What follows is a look at three possible senses of anarchy related to Proudhon’s work, together with a sketch of their possible relations as developments from one another. The intention here is to simply present some basic definitions as a kind of hypothetical framework, which can then be tested against close readings of the relevant texts.

Historical anarchy: In a society organized around the principle of authority, resistance appears as anarchy, whether it is the active resistance of those oppressed or simply the friction generated by the contradictions of an authority-based society. This is the sense that Proudhon most frequently gave to the term, drawing on existing usage, to describe various tendencies within existing societies: the violence emerging from political conflict, the “anarchy of the market,” etc.

Abstract anarchy: The various manifestations of historical anarchy then suggest, however dimly at times, a general principle or social form, which unites them. In The Federative Principle, Proudhon gives us anarchy conceived as one of four a priori forms of government. These forms emerge “necessarily” and “mathematically” from the logical consideration of government and can be characterized through the consideration of two factors: the opposition of the principles of authority and liberty (understood in part as the opposition between division and non-division of power), and the symmetry or asymmetry of the rulers and the ruled. Anarchy, or self-government, is characterized by division of power and symmetry between the rulers and the ruled. It is the “government of each by each.”

In that text, however, we are presented with this abstract anarchy, only to have it rejected as “an empirical creation, a preliminary sketch, more or less useful, under which society finds shelter for a moment, and which, like the Arab’s tent, is folded up the morning after it has been erected.” The obviousness of the forms is a “snare,” as none of those that first present themselves through logical analysis are ultimately practicable.

Just as monarchy and communism, founded in nature and reason, have their legitimacy and morality, though they can never be realized as absolutely pure types, so too democracy and anarchy, founded in liberty and justice, pursuing an ideal in accordance with their principle, have their legitimacy and morality. But we shall see that in their case too, despite their rational and juridical origin, they cannot remain strictly congruent with their pure concepts as their population and territory develop and grow, and that they are fated to remain perpetual desiderata. Despite the powerful appeal of liberty, neither democracy nor anarchy has arisen anywhere, in a complete and uncompromised form.

This appears, then, to be a decisive rejection of anarchy as a guiding notion. In its place Proudhon presents federation, the only system that he believes can truly fulfill the role of “all political constitutions, all systems of government,” which is “the balancing of authority by liberty, and vice versa.”

The question is whether this appearance is deceiving. There are quite a number of additional questions raised, but perhaps we can start here:

Did Proudhon stop being an anarchist, did he discover he had never been an anarchist or is there some some sense in which his rejection of this abstract notion of anarchy still leaves open the possibility of another anarchy, and thus another way of being an anarchist?

If we choose the first interpretation, then presumably we believe that the abstract anarchy of The Federative Principle was the same anarchy that Proudhon embraced as a positive goal, but that developments in his thought—perhaps the discovery in the 1850s that “the antinomy does not resolve itself”—led him to abandon that position.

The second interpretation seems a natural choice if we once again identify the abstract anarchy of the later works with the anarchy of the early works, but then recognize that this form of self-government could not remain “strictly congruent” with its “pure concept” in any analysis involving collective force and unity-collectivities, making it inadequate even in the earliest works, where at least the basic analysis of collective force was already at work.

The third interpretation requires that we recognize multiple senses of anarchy in Proudhon’s work—which we can certainly do given his explicit recognition of multiple senses in The General Idea of the Revolution—but also that we find a way of thinking about federation as not simply a replacement for an impracticable sort of anarchy, but as the key to some other form.

Each approach has consequences.

The first presumably preserves Proudhon within the anarchist tradition as a kind of early adopter or precursor, but then draws some kind of line between his mature work and anarchism. That then leaves us to ask what sort of anarchy was adopted by the anarchist movement as it emerged after Proudhon’s death—a question complicated by the fact that some of Proudhon’s late works, such as The Political Capacity of the Working Classes, were particularly influential in the period of the International and works like The Federative Principle seem influential in the present. If we think of Proudhon as an early adopter of an abstract anarchy later embraced by the explicit proponents of anarchism, then we are faced with the question of how we respond to Proudhon’s claim that such a notion is at best only approximately applicable to practice. The problem of collective force seems difficult to overcome, so we presumably forced to choose between the concept behind Proudhon’s declaration that “I am an anarchist” and the theory behind his claim that “property is theft.” If, instead, we think of him as a mere precursor, then we are left to determine just how the anarchy that emerged in later years differed from Proudhon’s conception and how it escapes his critique.

