Resolved: The Modal Ontological Argument is Sound

the problem in the argument is that it assumes a lot of definitions.

Maximally great being is defined as being which exists in all worlds.

that is existence already built in definition.

So saying "being which is defined as existing everywhere = exists", is a definitional tautology which only works as long as someone accepts a definition.

Likewise, definition of "possible" in modal logic doesnt really apply to reality, because saying that something is possible by our current knowledge is not saying it is possible by all knowledge out there.

So argument works as long as someone agrees to definitions. But why would someone agree to definition "maximally great being exists everywhere", and then argue it doesnt exist?

So, we can string together words and create non-sense within a reasonably coherent framework.

Though what the Modal Ontological Argument boils down to, is philosophically waffling verbiage that desperate theologians might resort to in moments of crisis...Often referred to somewhat disparagingly, as verbal diarrhoea

And sound is as sound is required to be.

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.