There is a great divide among the traditions of anarchism about the question of private property and economic organization.
Socialists vs Capitalists
In the end, both socialist anarchists and anarcho-capitalists
consider the other group as deeply misled,
and that the other group's notion of "anarchy" is not real anarchy,
but government in disguise, rejecting the name, but keeping the concept.
Thus, socialist anarchists and anarcho-capitalists
don't generally engage in any form of co-operation,
despite what might appear to be a mutual goal:
both groups want to get rid of the state,
but they have opposite opinions of what characterizes the state.
On the other hand anarchists of each kind
share a lot of literature and cooperate with the non-anarchists
in their respective socialist and
classical liberal traditions.
See also:
- anarcho-capitalist critique of left-anarchism
- libertarian socialist critique of anarcho-capitalism
Other anarchist traditions with respect to private property
Anarchists of other traditions vary in their appreciation of the respective socialist and classical liberal arguments above.
Some of them will consistently side with some of the above arguments, thus adopting the socialist or classical liberal tradition, though without forcibly doing it formally.
Some will mildly side with some of the arguments above, though without considering them a defining stance for their flavor of anarchism, and will consider the question as secondary.
Some do not care about this debate, and consider it a waste of time; they think that by getting rid of government, such problems find a natural solution.