Many people believe that there is: 1) no greatest number, 2) no greatest possible world, and 3) a greatest being (person, agent). The reason many people believe 1 and 2 is that there seems to be procedures to take a number (or world) and return a larger (or better) one. For any number (cardinal), take the powerset to get a larger number. For any world, stick some happy people in a far off corner to get a better world. (Of course, there is far from universal agreement on this second point.) The question arises: Is there any way to take a being, and return a better one?
One way is to try and link beings with the worlds they create. The idea would be that a being who creates a surpassable world is a surpassable being. This line of thought gives rise to a whole body of literature, some quite recent. Going in a different direction, here is another way that any being might be surpassable. Let us imagine that some virtues, e.g. courage, are traits wherein one wants to be at the mean that lies between extremes. We might imagine that 'courage-level' runs along a continuum from 0 (totally cowardly) to 1 (totally rash). Then, speaking loosely, somewhere in the middle is best. But, is it clear that any specific point is best? That is, what if the function, F, from courage-level (which runs from 0 to 1) to the value or goodness of the being goes as follows: F(x) = x for x in [0, 0.5] and F(x) = 1.01 - x for x in (0.5, 1]. Then there is no greatest being, as for any being, there is a better one. There is no greatest being, as beings get better as they approach 0.5 from the right on courage-level.
If there is an optimal point on a trait, call that trait 'closed'. If there is not an optimal point on a trait (for any level a being takes on the trait, there is a better level), as in the courage example above, call that trait 'open'. The question is, are all traits are closed? Or, what is the best argument to the conclusion that all traits are closed? In the absence of an argument regarding open and closed traits, the principle of indifference might suggest that courage is open with 50% probability and closed with 50% probability.
(One way to respond is to argue along these lines: certain traits/properties are fundamental (e.g., power, knowledge, freedom, goodness), these traits take maximal levels (individually and together), all other traits follow logically from these, and thus all traits take optimal levels and so are closed. Is there a relatively simple and convincing argument along these lines? Also, are there other ways to argue that all traits are closed? In particular, and thinking of approaching the question from a non-theistic angle, am I missing some sort of simple argument or reason as to why all traits are closed?)