At this point, it is tempting to simple note that there is a great deal of discontinuity in the early anarchist tradition and a certain amount of opportunism when it comes to the use of Proudhon’s work in later anarchist thought. But the theoretical questions still remain, if we want to attempt to establish continuity in the tradition. I am not entirely opposed to the project of attempting to understand Proudhon’s mature work as something other than anarchism in the received sense—if that is the only way to move forward with a serious discussion of Proudhon’s mature work—but I think other options still remain.

The second choice forces us to confront the possibility that adopting the language of anarchy was something of a wrong turn for those who took up Proudhon’s project, with whatever degree of fidelity. That opens a lot of potentially interesting paths of inquiry, from an examination of “libertarian socialism” as an already existing alternative (in the works of writers like Gaston Leval) to the exploration of possible alternate histories (such as my still largely nascent musing about atercracy, art-liberty, etc.) But while I am attracted to these research possibilities as ways of illuminating aspects of the anarchist tradition, I’m still basically convinced that:

Anarchy is a fundamentally useful concept, which nothing else can really replace. Proudhon’s social science is a powerful set of tools, which we have barely begun to understand and use. We don’t have to sacrifice one to the other.

That forces us to return to the analysis in The Federative Principle and ask ourselves if the movement from abstract anarchy to federation is perhaps not a break, but yet another development? The “pure concept” of self-government seems to fail when it encounters the effects of collective force. If we attempt to envision that “government of each by each” in practice, with even the most basic elements of Proudhon’s social science intact, we must account for the reality and even the “rights” of social “unity-collectivities.” And it becomes nearly impossible to address the question of just who or what will take the role of “each” without noticing that some of the possibilities might also answer to “all,” at least in some contexts. But if we are committed to the analysis that began with “property is theft,” then this is precisely what we should expect and, as complicated as the next steps promise to be, confronting them is no setback.

It’s important, I think, to treat the analysis in The Federative Principle as both advanced, in terms of Proudhon’s theoretical development, and a bit compressed. What seems to have stuck with us is the a priori principles, when the lesson of the texts seems to be precisely that we cannot simply stop there, given the potential disconnections between their “mathematical” and “necessary” nature and the “infinitely flexible” nature of politics as an “applied art.” Rigorous logical analysis is essential, but it appears that it also has its perilous side, if we do not follow through. As Proudhon said:

Logic and ingenuousness are primordial in politics: and that is exactly where the trap lies.

The third choice seems to be to follow Proudhon from abstract anarchy, through the difficulties and antinomies associated with its application, to federation—and then to ask ourselves if there is another kind of positive, practical anarchy that emerges in this new context, not simply as a kind of political autarky or as a negative ideal, but as the result—or resultant—of “the balancing of authority by liberty, and vice versa.”

Resultant anarchy: Let us simply propose a third general variety of anarchy, which does not arise directly from the application of a simple principle to a simple society full of simple, individual subjects, but emerges from the balancing of social forces, norms and institutions. And let’s borrow from Proudhon a word that he was fond of using in his later works: resultant (résultante). According to the OED, a resultant is “the vector which is the sum of two or more given vectors” or “the force that is equivalent to two or more forces acting at the same point,” as well as simply “the product or outcome of something.” So let us then say that we approach this other sort of anarchy as the sum of the various social forces in play (understood as vectors) approaches zero. And let us raise the possibility that we might speak of quantities or degrees of anarchy based on the intensity of the forces held in balance.

This third definition is presented here merely as a sort of hypothesis, a direction that subsequent research might pursue, as well as a potential escape from at least some of the difficulties that have emerged as we examined the first two. For those who might want to pursue the line of inquiry on their own, I can suggest that the most promising line of research seems to run from the 1840 discussion of “liberty” as a “third social form” and “synthesis of community and property,” through the study on liberty in Justice in the Revolution and in the Church and then on into the works of the 1860s.