-3-a); but I digress]. But since tautological entailment occurs in the context of logic (Pigden, 424), this shows that Maydole meant M2 "logical entailment" in M2. But if M2 references logical entailment, then so does M2’. And M2’s then looks at least as plausible as M2. If a description contains feature A and A entails B, then of course the description contains B. For example, in the actual world I am a bachelor (*hint hint, ladies*). Since being a bachelor logically entails being male, I must be male. Similarly, if a Fran-like feature (i.e. a feature in the description of Fran) entails another feature B, then B must be Fran-like. Since even in logically possible + metaphysically impossible worlds descriptions which include being a bachelor will include being male, this defense of M2 does not assume F2 Fran is metaphysically possible.  Finally, M3 should be blatantly obvious: being Fran means possessing all the features in Fran’s description and thus entails being Fran-like.

So we can now plug M1’-M3’into Maydole’s proof (2003, 301) and thus show that F2 Fran is metaphysically possible. A similar parody argument could be constructed for F2 Kengo. Maydole’s argument can therefore be used to “prove” the metaphysical possibility of all sorts of entities E to which one attaches F2, even entities we know are metaphysically impossible. One just needs to list the features of that F2 entity, label those features “E-like,” and then run modified versions of M1-M3. Furthermore, if one shows that an F2 being is metaphysically possible (i.e. a being to which Barcan’s Formula applies is metaphysically possible), then one has shown that being actually exists. A being V’s possession of F2, not perfection or supremacy, combined with simple modifications to M1-M3 is solely sufficient for Maydole’s argument to prove the existence of V (Maydole 2009, 580-581; Maydole 2003, 301; if, in fact, Maydole’s argument does work). In section II-B-1 and II-B-2, I argued for a similar point regarding NE and metaphysical possibility, not colloquial greatness or MG, being solely sufficient for running Plantinga’s metaphysical OA.

As long as my descriptions of F2 Kengo, F2 Fran, etc. include F2, the same logical argument Maydole employs to prove the existence of the supreme being works for my descriptions as well, regardless of whether my descriptions fail to include all the perfections or include some non-perfections or fail to be perfections themselves. So Maydole’s argument proves the existence of too much and thus Gaunilo-type counterexamples invalidate his argument. Maydole's argument therefore exhibits the central flaw Gaunilo tried to point out so long ago: OAs, if sound, could prove the existence of almost anything, including things we know do not exist. Therefore OAs must be unsound.

II-B-4-a-ii. More Flaws in the MPA, or “Hyper Cutter blocked 32-step logical proof’s Intimidate”

In this sub-section, I will discuss other errors present in Maydole’s argument and Pumbelo’s formulation of Maydole’s argument. I already rebutted Maydole’s argument in section II-B-4-a-i, so this sub-section is only for readers interested in a slightly more detailed, informal dissection of the MPA.

Pumbelo’s K1 admits of two readings:

K1a   :   If it's not metaphysically possible that a supreme being exists, every being in every metaphysically possible world has the property of not being supreme.

K1b   :   If it's not metaphysically possible that a supreme being exists, every being in every logically possible world has the property of not being supreme.

The atheist claims the supreme being is not metaphysically possible. So the atheist can accept K1a. However, the atheist can also hold that it is logically possible that a supreme being exists (see my conceptual/existential distinction in II-A-2 and III-C and the logical/metaphysical distinction in section I-B-2). Thus the atheist will deny K1b since a supreme being in a logically possible + metaphysically impossible world would not have the property of “not being supreme”. So this type of atheist affirms K1a and rejects K1b. Another type of atheist could reject K1a and K1b. This atheist claims the notion of a supreme being is incoherent and therefore logically impossible. To show this they could employ my argument from the section II-B-3-c, argue that some of the tri-omni traits are self-contradictory, or argue that they contradict one another when conjoined together. Since logical impossibility entails metaphysical impossibility, this type of atheist will deny Maydole’s proof for the metaphysical possibility of a supreme being. Since “being supreme” is incoherent, "being supreme" will entail some contradictory features “A” and “not-A.” By M2 and M3, “being supreme” entails only perfections. So A and not-A must both be perfections. But this contradicts M1. So if an atheist thinks the notion of a supreme being is incoherent, they will claim M1-M3 are mutually inconsistent. Thus this atheist would reject the MPA. For the sake of argument, I will go with the weaker atheistic position and assume that “being supreme” is a coherent notion [the curious Joycean is curious!]. Thus I will accept K1a, but not K1b.

K2 and K3 admit of two readings, corresponding to the two readings given to K1:

K2a   :   If every being in every metaphysically possible world has the property of not being supreme, not being supreme is a metaphysically necessary condition.

K2b   :   If every being in every logically possible world has the property of not being supreme, not being supreme is a logically necessary condition.

K3a   :   If not being supreme is a metaphysically necessary condition, not being supreme is a perfection. (from M2)

K3b   :   If not being supreme is a logically necessary condition, not being supreme is a perfection. (from M2)

K3a is false, since the entailment/necessity in M2 is logical entailment/necessity and metaphysical necessity does not imply logical necessity (see sections I-B-2 and II-B-4-a-i). K3b depends on reasoning that runs from K1b through K2b. Since the atheist rejected K1b, they can thus reject K3b as unsupported by Maydole's premise. K3a and K3b exhaust the possibilities for M2. Since the atheist rejects both K3a and K3b, they also reject M2. So atheists can reject M2, regardless of whether they think "being supreme" is coherent.

Moreover, K3a and K3b seem strange. They infer that “not being supreme” is a logically/metaphysically necessary condition for X simply because “not being supreme” shows up in every logically/metaphysically possible world in which X appears. If this were true then “2 + 2 = 4” and “water is H₂O” would be logically necessary and metaphysically necessary conditions, respectively, for any entity X. But this seems like the wrong sort of connection: it borders on trivial entailment. One type of trivial entailment involves using material conditionals to infer any premise from a false truth-apt claim: “If A then B” is false iff A is true and B is false. So if B is always true, then as long as A is truth-apt, “If A then B” is true and A thus trivially entails B (Pigden, 424) [truth-apt statements are capable of having a truth-value, where truth values come in two varieties: “true” and “false”; commands [ex: “Attack Caesar’s Legion!”] are one example of non-truth-apt statements].

K2b makes “not being supreme” as trivially necessary as "2 + 2 = 4".  K2a does the same for “not being supreme” and “water is H₂O.” How is “not being supreme” a meaningful necessary condition for anything? This might be easier to see with any example (the example is taken from Joyce 2002, 54-55). Suppose that it is a conceptual truth of mathematics that planar trilaterals are triangles and vice versa. So triangles on a plane have three sides in every logically possible world. Furthermore, imagine that a machine exists which examines planar shapes and if the shape has three sides connected to one another in a certain way (all three sides connected to one another with the space exterior to the shape completely separated from the space interior to the shape and none of the sides extending beyond the point where they intersect with the other lines, etc.), the machine places the shape in a box. In every logically possible world, the machine always selects triangular (i.e. 3-angled) figures given the conceptual truth that planar trilaterals are triangles. However, it would be incorrect to say the machine chose the triangles because they were triangles (Joyce 2002, 54-55) or that the machine's selection depends on a shape being triangular. Instead, the machine chooses shapes because they are ­planar trilaterals, not because they are triangles. It just so happens that every planar trilateral of a certain structure is also a triangle.

So we might say that non-trivially necessary conditions have some sort of explanatory connection to the thing for which they are a necessary condition. In the bachelor example from section II-B-4-a-ii, being a male came part and parcel with being a bachelor; it explained some of the features associated with being a bachelor. Every truth-apt claim logically entails “2 + 2 = 4” and metaphysically entails “water is H₂O.” But neither “2 + 2 = 4” or “water is H₂O” explain why some beings are on way as opposed to another. For instance: though "snakes are reptiles" entails both of these two statements, neither of them provide an explanation for the nature of snakes. Thus “2 + 2 = 4” and “water is H₂O” represent trivially necessary conditions. I am arguing that even if K2a and K2b are true and “not being supreme” is a necessary condition, then "not being supreme" is a trivially necessary condition. 

