In fact, the human mind thrives on comparisons and relations and there will be hardly any notion you can fully grasp without the help of such means. However, if for some strange reason you find the very word “greatness” objectionable, why nor replace it with some other term like “maximal perfection” or, which I would prefer, “maximal possibilities” respective “maximal potential”. Attributes to such a term can be most easily found.
Ok, let’s get into the details. Regardless of the name we use (greatness, perfection, whatever) we talk about a
composite attribute, as opposed to a
simple one. If one speaks of a simple attribute - for example: height - then it is meaningful to speak about the tallest mountain. The first problem with “greatness” is that it is a subjective concept. Your concept of a “great” statesman is not necessarily the same as mine, or your neighbor’s. You may choose a different set of simple attributes which comprise “greatness” for you, while I may choose a different set of them.
How can this be reconciled? It cannot. “Greatness” cannot be defined in a manner which will be acceptable to everyone.
Second problem: if one chooses the definiton of “greatness” as being “outstanding” in
every respect, then some of these simple attributes will contradict each other. The same mountain cannot be the tallest and smallest, at the same time.
Third problem: Even if we would speak of “simple” attribute like “taste”, how can one compare a great tasting steak to a great tasting ice-cream? It is impossible - they are incommensurate. If we would ponder a more complicated case, which person is “greater”, a great politician, or a great athlete? They cannot be compared.
Therefore “greatness” is not an objective and meaningful term. It is at best a sloppy description that someone wishes to use to express his or her
personal preference.
Kant has convincingly argued that contingent existence is not a property but just the shere fact that an object with its attributes is placed in space and time. However, Anselm never argued for contingent existence being a property and even made so explicitly clear in his reply to Ganilo. Contingent existence means that a being also could not exist, could be conceived of not existing. Obviously, for something that also could not exist, existence cannot be a property but just means that it is placed in space and time. But if we recapture our definition here, we see we’ve said that necessary existence would be more perfect/great etc. than contingent existence because necessary existence can by definition never come to an end and a being with necessary existence cannot be conceived of not existing. Thus we clearly must say that necessary existence is a property because otherwise there would be no inherent difference between a being that could also not exist and a being that cannot not exist – which would be absurd. – The attribute “necessary existence” can only be applied to a maximally great being. It’s quite useless to postulate a being with less than maximal greatness that nevertheless exsists necessarily. Because if a being is maximally great it must be conceived to exist in every possible, conceivable world. But with a necessary being it also always must be possible to conceive of world where that being exists self-sufficiently, all alone. And now it’s been made plain that the notion of a less than maximally great being is logically contradictory since it couldn’t exist in a world all of its own(because the maximally great being would also have to exist in this very world, which, however, could not be).
Emphasis mine in both cases. In the light of what I said above a “maximally great being” is a meaningless term. The rest is just icing.
Neverheless, we can contemplate the idea of “possible worlds”. The term “world” is an abstract concept, which is the philosophical equivalent of the mathematical term “set” or “collection”. A logically possible world is one, which contains no logical contradiction. That is the only restriction, the number of “entities” in a world is not defined. (I prefer the term “entity”, because “being” has other connotations (like being “alive” and being “conscious”).
Now, having two possible worlds (sets of entities) it is obvious, that they can be disjunctive. There is
no logical requirement that says: “if an entity exists in one possible world, then it also must exist (logically) in any other world”. Therefore, there is no basis to argue that there will be an entity, which exists across all possible worlds.
One of the possible worlds is the empty world, the equivalent of a matematical empty set. It contains no entities, therefore it contains no logical contradictions.
If you object and say that it is not “really” a world, you are still in trouble. The number of elements in the world is undefined, it can be zero, one, two, any number of “n”. You may wish to say that a “world” must have at least one element in it (which is not stipulated in the definition above). If such a restriction is applied, you still cannot assure that the two worlds will not be disjunctive. One possible world may contain exactly one electron, whilc another one may contain exactly one positron - no common element.
Conclusion: apart from the fact that “maximally great” is an undefined and undefinable concept, the idea of possible worlds does not come to the rescue. Possible worlds do not necessarily have a “common” element.
Q.E.D.
“Greatness” is an adverb, meaning it’s a predicate and can certainly be used in the “abstract sense” for anything regarded as comparatively the best. See the following definition from 