The first chapter of John Dewey’s The Public and Its Problems lays out the structure of his conception of political theory. I discuss the method he proposes to follow here. In this post I give his definitions of public and state, and a brief sketch of the argument.
Dewey starts with the observation that we live in groups of people from the beginning to the end of our lives. We are in a strong sense created by those groups. Their influence shapes us in deep as well as shallow ways. All of our actions take place in the context of such groups.
People’s actions have consequences, direct and indirect. Some actions mostly affect the parties to the transaction, as a discussion between friends about the weather. Others have indirect effect, as friends joining for dinner at a restaurant. We call these private, because they don’t affect large numbers of people and do not have any significant impact on others.
Other actions affect a larger group, directly or indirectly, or affect a few people strongly. For example, a Pastor of a church gives a sermon, which causes changes in members of the congregation. A neighbor puts up an ugly fence, hurting property values. If the group is large enough, we call the action public. Most of our actions are private. A few have such an impact that we as a society want to encourage or discourage them.
This leads to this definition:
The public consists of all those who are affected by the indirect consequences of transactions to such an extent that it is deemed necessary to have those consequences systematically cared for. P. 69.
We delegate the task of coping with the consequences of public acts to people we designate as officials. This point is necessary to Dewey’s thought, because the thing we call the State only operates through individuals. Some single person issues a regulation. Some single person decides who should be prosecuted for a crime. He takes up the nature of the State in more detail in Chapter 2.
The precise form of the institutions these officials work at, the selection of officials. and other details arise from the historical context. In the US, for example, we have some institutions and forms from England, others from other countries, some created here based on theories current at the time of the founding of the country, some generated here in response to problems that are specific to this place, and some arising in response to subsequent events and changes in social attitudes.
… [W}hen a family connection, a church, a trade union, a business corporation, or an educational institution conducts itself so as to affect large numbers outside of itself, those who are affected form a public which endeavors to act through suitable structures, and thus to organize itself for oversight and regulation. P. 79.
These “suitable structures”, are groups of officials acting through institutions. Of course, these institutions may not suffice. In that case change is necessary. The newly emerging public created by changing conditions may be unable to force the State to adapt to new problems This can have disastrous consequences:
The public which generated political forms is passing away, but the power and lust of possession remains in the hands of the officers and agencies which the dying public instituted. This is why the change of the form of states is so often effected only by revolution. The creation of adequately flexible and responsive political and legal machinery has so far been beyond the wit of man. An epoch in which the needs of a newly forming public are counteracted by established forms of the state is one in which there is increasing disparagement and disregard of the state. General apathy, neglect, and contempt find expression in resort to various short-cuts of direct action. And direct action is taken by many other interests than those which employ “direct action” as a slogan, often most energetically by intrenched class-interests which profess the greatest reverence for the established “law and order” of the existing state. P. 81.
This leads to the assertion that the form of the state must be constantly scrutinized and changed. That doesn’t suit the “intrenched class-interests”. It also leads to this formal definition;
… [T]he state is the organization of the public effected through officials for the protection of the interests shared by its members.
Finally Dewey says that the important thing to understand is that we can’t understand the public and the state by looking for or asserting the existence of special forces outside of intentional human action.
1. Dewey’s method turns on facts, but not on the kinds of facts we saw in Arendt’s The Origins Of Totalitarianism or Polanyi’s The Great Transformation. The latter two trace out long historical sequences and use them to understand the then current situation. If followed this method we’d have to look at the organization of hundreds and thousands of societies, from tribes to clans to kingdoms, to the different city-states of ancient Greece, to the empires of the Persians and the Dynasties of China and on and on. That’s not what Dewey did. 
Dewey also relies on facts, but he uses facts about the way human beings interact. They are more like the facts used by John Rawls in his book A Theory of Justice.  It’s a way of weeding out contingency in the hope of finding a generalizable statement of the problem.
2. The most common way to understand the nature of the state is the theory of the Social Contract. The following begins this thorough discussion.
Social contracct theory … is the view that persons’ moral and/or political obligations are dependent upon a contract or agreement among them to form the society in which they live.
There is no such a contract, of course, and no one actually assents to it in any meaningful way. It’s merely a construct. Dewey addressed social contract theory in a 1888 essay, The Ethics of Democracy.
The notion, in short, which lay in the minds of those who proposed this theory was that men in their natural state are non-social units, are a mere multitude; and that some artifice must be devised to constitute them into political society. And this artifice they found in a contract which they entered into with one another. …
The fact is, however, that the theory of the “social organism,” that theory that men are not isolated non-social atoms, but are men only when in intrinsic relations to men, has wholly superseded the theory of men as an aggregate, as a heap of grains of sand needing some factitious mortar to put them into a semblance of order.
Sadly, Dewey got this wrong. Social Contract theory remains dominant and Dewey has receded.
 Aristotle seems to have done it, gathering and classifying 170 constitutions.
 Here’s an explanation of the veil of ignorance, the basic starting point of the book.