It's natural in the sense that you have it if you are the only person on an island somewhere, assuming there's no aircraft or satellites going overhead. In that situation you could literally say anything you wanted, as long as you can collect food and water and not die of some other cause before you finish saying it. Kind of goes for other things to a lesser extent, for example you have total privacy and there's no one there to take away any guns you have, but you do have to think about other people more in those cases, as the island thing is just a thought exercise.

Sound like you're defining "rights" along the lines of "what you can do in isolation, as long as it doesn't affect anyone else". Does that seem correct?

I think that's how most people define natural rights unless they want to invoke some sort of creator.

I don't see how what man can do away from everything and everyone should have any relevance to what man should be allowed to do in a society

What's the logic there?

Yeah that's where everything gets complicated, obviously people's natural rights can conflict and that's where you need to set up some sort of rules based system, but the point is that you don't infringe on someone's natural rights unless there's a direct conflict with someone else's natural rights. For example your natural rights to bear a weapon cause a conflict if you are bearing them in someone's house in order to rob them after you just broke in. Conflicts with their right to have property, etc.

That's not what I meant

It seems like your position is "natural rights should guide or at least influence societal rights", and you consider that to be self-evident or maybe axiomatic

I don't see why natural rights would be part of the discussion altogether

They are natural in that you have them by virtue of existing; if you were alone on a deserted island you would be able to exercise them. The traditional interpretation in the US is that they come from God: "We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness."

Considering all the slaves the authors of the declaration of independence owned, I don't know how to reconcile those thoughts.

Of the five main drafters of the Declaration, Thomas Jefferson was the only slaveowner. Jefferson was definitely a huge hypocrite on this question, but he at least had the decency to feel guilty about it. In fact, Jefferson's initial draft of the document included a paragraph condemning slavery and blaming the British crown for it—though unfortunately, this passage was excised from the final version.