Resolved: The Modal Ontological Argument is Sound

Thank you, Rational Theist, for this debate! May it prove to be an intelligent and thought-provoking discussion!

The Ontological Argument for God is very old. Some form of it dates back to at least 1078 when it was proposed by Anselm of Canterbury. Since then, various philosophers have put forth other versions of it with minor adjustments. My opponent claims to be using the version put forth by Alvin Plantinga, which is possibly true, though I recognize it as the one used by William Lane Craig. However, you can only do so much to fix up a building that is built on a broken foundation, and the MOA is built on a bad foundation indeed. Allow me to explain.

Definition Troubles

My opponent says that a Maximally Great Being would have omnipotence, omniscience, moral perfection, and necessary existence. What is unclear to me is whether these qualities are antecedent to being maximally great or a consequent of it. If the former, then the definition of an MGB is entirely arbitrary and unjustified. The latter is also problematic, because 'greatness' is inherently subjective in most contexts. Even in mathematics, when something can objectively be greater than something else (for a particular definition of greatness), it is only a relative term - no number has the inherent quality of 'greatness'. This is relevant because an MGB may not even be a coherent entity in the first place. However, there is an even greater flaw with the MOA.

Proof That the MOA Begs the Question

Begging the question is when the conclusion to an argument is wholly contained within one of the premises. Arguments that beg the question are entirely useless, because one is forced to either just assume the conclusion without sufficient justification, or find a different argument to prove the conclusion independently, in which case the argument that begs the question is wholly redundant. The MOA is such an argument, and it is fairly easy to demonstrate this fact. Let us take a classic problem in mathematics, that of P versus NP. Consider this erroneous proof:

1. It is possible that P = NP.
2. If it is possible that P = NP, then P = NP in some possible worlds.
3. If P = NP in some possible world, then P = NP in every possible world.
4. If P = NP in every possible world, then P = NP in the real world.
5. If P = NP in the real world, then P = NP.
6. Therefore, P = NP.

P3 is simple to prove, as P = NP is a mathematical statement, meaning that it isn't derived from any contingent truths, so it is either necessarily true or necessarily false. It can't be a contingent truth. So this argument would seem to be sound, except that we could just as easily 'prove' that P ≠ NP, and it's obviously impossible for both statements to be true at once.

The problem here is with the first premise - what do we mean when we say that it is 'possible' that P = NP or that an MGB exists? To be sure, P = NP is an epistemic possibility (meaning, we do not know that it is false). Brilliant mathematical minds from across the globe have been trying to solve the P versus NP problem for decades, yet no one has been able to do so. However, the form of the logic used in the MOA is not syllogistically valid if P1 is taken to refer to mere epistemic possibility. Consider this statement:

If Germany borders China, then it is possible to travel directly from Germany to China without passing through any other countries.

This statement is true, but it is vacuously true. The antecedent does entail the consequent, but the antecedent is false, so the statement is true in a way which is meaningless. Now, consider the 'proof' that P = NP reanalyzed like so:

1. It is [epistemically] possible that P = NP. (We do not know that P = NP is a false statement. It may actually be false, but we do not know that it is false.)
2. If it is possible that P = NP, then P = NP in some possible worlds. (Vacuously true if P ≠ NP)
3. If P = NP in some possible world, then P = NP in every possible world. (Vacuously true if P ≠ NP)
4. If P = NP in every possible world, then P = NP in the real world. (Vacuously true if P ≠ NP)
5. If P = NP in the real world, then P = NP. (Vacuously true if P ≠ NP)
6. Therefore, P = NP.

It is now obvious that the argument is invalid - the premises do not entail the conclusion. Moreover, we also have to reconsider premises 2 and 3:

1. If it is [epistemically] possible that P = NP, then P = NP in some [epistemically] possible worlds.
2. If P = NP in some [epistemically] possible world, then P = NP in every [epistemically] possible world.

