When we say 'Ed is mean', 'Ed' is the subject and 'mean' is the predicate. Can any existing thing or any notion of existence itself be considered meaningful if it cannot possibly fit into these two categories of subject and predicate?
Subject and predicate are linguistic categories; thus, from a logico-linguistic point of view, we have to consider also so-called Syncategorematic terms, such as the connectives : “and”, “or”, “if … then”, etc.
In a sentence like :
"Courage is a virtue"
we are predicating virtuosity of the subject courage; is thus courage an "existsing thing" ?
Wittgenstein is famous for answering "yes" to this question by distinguishing "know what" of propositional knowledge and "know how" of linguistic competence and other skills. Wittgenstein's position (in his late period) generally was, contra Frege and others, that meanings in a language are not reducible to propositional semantics and logical form, meaning is use. He likens language use to playing a game, and games have meaning beyond positions and following the rules:"imagine people amusing themselves in a field by playing with a ball so as to start various existing games, but playing many without finishing them and in between throwing the ball aimlessly into the air...".
More generally, the classical notion of fully expressing meaning in propositional knowledge, "essences", was rejected by modern philosophers of life and existentialists among others, Nietzsche and Heidegger are famous examples. Existentialist motto "existence precedes essence" signifies this rejection. Of course, non-propositional knowledge, being inexpressible in language, makes it hard to give examples by using it, but one can point to person's awareness of her own feelings, which is hardly reducible to subjects and predicates. The popular notion of qualia tries to capture the difference. Mary the color scientist may know everything about color propositionally, but she still gains new knowledge when exiting her black and white room and experiencing red for the first time. Religious mystics described their experiences as meaningful but ineffable throughout the centuries.
On a side note, although noun/verb distinction is very common in natural languages, and underlies the subject/predicate structure of sentences, there are exceptions. "A feeling for what a language without a noun-verb distinction is like comes from Straits Salish. Here, on the analysis by Jelinek (1995), all major-class lexical items simply function as predicates, of the type “run”, “be_big” or “be_a_man”", see Evans-Levinson.
In Physics I.3 b25, Aristotle points out:
Even our more recent predecessors were anxious to avoid making the same thing one and many at the same time. This is why some of them, like Lycophon, eliminated the word 'is', and others tried to alter the way we speak, by saying 'He pales' instead of 'He is pale', or 'He walks' instead of 'He is walking'.
This is because to the eye the thing presented to us is a unity, which is why he goes on to say:
They wanted never to add 'is' in case they turned what is one thing into a plurality.
But he argues that, even if a thing is one in fact:
ie. seen as a unity, in the way that a word is made of letters, but we grasp it as a unity; to emphasise this, we could do something along the lines of Lycophron and just eliminate the space
However Aristotle writes
things can be many either in definition ... or by division
'Ed is mean'
One could argue further that this is because that there is neccessarily change in the phenomenal world ie Nature
Otherwise, as he points out a little earlier:
if they mean everything to be one in definition (like 'mantle' and 'cloak') [and also for our purposes - meanEd] they will find that they are committed to the Heraclitean thesis: there will be no difference between what it is to be good, and what it is to be bad, good and not good will end up identical, and so will man and horse, and their doctrine will not be about things being one, but about things not being anything at all.
ie because we live in a world which has change, and this has parts, then we are committed to descriptions which too have parts.
So we know our description of 'meanEd' will have parts; the minimal number must be two; one part will have the capacity to cause change - the subject; the other the capacity to receive change - the object
But this isn't the division in definition that you ask: subject - object; but rather that which qualifies: object - qualifier
In linguistic terms, the object is named - so a name - and so a noun; and the qualifier is descriptive, and in two ways, either attributively and so an adjective, or predicative via a linking copula - in English, 'is'.