Ah, but there are two forms of morality, I would argue. Subjective morality and objective morality. Objective morality is predicated on the things I've outlined already, with subjective morality simply being your individual opinion of what is right and wrong.

The philosophy there is primarily in regard to an explanation as to when a utilization of violence should even be acceptable. For example, I am a staunch atheist, I believe all organized religion is utterly destructive and nonsensical - From a utilitarian perspective I believe it would be better for humanity to outlaw all religion, but I am not an authoritarian, and even though I see all religion as fundamentally immoral, it seems clear to me that we should not use violence to outlaw religion.

In fact, you don't need to, not in a free society.

Because it isn't the religion we need to worry about, it's certain actions. If someone wants to make a moral claim that you should be allowed to marry a 6 year old (Islam), it shouldn't matter what the reasoning is. Gods, religious figures, other authority figures - all irrelevant. It should be universal that good people take up arms and stop anyone from engaging in sexual relations with a 6 year old. This is in fact nearly self-evident, the only people in the world who disagree with this have to use ridiculous, ethereal, nonsensical woo woo claims to quantify to anyone with even the slightest bit of a rational mind.

You ask:

"So let’s make this incredibly simple: What principle of formal logic establishes that the first person to desire exclusive control of something gains a moral right to exclude everyone else?"

You do this through reductionism. You imagine a thought experiment such as follows:

If you are the only person on earth and you are walking through the forest and come across a diamond and suddenly, you desire exclusive authority over that diamond (I.E: You do not want anything to happen to it and want it to remain with you in ways in which you can manipulate.) Who owns that diamond, and why?

Well, you do, because ownership is predicated on us - on humans. The entire discussion surrounding ownership is only valid for mankind. We do not concern ourselves with if we believe that the ants own their anthill, or the squirrel owns the tree. Some might in some form or another, but that's a discussion for another time.

So you would own that diamond simply because there are no other human beings of which there can possibly be a will conflict with. It's a default state. Ownership only even arises when there's a will conflict between humans. You are free to hold exclusive authority over everything you come across if you were the only human on earth.

So you then have to simply - and logically here - conclude that ownership is a construct of which side we "aught" to take during a will conflict between at least two humans. In fact, even if you have more humans in the world but not a single one of them cares about that diamond but you, then you still own it because there are no will conflicts surrounding that diamond.

The only time ownership matters is during the scrutiny of who should hold exclusive authority over something, and someone will ALWAYS hold exclusive authority so long as there is at least one human who desires such. Again, there's no such thing as "public" property - that's nonsense. There is always someone - some government official - who has that final say, and it's never, ever you or I, regardless of how much of our money was taken to procure it.

Ask the authorities when you're escorted out of one of our state parks while it's closed why you can't enjoy your property and see what they say.

If ownership means other things outside of this then the idea itself has no essence, so it means nothing at all. If the definition of ownership is predicated on arbitration of some authoritarian system then whatever that system claims becomes what it is, which means again that it has no essence so really it's a nothing idea. That's stealing and "claiming" it isn't theft because you defined ownership which of course also then means you define theft. That's not how ideas work, those are semantics arguments.

So we can reduce the idea into its fundamental constitute parts and we can only conclude what I've described. There's nothing else you can conclude because the reality is that the idea to own something is a nothing the moment there are no will conflicts surrounding a "something".

So now let's imagine someone comes along and sees you with that diamond and now they want it. Which should we side with? You, who already own that diamond by default, or this new person, who didn't even know that diamond existed all the while you held it, until just now? And why?

We could make an infinite number of arbitrary reasons why the other person should have that diamond, but again, subjectively, you cannot rank the value of your opinions, so even if that person was to say they never got a turn owning it and you did and that's, "fair", that's just an opinion. Your reasons for continuing to own that diamond are just as valid.

But the thing is, if THEY were in your shoes, they would agree with your current will to continue to hold exclusive authority over that diamond as well.

And in addition, since we can only fundamentally define ownership in this way we can also only define theft in one way. Again you can use reductionism to construe what theft can only be. Again, if theft is defined arbitrarily then it's a nothing. Theft must be taking something from someone that they already own without their permission.

Generally the Law of Identity, Non-Contradiction, and mutual exclusion are what philosophers use to understand a fundamental principle of things like ownership.

So it cannot be both true and false at the same time. Regarding property and ownership, this is a principle of exclusion whereas if person A has exclusive authority over object X, then person B cannot. This is how theft is analyzed as well, because an attempt from person B over object X would be an attempt at theft due to the non-contradiction law.

In addition, Plato created the concept of essence through use of his Theory of Ideas (forms). This idea was then used by Aristotle in his philosophy of essence. This is the fundamental, immutable characteristics of what constitutes an idea, as independent from any other idea.

In short, when using words, you are either conveying one singular idea, or you simply think you are but you're really talking about something else entirely (semantics) because you yourself do not really know what it is you're talking about.

It would be like a layperson saying they own a car and when asked what ownership is they give you a reply like, "the law says I own it". They would be the first people to also argue that the state cannot take that car from them because they own it the very second the state changed the law saying they no longer own it.

They simply do not comprehend the fundamental nature of what must manifest the very idea of ownership which is why the blatant contradiction in their reasoning.

I would argue that almost everyone thinks of these things in a very rudimentary way, which is why we have so much authoritarianism/statism in the world today, and always have.