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> You state this, but I am an anarchist and I don't consider the private production of wealth to be theft.
> I'll assume you meant under some kind of collectivist anarchy.
It sounds like you're coming from a pretty individualistic and capitalistic place, so I'm going to try to convey some of my underlying positions. I'm an individualist and an egoist, but I believe that the best way to maximize individual autonomy is through a collectivist form of anarchy. Many others agree, so you'll find plenty of anarcho-{collectivist,communist,socialist}s who aren't particularly altruistic. Personally the word altruism leaves a bad taste in my mouth. I just don't think private ownership is easily implemented, and I think some forms of it are unethical.
The difficulty of implementing private ownership lies in the logistics of enforcing ownership. Common ownership is easy because no one owns most of the resources, and everyone just kind of takes what they need. I'm coming from a post-scarcity (https://en.wikipedia.org/wiki/Post_scarcity) position, which mostly just means we kind of share the work of producing and obtaining resources such as food and clothing and everyone just kind of does what they feel like doing. All time is spare time, no one is obligated to work in any way, but it's probably a bit frowned upon to do nothing all day.
The ethical issues come from coercion. Most capitalists believe that if I choose to work for a particular company in exchange for a wage, I made that decision of my own free will. Most anarchists believe that capitalism is coercive, that the economic system drives me to accept a deal I wouldn't ordinarily accept. I think this is readily apparent when imagining post-scarcity communities like I've described above. Would I trade my labor and time for a wage if I didn't need to in order to survive, or would I devote my time to self-actualization, to art, or even to working in the same way I would have done for a wage, only in exchange for partial ownership of the fruits of my labor instead? This is why most anarchists say that anarcho-capitalists aren't truly anarchists, that capitalism creates involuntary hierarchies.
With that said, it doesn't make sense (to me, though Kropotkin might not agree) to claim that all forms of private ownership are theft. I think we'd agree that the things you create with your loom are yours and yours alone, and the loom would be yours too. I don't personally find the idea that everything I create can be taken from me because it's not "really mine" at all appealing. I just think post-scarcity "collectivism" makes the most sense as an individualist and egoist.
> if I have beautifully patterned cloth for sale people will trade for it out of convenience.
I'm glad you said this because it helped me conceptualize the distinction between access to resources and access to things we've created. I think it's likely that people would continue to trade in items like this. I can see trading jewelry for a painting, something I've made for something you've made, etc. Items of sentimental value or of appealing craftsmanship rather than monetary worth. The current notion of monetary value comes from scarcity (with some exceptions), and post-scarcity renders this notion obsolete.
> This is not what happened in the ungoverned old american west
> I would also like to note that by definition, defending anything with or without force is not an act of aggression.
> The real question I'm asking is not if or why capitalism would not be tolerated, but how it would be eliminated.
> >what stops the existence of capitalism is the nature of the chosen anarchist system.
> How exactly does that work?
I assume the old west was full of people who believed in property rights, and that leaving didn't function as a signal that you've surrendered ownership. The nature of the anarchy determines how these kinds of things work. If we form the society on the basis that land is commonly owned, and you insist that the acre of land in front of your house is yours but you don't use it for anything, someone may plant something on it. If you then destroy what they've planted, you may be the one committing theft, not them. It very much depends on the bases of the established society.
As for how they would stop you from participating in something similar to capitalism, it would most likely be by denying you access to the available resources and ostracizing you from the community. But as long as your trade wasn't exploitative, I doubt anyone would mind. I figure trade isn't going away.