But if we accept "dynamism" as an axiom, then you have no way to know what A is at any given time. For it to be an objective truth, you have to assume that it remains unchanged. If its properties changed due to dynamism -- well, then, the idea that A is an objective truth is no longer true -- what was true at one instant may not be true the next.
Thus, even "A is A" requires you to make non-objective assumptions about the nature of any A you happen to be considering.
You have no idea how hard it is not to be sarcastic. I have very patiently pointed out in other posts, "A is A" is epistimological, not metaphysical. "A" can be any concept. For example, let A be a clock.
Now a clock cannot be a clock unless there is change, namely, the moving of the hands of the clock (or the changing of the numbers if it is a digital clock). In this case, A would not be A if there were not change (or A is a broken A).
Why is this so hard to understand?
Here are some more As that could not be As if there were no change: an explosion, a flame, a river, a symphony, a dog, a cat, (or any other living organism).
I think the problem is that you do not understand the identity of a thing is determined by its qualities. Some changing characteristic is a quality of many things, including all living things.
Now consider your statement, "but if we accept "dynamism" as an axiom, then you have no way to know what A is at any given time." So, let's assume you have a child. Your statement would mean, since children almost never cease to be in motion, you could never know your child was a child, much less yours, because it was changing. You must live in a very uncertain world.
Hank
Thanks for your patience. To be quite honest, I'd never considered debating "A is A" until I brought it up with you. I confess I don't know how it's going to turn out. As it is, even if "A is A" is true, objectivism cannot do anything with it without making a large number of assumptions, beginning with the answer to the following question: "so what?"
But let us plow on.
I have very patiently pointed out in other posts, "A is A" is epistimological, not metaphysical.
Epistemology: the study or a theory of the nature and grounds of knowledge especially with reference to its limits and validity. (Webster)
In terms of "A is A," you're saying that "A is what it is." There is here a tacit assumption: that A will never be anything other than what it is.
"A" can be any concept. For example, let A be a clock.... Now a clock cannot be a clock unless there is change, namely, the moving of the hands of the clock (or the changing of the numbers if it is a digital clock). In this case, A would not be A if there were not change (or A is a broken A).
Actually, the idea of hand movement or some other expression of the passage of time is nothing more than part of the concept of "clock" -- something that denotes the passage of time. But of course, relativity makes "the passage of time" a contingent matter, and in some frames of reference (e.g., that of a photon), it may have no meaning at all.
Actually, your choice of "clock" as an example is an unfortunate one. "Clock" has no fixed definition: it can be a candle, or a pendulum, or drips of water or sand, or the hyperfine electron transitions in an excited cesium atom, or just about anything we can figure out how to use for the purpose of measuring time. And in the process of measuring time, it must be remembered that the units by which time is measured are merely conventions, adopted because they are convenient. There's no intrinisic reason the second couldn't have been defined as longer or shorter than it currently is (and indeed it has been redefined numerous times over the past 100 years or so).
Your assertion that "'A' can be any concept," is on shaky ground here. In the case of clocks, "A" is a clock only when we decide to call it one. Before that, it's a cesium atom, or an annoying drip in the kitchen sink. And of course, "the passage of time" doesn't have a fixed meaning.
Indeed, "clock" had no meaning until somebody decided that they needed to measure the passage of time in the first place. Before that, and certainly before the advent of humanity, "clock" had no identity at all.
Thus, we have found a case where A was once ~A, and only became A when we decided to define it as such. Now, if I properly recall your definition of "axiom," this isn't supposed to happen to axioms.
Therefore, "A is A" does not satisfy your definition of "axiom."