Hi, minarchist here. You are almost right in the distinction between right and left anarchism being about private property. But it's a little more profound. The main difference radicates in the conception of legitimate power. For a right anarchist, power is illegitimate only when it's carried out through violence. Meanwhile, for a left anarchist almost any power hierarchy is illegitimate in itself. To the extent that private property could give rise to power hierarchies, a left anarchist will reject it. But it's only a particular case derived from the core belief.
> "anarcho-capitalist" is inherently paradoxical
Well, anarcho-capitalists believe that there are ways to provide property rights outside the state. As a minarchist, I'm skeptical about it, but if you believe it there's no paradox.
On the other hand, I do find deeply paradoxical the left anarchist stance on rejecting capitalism but also (AFAIK) reject any means to stop its emergence in society.
> There is also another conversation to be had about minarchist/libertarian ideas basically wanting to remove all the good bits of the state [...] but keeping the bad parts
As a minarchist, I strive for reducing the weight of the state as much as humanly possible. Justice, defense, and a minimal social security net are the only services I can't think how to provide without the state. If you think these are the bad parts I'd love to hear a viable alternative, maybe you can make me fully anarcho-capitalist ;).
I agree with you on the more nuanced distinction, I just didn't want to open the discussion of what legitimate power structures constitue.
Re your criticism of left-anarchism, one of the big unsolved challenges in my eye is exactly your point: how do you keep per from pooling? In a sense, you also need a "state" but one which has as it's explicit goal the self dissolution - which is of course the same paradox that ancaps face. The difference to me is that it seems to me more feasible to build societal systems and cultures that disperse power if we build our ideology around consent and cooperation than to build a society where the central building block is the by-necessity cooperation of small dictators who somehow are supposed to also respect their weaker neighbors private property rights. The former seems like positive feedback loops are possible (and we see spontaneous cooperation like this emerge throughout history, without any powerful person pushing it) while the latter...was the robber barons and cleptocrats of the 19th,20th and 21st century
Re your question, I don't like to quibble to much about this if it doesn't have a possible payoff, but do you believe in e.g. environmental regulations, provision of public goods via a regulated healthcare system, basic education etc? If yes then I think your position might be rare amongst self identified minarchists. If not, then do you see how e.g. natural monopolies like healthcare or highly influential realms like healthcare are open to power concentration and state hijacking?
> "anarcho-capitalist" is inherently paradoxical
Well, anarcho-capitalists believe that there are ways to provide property rights outside the state. As a minarchist, I'm skeptical about it, but if you believe it there's no paradox.
On the other hand, I do find deeply paradoxical the left anarchist stance on rejecting capitalism but also (AFAIK) reject any means to stop its emergence in society.
> There is also another conversation to be had about minarchist/libertarian ideas basically wanting to remove all the good bits of the state [...] but keeping the bad parts
As a minarchist, I strive for reducing the weight of the state as much as humanly possible. Justice, defense, and a minimal social security net are the only services I can't think how to provide without the state. If you think these are the bad parts I'd love to hear a viable alternative, maybe you can make me fully anarcho-capitalist ;).