The argument that people can appropriate unowned land by mixing their labor with it has a lot of problems. Labor is not a substance, and so it cannot be mixed. Even if it could be mixed, it is not clear why mixing it with something transforms the unowned particles into owned particles. Even if you can get past the weird mechanics of mixing, such appropriation would seem to violate ordinary libertarian ethics of non-aggression because everyone except the appropriator has their previously-existing access to the land violently taken from them without their consent.
These are all problems that have been discussed extensively and advocates of the theory lack a convincing retort. But there is another fundamental problem that I have not seen discussed before. And that problem is this: “land” ambiguously refers both to “soil” and to “space” and the mistaken conflation of the two is what really drives the entire labor-mixing theory.
When you ask someone what they mean when they say that someone has “mixed their labor” with a piece of land, they usually reach for an agricultural example: a person mixes their labor with the land by cultivating the soil and planting crops. Insofar as agriculture was the overwhelming purpose of land at the origin of this theory, this makes sense. But the example does not explain how space comes to be own.
If someone cultivates the soil, then the labor-mixing theory should say that they own the soil, not the space the soil sits in. The space the soil sits in, which can be described by reference to lines of longitude and latitude or by drawing lines on a map, is not mixable. It’s a container. It’s territory. It’s not soil.
The difference between “soil” and “space” is very easy to see once you recognize that soil can be moved to a different space. The layer of topsoil a person has mixed their labor with could be shoveled into a truck and moved elsewhere. And, if that were to happen, the owner of the soil would not have had anything they mixed their labor with taken from them.
The same is true of any other labor mixed in any other space. A house built on some piece of land could be loaded onto a special truck and moved. I’ve seen them do it on TV. So could any other structure. For any given land claim, the objects that the labor was mixed with could be isolated and moved outside of the space.
So how does someone ever come to own the space itself rather than just the objects that were sitting in the space when labor was mixed with them? This is not a trivial question because it is in fact the space that is so valuable. That’s what land rents (these days especially) are being paid to: not to soil but to space.
As far as I can tell, the labor-mixing theory has no actual argument for how space can be owned, but has instead equivocated between different uses of the word “land” to move deceptively from “soil can be owned” to “space can be owned” without providing a separate argument for the latter.