The Modal Ontological Argument is a restated version of St. Anselm’s original Ontological Argument for the existence of God. This version of the argument formulates Anselm’s reasoning using formal modal logic and Possible World semantics.
There are several forms of the Modal Ontological Argument, but one of the simpler and seemingly more common variations is constructed as follows:
Definition: A Maximally Great Being is Maximally Excellent and necessarily exists.
1. It is possible that a Maximally Great Being (MGB) exists.
2. If it is possible that a MGB exists, then a MGB exists in some possible worlds.
3. If a MGB exists in some possible worlds, then a MGB exists in all possible worlds.
4. If a MGB exists in all possible worlds, then a MGB exists in the actual world.
5. If a MGB exists in the actual world, then a MGB exists.
You may think this is the most blatantly irrational argument you have ever seen, and I would not disagree with you. But it can be confusing so it’s important to understand the argument and the peculiar reasoning underlying its choice of definitions.
In this article, I will explain the argument’s terminology and reasoning before presenting my objections to it.
The terms and concepts that must be understood are: Modal Logic, ‘Possible World’ semantics, Metaphysical Possibility, ‘Essential’ properties, ‘Necessity’ in Modal Logic, Modal Axiom S5, and the definition of a Maximally Great Being (i.e. God) used in the MOA.
2a. Modal Logic
Modal Logic is a type of formal logic that uses terms such as “possibly” and “necessarily” (called “modals” or “modal operators”) to express the truth or falsehood of a proposition. The logical relationships between these statements in an argument can be used to deduce a conclusion which is also expressed in these terms.
2b. ‘Possible World’ semantics
Possible World semantics is a system of terminology that refers to hypothetically possible states of reality by the term “possible worlds”. This includes the actual reality as well as what reality seemingly could have potentially been.
In more precise terms, a “possible world” refers to a set of all the logically possible statements that describe a single, complete, possible reality. For example, one could say that the statement “The Axis powers were victorious in WWII” is true in some possible world.
With ‘possible world’ semantics, the term “actual world” refers to the actual state of reality, which is one of many possible worlds. The “actual world” is the set of all true statements that describe reality as it actually is. We may not know what all these statements are of course, but this is what the term implies.
2c. Impossible, Contingent, and Necessary propositions
Propositions can be classified as either “impossible”, “contingent”, or “necessary”.
Impossible propositions are ones that could not be true in any possible world.
Contingent propositions are ones that can be true or false depending on the circumstances. These are true in some possible worlds but not in others.
Necessary propositions must be the case. They must be true by virtue of their own nature rather than as a result of conditions of any particular world. When using Possible World semantics, asserting that a proposition is “necessary” means that it is true in all possible worlds.
2d. Modal Axiom S5
This axiom of modal logic is a key part of the MOA. It is often misunderstood and can be confusing when you first hear it, but it does make sense. This axiom is not where the MOA’s problem lies, but it should be understood anyway so that we do not make invalid criticisms of the MOA.
Modal axiom S5 states that if some proposition is necessarily true in at least one possible world, then it must be true in all possible worlds (which includes the actual world).
You may hear people phrase this as “If something is possibly necessary, then it is necessary.” Due to the difference in semantics between everyday speech and modal logic, the axiom may sound absurd, but the logic it is meant to convey is perfectly sound (and is already understood by everyone, I imagine, although they do not phrase it in this way). Remember that what “necessary” means (i.e. “necessarily true”) in this context is something that definitely has to be true no matter the circumstances, due to its inherent nature, not because it follows from other conditions or propositions.
A common example is mathematics. It could be said that 2+2=4 is necessarily true. Or in other words, we consider it to be true in all possible worlds because to say otherwise would seemingly be incoherent. And therefore, according to Modal Axiom S5, if 2+2=4 in at least one possible world, then 2+2=4 is true in all possible worlds.
So if there were some other statement that we had reason to consider necessarily true, then logically it would have to be true in all possible worlds – and thus also true in the real world we live in.
2e. ‘Essential’ properties
When analyzing the possibility of an entity existing, we must clearly define that entity. An entity can be most specifically defined in terms of a set of properties.
We can classify these properties in two ways.
The properties that comprise the minimally required description of the entity are called “essential properties”. It would be incoherent to say that an entity could lack one of its essential properties and still possibly exist, because those properties are what define the entity.
These are contrasted with properties called “accidental properties” (also called “contingent properties”) that are superficial in the sense that they could have been different or be changed yet the entity would still be considered the same entity.
The Stanford Encyclopedia of Philosophy discusses the concept at length, but they summarize it like this: “an essential property of an object is a property that it must have while an accidental property of an object is one that it happens to have but that it could lack.”