Since K3 includes trivially necessary conditions, K3 needs to be modified. And since K3 comes from M2, Maydole should revise M2 to avoid trivially necessary conditions and tautological entailment. But Maydole does not do this. Instead he introduces two new premises to exclude non-tautological entailment:

M31   :   For every Z, all of the nontautological essential properties entailed by Z are perfections

if and only if the property of being a Z is a perfection.

M32   :   Every nontautological essential property entailed by the property of being supreme

is a perfection. (2009, 581)

He then uses M31 and M32 to argue for M3, while not appropriately modifying M2. Don't believe me? Compare step 16 on page 301 of Maydole 2003 and step 8 of the first proof on page 591 of Maydole 2009 (modified in the way Maydole suggests on page 581). The former came before Oppy's "tautological entailment objection" and the the latter came after the objection. Yet the latter is not modified so as to avoid the charge of trivial deduction. So both K3 and M2 still fall to Oppy's abhorrent counterexamples. Maydole could modify M2 in a way that avoids Oppy's criticism. But the revised premise would blatantly beg the question: the revised premise, on its own, would logically entail the "being supreme is possible" while "being supreme is possible" would entail the revised premise (Landini, 127-8). Now wonder Maydole avoided revising M2.

We can approach the question-begging nature of Maydole's argument in another way. Remember: the atheist asserts that "being supreme" is metaphysically impossible. This results from the "supreme being" containing a metaphysically impossible descriptor D. D might turn out to be entire description of the supreme being or only part of its description. To rebut the atheist, Maydole assumes that "being supreme" is metaphysically impossible and tries to show this contradicts M1-M3. So Maydole needs to assume that the "being supreme" logically entails a metaphysically impossible descriptor D. If one of his non-logically necessary premises, on its own, logically entailed that "being supreme is metaphysically possible" and vice versa, then his argument blatantly begs the question (see section II-A-1-b). Since Maydole knows what a question-begging argument is, he employs three (supposedly) non-logically-necessary premises M1 to M3 as opposed to one premise. 

Since D is included in the description of the supreme being, then supremacy non-trivially entails D. So by M2 and M3, D is a perfection. There is no reason to suppose that D being a perfection conflicts with M1. So if an atheist can say "supremacy includes a metaphysically impossible descriptor D" without contradicting premises M1 to M3, then how does Maydole's reductio work? We can see the problem by noting Maydole;s response to Thomas Metcalf. Metcalf introduced a candidate for D, though he did not intend to use his example for this purpose. He employed his example in a counterargument against Maydole's MPA. Maydole accepts Metcalf's argument as valid; so if Metcalf's premises are true, his conclusion is true. However, Maydole denies that Metcalf's argument is sound; so at least one of the premises is false (Maydole 2005, 136). According to Maydole, Metcalf's argument is unsound because D is not possible and thus cannot be a perfection: "sans a good argument that being greater, even, than the greatest being [i.e. Metcalf's D] is a perfection, the MPA advocate could equally argue that the property being greater, even, than the greatest being is not a perfection. For if it were a perfection, then it would be instantiable, because all perfections are instantiable—as also implied by the premises of MPA (Maydole 2005, 135)." Instantiable traits are metaphysically possible and vice versa (Craig, “Graham Oppy on…”). So Maydole is arguing that D is not metaphysically possible and thus cannot be a perfection.

Maydole makes a couple of errors in his response to Metcalf. First, he incorrectly asserts the OA critic needs to prove that D is a perfection. "D is a perfection" is entailed by M1 and "being supreme is metaphysically impossible", the very premise Maydole needs to assume for his reductio. The OA critic can choose to provide an example D that is both metaphysically impossible and a perfection, though they need not. The atheist could argue that any of the following could be D: all-existence, omnipotence, omniscience, making human beings that engage in specified interactions C and always choose to do what is right (most free will defenders will claim this is metaphysically impossible for a certain Cs) or... 

Second, we can now see Maydole's argument in all its question-begging, nigh circular, glory. His MPA rests on including Barcan's formula in his account of supremacy and showing that the "being supreme is metaphysically possible". His argument for "being supreme is possible" hinges on showing M1 to M3 conflict with "D is metaphysically impossible". So, he claims that D cannot be a perfection and thus not apart of the nature of the supreme being because... the MPA shows that all perfections are metaphysically possible. So either Maydole begs the question by assuming all perfections are metaphysically possible, which directly conflicts with the premise he was supposed to be assuming for his reductio [thanks to Rayndeon (personal communication) for bringing this to my attention], or he argues in a circle.

To summarize: Maydole faces a dilemma. He can allow for trivial entailment in M2 or he can block it by limiting M2 to non-trivial entailment. If he goes with the former he: 1) fails to rebut to Oppy's counterexamples of abhorrent or impossible perfections (Oppy 2004, 205; Landini, 127), 2) remains susceptible to my "nontrivial-necessary-conditions-must-be-explanatory" argument, 3) is susceptible to Gaunilo-type counter-examples, and 4) atheists can reject M2 regardless of whether they think "being supreme" is coherent. If he goes with the latter, he: 1) is susceptible to Gaunilo-type counter-examples, and 2) atheists can reject M2 regardless of whether they think "being supreme" is coherent and the only viable way to avoid this begs the question (Landini, 127-128).

II-B-4-b. The Flaw Generalized, or “anything you can do, I can do better”

Gaunilo-type objections generated via feature F rebut most, if not all, OAs. For instance, on one plausible construal of St. Anselm’s argument, Anselm argued that God could not exist in the understanding without existing in reality (Oppy 2011, section 8.1). This would thus count as St. Anselm’s F. Call this “F3”. God, as the greatest conceivable being, presumably possesses F3. But plenty of other descriptions could possess F3. This fits well with section II-B-1, where I argued that many concepts/descriptions other than the MGB entail NE. Similarly, many other concepts/descriptions could entail F3. So if St. Anselm believed his argument worked for God, this same argument would prove the existence of too many other beings. This was the lesson Gaunilo intended to teach with his island example.

Since Gaunilo, unfortunately, too many critics of the OA focused on making their counterexamples “great beings” (Oppy 2011, section 5). The critics attempt to point out a GMP God lacks, as I did in section II-B-3-b, or construct an account of a maximally great cake or island or… in order to reduce the OA to an absurdity. Though these strategies can work, one can take a much more direct strategy: simply include the OA proponent’s F in one’s counterexample. Even if the OA proponent thinks “greatness” or “supremacy” or… entails F, the proponent has not shown the reverse entailment holds (see section II-B-2). So a description such as “Kengo possessing F” would work as a counterexample, regardless of whether Kengo is great or supreme or.... I call this the F-strategy for generating Gaunilo-type objections and I have employed it in rebutting the OAs of Plamtinga, Maydole, and Anselm. This strategy should work against most, if not all, OAs.

The F-strategy also provides other benefits. For instance, it allows the OA critic to parallel the OA proponent’s justification for including NE in their deity’s nature. OA proponents such as Malcolm attempt to show that a description of their God including feature F is coherent and take this to be sufficient in defending their OA God (see: Reitan; Rayndeon, section §IV; Oppy 2011, sections 2 and 6). But I argued in section II-B-2 that “F Kengo,” “F MDB,” etc. are just as likely, if not more likely, to be coherent concepts. Or suppose the OA proponent claims that since God cannot come into existence or cease to exist, NE must be included in the description of God. Malcolm may propose this defense. This defense fails since neither metaphysically NE or logically NE have anything to do with coming into existence or ceasing to exist. But suppose I ignore this point and accept the OA proponent's argument. Then since F Kengo, F MDB, etc. are also deities, they cannot come into existence or cease to exist. The OA critic can therefore employ the same reasoning to show that F Kengo's, F Fran's, F MDB's, etc. descriptions must include NE. So once we no longer allow OA proponents to employ ad hoc, special pleading to grant NE to their God and their God only, Gaunilo-type objections rebut most, if not all, OAs.

