> ...how else would you or anyone define it?

A geographic location where there exists a monopoly on violence. For example: the USG gets to decide who is allowed to kill who and under what circumstances, exclusively, for a specific location. That monopoly can be made clear through laws, but it isn't necessary - consider monarchies with no legislative bodies. Also consider the fact that laws cannot be established without a monopoly on violence, which a lot of people seem to get confused about - thinking the authority over violence is somehow derived from law...

> And are we talking philosophical or real world examples?

I'm really tempted to launch into a rant about cognitive dissonance here, but I'll just save time and say that is a distinction without a difference. As far as examples, like I said, pick any monarchy without a legislative body - Native American history has plenty of that.

To me, the difference between philosophical positions and ones which can survive the tests of the real world are pretty important. But I suppose that's my opinion as an engineer. I've studied a lot of philosophy that's logically self-coherent but completely impractical to let anywhere near physical matter.

I would say that "a geographic location where there exists a monopoly on violence (such as a monarchy without legislature)" nonetheless has implicit laws that guide its hand. And by which it is judged! Indeed, transgressing unwritten social contracts has led to the downfall of most monarchies throughout history. Or to put it another way, co-opted power structures are necessary for the governance of any sufficiently large group, above and beyond sheer force. And power-structures require some sort of bargaining and negotiation even if it's rather one-sided.

Laws as instruments to communicate expectations are what makes scalable organization possible past a certain point, whether they're explicit or implicit.

That's why you don't see any long-lived civilizations with true violent anarchy as a form of government.

> ...difference between philosophical positions and...

Philosophy is a pretty huge domain, where one end of the spectrum is navel gazing Platonic forms and the other is the propositional logic that informs compiler design. It sounds like you describing the trap that medieval scholars fell into, where they would recursively construct syllogisms until they found themselves talking about how many angles could dance on the head of a pin. This is what happens when you fail to check your premise, you end up with a logically consistent delusion. So the "self-coherent but completely impractical" philosophy you've condemned is just a condemnation of poor logic - which doesn't do your utilitarian argument much good.

As far as the the rest, you've now changed the topic from "what defines a state" to "what defines a well judged, scalable, long-lived civilization".

> ...anarchy as a form of government...

One of those words doesn't mean what you think it means :)