For example, any definition of an individual human named Priya would probably need to include the properties that define humans as a species as well as those factors that fundamentally make her a distinct individual. However, Priya could also be born without one arm, be raised into a certain religion, or like spicy food. If any of these properties had been different or end up changing by any means, the individual could still fundamentally be considered Priya. (There is an interesting discussion to be had regarding what qualities really define a person, and how vague and malleable distinct selves actually are, but that’s a topic for another article)
There are, of course, myriad more essential and accidental properties that could define an individual, and we could debate which properties should be considered essential, such as certain aspects of someone’s personality. But for the illustrative purposes of this example, being human would be one of Priya’s essential properties. If a being lacked this property, then in what sense could it possibly be considered to be Priya? However, being born with one arm, raised as a Vaishnava Hindu, and liking spicy food would be accidental properties, because if any of these properties were different or happened to change, that entity would still be considered Priya.
2f. Definition of a Maximally Great Being (i.e. God)
In the MOA, the original creator of the MOA, Alvin Plantinga, refers to God as a Maximally Great Being. He defines this MGB as a being than which it is not metaphysically possible that there be one greater. Plantinga asserts that this means that God’s essential properties are: being immaterial, omnipotent, omniscient, and morally perfect, and must exist (i.e. “exists necessarily”, or “existence” is a necessary property of God).
3. The MOA’s reasoning explained
3a. Intended purpose of the MOA
The MOA is an unusual argument because it does not actually attempt to prove anything other than that the first premise expresses the same meaning as the conclusion.
This is crucial to understand:
The MOA does nothing except restate the first premise in other ways. The conclusion that God exists is already stated – not even only assumed – in the first premise. This is because the argument openly and explicitly utilizes a definition of God that includes necessary existence among its properties. Again, the MOA itself is not trying to prove that God is necessary. It begins with the assertion that necessity is an inherent, essential part of the definition of God. So obviously if you do not accept its definition of God then you won’t accept the first premise of the MOA and the argument leads nowhere.
For this reason I honestly question what use the MOA even has, because the entire argument is really within the definition of God it uses. Anyone who is aware of the definition being used will already agree or disagree with the MOA’s conclusion on that basis before ever reading the MOA.
So the topic of debate is only its proponents’ justifications for the definition of God being used and the MOA’s first premise which asserts that a being by that definition is possible.
Remember the beginning of the MOA:
Definition: A Maximally Excellent Being is immaterial, omnipotent, omniscient, and morally perfect.
Definition: A Maximally Great Being is Maximally Excellent and necessarily exists (i.e. exists in all possible worlds).
Premise 1. It is possible that a Maximally Great Being (MGB) exists.
Many people hear the first premise and mistakenly think it means “It is possible that a being exists which is immaterial, omnipotent, omniscient, and morally perfect.”
This may be because this is the definition of God used in most religious debates they tend to encounter, or because they take the term “Maximally Great Being” at face value instead of reminding themselves of how that term has been defined for this particular argument.
But regardless of the reason, many of these people will accept the premise as true then become confused by the remainder of the MOA since it won’t logically follow from what they thought the first premise meant. Just remember that the first premise references Plantinga’s definition of a Maximally Great Being, not a Maximally Excellent Being.
3b. Justification for why a MGB must be necessary
This is critical. The belief that one can define a MGB as a necessary being is solely the entire basis of the MOA. This is the actual point that debate centers around, not the MOA itself.
Plantinga argues that a MGB must exist because if a being lacks existence then it does not really have those properties, and thus contradicts its own definition. He makes this assertion numerous times in his writings, but this excerpt will serve as an example:
“…obviously a being can’t be omnipotent (or for that matter omniscient or morally perfect) in a given world unless it exists in that world.”
I will address this point in section 5b.
4. Invalid Objections to the MOA
Before explaining my own objections to the MOA, I would first like to list some common but invalid objections to the argument so the reader has an accurate understanding of the MOA and will be fair in their own debates on this topic.
4a. The meaning of “necessity”
Some people may misinterpret the notion of God being “necessary” to mean that God may have to exist in some possible world as a result of the state or conditions of that particular scenario. As a result they claim that the MOA actually just proves that God “necessarily” exists only in worlds where he does exist.
But remember that this is not the meaning of “possible” and “necessary” being used in an argument utilizing modal logic format. “Necessity” in Modal Logic refers to existing by virtue of its own nature and not as a result of any other conditions in any hypothetical reality.
When the appropriate definition of “necessity” is applied to the objection, we see that the objection is nonsensical.
4b. Swapping premises
Some people argue that the MOA is flawed because they think that Premise 1 could logically be replaced with an equivalent statement “It is possible that God does not exist” and that this would make the MOA’s logic prove that God does not exist. Because of this, they claim that the argument’s logic is flawed and does not prove either conclusion.