In conclusion, Gaunilo-type objections reveal a major flaw in Plantinga’s metaphysical OA: the entire argument hinges on NE and one can place any set of properties one wants around NE, as long as the resulting entity is metaphysically possible. This serves as a reductio ad absurdum for the metaphysical OA since: 1) maximal greatness [the description the metaphysical OA proponent claims entails NE] entails contradictory properties and thus is logically incoherent [though the atheist need not accept this claim in order to show that the MGB is metaphysically impossible], 2) the metaphysical OA cannot prove the God theists want since their God lacks some GMPs, 3) the argument leads to the contradictory conclusion that multiple omnipotent beings exist, and 4) the argument could prove the existence of entities we know do not exist. This last rebuttal can be generalized to most, if not all, OAs by replacing NE with whatever feature F the OA proponent believes suffices for showing God exists. Thus most, if not all, OAs fail.

II-C-1. A Helpful Modal Thought Experiment, or “pandemic: the OA goes viral”

First, some definitions: Single world property (S) refers to a property something possesses independently of what goes on in other possible worlds. For example: "being blue," "being possible," and most other properties. A transworld property (T) depends on goings on in every possible world. For example: "being necessarily green," "being impossible," “transworld depravity (Plantinga, 40),” etc. Plantinga endorses this distinction when he writes, “a being’s excellence in a given world W, let us say, depends only upon the properties it has in W; its greatness in W depends on these properties but also upon what it is like in other worlds (Plantinga, 67).”

When we want to determine whether something possesses an S property, we examine single possible worlds. However, we use different methods for determining if something has a T property. We need to make arguments about multiple possible worlds. This involves an entirely different epistemology. It is the epistemic difference between determining if my car could have been yellow vs. whether there was no way the would could have been such that my car was not yellow. The epistemologies involved make proving the former easy, while making the latter quite hard. Unfortunately, P1's phrasing causes some people to apply an S epistemology to determining if something has a T property. So instead of trying to show that God exists in all possible worlds, they instead look for a necessary God in one possible world (in this case, the T property is "necessary existence"). But that is the wrong epistemic method and leads to a much too easy result that could prove the necessary existence of almost anything (Gaunilo strikes again!). An analogy might help. This analogy provides intuitive guidelines for how to treat different modal claims; along with helping people new to modal logic reason their way through Plantinga’s argument:
[NOTE: “possibility/impossibility” in this context does not refer to epistemic possibility/impossibility but metaphysical possibility/impossibility (see section I-B-1 for the distinction)]

New York   =   the space of possible worlds

New York resident   =   a possible world

Punpun (a specific resident of New York)   =   the actual world

Flu   =   S property

Epidemic flu (Eflu)   =   T property

A flu outbreak strikes New York. A person has Eflu iff: 1) they have the flu, and 2) every New York resident has the flu. So we could run an argument parallel to Plantinga’s metaphysical OA as follows (see section I-C: Q1-Q3 are analogous to P1-P3 in Plantinga’s metaphysical OA, while D1-D2 are analogous to C1-C2):

Q1   :   A New York resident has the Eflu.

Q2   :   If a New York resident has the Eflu, then every New York resident has the Eflu.

D1   :   Every New York resident has the Eflu.

(from Q1 and Q2).

Q3   :   If every New York resident has the Eflu, then Punpun has the Eflu.

D2   :   Punpun has the Eflu.

(from D1 and Q3).

Q2 (P2) trips up most people new to modal logic. Most people are used to dealing with S properties such as omnibenevolence, omnipotence, blue, omnipresence, smart, fast, etc. These are analogous to the flu.  So when most people read P2 (Q2), they unknowingly substitute in the “MEB” (flu) for the “MGB” (Eflu) and thus P2 (Q2) makes no sense to them: how does the mere possibility of a God entail that God exists necessarily or exists in the actual world? But now we can see the metaphysical OA’s central move: by including necessary existence in the features of the MGB, theists defined the MGB as metaphysically NE. Similarly, one can define the Eflu as a flu infecting everyone in New York. So just as admitting that one patient has the Eflu would commit you to saying that the patient has a virus they could only have if everyone else had the flu, saying the MGB exists in a possible world commits you to saying that there is a possible world that has a being it could only have if every possible world contained the MEB. So when you concede Q1 (P1), you concede that every resident has the flu (every possible world has an MEB). Since for each particular person P (possible world), P has the flu (an MEB) and every other resident has the flu (every possible world has an MEB), then P has the Eflu (that world has an MGB). Applying this reasoning to every resident (possible world) gets us to D1 (C1). And if every resident has the Eflu (every possible world has an MGB), then of course Punpun has the Eflu (the actual world has an MGB). So D2 (C2) follows. This is the intuitive idea behind the formal proof presented in Maydole 2009 (590).

{Here is your homework assignment: use this flu thought experiment to show: a) how D1 [C1] entails Q1 [P1] and D2 [C2], and b) how D2 [C2] entails Q1 [P1] and D1 [C1]. Homework answers available at Alighieri, and Rayndeon, section §III}

II-C-2. An Epistemological Error, or “could I please switch to an a-religious epidemiologist?”

Suppose a curious doctor wondered whether anyone in New York suffered from the flu. This is analogous to thinking about possible S properties (ex: “is it possible for cats to be green?”). The doctor requires only one person with the flu. To find such a person, she can screen people one-by-one or just scan around for someone with flu-like symptoms and then examine them. This is a confirmatory S method and it serves as an analogy for conceiving of different possible worlds. If the doctor wanted to determine if Punpun had the flu (analogous to thinking about S properties in the actual world [ex: “do green cats actually exist?”]), she would just apply her methods to Punpun. Conversely, suppose a bemused epidemiologist wondered if anyone in New York suffered from the Eflu. It would not make sense to just look at one patient and say “oh, you have Eflu” (analogous to conceiving of one possible world to determine if it contains an MGB). The epidemiologist either needs to screen everyone in New York to determine if they all have the flu or provide some other argument for thinking that the flu was so bad that it is incredibly unlikely that someone in New York was uninfected (ex: maybe in lab tests the flu had a 100% infectivity rate, maybe everyone in New York is displaying flu-like symptoms, maybe the flu infected an ancestor common to all humans and is being re-activated, etc.). Analogously, one could argue that we cannot make sense of worlds where certain logical truths do not hold, so such possible worlds do not hold. The epidemiologist’s confirmatory T methods thus contrast with the doctor’s confirmatory S methods. The rebutting S/T methods distinction parallels the confirmatory S/T distinction.

