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This is intentionally provocative. Actually, it is possible for collectivist anarchists and anarcho-communists to be anarchist. Bakunin and Kropotkin were. But (the point is) most people who self-label that way today are anti-propertarian first, and anti-statist secondarily if at all. E.g. Given the choice between no States and no private property, the vast majority choose no private property. (I've done polls.) Thus, they fail the purity condition, and should be referred to as anideotists - anti-propertarians - not anarchists.