One of the most common objections that Internet atheists give to this argument is that there is no such thing as a great-making or lesser-making property. Greatness, they say, is a subjective thing. It is not really an objection to this argument for the existence of God, but to perfect being theology. William Lane Craig discussed this objection in one of his questions of the week. The questioner argued that the idea of a greatest conceivable being is inherently subjective. Craig responded:
To say that I tacitly endorse Anselmian Perfect Being Theology is an understatement, Aditya. I am an enthusiastic proponent. As I explain in Philosophical Foundations for a Christian Worldview, I see the conception of God as the greatest conceivable being as one of the guides for systematic theology’s formulation of the doctrine of God. . .
This objection seems to confuse God’s being the greatest conceivable being with our discerning what properties a greatest conceivable being must possess. I’ve already acknowledged a degree of play in the notion of a great-making property. For example, is it greater to be timeless or omnitemporal? The answer is not clear. But our uncertainty as to what properties the greatest conceivable being must have does nothing to invalidate the definition of “God” as “the greatest conceivable being.” Here Anselm’s intuition which you mention seems on target: there cannot by definition be anything greater than God.
Now you might think, “But what good is it defining God as the greatest conceivable being if we have no idea what such a being would be like?” The answer to that question will depend on what project you’re engaged in. If you’re doing systematic theology, then you have that other control, namely, Scripture, which supplies considerable information about God, for example, that He is eternal, almighty, good, personal, and so on. Perfect Being theology will aid in the formulation of a doctrine of God by construing those attributes in as great a way as possible. On the other hand, if your project is natural theology, which makes no appeal to Scripture, then you will present arguments that God must have certain properties. Note that mere disagreement about whether a property is great-making does not imply that there is no objective truth about the matter. When we have a disagreement, then we may present arguments why we think it is greater to have some property than to lack it. The fact that some properties (like timelessness) are not clearly great-making does not imply that no properties are great-making or that the concept of a greatest conceivable being is wholly subjective. . .
There is a more fundamental confusion underlying the second question, and that is the confusion of conceivability with imaginability. These are not the same. A thousand sided polygon is unimaginable, but it is hardly inconceivable. Conceivability is taken to be co-extensive with metaphysical possibility. So the greatest conceivable being is the same thing as the greatest possible being. It is, as Plantinga says, a maximally great being, the greatest being possible. True, Plantinga does give content to this notion in terms of specific properties, but those properties are obviously chosen because he thinks of them as great-making properties which a maximally great being cannot lack. Maximal greatness is doubtless not exhausted by the properties he mentions. His version of the ontological argument is based, in effect, on one of those incomplete, inadequate conceptions of God that you mention in this question.Even in secular literature, the field of ethics and the field of aesthetics are both filled with statements about objective values such as greatness. Some ethical theories talk about "ideal observers" and about contracts signed by "better versions of ourselves."
A Precise Formulation of the Modal Perfection Argument Terms
Putting this objection aside, we can formulate a more exact definition of a Maximally Great Being, at least as far as the argument is concerned. A being has Maximal Greatness if and only if that being has the properties of omniscience, omnipotence, and omnibenevolence in every possible world. Thus, A being is a Maximally Great Being if and only if that being has Maximal Greatness. This entails that the being exists in every possible world, since a being that does not exist cannot have properties such as omnipotence.
Let me cut off one objection really quickly. One might object that unicorns do not exist, and yet have properties, such as having one horn. It is not true to say that unicorns possess the property of having one horn. When we say that unicorns have one horn, what we really mean is that if unicorns had existed, they would have one horn.
We can also define great-making and lesser-making properties as follows. A great-making property is a property that a being would need to have in order to be a Maximally Great Being.
Obviously, the four properties just mentioned are Great-Making properties. These omni properties entail other properties, such as knowledge, will, potency, love, and many others. They also entail properties such as "being self-identical" which all things have. This makes the new formulation less intuitive. We do not think of "being self-identical" as a great-making property, but there is nothing incoherent in saying that it is so. We can then run a more efficient version of the Modal Perfection Argument, and one that does not even need Lesser-Making properties.
Advance Warning to Skeptics
Since the Modal Perfection Argument is valid, the only way to deny the conclusion rationally is to deny one of the three premises. As Marianne Talbot is fond of saying, it is not enough to fold your arms and say that you just think a premise is false, and that you are unconvinced. Philosophy is not concerned with your personal feelings or opinions. You need to give an argument for why anyone else should think that the premise is false. Since premises 1 and 3 are tautologies (true by definition), I suggest that the skeptic go after premise 2. But you need an argument for that, and preferably an example of a property that an omnipotent, omniscient, and omnibenevolent being would need to have entailing a property that an omnipotent, omniscient, and omnibenevolent being could not possibly have.
The Modal Perfection Argument
1. Maximal Greatness is a great-making property
2. If a property is a Great-Making property, its negation is the lack of a Great-Making property
3. A Great-making property do not entail the lack of a Great-Making property
Premise 1 is a tautology. It states that the property of having the properties of omniscience, omnipotence, and omnibenevolence in every possible world is itself essential for a being to have omniscience, omnipotence, and omnibenevolence in every possible world.
Premise 2 is a tautology. If a property is essential to being a Maximally Great Being, then by definition, a Maximally Great Being cannot lack this property.
Premise 3 is not a tautology, but it seems virtually impossible to deny. If we say that great-making property entailed the lack of a great-making property, we are saying that a property that a Maximally Great Being would need to have in order to be a Maximally Great Being entails the lack of another property that a Maximally Great Being must have. How could a property be essential for omniscience and simultaneously entail a property that an omniscient being cannot have?
If it were not possible that a Maximally Great Being exists, then the property of Maximal Greatness would not be instantiated in any object in any possible world. This means that:
Necessarily, if a being has a property, then that being lacks Maximal Greatness.
Which is equivalent to saying that for any property, that property entails the lack of Maximal Greatness.
Which is equivalent to saying that every property entails the lack of Maximal Greatness. By premise 3, this means that no property is a Great-Making property. But we just said that Maximal Greatness (not to mention omnipotence, omniscience, and omnibenevolence) is a Great-Making property.
Therefore, the proposition: "it is not possible that a Maximally Great Being exists" which is equivalent to "it is possible that a Maximally Great Being does not exist" results in a contradiction.