So here is a list of claims, and whether one should use S or T methods to confirm them:

S   :   Punpun has the flu, Punpun does not have the flu, Punpun does not have Eflu, Someone has the flu, Someone does not have the flu, Someone does not have Eflu, Everyone does not have Eflu, No one has Eflu

T   :   Punpun has Eflu, Someone has Eflu, Everyone has the flu, Everyone has Eflu, Everyone does not have the flu, No one has the flu

The same methods apply even if we rephrase the doctor’s problem and the epidemiologist’s problem as: 1) Doctor: “No one has Eflu” (analogous to “It is metaphysically impossible that an MGB exists”) and 2) Epidemiologist: “At least one person has Eflu” (analogous to P1 of the metaphysical OA). Re-wording the statement does not increase or decrease the underlying epistemic burden. Despite the re-wording, we still address 1 via S methods and 2 via T methods. Furthermore, 1, even though it implies the utter non-existence of a property, is not an overly strong conclusion and does not require extraordinary evidence. We still address it via S methods: if the doctor found one patient who did not have the flu, this would prove 1. In fact, the denial of 1 is the particularly strong conclusion: it implies that everyone has the flu, and everyone has the Eflu, and so must be supported via the confirmatory T methods. Conversely, even though 2 is re-worded to make it look like a modest S claim, it is still really a claim about existent T properties and to confirm it one still needs to employ confirmatory T methods, not confirmatory S methods; i.e. do not just look into one patient (or conceive of a single possible world) to look for your T property. You instead screen every patient or make a persuasive argument for thinking everyone has the flu. And rebutting 2 is quite easy: it involves rebutting S methods such as showing there is one person who does not have the flu (or conceiving of a possible world without an MEB).

These distinctions are why proving that “necessarily instantiated S” [ex: “necessarily existent,” “necessarily blue,” etc.] usually is, and should be, so much harder than proving that “possibly not instantiated S.” This is why it such a rare occurrence for someone to show that something necessarily exists, such as a mathematical object, while it is no big deal if one can show that it is possible something does not exist, such as trees or non-physical minds. So we should feel uncomfortable with how easily some people accept P1 of the OA when it implies that, “necessarily instantiated S”; i.e. the NE MEB. The epistemic problem with P1 should now be clear: its wording entices people into applying confirmatory S methods (“Well, I can imagine a world where an MGB exists”) instead of the appropriate confirmatory T methods or rebutting S methods (“why should I think an MEB exists in every possible world?”; “why do you think I cannot conceive of a world without an MEB?”).

On a related note: some theists accuse atheists of being dogmatic when atheists affirm P1’s negation and thus claim, “it is metaphysically impossible for an MGB to exist.” I disagree with this accusation for various reasons. First, given the distinction I made in section I-B-2 between metaphysical modalities and logical modalities, the atheist can claim that the MGB is metaphysically impossible without having to show something so strong as that the concepts of “MGB” and “MEB” are incoherent/logically impossible. Second, the theist may be equivocating between two definitions of God. Proponents of the modal OA often equivocate between defining God as the MEB versus defining God as the MGB and so confuse saying the latter is metaphysically impossible with saying the former is metaphysically impossible. They therefore assume the atheist’s position is much more extreme than it need be. Once we prevent this equivocation, we see that the atheist is simply applying the doctor’s rebutting S methods (see section II-D): “suppose I concede that someone has the flu (a possible world contains an MEB and thus the MEB is not metaphysically impossible). I can still deny that Punpun or some other person has the flu (I can say the MEB does not exist in a possible world) and thus no one has the Eflu (the MGB is metaphysically impossible).”

Third, the atheist’s 1-like claim is no more extreme than other everyday claims. 1-like statements can be innocuous because everyone commits to1-like statements. For example, whenever we deny the actual existence of some thing X (invisible non-physical unicorns and hobbits, for example), we commit to the claim, “it is metaphysically impossible for an NEX to exist” where NEX = NE + X (i.e. NEX is a metaphysically necessarily existent X). Or if you simply lack belief in X and think we lack sufficient efficient evidence to think X exists, you are committed to thinking that we lack sufficient evidence for thinking an NEX is metaphysically possible. In fact, if you accept that it is metaphysically possible for X not to exist, you just granted that the NEX is metaphysically impossible. And we are usually quite willing to allow that a proposed X that has only S properties could fail to exist in at least one metaphysically possible world; the world can been such that X did not exist. Again, one does not need to show that the concept "NEX" is incoherent in the way "married bachelors" are in order to show that it is metaphysically impossible that anything matching/referenced by the concept "NEX" exists. So unless theists are going to say that denying the existence of hobbits and the like (or maintaining that is metaphysically possible that those entities do not exist) remains too strong a position and thus forfeit their right to deny the existence of anything, then they should not claim the atheist’s position is too strong. No special pleading or ad hoc adjustments of epistemic standards when the subject of discussion is God.

Saying an NEX is metaphysically impossible in nowhere near as extreme as saying X is metaphysically NE (or equivalently: an NEX is metaphysically possible). Re-defining God to include NE is just a empty logical maneuver which: 1) if it worked would then prove the existence of almost anything [see section II-B] and, 2) misdirects people into incorrectly applying the epistemic standards for "X is metaphysically possible" to "NEX is metaphysically possible." "The MEB is possible"  =/=  "the MGB is possible". The latter claim is just a rephrasing of the statement "the MEB is metaphysically NE" [i.e. "there is no way to describe the way the world could have been such that, if that description were actual, the MEB would not exist"] and our epistemic methods should reflect this. Similarly, "X is metaphysically impossible"  =/=  "NEX is metaphysically impossible."The latter claim is quite modest and can be supported simply showing it is metaphysically possible that X does not exist. To paraphrase Rich Talylor: our initial episitemic assumption is "X is contingent (i.e. X is possible and not-X is possible)." Metaphysical OA proponents modify this into "NEX is possible (i.e. X is necessary and not-X is impossible)." This is simply an ad hoc revision of epistemic standards: no theist would accept it if NEX was replaced with anything other than their preferred deity. This all amounts to epistemic special pleading. So until we are provided with evidence to the contrary, our primae facie epistemic assumptions are as follows: if X has only S properties (no T properties), then we assume X is metaphysically possible and metaphysically NEX is metaphysically impossible.

In conclusion, the thought experiment I offered in this section reveals one epistemic problem with the metaphysical OA: the phrasing of P1 encourages people to employ the incorrect epistemological methods for determining if P1 is true.

II-D. Unsupported Modal Intuitions, or “…and the dualists rode in on pale horses…the OA trembled”

As I argued in section II-C-2, an atheist has just as much, if not more, justification for their modal intuition that “it’s metaphysically possible that an MEB does not exist” (and its logical equivalent, the affirmation of P1’s denial: “it’s metaphysically impossible for an MGB to exist”) than the theist has for their modal intuition P1, since the atheist employs the correct epistemology while the theist does not. I will build on that argument in this section.

Some philosophers remain skeptical of human modal intuitions (Vaidya 2007). But this cuts both ways: such skepticism would undercut both our trust in anti-P1 modal intuitions and our trust in the truth of P1. So, for the sake of argument, I will assume that at least some modal intuitions are reliable. So how does one decide between anti-P1 and pro-P1 modal intuitions? Both atheists and theists employ similar methods. For example, the (presumed) atheist property dualist David Chalmers argues that it is conceivable that a physical duplicate of me could lack qualia, therefore a metaphysically possible world holds where the qualia are different though all the physical properties are the same. Thus qualia are not physical. (Chalmers 1996, 94-99). Plantinga runs an analogous argument for the notion of a “self” as non-physical (Youtube, LennyBound’s “Alvin Plantinga and the Modal Argument”) and also endorses the “conceivability” method in the quote cited at the end of section I-B-1. Yet this “conceivability” method also grounds the atheist’s modal intuition: they conceive of a world without an MEB and thus employ a rebutting S method against P1. Even Plantinga admits that atheists can conceive of a world without God (see section I-B-1). But conceiving of a single possible world with or without a being in it is an S method (see section II-C-2), and therefore should not be used to confirm P1, which involves the instantiation of a T property. If theists want to employ confirmatory S methods, then they need to conceive of a possible world where an MEB, not an MGB, exists. But even if an atheist concedes that an MEB is metaphysically possible, that is not enough to support P1 of the metaphysical OA, which claims that an MGB is metaphysically possible. So the atheist has the leg up here since they can use conceivability arguments to rebut P1 while theists cannot use conceivability arguments to support P1.

