This view on land property started with Locke and Rousseau, Locke saying that land can be property, Rousseau disagreeing. Rousseauan thought continued to Proudhon, and that view on land property is found in Georgism/ Geolibertarianism.
What kind of paradox, if you would be so kind to elaborate? If anything here is paradoxal is how can one support both the labor theory of property and the notion that land can be property.
Selfownership is an axiom a part of which says we own our actions, and we own our labor. From that follows that what we create or, in Locke’s words, what we mix our labor with to remove it from the state of nature- is our property which we can consume, sell or whatever. So the product of our labor is our property.
Homesteading principle is a Lockean addition to that definition of property which says that because exclusive use of land was necessary for acquiring property (eg. growing crops or whatever) it too becomes property. This dialectical jump, or leap of faith, or non sequitur, no matter how we call it, is given a justification of “it is necessary”. This justification fails when we have Proudhonian explanation in mind- that land needs not be considered property, ius in re, in order for someone to have exclusive use of it, but it is enough for it to be a “possession”, ius ad rem, meaning that homesteading principle is not justified as an addition to the definition of property we have, that follows from the selfownership axiom, that products of labor are propetry.
Being that land is not a product of labor, and that therefore- one cannot have property over it, one can only use or abandon it. That use of land, in order to be exclusive, people agree to be ius ad rem, meaning “a right to a thing” in Latin, that is- “a right exercisable by one person over a particular article in virtue of a contract or obligation incurred by another person in respect to it and which is enforceable only against or through such other person. It is thus distinguished from jus in re which is a complete and absolute dominion over a thing available against all persons”.
Being that land is unowned, everybody has the right to go there, by the virtue of his right to freedom (of movement). And being that one, by his use of the land, has impaired others in their right to freedom, he owes them some sort of recompensation, called “land value tax”.
As the quote of Thomas Paine (which is on the wikipedia article about geolibertarianism, which you probably read) says: “Men did not make the earth. It is the value of the improvements only, and not the earth itself, that is individual property. Every proprietor owes to the community a ground rent for the land which he holds.”