OK. I can accept that existence exists. I will even grant "conscious" as real, though I cannot go further to define what it really is.
But I cannot accept that "A is A" is axiomatic, because it requires us to be able to define what A really is in the first place. For example, suppose I have a wooden chair. Is it the same wooden chair that stood before me a minute ago, right down to the very last quark? Can I prove that? And if there's a quark's worth of difference, can I really say that "A is A" in this case? I suppose you can defer to something like Plato's "forms," but then you'd have to prove them, too.
The point is, if we want to actually use "A is A" for anything useful, we need to define in some manner what "A" is in the first place -- which ultimately requires us to make assumptions about A. And what's more, we have to choose the proper "A" from among a wide array of possibilities.
Looking at this from the practical perspective, the problem of defining "A" turns out to be quite difficult. In this thread, the A's in question are things like "self-interest," and "happiness," and as we've seen these particular choices are in no way axiomatic, according to your own definition of the term.
Now let's look at your proposed other axioms. None of them satisfies your conditions for being axiomatic.
Plurality. (There must be more than one thing.)
This axiom requires us to assume that there is in fact more than one thing. You can objectively prove (to yourself, not me) the existence of one only thing: yourself.
Dynamism. (There must be change.)
This contradicts "A is A," and it also requires you to assume a whole bunch of things about the ultimate structure of the universe. Suppose, however, that I posit a viewpoint that lies "in eternity," which sees the universe in the same sense we see a completed book. (The statement "existence exists" seems to suggest that such a viewpoint is logically possible.) In that case, the concept of dynamism may not be meaningful.
Differentiation. (All existents are different.)
A mighty broad statement, the truth of which is muddied by such things as quantum entanglement, not to mention Dr. Heisenberg's little theorem.
A is A is not "metaphysical" it is epistemological. Your father is your father, no matter how much he changes. If this is not true, you could not even state your criticism. What you mean by, "same wooden chair?" does that have a meaning? If it does not, your quesion is meaningless. If it does, apply it to the present case.
If we want to actually use "A is A" for anything useful...
Are algebra and symbolic logic a problem for you. I'll humor, your father is your father.
Plurality. (There must be more than one thing.)
Your criticism begins, This axiom requires us ... and falls down there. Remember, you cannot use or imply the concept you are trying to deny in its refutation. You've already implied a plurality.
Dynamism. (There must be change.)
Your criticism, This contradicts "A is A," (your father never did anything?) and it also requires you to assume ... an assumption (or any other mental phenomenon is an action and all action requires change)You cannot imply an action in your refutation of dynamism.
Differentiation. (All existents are different.),p> Your criticism, A mighty broad statement, the truth of which is muddied by such things as quantum entanglement, not to mention Dr. Heisenberg's little theorem.
You've made way too much of this, and your criticism is totally irrelevant. (It might not be irrelevant to what you think it says.) It only means if there are two things which are really two things and not aspects of the same thing, for example, there must be something different about them, or they will not be two things. There must be some quality that is different for any two things, even if every other quality is the same and the only difference is their location, for example.
Hank