Maybe theists have other arguments in favor of P1. Or maybe not. As Theophage persuasively argues (Youtube, “Refuting the Modal Ontological Argument” and “Must Maximal Greatness be possible?”), Plantinga presents no arguments in favor of P1. I also found no arguments from Plantinga for the truth of P1; he only claims, “that there is nothing contrary to reason or irrational in accepting this premise (Plantinga, 71).”

{Side-issue: this is one reason (of many) I deeply respect Plantinga (also see the end of section I-B-1). He understands his critics’ thought-process while not blatantly over-estimating the strength of his own arguments: “What I claim for this argument [his modal OA], therefore, is that it establishes, not the truth of theism, but its rational acceptability (Plantinga, 71).” Even Maydole notes that, “it would be philosophically arrogant for me to claim that the Modal Perfection Argument proves once and for all that God exists. Even though I think that it is arguably sound, it does have premises, presuppositions and inference rules, some of which can and, perhaps, should be challenged. I have tried to address some of these challenges (2003, 311).” Craig, and those others who offer the modal OA as evidence or “logical proof” of God’s existence, should take notes.}

But Plantinga does not have an argument for this claim either, while atheists have arguments against the P1. For example, the aforementioned “conceivability” method provides a reason for denying P1. Also, atheists provide other arguments for the possible non-existence of the MEB (ex: see the last paragraph of Rayndeon, section §IV), which rebuts P1. Similarly, every argument against the existence of an MEB in the actual world entails, by extension, the falsity of P1. For instance: the problem of non-belief/divine hiddenness, suffering, the issues regarding omnipotence and omnibenevolence I hinted at near the end of section II-B-3-b, the incoherence of an atemporal functioning mind, the evidential and logical problems of evil (and no, Plantinga’s transworld depravity defense against the logical problem of evil fails, ironically, for many of the same reasons his OA fails; for one sound logical problem of evil, see Meow Mix), omniscience paradoxes, etc. Since metaphysical impossibility does not entail incoherence (see section I-B-2), these arguments need not show that the MEB or the MGB are incoherent notions, though many of them purport to do so. Instead, the argument simply need to show the MEB likely does not exist in the actual world; that alone entails the falsity of P1. Furthermore, in section II-C-2 I argued that rephrasing "the MGB exists in every metaphysically possible world" or the "the MGB exists in every metaphysically possible world" into P1 does not affect the epistemic status of either claim; the latter claim requires exactly the same evidence the two former claims. So any negative atheist argument which shows that belief in the MEB is unjustified/lacks sufficient evidence also shows that P1 lacks sufficient evidence/is unjustified. Not so for theistic arguments which supposedly support P1.

Most plausible religious arguments provide evidence for a vague, deistic being, not an MEB or MGB. Other religious arguments conclude only that an MEB, not an MGB, actually exists and thus fail to support P1. For example, Craig’s Kalam argument does not lead to the conclusion that an MEB exists in every metaphysically possible world and has the same character traits in every possible world. This is one reason why telemantros’ argument from the end section II-A-3 is unsound. The argument involves no modal claims. Similarly, the teleological argument, if sound (which it is not), only provides evidence for the existence of an MEB in worlds like ours; the argument makes no modal claims about all possible worlds. But these arguments need to make such modal claims if they support P1; i.e. show an MEB exists in every possible world and thus an MGB actually exists. So some theists, such as telemantros, subtly equivocate between two definitions of God: God as the MEB and God as the MGB. They thus confuse arguments that provide evidence for the possibility/actual existence of the MEB with arguments that provide support for the possibility/actual existence of the MGB.

In fact, I can think of few theistic arguments, outside of bare assertions or appeals to scripture/irrelevant authorities, which aim to support P1. So even if I agree with Plantinga that P1 is not obviously irrational (which I do not), there is sufficient evidence for denying P1 and insufficient evidence for accepting it unless theists present a sound argument for P1. And even if theists could provide sound arguments for P1, this would be pointless for the reasons I discussed at the end of section II-A-3. I await theistic replies to the contrary. I know some theists will attempt to use the moral argument to support P1 [Youtube, parts 1 and 2 of KnownNoMore’s series “Why I Reject the Euthyphro Dilemma (and the moral argument as well)”]. Fortunately, meta-ethics is my philosophical strong-suit so I can think I can rebut any such argument. I will attempt to do so in a separate paper.

So if by “God” a theist means the MEB, then my arguments do not show that God is metaphysically impossible; but that is only because the theist has agreed to not define their God as metaphysically necessary. The moment the theist changes their mind and gives in to the temptation to define God as the metaphysically necessary MEB (i.e. God   =   the MGB), God becomes metaphysically impossible. Given section I-B-2's distinction between metaphysical and logical modalities, one can show the MGB is metaphysically impossible while still allowing the theist to claim the MGB is coherent and thus logically possible. Furthermore, since the metaphysical OA solely hinges on metaphysically NE, God needs to be defined as an MGB, not an MEB, for the metaphysical OA to show that God exists. So either the theist sticks with a definition of God that does not include metaphysically NE and thus forfeits the metaphysical OA (a relatively minor loss) or the theist defines God as metaphysically NE and thus makes God metaphysically impossible.

In conclusion, the atheist has solid arguments for denying P1 and thus saying that the MGB is metaphysically impossible. This does not entail saying that the MEB is metaphysically impossible and so, as per my arguments at the tail end of section II-C-2, the atheist’s claim is not overly strong; saying an NEX is metaphysically impossible is quite a modest conclusion when compared to saying that X is impossible (where X includes only S properties) or an X exists in every metaphysically possible world (equivalently: a metaphysically NEX is metaphysically possible). Theists should thus not slip metaphysical necessity into their description of God and then act surprised that the resulting being is metaphysically impossible.

III. The Fall of Logical OAs

III-A. The Logical OA is Less Plausible than the Metaphysical OA, or, “logic gets picked on”

The logical OA pales in comparison to the metaphysical OA. The logical OA has most of the problems noted in section II, but also comes with an additional problem in section II-D’s discussion of obviously irrational modal intuitions. Namely: much more skepticism and confusion exists regarding our epistemology for metaphysical modality versus our epistemology for logical modality (for a discussion of modal epistemology see Vaidya 2007). For example, some philosophers argue that conceivability fails as a sufficient test for metaphysical possibility (Chalmer’s, chapter 2; Youtube, ConsciousnessOnline’s “Richard Brown -The 2D Argument Against Non-Materialism”). Other philosophers, much fewer in number, argue that metaphysical modality amounts to the same thing a logical modality (Chalmers 1996 may advocate this view in chapter 2). Yet the guidelines for logical possibility and logical necessity remain quite clear: it boils down to conceptual truths. This makes it much harder to use uncertainty about modal intuitions/modal epistemology to argue that one’s logical modal intuitions are not obviously irrational versus using similar uncertainty to defend one’s metaphysical modal intuitions as not obviously irrational (see paragraph II of section IV). The clarity of logical modality’s epistemology, I argue, provides a very easy method for dismissing both Malcolm’s argument and the logical version of Plantinga’s OA.

III-B. The Logical Version of Plantinga’s OA, or “+/- ?”

The sets of properties specified by each description are as follows, as per section I-C:

MEB   :   {omnipotent, omniscient, morally perfect}

logically necessary MEB (i.e. the LMGB)   :   {omnipotent, omniscient, morally perfect, logically necessarily existent}

Logical necessity is characterized by conceptual truths, as I discussed in section I-B-1. It is a conceptual truth about logical necessity that if X (ex: X  =  MEB) is logically necessary (thus leading to the LMGB), not-X must entail a contradiction or a denial of a conceptual truth. So logically necessary existence (or logically NE) involves existence coupled to conceptual truths. More specifically: it is a conceptual truth about logically NE that if a being is logically NE, then denying the existence of that being minus logically NE must entail a contradiction or the denial of a conceptual truth. The contradiction is not supposed to be in denying the being with logically NE: it is in denying the existence of the being minus logically NE. To put it more simply, a  logically NE cat is incoherent not because of whether or not one can deny the existence of an LNE cat without contradicting oneself, but because one can deny the existence of a cat without contradiction or denial of a conceptual truth. An example might help.

