But when it is used to describe a political ideal, anarchy is a term used in two different ways in describing two very different political views. It is worth noting that although it is likely that adherents of either view will surely have many disagreements with the other, it is not correct to think of them as being diametric opposites.
Prominent anarchists of the traditional sort include EmmaGoldman?, MikhailBakunin?, and NoamChomsky?. We have a comprehensive discussion of TraditionalAnarchism.
The most prominent theorist of AnarchoCapitalism is DavidFriedman?, son of NobelPrize/EconomicSciences winner MiltonFriedman?. We have a comprehensive discussion of AnarchoCapitalism.
Proponents of these two views sometimes view each other with some hostility. Proponents of TraditionalAnarchism may view AnarchoCapitalism as either a grave misunderstanding of anarchism proper, or a special case of the rejection of government authority in favor of capitalist authority. Terms such as "baseless" and "oversimplistic" may be used.
Advocates of AnarchoCapitalism may contend that TraditionalAnarchism is ill-defined, and most likely will reject the view that there is any such thing as 'capitalist authority' and that many anarchists are economically illiterate.
This page will not settle any disputes between the two, but hopes instead to acknowledge the facts of the situation (that both use the term, rightly or wrongly), and to point to separate treatments of both.
You can see a little bit of the lively debate here: /AnarchyTalk