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This post concerns St. Anselm's version of the ontological argument for the existence of God. Part of this argument concerns Anselm's definition of God, which is, in so many words, "that than which nothing greater can be conceived."

First, let me say that the point I want to make has nothing to do with whether existence is a predicate. That is a separate issue ably debated by a number of philosophers.

Instead, I want to talk about whether greatness can be considered an essential property of a thing as opposed to a speaker evaluation of a thing.

As many of you know, Anselm reasons that God must exist apart from our thoughts, since that which doesn't exist apart from our thoughts would not be as great as that which does. Absent objective existence, God would not be that than which nothing greater can be conceived.

It seems to me that this argument depends on the notion that greatness can be an intrinsic property of something, including God. If greatness is only a speaker evaluation of God, rather than a property of God, then this evaluation is a property of the speaker. Since greatness itself cannot be intrinsic to anything as a matter of objective fact, then the ontological argument can't prove what it purports to.

Second, let's consider some of God purported attributes:

omnipotence: The ability to do anything. (I do not believe that it should be necessary to qualify this with phrases as in "anything logically possible," since logical impossibilities are not actual things that no agent can do, but instead meaningless verbiage. "Round square" is not a shape that can't be drawn. The phrase is instead meaningless verbiage a set of points that both are and are not equidistant from some center point.)

omniscience: The knowledge of every state of affairs. (Again, it should be unnecessary to qualify this with phrases as in "every extant state of affairs," since there are no states of affairs that don't exist, either physically, mentally, or both.)

incorporeality: Lacking a physical body. (I don't believe that there are good reasons to dismiss 'incorporeality" as a self-contradictory expression. As others have stated, supposing this incoherence makes a needless mystery out of why the term "incorporeal spirit" is used and understood cross-culturally around the world. What is more, gravity does not have a body. Neither do the other known forces. Yet it would be silly to assume that these forces cannot cause events.)

For my money, these supposed attributes of God are clear, if abstract.

Third, let's take a look at greatness: Patton was an unusually competent warrior, so he is called great. Mohandas Gandhi made influential use of non-violent resistance to undermine an oppressive colonial power, so he is called great. Vladimir Horowitz played the piano exceptionally well, so he is called great. Although the Great Wall of China did not stop invaders as it was meant to, it is very big, so it is called great.

The only relevant property that any of these "great" things have in common is that people exalt them, each for a different reason, i.e., on account of different properties that these "great" things have.

Finally, let's take a look at God's greatness. We might say that God is great because of his omnipotence, but anyone who has contemplated the problems of Evil and Natural Suffering might say otherwise. We might say that God is great because of his omniscience, but since God does not share arbitrarily large amounts of his knowledge with human beings, what's so great about his being a know-it-all? As for incorporeality, what the heck is so great about that? Empty space is incorporeal by definition. Yet almost no one exalts it, worships it, or calls it great.

tl;dr: Anselm's version of the ontological argument doesn't work because greatness is not an inherent or defining property of anything, but is instead a speaker evaluation of any number of collocations of properties, which evaluations will vary across contexts, speakers, and social groups. God doesn't exist necessarily just because some folks think he's great.

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    In the usual interpretations of the ontological argument, greatness is not a particular property, but just a shorthand. In Leibniz's and Gödel's versions, a shorthand for all "positive qualities", in Plantinga's, for just power, knowledge and benevolence. But there are still "inherence" issues with those explications of "greatness", see e.g. discussion and references in the thread on Leibniz's perfections.
    – Conifold
    Oct 16, 2023 at 5:31
  • Perhaps God never feels or claims any inherent greatness if God exists, not unlike Gödel's second incompleteness theorem, all ontological arguments are arguments only from human's perspective wherefrom greatness or goodness could be said to be inherent or intrinsic as some form of guidance to have the potential to arrive at some place... Oct 16, 2023 at 6:35
  • Compare with Great man theory: it refers to men "full of qualities", not to tall men. Oct 16, 2023 at 14:50
  • What was the word that Anselm himself used? Google Translate gives magnitudo, magnificentia, and majestas for the input greatness. Any of those would yield a different sense for the kind of comparison Anselm intended between existence-in-the-understanding and existence-outside-the-understanding. Oct 16, 2023 at 17:35