Suppose I have the concept “horse” and want to know whether the concept of a “horned horse” is coherent or incoherent. I do not determine this by showing there is some description (say, “unicorn”) that entails “horned horse,” since that description itself could be incoherent. That would be analogous to showing that the description “maximally great being” entailed the concepts LMGB or NE. This goes hand-in-hand with my claim in II-B-1 that the concept MGB was not special just because it entailed NE; any description could be constructed such that that description entailed NE. So if I want to know whether a “horned horse” is coherent, I instead determine whether any of the conceptual truths about “horned” conflict with any of the conceptual truths about “horse”. There are a number of ways of doing this. For example, if I showed that the concept “horse” entailed the concept “horned,” I would have shown the concept “horned horse” was coherent if “horse” was coherent (analogous to showing that the MEB entails NE without redefining the MEB into the MGB). Or I could show that “horned” conceptually entailed “horse” and thus a “horned horse” would be coherent if “horned” was coherent (analogous to my request in II-B-2 that theists explain why a being X that is NE must have the other GMPs [supposedly: the features of the MEB]). Since none of the conceptual truths about “horned” contradict the conceptual truths about “horse” and both “horned” and “horse” are coherent concepts, the concept “horned horse” is coherent.

Suppose one now proposes the concept of a “married bachelor.” Again, it is irrelevant whether one can or cannot construct a description that entails “married bachelor.” Instead, what matters is whether any conceptual truths about “married” conflict with conceptual truths about “bachelor.” And in fact, some of the truths do conflict: bachelors, by definition, are unmarried. So the concept “married bachelor” is incoherent. So now take the LMGB (or the MEB + logically NE). The question is not whether there is a description entails the traits of the LMGB. Instead, the question is whether any conceptual truths about “logically NE” conflict with conceptual truths about the other features of the “LMGB” (i.e. the features of the LMGB minus logically NE or, more simply, the features of the MEB). One conceptual truth about a logically NE being is that you cannot deny the existence of the being minus logically NE, without entailing a contradiction or the denial of a conceptual truth. Since one can deny the existence of the MEB without contradicting oneself or denying a conceptual truth, the notion of a “logically necessary MEB” or “an MEB that exists as a matter of logical necessity” is incoherent.

Again, as in the case of “bachelor” and “married bachelor” where I showed the latter concept was incoherent without having to show the former concept was incoherent, I have shown that the LMGB is logically impossible without having to show that the MEB is logically impossible. So if by God a theist means the MEB, then my argument does not show that God is logically impossible; but that is only because the theist has agreed to not define their God as logically necessary. The second the theist changes their mind and gives in to the urge to define God as the logically necessary MEB (i.e. God   =   the LMGB), God becomes logically impossible. Furthermore, since the logical OA solely hinges on logically NE, God needs to be defined as an LMGB, not an MEB, for the logical OA to show that God exists. So either the theist sticks with a definition of God that does not include logically NE and thus forfeits the logical OA (a relatively minor loss) or the theist defines God as logically NE and thus makes the concept of God incoherent. Theists should thus not sneak logical necessity into their description of God and then act surprised that the resulting description is incoherent.

{Hilarious side-issue: If God's existence is logically necessary, then "it is not the case that God exists" is logically impossible/incoherent/self-contradictory. An OA proponent commits to this claim when they say, "you need to show God is incoherent in order to rebut the OA," since coherence goes with logical possibility, not broadly logical possibility. And as I noted in section II-B-4-a-ii, one can logically derive any conclusion from a logically impossible premise (Pigden, 424). This is because any deductive argument can be rephrased as a material conditional "If P then C", where P is the conjunction of all the argument's premises and C is the argument's conclusion. A material conditional is true if its antecedent is false and its consequent is truth-apt. This leads to unfortunate results for the proponents of logical OA. For instance, Wes Morriston (20-23) notes that many moral arguments for God take the following form:

1   :   If objective moral values (or requirements or...) exist, then God exists.

2   :   Objective moral values (or requirements or...) exist.

3   :   God exists

(from 1 and 2)

Even if a theist does not explicitly statement their argument in this way, they normally commit to something like this. However, 1 is logically equivalent to the following:

1'   :   If it is not the case that God exists, then it is not the case that objective moral values (or requirements or...) exist.

In fact, Craig often employs premise 1' in his moral arguments for God. But now the problem should be clear: one can replace the consequent of 1' with any truth-apt claim and 1' would still be true. For instance, I could change the consequent to something ridiculous such as: "then Barack Obama was never elected President" (or "then Yuno is not perfect"), “2 + 3 = 7”, or "God exists". You can thus infer anything from a contradiction. If this is so, Craig should not be employing this style of reasoning in his arguments. He cannot draw any implications from a positive atheist's denial of God's existence, unless he admits he could derive any claim he wanted from this incoherent assertion. The same holds true for any theistic argument that takes the form "If P, then God exists. P. Therefore God exists;" i.e. this holds true for nearly, if not all, arguments for God since most, if not all, arguments for God can be rephrased into this form. Theists cannot try to defend their argument by noting the implications of God's non-existence since God's non-existence would imply the truth (and falsity) of any and every claim. Since theists do think that only certain claims can be inferred from God's non-existence (such as the meaningless of life or the non-existence of objective moral requirements) this shows that, contrary to their voiced opinions, most theists do not think "God exists" is analytically true and thus they do not believe that God's existence is logically necessary.

If God is defined as the MEB, then this implies that the LMGB is incoherent and that the logical OA cannot prove God's existence. And if God is defined as the LMGB, this still implies that the LMGB is incoherent: the theist accepts that the existence of God (i.e. the LMGB or "logically NE MEB") is not logically necessary, which is a contradiction. So if the theist thinks the atheist must show that God is incoherent in order to rebut the modal OA (i.e. the theist employs logical modality, not broadly logical modality, and thus means the LMGB when they say "God"), the theist has a choice: accept that God's description is incoherent or cripple most (if not all) arguments for God's existence [other than the logical OA, which is beset by its own problems]. The logical OA is a virus that infects and lyses every other argument for God. Theists should therefore immediately dispose of it. Thanks to Wes Morriston, brilliant theistic philosopher that he is, for inspiring this argument.

