Political Memes

It just doesn't fit in the definition.

As stated in the other comment: You're missing the distinction between states and government.

and entity that enforces rule of law

But why is anything concerning the law outside of the governing body? Your definition doesn't seem complete.

Apart from details of the management body: I agree to your code of conduct for a democratically run. Cooperative. But didn't you imply that socialism automatically implies authoritarianism? Where does authoritarianism enter the picture, if the decisions are made bottom-up?

Anarchy is the organization of society on the basis of voluntary cooperation, without political institutions or hierarchical government.

Here we come to the definitions problem again. Anarchy is usually understood as the absence of any hierarchy. Economical hierarchy (I own something that you need to survive) is a form of hierarchy. Also, as "politics" describes anything concerning decision making in groups: Good luck having a society without political institutions. Even private corporations are political institutions. Why you exclude the economic sector from your exclusion of hierarchy, I also don't really know (well I'm guessing that it's convenient for your ideology, but that's just a guess).

If all means of production are completely privately controlled, then there is necessarily no state involvement, because as soon as it’s introduced, there would be some means that are not privately owned.

But without any state involement: How are the property relations maintained? Private armies? That would result in warlord-feudalism.

You can also view capitalism through class-relations: The owners of the MOP and the people they employ. The employed have to follow the orders of their private boss in order to survive. If you switch out the private property owning boss with a party bureaucrat and the class relations don't actually change, that's called state capitalism. That's how language works. Adding a word to another word can create a new term.

Two different statements, and you can’t derive one from the other.

Lol, are you seriously trying to formal-logic me? A monopoly on violence is a necessary feature of a state (state -> monopoly on violence). If the means of production are privately owned, class tensions between the people with private ownership of the means of production. If these tensions are not resolved (which the owners have no incentive to in capitalism), they would lose their property through the violence of the employed class... or they'd "invent" something that pacifies class tensions with a monopoly on violence. A state.

It’s also not even true, if we ignore the theoretical voluntary cooperation in the hypothetical, in the case of no statehood property would be protected by private militia. One person’s militia would have no reason to protect other property inherently, and no one else would be restricted by the state from doing the same.

That's what we had in the middle ages in Europe. It's called feudalism. Or warlord-ism. People with more economical power have more resources to fund a private army. And why would I refrain from overpowering my market rivals, if I have the means to do so?

Private ownership stems from the human intuition of personal property.

The jump from personal to private property is incredibly big. Native Americans didn't have any concept of absentee-ownership. Or of ownership of anything that other people need.

In reference to tribal people, it’s a little silly to lump them all as one type of culture, but even still, they tend to have a lot of respect for personal boundaries and property, and this includes the means of production. When a tribal hunter takes home a hunt, they use it to provide for their family first and foremost, and unused excess is given to neighbors.

Lol, you A) have no idea of antropology and B) are committing the same thing that you are claiming is silly. :D No, that's not how "a tribal hunter" generally behaves. Immediate return societies are overwhelmingly incredibly egalitarian (and don't really have the modern notion of one's family, which must come first). They share everything.