This is problematic, because P3 is also invalid on its own - since it is epistemically possible that P ≠ NP, it is not true that P = NP in every epistemically possible world even though P = NP is an epistemic possibility. We can rewrite:

1. If P = NP in some [epistemically] possible world, then P = NP in every [metaphysically] possible world.

...But this is not valid, either. Clearly, the logic being used here is only valid if we are talking about metaphysical possibility - that is, non-contradiction. Let's rewrite our argument to be logically valid:

1. It is [metaphysically] possible that P = NP.
2. If it is [metaphysically] possible that P = NP, then P = NP in some [metaphysically] possible worlds.
3. If P = NP in some [metaphysically] possible world, then P = NP in every [metaphysically] possible world.
4. If P = NP in every [metaphysically] possible world, then P = NP in the real world.
5. If P = NP in the real world, then P = NP.
6. Therefore, P = NP.

At last, a valid argument! But wait, saying that P = NP is a metaphysical possibility is logically equivalent to actually saying that P = NP! We've assumed our conclusion right there in the first premise. So it goes with the MOA as well. Indeed, making things as logically tight as possible, we can rewrite the first premise of the MOA using formal symbols as follows:

1. ◊□M

...Where 'M' means 'a being which is maximally good exists'. (The diamond symbol used refers to possibility, while the square symbol indicates necessity.) However, under modal logic, the very system my opponent is using, ◊□A → □A. Thus, the first premise can be rewritten as follows, without it affecting the validity or soundness of the argument:

1. □M

In other words, the very first premise of the MOA states that an MGB necessarily exists, without justification. Despite what my opponent suggests, this is anything but a modest claim.

The Impossibility of Necessity

My opponent tries to define an MGB as having necessary existence. However, you cannot simply define an entity as being necessary, unless you are taking its existence to be axiomatic. Rather, necessary existence must be demonstrated.

In ontology, when we say that something is necessarily true, we are saying that it is impossible for it to fail to be true, even hypothetically. For a necessary truth to fail to be true is logically incoherent and meaningless. For instance, the mathematical statement "2 + 2 = 4" is a necessarily true statement because it is derived solely from logical and mathematical axioms - things which are held to be inherently true. In order to prove anything logically, there must be some things which are taken to be true axiomatically. Otherwise, we would never actually be able to prove anything.

However, it is only appropriate for us to take as axiomatic statements which relate to metaphysical truth - truths about the fundamental nature of reality and logic itself. For instance, we cannot take "the speed of light in a vacuum is constant" as an axiom even though our understanding of physics relies on it, as it does not follow from the basic laws of metaphysics. We can imagine a world where physics are completely different from our own world, and this does not contradict the fundamentals of logic itself.

This is relevant, because an MGB as defined is not a metaphysical entity. It must have at minimum:

1. A mind to have knowledge, since it's omniscient
2. A will to exert its power, since it's omnipotent
3. A will that is free, since a morally perfect entity would always choose the morally correct course of action in any situation, and ought implies can. (If an entity has no moral obligations, then calling it morally perfect is meaningless, unless my opponent wishes to argue that I'm typing on a morally perfect keyboard.)

An entity with a mind and a free will is not a metaphysical entity - it goes beyond statements about the fundamental nature of reality and logical reasoning. From basic axioms like the law of identity, the law of the excluded middle, and the axioms that anchor modal logic itself, we cannot prove that "a mind with a free will exists" is a true statement. At best, we could prove that it is possible (and even then, free will is a tricky subject and I am not willing to concede that it is possible in a meaningful way), but not that it is necessary. It simply does not follow from metaphysical necessities. Therefore, any entity with omniscience, and/or omnipotence, and/or moral perfection is inherently a contingent entity.

However, this contradicts the definition of an MGB as having necessary existence! Thus, maximal greatness either can't include necessary existence, or it is simply logically incoherent. Either way, the MOA is unsound.

My opponent may object to the validity of this logic. However, I ask them this: what is logically incoherent about a world with no MGB? If it is my opponent's claim that an MGB is a non-contingent entity (which hasn't been demonstrated), and it is even an epistemic possibility that an MGB does not exist, then we cannot soundly conclude that an MGB is a metaphysical possibility. And if we cannot soundly conclude that an MGB is a metaphysical possibility, then we cannot conclude P1 of the MOA. Therefore, it has not been demonstrated to be sound - and that's precisely the burden of proof my opponent has. He has been unable to meet it.