I am not claiming that one cannot argue for a logically necessary conclusion nor that one cannot examine the implications of denying a logically necessary truth. Instead, my claim is that if you think statement L is logically necessary and you decide to examine the implications of not-L, then you should immediately note that you can infer anything from not-L. Of course, most analytic philosophers follow this rule. For instance, if an analytic philosopher thinks "2 + 2 = 4" is a conceptual (i.e. logically necessary) truth, the philosopher will only examine the implications of denying this truth in order to explicitly show a contradiction. This is all that’s required to show that the original statement is an analytic truth. The philosopher will not (as Craig does for "God exists") stand in front of an audience and wax philosophical about the horrific theoretical and practical results of accepting that "it is not the case that '2 + 2 = 4'," as if contradictions do not imply the truth (and falsity) of every claim. If a theist really believes they can draw meaningful conclusions from a positive atheist’s denial of God’s existence, the theist has already accepted that God’s existence is not logically necessary. (8/2/12)}

III-C. Rebutting Theistic Replies, or “logic leans right”

Theists could retort that that my argument in section III-B depends on assuming that the existence of an MEB can be denied without implying a contradiction or denying a truth of logic. And isn’t that unfair? This objection fails for a number of reasons. First, I could employ the conceivability argument from section II-D in my own defense. It is conceivable that an MEB does not exist so it is metaphysically possible that an MEB does not exist. And since it is metaphysically possible that an MEB does not exist, it is logically possible that an MEB does not exist. So the existence of an MEB can be denied without contradiction. Any argument for the possible non-existence of the MEB would therefore entail that the MGB is incoherent (see section II-D). Second, all the positive atheistic arguments I mentioned in section II-D support the non-existence of an MEB in the actual world. This implies the non-existence of an MEB in a logically possible world, contrary to the logical version of P1. Third, every negative atheistic argument undermines the logical version of P1. Negative atheists argue that belief in the actual existence of the MEB is unjustified/lacks sufficient evidence. So of course they also think that belief in the necessary existence of the MEB is unjustified/lacks sufficient evidence. And since the logical version of P1 is equivalent to saying the MEB's existence is logically necessary, then negative atheistic arguments undercut any support for P1. Fourth, there may be some persuasive atheistic arguments for the incoherence of the MEB (ex: Youtube: TheoreticalBullshit’s “Omni VERSUS Omni!”, Theophage’s “The New God Debate: Theophage’s Opening Statement” and Theophage’s follow-up videos), which would, of course, entail the incoherence of the LMGB. Since the existence of the LMGB entails the existence of the MGB [logical necessity entails metaphysical necessity] showing the MGB is incoherent also shows that the LMGB is incoherent. I provided arguments for the incoherence of the MGB and the MEB in the latter half of section II-B-3-c. So atheists have further grounds for thinking the concept "LMGB" is incoherent.

Fifth, as I discussed near the end of section II-C-2, people constantly deny the actual existence of different beings (hobbits, invisible unicorns, Kengo, etc). But denying the actual existence of X entails accepting that the concept “the logically necessary X” is logically contradictory. X’s non-existence in the actual world implies X’s non-existence in a logically possible world, conflicting with a conceptual truth about logically NE; namely: logically NE things exist in every logically possible world. We are even willing to accept that it is logically possible for entities which are not abstract (planets, a given non-physical mind, Daxter, etc.) to not exist, until we are presented with contrary evidence. Theists should not (in an ad hoc manner involving special pleading) increase the burden of proof when the being in question is their own God. Even Plantinga avoids this burden shift in the quote from the end of section I-B-1. He freely admits that “God exists” is not analytically true and can thus be denied without contradiction or denial of a conceptual truth. He holds to this position in his later work. This is why he phrases his modal OA in terms of broadly logical necessity, not logical necessity. Even Craig accepts that one can deny God’s existence without contradiction (when he isn’t engaged in double-speak; Craig, “Does the…?”). As I discussed in section II-B-1, the theist bears the burden of proof in showing that "the MEB exist" cannot be denied without a contradiction and thus the LMGB is coherent. After all, conceptual truths may be unobvious (Joyce 2006, 149; Pigden, 427; Plantinga, 220), so just because the LMGB looks coherent to an apologist does not mean the concept is coherent. Especially since some apologists have been known to say anything in defence of God's existence (*cough* William Lane Craig *cough*). So until we are provided with evidence to the contrary, our primae facie epistemic assumptions are as follows: if X has only S properties (not T properties), then X is contingent and thus X is logically possible and logically NEX is logically impossible. Unless OA proponents forfeit their right to deny the existence of any non-abstract object or present an argument for why denying the MEB’s existence entails a contradiction or a denial of a conceptual truth, my argument against the logical version of Plantinga’s OA remains unaffected.

And how would theists even go about providing such an argument? Even if the theist provides an argument for the logical version of P1, then as I argued at the end of II-A-3, the resulting logical OA uninformatively begs the question and lacks argumentative force because it presupposes the strongest form of theism in its first premise; namely: that theism’s truth is conceptually necessary (i.e. “God does not actually exist” is self-contradictory). Additionally, since logic is conservative, one only gets out as much as one puts in. Because none of the rules of logic have predicates referring to omnipotence, omniscience, etc. (let alone God), it is extremely unlikely that theists will be able to show that logical formalisms (a genus in the family “conceptual system” [see section I-B-1]), on their own, entail the existence of God. The transcendental argument for God from logic may or may not help here. The argument does not show that denying God’s existence entails a contradiction or the denial of a conceptual truth. The argument instead makes a metaphysical claim about God’s existence in relation to the existence of abstract objects. If it is a metaphysical, not conceptual truth, that abstract objects imply the existence of a God, then the transcendental argument, even if sound (which it is not), would not support the logical version of P1. Instead, the theist would need to show that it is a conceptual truth that abstract objects entail a God and that abstract objects are logically NE. I await such an argument (and for theists who look to Craig for aid: Craig’s a nominalist).

Alternatively, some theists might be tempted to engage in an obviously irrational move that dates back to at least St. Anselm. These theists will ignore my warning in section III-B to examine not whether the LMGB could be denied without a contradiction, but whether the MEB can be denied without contradiction. They will then say something like, “it is obviously contradictory to deny the existence of a logically NE MEB (i.e. the LMGB). After all, the LMGB is defined as existent. So the LMGB must exist.” This argument has many problems; I hope no theist feels tempted to pursue it. First, the argument ignores the warnings and arguments I gave in section III-B. Second, the argument would prove the existence of many things, since for any logically possible being X, one would need only attach logically NE to that being’s description and then use the theist’s argument to show that being existed (Gaunilo sneak attack!). So at this point the OA defender blatantly attempts to define God into existence.

Third, the argument commits a basic category error. “Exist” can be used in a definitional (or conceptual) sense (“by definition, God is an existent being”) and an ontologically-committing sense (“God actually exists”) [Oppy 2011, sub-sections 1 and 2 of section 4]. The former sense does not commit one to claiming that God exists in the real world (compare with: “by definition, Santa Clause exists”) while the latter sense does. For the claim N, where:

N   :   the logically NE MEB does not exist

the “logically NE” in N must be definitional, not ontologically-committing; otherwise no atheist would assert N and the theist’s reply begs the question. But then a dilemma arises: the “exist” in N is either definitional or ontologically-committing. If it is definitional, the atheist does contradict themselves when they assert N. But that is not what the theist needs for their argument, since this would only imply that atheists cannot deny a definitionally existent deity definitional existence. That is no more interesting than saying, “if Santa existed then it would be incorrect to say that Santa did not exist.” Definitional existence just makes a claim about what would be true if a concept had a referent in reality. So what if the “exist” in N is given an ontologically-committing reading? Then N is not contradictory. The atheist is simply denying that the concept God has a referent in reality. On this interpretation, N could be read as saying “if God actually existed, then God would exist necessarily, but it turns out that in the real world, God does not actually exist.” Some theists may conflate definitional and ontologically-committing existence and thus believe that N is contradictory. Once we clear up this equivocation, the theistic reply here falls apart.

In conclusion, I do not think either of the theistic arguments surveyed in this sub-section adequately defend the logical version of P1 against my argument from section III-B.

III-D. Malcolm’s Argument, or “why bother?”

My rebuttal of Plantinga provided all the tools necessary for dismantling Malcolm’s argument. In section II-B-4-b, I used Gaunilo-type counterexamples to rebut Malcolm’s argument. But Malcolm’s argument has additional flaws, as seen when we attempt to define the God his argument seeks to prove. Malcolm has two options for his definition of God: to include or to not include modal necessity in his definition. I will survey both options in turn.

