Friedman's paradox?

In “Capitalism and Freedom (1962),” Friedman discussed property rights mainly in the context of the limited role of government. He argued that the justification that the government may exist is that it has a role in defining and protecting property rights. Yet, he did not explicitly discuss or make any arguments about the basis of property rights claim by an individual. The only explicit argument that he made was “the existence of a well specified and generally accepted definition of property is far more important than just what the definition is (p.27).”

One thing we can infer from this argument is that property rights is basically a constructed definition that is generally accepted. But at the same time, he also argued that it is the role of the government to make such definition. Corollary, in Friedman’s view, government is the only source of property rights.

I found this position quite problematic. The whole point of Friedman’s argument in “Capitalism and Freedom” is about how the government is merely a tool to serve individuals’ interests. This means, individuals exist before any forms of government. That should imply that before there was government, there have already been property rights. But this contradicts the earlier statement that defining property rights is the role of government.

Anyone has an idea on explaining this paradox?