But this objection is invalid because under the MOA’s definition of a MGB including the property of being necessary, the proposition “It is possible that God does not exist” is not a claim that can be made since it would be a contradiction. In Possible World semantics, this point reads as “God does exist in all possible worlds”.
Consider if something like the number 3 or the notion of a square were the subject of this argument instead of God. If you accept the notion that it is inherently “necessary” (that is must exist by virtue of its nature), then there is no way to refute its existence. Stating that it is possible that it does not exist would be nonsense. The same is true for the definition of God in this argument. So the question we need to focus on is this:
Is it actually coherent that the definition of God includes the property of being necessary?
5. The Primary Flaws
5a. The concept of existence; why a MGB is not a necessary being
Critics of ontological arguments such as Kant and Caterus are still correct about them, even regarding this modern version.
The nature of the concept of existence – be it contingent existence, impossible existence, or necessary existence – either renders it a unique type of property that is distinct from properties which can define essential essence, or simply means it cannot be classified as a property at all.
In either case, the MOA uses the concept of necessary existence in a way that is incoherent. Existence is a concept that describes a relationship between a conceptual entity and reality – that is, whether the description of an entity matches an entity in the actual world.
So the concept of necessary existence can only coherently mean that an entity must exist in reality by virtue of the combination of properties that define its essential essence. In other words, the only way an entity is “necessary” is if the nature of an entity’s combination of essential properties cannot conceivably be missing from reality.
And since an omnipotent, omniscient, perfectly good being lacks such implications it is indeed impossible for it to be necessary in even one possible world, and therefore the key premise of the MOA is false.
5b. Existence and non-existence do not alter a thing’s essential qualities
The notion that existing increases the “greatness” or “perfection” of a property is a confusing idea in the definition of God used in all forms of the Ontological Argument. As I mentioned in section 3b, the MOA rests entirely upon the claim that a being only possesses its essential qualities if it exists:
“…obviously a being can’t be omnipotent (or for that matter omniscient or morally perfect) in a given world unless it exists in that world.”
But this is a simple and blatant error in logic. Plantinga is conflating concept definitions with instantiation in a possible world.
Whether a MGB – or any other being – has certain properties is purely a matter of concept definition; existence refers to the instantiation of a concept’s properties (i.e. a MGB) in a possible world. So a thing not existing is a fundamentally different situation from lacking its essential properties. Remember, a thing possessing a property in definition is different from that thing’s properties being able to impact the real world. Whether it can impact the real world is a matter of instantiation in a possible world.
Consider an example: it is nonsensical to claim that the property of omnipotence of an omnipotent being could be increased by that being existing in actuality. By definition this being is already as powerful as logically possible. The essential properties of this entity are unrelated to whether the entity actually exists or not, or how many possible worlds there are in which it exists.
When we apply these principles to the MOA’s definition of God, we reveal this point:
If you say that a MGB by definition can only be one that exists (regardless of whether your reason is that you think existence is necessary to maximize its properties or because you think existence is itself a property that increases “greatness”), then a MGB is still a contingent being. This is because all you have said is that a being only meets the definition of Maximal Greatness if it is Maximally Excellent and exists.
Nothing about this definition implies that a being with Maximally Excellent properties must necessarily exist.
1) “Greatness” is a subjective term, and has no clear meaning in the MOA
The use of the term “maximal greatness” to describe the defining property of God is problematic because “greatness” refers to subjective and relative notions or to measures of objective factors. Greatness cannot be treated as a quality of its own that could be possessed by an entity. To do so renders it vague and meaningless, and therefore the qualities attributed to a MGB are arbitrary and cannot form the basis of an objective point about the existence of a being.
Originally this article contained my full explanation of this point in detail but I have removed it since it made this article obscenely long and I wanted to keep my points on this page restricted to the most direct objections to the MOA. I will revise these additional points for posting to a separate, supplemental article devoted to that subject alone.
2) The Problem of Evil
I view the Problem of Evil as evidence that blatantly contradicts the possibility of God as defined by Plantinga. You can read my arguments in favor of this view and my responses to objections against it in the article at this link.
I have placed this objection in this section rather than listing it as a primary flaw of the MOA because the meaning of terms such as “goodness”, “moral perfection”, “omnibenevolence, or being “perfectly good” used in the definition of God are defined in different ways by different Theists, and sometimes not defined at all. And since the Problem of Evil is only relevant to the concept of a deity that wishes to reduce the suffering of other beings, not all definitions of moral goodness, the Problem of Evil cannot be said to apply to all forms of the MOA.