You missed the point; I must have been unclear. I'll try again.

The income you and I have today is inextricably tied to the system of government, taxation, and trade that we are in. You can't talk about holding one fixed and changing the other in any meaningful way.

Now the toy examples - two guys on an island have some of their own problems. If it's just you and I on an island we won't bother with currency or payment (this is part of why it's a toy model). Their tends to be furious hand-waving between this sort of example and a "real" economy, and part of the reason for that is much of the mess as it scales up in practice (e.g. in actual history) tends to be creation of exactly the sort of institutions OP is trying to elide. I'm not sure I buy it, but there is at least an argument to be made that they are necessarily tied together.

You can talk about purely theoretical systems with a different basis - but they are completely different systems. Ones that nobody has actually worked out how to implement, for that matter, though there is lots of theorizing. Always worth remembering that the majority of economic theorizing seems to have a fairly loose connection to the observable world.

Fwiw: the desert island scenario, along with Smith's bartering villages are flawed enough to be probably best avoided.

Natural rights should hold in simple and complex examples, without resorting to utilitarian arguments.

> The income you and I have today is inextricably tied to the system of government, taxation, and trade that we are in.

Yes, that is our current context.

> You can't talk about holding one fixed and changing the other in any meaningful way.

Yes, the world is complex. I simply wish to see one with more voluntary interaction and less coercion. Too few hold liberty as a political value, settling for lesser subjective things such as "fairness."

I was using "complex" in a way that should have been made tighter. I meant that the issue of property itself is very complex, in a way that makes their clear definition as a right at the same level as "basic human rights" at best very difficult, which is why it has not been done successfully.

Thr currency you receive in private trade is unquestionably your own private property. The fact that income tax law requires you to surrender your privacy rights and disclose all of the transactions you engaged in in order to collect an income tax is an indication that the activity being taxed is private.

It doesn't, because it's an overly simplistic example.

Here is a better one: on the island there is you, me and Bob. Bob does not participate in our trades, but is responsible for things like protecting the island from neighboring tribes, putting out forest fires we accidentally start while camping, and building the paths and roads we use to get around the island.

These things not only benefit us, it can easily be argued that our everyday trades would not be possible without them. Without roads I would not be able to reach you, without Bob's protection I would be robbed or worse on the way to meet you.

This is why Bob is inherently entitled to a portion of our income. Without Bob, the environment in which you and I can comfortably conduct business would not exist.

This still isn't a great example. It would be perfectly simple for you to come to a voluntary arrangement with Bob in exchange for his protection, without suggesting that he's inherently entitled to anything.

The real counter-examples comes at larger scales. At a certain point it becomes impractical for a large number of people to individually make voluntary agreements about their responsibilities to each other, so generally people agree to some system of deciding rules, and agree to the outcome of those decisions in advance, without consenting to each one individually.

Yes, obviously it's not a great example, but I used it because the parent seemed incapable of contemplating any scenario more complex than "a few people on an island".

And as long as we stay on that island and live our lives trading coconuts, we can live without much government or taxes. Well, at least until you kill me in my sleep and steal all my coconuts.