Thank you for reading! I yield the floor.

Thank you, Rational Theist! Unfortunately, much of my case remains largely uncontested. Allow me to explain.

On Whether the MOA Begs the Question

My opponent draws a distinction between de re and de dicto modality. While it is true that the form of the argument my opponent uses does not directly state "it is possible that it is necessary that an MGB exists", necessary existence is still a stated property of an MGB, and if it is possible that an entity exists, it also must be possible for all its properties to exist, both in isolation and in combination. Thus, possible necessary existence is an inherent part of the first premise. In fact, the third "premise" of the MOA as stated by my opponent is simply a restatement of the fact that, under 5S Modal logic, possible necessity is the same as necessity.

In fact, the MOA as presented here has several statements that can be left out entirely - premise 2, for instance, is basically just stating ◊MGB → ◊MGB... which is axiomatically true. P3 has already been discussed, P4 is just a restatement of the 5S axiom □A → A, and P5 is wholly redundant. P1 is the only actual premise in the entire argument, everything else except the conclusion is something that simply cannot fail to be true under the axioms of 5S modal logic. Therefore, the argument can be rewritten like so, without changing its validity or soundness:

1. It is [metaphysically] possible that an MGB exists.
2. Therefore, an MGB exists

This formulation is problematic - a typical deductive argument has at least two premises, such as the classic "Socrates is mortal" argument, or other arguments for God like the Kalam Cosmological Argument. The fact that there is only one actual premise here indicates possible question begging, and whether he realizes it or not, my opponent actually confirms this when he tries to refute an inverse form of the MOA, stating:

For this argument to work my opponent needs to show why it is impossible for a maximally great being to exist.

In other words, I'd first have to disprove the existence of an MGB in order to prove that... no MGB exists. Well, true enough, but the form of the argument used is exactly the same as the positive MOA, the only difference being that positive "exists" statements are swapped for negative "does not exist" statements -- otherwise, the form of the logic and all terms are identical. Therefore, for my opponent's argument to be demonstrated as sound, he must first actually prove that an MGB exists. Notably, he did nothing to actually do that in the first round of this debate; he merely presented the argument and said that "there is nothing logically incoherent about [an MGB]." In other words, he merely stated that the first premise of the MOA is true and left it at that. That is not how the burden of proof works. My opponent has to actually demonstrate the truth of the premises he is using.

Now, he has actually provided some new arguments in this round! Unfortunately, they are very flawed.

The Incoherence of Maximal Greatness

I made (what I considered to be) a fairly simple argument in Round 1:

What is unclear to me is whether these qualities are antecedent to being maximally great or a consequent of it. If the former, then the definition of an MGB is entirely arbitrary and unjustified. The latter is also problematic, because 'greatness' is inherently subjective in most contexts. Even in mathematics, when something can objectively be greater than something else (for a particular definition of greatness), it is only a relative term - no number has the inherent quality of 'greatness'. This is relevant because an MGB may not even be a coherent entity in the first place.

While my opponent has attempted to shore up the idea of maximal greatness, he hasn't really addressed the point that, outside of mathematics, 'greatness' is a largely, if not entirely subjective concept. Rather, he simply treats greatness as objective and ignores the fact that I already contested this idea. Moreover, his attempted "proof" at the impossibility of the non-existence of maximal greatness is logically incoherent. Look at this statement which my opponent holds to be true:

Maximal greatness is the greatest "great-making property," therefore, Maximal Greatness cannot entail its negation of non-Maximal greatness.

This is impossible, and it is easy to demonstrate why:

1. A → A
2. If A has a truth value, "A ∨ ¬A" is true
3. ¬(¬A) = A

All of these are axiomatically true. We can further deduce:

1. A → ¬(¬A)

Now, let MG mean "the existence of maximal greatness". We can deduce the first statement below from the law of identity, the first axiom I mentioned above. The second comes from my opponent's own statement about maximal greatness not entailing the negation of its own negation. The others are simple logical deductions from the first two statements.