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Greatness is a difference of increase, so that X is greater in respect to something if X has more of this something than others. The Great Wall of China is greater in size than the wall of the average bedroom not only because it's evident, but also because you can measure the Great Wall with multiple bedroom walls. Clearly this will be the case regardless if people exalt the Great Wall or not or even if they called it the Smallest Wall of China. Likewise, a warrior's competence isn't dependent on praise or labels - clearly a warrior who can't win any battles is lacking something which the winning warrior has more of. Vladimir Horowitz has something which I, who can't play the piano, clearly haven't - even if Horowitz's pianist skills were absolutely unknown to the public, he wouldn't cease to be greater than me. Gandhi did something which most people couldn't pull off, even if everybody had been thankless to him in the end.

Indeed, none of the traits in your examples are truly "essential" to those who possess them. They are, in fact, accidental. Vladimir Horowitz wasn't born a pianist and he can lose his skills. Greater walls can be built than the Great Wall of China, and it can nevertheless be dilapidated. But they still are inherently great insofar as what they have more than others is independent of human appraisal.

St. Anselm, however, talks about God being essentially great. So, in what respect is God greater? Since we're talking about essences, we won't be comparing accidental traits such as size and piano skills but rather something more fundamental: what something is, which determines whatever accidents the entity can or cannot have. This "what" refers to being, so if we're comparing anything between essences at all, it's being itself. So a greater essence is one which has more being than another. And "greater being" means more of its existence pertains to the entity itself. Consider rocks, for example, which can't move unless moved by others, while animals can move on their own. Animals are essentially greater than rocks, they have powers which rocks intrinsically lack, not circumstantially, but because rocks are limited in their very being in ways which animals are not, and depend upon others in order to act. Again we have something inherently greater than another, again it's independent of human evaluation, and this time it's essential.

Therefore, if God is to be maximally great in essence, this is to be understood as God having an essence which in no way lacks any being, with no limitations, no dependencies, nothing derived from another whatsoever. Indeed, this is why St. Thomas Aquinas says God's essence is identical with His existence, and in this way non-existence can't be associated with God not even in principle. However, Aquinas does not regard this identification as self-evident. He provides arguments that purport to show that if limited beings exist at all, then the existence of a perfect and self-subsistent source of all being is entailed in order to account for their existence. Either way, what I have said should more than suffice to say that inherent greatness exists - not only in particular cases, but also in the case relevant to Anselm.

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Anselm's argument hinges on the definition of greatness encompassing the assumption that real is 'greater' than imaginary, but otherwise doesn't pin down exactly what great means. On that basis you can use his argument to prove the existence of almost anything. Let's define, for example, the Ocram Elephant to be the elephant greater than which no elephant can be conceived. If you now imagine an impossibly huge elephant the size of the Moon, Anselm's logic will tell you the Ocram Elephant must exist, since an existing elephant the size of the Moon is greater than an imagined one. So, Anselm's argument does work, in the sense that if you pick any definition of greatness you like, you can prove that more or less any sort of entity possessing that sort of greatness to a maximum degree must exist, since a real one must be greater than an imaginary one.

Indeed, a key feature of the argument is that it sidesteps any physical constraints. Suppose we could prove, for example, that it was not physically possible for an elephant to be larger than a given size. In applying Anselm's argument to the Ocram Elephant, I allow myself to conceive of an elephant larger than the largest possible elephant, and then prove that it must exist because an existing version of it is greater than an imaginary version.

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    In short: when you define God as existing, then it's not all that difficult to conclude that God exists. It's merely begging the question.
    – NotThatGuy
    Oct 16, 2023 at 7:39
  • Compare with Gödel's ontological proof for the notion of a "positive property": greatness mist not be read in spatial/physical terms. Oct 16, 2023 at 7:50
  • "Let's define, for example, the Ocram Elephant to be the elephant greater than which no elephant can be conceived." Han Solo can imagine a much bigger elephant. :D
    – RonJohn
    Oct 16, 2023 at 17:07
  • @RonJohn undoubtedly, but let's no forget- size isn't everything! Oct 16, 2023 at 17:14
  • Size might not be everything, but quantity has a quality all it's own. (Stalin did not say that.)
    – RonJohn
    Oct 16, 2023 at 17:20

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