Rothbard very briefly mentions (in The Ethics of Liberty) why the Columbus claim to own the entirety of a newly discovered land was invalid; he could only own land he homesteaded, or mixed his labour with.
But what does this mean exactly? If Columbus built a fence round the whole island would it be legitimate?
If not, what exactly would he have to do to the land to homestead it? Could he leave any patch in its natural state?
The purpose of property rights is to resolve conflicts over scarce resources. Rothbard uses a very crude and old-fashioned example of mixing one’s labor with the soil, because doing so demonstrates an intent to use scarce resources in the production of goods. If someone attempts to interfere with that an arbitrator will have to delimit the property rights of the first user.
Claiming a continent, on the other hand, does not interfere with anyone’s use of that continent, and neither does it create any interference with future use of the continent. Columbus is not using it at all.
The point “mixing ones labour with the soil” creates an objective link between the homesteader and that piece of land. Just as much as I use my body as a means to acheive my ends, say through eating (the end being staying alive) the piece of land becomes an extension of my body as means to attain my ends, whatever they may be.
OK, suppose my end is to create a piece of art. My artwork is going to be an obelisk sitting in the middle of an unspoilt island. The island being unspoilt is a crucial part of the artwork. If somebody turns up on my island and builds themselves a hut, do I have the right to evict them on the grounds that they are on my island, which I used as a means to create my end?