Self-ownership is the normative claim that a person ought to own their body as private property and in virtue of this ownership have exclusive rights of control and use over their body. One of the main replies by Anarcho-Capitalists to those who reject self-ownership is that if people do not own their body as private property, then who does? And if a person does not own themselves, then other people can own them as property. Thus we must believe in self-ownership or believe in the legitimacy of people owning other people, as in slavery.
This argument however fails. The fact that x belongs to the set y, which is the set of things that are un-owned, does not entail that z person can legitimately claim ownership of x. It is only entailed if x belongs to the set of things that can be legitimately owned. The set of things which can be legitimately owned merely intersects with the set of things which are un-owned, rather than being identical with it. For instance a piece of land may be un-owned and yet be capable of being legitimately owned, while the the earths atmosphere is un-owned and cannot be legitimately owned. Likewise a person’s body belongs to the set of things that cannot be legitimately owned and the set of things that are un-owned. Therefore, it is not the case that if something is not owned it necessarily can be owned and that if people do not own themselves then they can be owned by other people.
While self-ownership itself justifies slavery. Since if my body is property, and I have rights of use and control over my body, then I have the right to transfer ownership of my body via voluntary contract, just as I can do so with any given thing I own as property, such as a chair. A person therefore has the right to voluntarily transfer ownership of their body to others, and so voluntarily become owned as private property by others. A slave is a person who is owned as property by another person, therefore It is self-ownership, not it’s denial, that entails slavery.