Let me preface by saying I'm not attacking the merits of the belief; I do not like centralized government either and I still support capitalism. However, anarchism means "without rulers," but capitalists believe in private property rights, meaning if you have your own land, you can make your own rules on it, therefore you are a ruler. So instead of supporting a big central government, ancaps support very decentralized governments. They are anti-statists, but that is not the exact opposite of anarchy. Instead of anarcho-capitalism, it just seems like capitalism in its purest form.
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I agree, however, that anarcho-capitalism is very much in the spirit of capitalism. Capitalism states that the individuals and organizations exchange capital on a free market, and the lack of external regulatory body (such as government) interfering in this exchange is simply the logically self-consistent implementation of capitalism.
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I guess it just depends on how we interpret "anarchism." It comes from the greek "an-" (without) and "arkhos" (rulers) so it translates to "without rulers" but in the context it's commonly used, it refers to self-governed societies. A self-governed society would have a government, right? Just a very small one that has sovereignty.
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