A common fallacious anarcho-socialist claim is:
A common definition of the state that anarcho-capitalists use is that it is a territorial monopoly on ultimate decision-making power.
A common definition of property that anarcho-capitalists use is that it is ultimate decision-making power.
This makes the ownership of territory, i.e. land, incompatible with anarchy, because it is identical to a state.
There are several easy refutations:
- Misunderstanding of 'monopoly.' A State is a territorial monopoly by Max Weber's definition, i.e. a monopoly that disregards ownership. Private property (and socialist collective property) is not a territorial monopoly, since its legitimacy depends on local property conventions. The State's monopoly is (by definition) regardless and in spite of property rights and conventions.
- Equivocation of 'ultimate decision-making.' The term "ultimate decision-making power" is a fallacy of equivocation. A State has a monopoly of decisionmaking of all types, in particular legal decisions. A property owner has decision making power in a very limited way - over some particular use of some resource. It is not “ultimate” in the same sense of all-encompassing like a State, since it does not address legal issues at all, other than the narrow question of using some particular resource. For a more detailed elucidation, read The Difference Between a Proprietor and a Sovereign by Properal.
- Self-annihilation. The argument is self-annihilating. If it "worked" against private property (anarcho-capitalism and mutualism) it would also work equally well against collective property. If valid, it would refute all property systems, collectivist and individualist alike. If private property is a State, by the same (faulty) reasoning, a collective farm or factory is also a State, as is a commune. It destroys its own position!
- Straw man. Note that the second claim, that anarcho-capitalists define property as "ultimate decision-making power," is false - a straw man. Anarcho-capitalists do not define property that way.