[Zygote]

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But "statists" entire belief system, at least in the political sense, isnt based on an a concept of absolute, inviolable property rights. Anarchists/libertarians do believe in that. Get it now?

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Anarcho-capitalists do, most anarchists don't.

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Lets say a state of anarchy is created. Now an anarcho-capitlist stands his ground and proclaims that the land he stands on his to preach from.

An anarcho-socialist comes along and wants to make use of his share of the property that the anarcho-capitalist claimed to be of his right of use. The anarcho-capitalist refuses and, trying to play devil's advocate, says if this society is socialist then before you protest my action you need permission to preach from the land you stand on. The anarcho-socialist redirects this argument to him. This continues back and forth ad-infinitum. In the least both anarchists must concede that all have the right to use their body and the land they stand on. This is inherently anarcho-capitalist and private property based. How far the private property extends is debateable, this much is not, however.

The question is what basis of action does the anarcho-socialist have against the anarcho-capitalist in terms of protesting the anarcho-capitlist's attempt for private property use? How can he accomplis his goal without either creating a state or admitting he's at least a hypocrite anarcho-capitalist?

In anarchy, there can be quasi socialists but they must respect private property to prevent descending into a state. A kibbutz can live side by side capitalist institutions but they can't make all the land under kibbutz rule without become a state.