Before Aristotle began to try to define citizenship at the beginning of Book Ⅲ of the Politics, he briefly brought up the question of when an action can be said to be taken “by the state” as opposed to, say, by a particular person or group of people in the ruling class.
What is the character of the state, and to what extent is it independent of or separable from the people (or territory, or edifices) that are part of it? If a government abruptly changes its constitution, or its qualifications for citizenship, is it now a new state? If so, has the old one then entirely ceased to exist, or has it transformed into the new one?
For example, Aristotle says, when a revolution transforms a government from an oligarchy or tyranny into a democracy, the people who take over are often reluctant to acknowledge that the debts and other obligations taken on by the former government are legitimate and binding on them. (This can also work in the other direction, as for instance when the new United States tried to dodge its war debt to France on the grounds that they owed the money only to the French Sovereign, who had since been conveniently overthrown and decapitated.)
It would be nice if we could just use the continuity of territory and inhabitants to define a continuous state. But this can become confused when what was formerly a single state divides (e.g. Yugoslavia), or multiple states merge (e.g. East and West Germany).
“[W]hat is the criterion for regarding the state as a unity?” Is being in the same city enough? Or being of the same race of people? Aristotle references the case of the city of Babylon, apparently the mega-city of its day: so large that when the outskirts of the city fell in an invasion, the folks downtown didn’t find out about it until after their festival was over two days later. Could they really be considered a single polis under such conditions?
Perhaps when a population continues to live under the same constitution, even as new people are born into that population and others die from it, they can be said to be the same state. It’s the constitution that matters. But that leaves open the question of how much change in a constitution signals the creation of a new state, and to what extent the obligations of the old state are binding on its citizens in such a case.
I don’t want to go down what I assume would be a fathomless rabbit hole of international law about these subjects. Suffice it to say that Aristotle’s concerns remain live ones today. For example, a sample reference that I arbitrarily chose from many I could have opened (Alfred R. Cowger Jr., “Rights and Obligations of Successor States: An Alternative Theory,” 17 Case Western Reserve Journal of International Law 285, 1985) says:
The traditional theories of successor [state] rights and obligations have never been broadly accepted by scholars or nations and even seemingly straightforward fact patterns have been confused by definitional difficulties… [E]ven if some traditional principles could be fathomed from custom and practice, these principles have been so ambivalently analyzed that their legal repute is doubtful.
So it is not surprising that Aristotle raises these questions without having confident answers of his own, and his humility here is probably to his credit. It is apparently not an area where there are easy answers he simply overlooked.