Suppose by “God” Malcolm meant something which makes no reference to T properties or modal necessity (such as the MEB). Furthermore, suppose we grant the theistic claim that the MEB is coherent; any plausible OA requires this claim in order to work. p1 would then be false since nothing about the nature of an MEB (as contrasted with the LMGB) entails that the MEB is either logically NE or logically impossible. Instead the “logical necessity/impossibility” dilemma only arises when God is defined as the LMGB. The falsity of c2 results from the same reasoning: the description of the MEB does not contain logical NE. However, on this interpretation, I would not have shown that p3 or c1 are false. This is irrelevant since p3 and c1 alone are not enough to get Malcolm to his conclusion that God exists.

So Malcolm, as a proponent of modal OAs, must somehow slip necessity into his definition of God. Malcolm has two main options for doing this: logically NE and metaphysically NE.

If Malcolm includes logically NE in his definition of “God” (i.e. God  =   LMGB), then since I argued in section III-B that the LMGB is incoherent and thus logically impossible, c1 would be false. This also means p3 is false since God’s nature would be self-contradictory. However, p1 and p2 could still be true, though this would not be enough to get Malcolm to his conclusion that God exists. If Malcolm defines “God” as the metaphysically NE MEB (i.e. the MGB), then p1 is false because metaphysical necessity does not entail a dilemma between logical necessity and logical impossibility; that would make the mistake of mixing modalities, which I argued against at the end of section I-C, and inferring logical necessity/impossibility from metaphysical necessity/impossibility, which I also argued against in section I-B-2. c2 would be false for similar reasons. Again, I would not have shown that p2, p3, or c1 were false, but these premises are not enough to get Malcolm to his conclusion. If Malcolm instead meant “broadly logical” in premise p1, then as per the prohibition against mixing modalities, in order for his argument to remain valid all subsequent uses of “logical” would have to refer to “broadly logical.” But then p2 would be false since, as I discussed in section I-B-2, broadly logical impossibility (or metaphysical impossibility) does not entail logical impossibility (or self-contradiction). So Malcolm would not be able to infer c2 from p1-p3. Also, c1 would be false since I argued in section II-D that a broadly logically NE God is broadly logically impossible and I argued in section III-B that a logically NE God is logically impossible and thus broadly logically impossible.

So until Malcolm presents a plausible, non-ad-hoc definition of God that fits with his argument and addresses my objections in this paper, his modal OA remains unsound.

IV. Why Theists Still Defend Ontological Arguments, or “please have a seat on the couch”

In this section, I will do a bit of armchair psychoanalysis. First, let me be clear: I AM NOT asserting that proponents of the OA are being deceptive or intentionally disingenuous in advancing the argument (well…maybe Craig is [see section II-A-3]; but again, that’s neither here nor there). Far from it. The most obvious reason theists defend OAs is because they think OAs are sound. However, I think that some theists have other philosophical inclinations which also help explain their defense of the argument. I already examined one of those inclinations in section II-C-2: a tendency to apply S methods to T situations.  I will discuss three others: implicit usage of epistemic possibility, tepidness about defending God’s actions, and a lack of alternative evidence for God’s nature.

Youtube proponents of the modal OA (ex: migkillertwo, telemantros) distinguish between epistemic possibility and metaphysical possibility. I made the same distinction in section I-B-1. Atheists can misread P1 as referring to epistemic possibility and thus be confused about how not being absolutely sure God does not exist implies that God must exist. But again this cuts both ways. Theists can treat P1 as a metaphysical thesis, while using epistemic possibility to drive their argument. For example, as I discussed in section II-D, Plantinga claims only that P1 is not obviously irrational: we are not so sure of not-P1 (or not so unsure of P1) that we would say we are rationally obligated to not believe P1. But this is mere epistemic possibility. A theist in this mindset could say, “since P1 is not epistemically impossible (or obviously irrational), why can’t I tentatively accept P1 and thus tentatively accept the conclusion that God necessarily exists?” We saw a variant of this position at the end of section II-C-2 when I said theists might claim that the atheist’s denial of P1 is too strong or dogmatic; the theist may have thought the atheist was claiming P1 was epistemically impossible. The theist now works at things from the other end, trying to bolster epistemic confidence in P1 up to sufficient levels, even though (as I noted in section II-D) they lack sufficient evidence for P1. Once we get clear that denying P1 does not commit one to anything extravagant, that the not-P1 is more plausible than P1, and that P1 not only presupposes theism but presupposes the necessary truth of theism, then the air of epistemic respectability surrounding P1 vanishes, as does most of the rational motivation for accepting P1. The modal OA cannot be used a rational defense of God’s omnibenevolent nature and thus the modal OA fails as an indirect defense of God’s actions.

I have always been curious about how some theists defend God’s actions and inaction. Whenever I mentioned some unnecessary suffering in the world or some atrocity committed/ordered by a deity in a Holy Book, some theists would not bother explaining why a caring, omnibenevolent being would allow for such things. They would instead just say that the objection was moot since morality required God (this defense fails, as I will argue in a separate paper; see my comments from around 5/23/12 on TheCartesianTheist’s Youtube video “The atheistic moral problem” for a snippet of my views). I quickly realized that this reply just a convenient way for the theist to avoid the question (TheoreticalBullshit reached a similar conclusion via a different route in “A Treatise on Morality” from 18:30 to 19:58 [Youtube]). It is hard to come up plausible reasons why a caring being made this universe and then sat back and observed/ordered human + animal suffering without helping the helpless (see the Kengo and Fran examples from section II-B-2). And just as with the “morality requires God” argument, the theist uses the modal OA to avoid this difficulty by unnecessarily smuggling goodness into God’s description: the theist modifies the concept of GMPs as a method for introducing “omnibenevolence” into God’s nature even though “omnibenevolence” is completely unnecessary for the modal OA (as I discussed in sections II-B-1 and with my second objection in section II-B-3-a). And the OA comes with the added bonus of making those smuggled omnibenevolent traits necessary. No wonder theists hang on to the argument.

As I argued in section II-B-1, the OA is parasitic on NE and thus any properties one chooses to attach to NE are just along for the ride. So theists can (unknowingly) use the OA to smuggle in all the properties they wanted for God, but could never actually provide evidence for. On a related point, isn’t it curious that, besides theists arguing for God, no one uses OAs to argue for the existence of things they believe in? Yet if my Gaunilo-type arguments in section II-B-1 and II-B-2 were correct and a person believed modal OAs worked, that person could use the OA to prove the existence of almost anything they wanted. So if someone wanted an all-powerful galactic overlord Xenu to exist, they could just stick metaphysically or logically NE on to the description of that Xenu (or construct an ad hoc account of “greatness” or “awesomeness” or… such that the account produced a description of the NE galactic overlord they wanted) and use modal OAs to argue that the galactic overlord necessarily exists.

Yet instead of doing this, most people try to find strong evidence for things they believe exist. But (and this is just my conjecture based on experience, reading theistic arguments, and my discussion in section II-B-1) theists lack such sufficient evidence for thinking a being with the “omni-” attributes exists. So they resort to OAs to smuggle those attributes into existence. So it is not just a matter of smuggling moral properties into God’s nature so that God cannot be criticized; many theists use OAs to provide support for all those other non-moral properties of God for which they lack sufficient evidence. Craig clearly uses the OA to do this; along with the “moral deflection” usage I noted two paragraphs ago. So theists get all the properties they wanted for God, but lacked evidence for, in one fell swoop. And the modal OA has the added benefit of making God’s traits necessary, so the theist does not have the bother themselves with charges about how God’s nature “could have been different,” or how God “could possibly not exist.” Yet I have argued that OAs are fallacious, so theists should stop using them. However, unless theists come up with other arguments for God’s existence and the attributes of God’s nature to fill the needs discussed in this section, ontological arguments will continue to crop up for decades to come. And atheists will have to waste more time debunking them, lest some theists equate an atheist’s disinterest in an argument with an atheist’s acceptance of that argument as sound.

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