1. MG → MG
2. MG → ¬(¬(¬MG))
3. MG → ¬MG (from 2)
4. ¬MG (from 3)
5. MG (from 1)

However, this blatantly contradicts the law of the excluded middle, one of the axioms I restated above. MG and ¬MG are both held to be true simultaneously, and "maximal greatness exists" certainly has a truth value. Since its existence as defined leads to a contradiction, however, it must not exist as defined. In fact, Pro's 'proof' relies on assuming that the impossible entity, a maximally great being, does actually exist, and shows how its negation leads to statements needing to be both true and false at once. However, this is only true because an MGB as defined entails contradicting statements to begin with, so its negation might naively seem to also be impossible, but really, it's the definition itself that is incoherent.

Maydole's proof is likewise flawed, as it relies on circular logic to prove that existence is a property by defining a property of all existent entities as being "great-making". Of course, one could simply challenge this statement to begin with, and no progress has been made.

My opponent attempts to touch some intuitive sense of greatness by arguing, say, that an actual friend is greater than an imaginary friend, that love is better than hate, etc. Therefore, Pro argues, to deny the coherence of maximal greatness would be nonsensical. However, the response to this is simple, and I already gave it within one paragraph in my opening. Greatness means different things in different contexts.

For instance, F. Scott Fitzgerald famously referred to his character, Nick Gatsby, as The Great Gatsby in the title of his most famous work, and this is certainly very meaningful in a literary sense. His book could be said to be a great book. And there are a great many stars in the universe -- far more than the number of grains of sand on Earth, in fact. Are all these forms of greatness equivalent? Not at all! Being maximally great in one way does not necessarily entail maximal greatness in another.

My opponent states that to exist necessarily is greater than to exist contingently, and to exist contingently than to not exist. In other words, existence itself is taken to be inherently great. But this also means that, if some omnipotent, omniscient, omnipresent, omnibenevolent being existed in our world, but not any hypothetical worlds that don't exist, then its greatness would be diminished. A reader might point to the idea of a multiverse, but under ontology, if the multiverse theory is true, then the multiverse itself would be the actual world. Any possible world not contained within the actually existing multiverse would simply be a non-real hypothetical. The idea of God's greatness being diminished by not existing in mere hypothetical worlds seems silly and absurd, but that just highlights the fundamental problem with the MOA in all its forms - greatness of existence is conflated with the greatness of grandeur - that which people intuitively associate with the quality of being 'great'.

What is sneakily left into the MOA, and which most people do not easily catch, is that this latter maximal greatness (that of grandeur) is held to be subsumed under the greatness of existence, but this has in no way been substantiated by my opponent, and I contest this idea. I submit that my opponent is merely using the fallacy of equivocation, labeling necessary existence as 'great' and therefore lumping in everything else that intuitively feels 'great' to us without sufficient justification. The logic being used here is fundamentally unsound, and there is no reason a necessarily existing entity would also necessarily have omnipotence, omniscience, etc.

On the Inverse MOA

As I stated above, my opponent makes reference to a counter-MOA (let's call it the Modal Ontological Counter-Argument or MOCA). While I did sort of hint at it during my R1, my opponent completely missed the forest of my argument for the trees. I stated clearly:

Maximal greatness either can't include necessary existence, or it is simply logically incoherent. Either way, the MOA is unsound.

My opponent zeroed in on the first half of this statement, and ignored the second. I provided what I considered to be a fairly straightforward argument for why I feel an MGB is an impossible entity, and Pro has not substantially responded to it. Put simply, my argument is that omnipotence, omniscience, omnipresence, and moral perfection are all incompatible with the property of necessary existence. It is like how Bigfoot is a possible but not actually existent entity (presumably), but a "necessarily existing Bigfoot" is clearly an impossible entity, since Bigfoot is obviously a contingent entity. I believe that the inclusion of necessary existence in the definition of an MGB turns it from an entity whose possibility is at best debatable, to a being which is actually impossible. That is my argument, and Pro has provided no clear, direct rebuttal. He has still been unable to meet his burden of proof.

Thank you for reading! I yield the floor.

Unfortunately, I am going to have to waive this round. I spoke to Kohai over private message and we agreed to essentially turn this into a three round debate. I'll post my concluding round next. Thank you!

FORFEITED