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Network and Self-Reference

Even today theoretical endeavors in sociology seem to be informed by some idea of a networking going on between different elements of social action framing and thereby sustaining each other. Indeed, to talk of anything "social" always means to look at a combination of restriction and support as the characteristic features of relations. Jon Elster of late conceives of a general theory of constraints produced by the actors as a commitment and a sort of stake, which is negotiable among them. Stephan Fuchs is interested in networks that allow for variation. And Andrew Abbott looks at self-similar structures of the social that are defined by fractal distinctions which both single out certain features and use them to delimit their connection to other structures. Similar attempts abound.

What we propose here is to combine the ideas of network and of self-reference. Network synthesis means that any element of the network, referring to other elements of the same network, at some point will end up referring to itself, thereby discovering, and exploiting, the circularity, which means heterarchy (Gotthard Günther), of the network. Note in passing that David Stark has recently rediscovered the usefulness of the concept of heterarchy for the description and explanation of social organization bootstrapping itself by embedding within the network it needs as its own precondition.

The single tool most apt for the combination of network and self-reference is George Spencer-Brown's concept of the form of distinction, advanced in his 1969 book on the *Laws of Form*. Based on the idea of the distinction as an operation to be actually undertaken Spencer-Brown defines the "form" of the distinction as "the space cloven by any distinction, together with the entire content of the space" . This means that there are at least three values defining any one distinction, which are (1) the marked state, indicated by the distinction (the "inside" of the distinction), (2) the unmarked state, the state not indicated by the distinction (the "outside" of the distinction), and (3) the distinction itself, separating the two states or sides of the distinction by being drawn. Since the distinction is an operation actually being drawn it may be taken to be identical to the observer drawing it.

We take this form of the distinction to single out the minimal constellation of a network able to synthesize, in that it defines reference, as indication, self-reference, as the distinction being drawn by an observer, and a general network value, as the unmarked state being indeterminate, yet to be determined by further choice, i.e., distinction. The one idea introduced by Spencer-Brown, which is sociologically perhaps the most intriguing one, is the possibility to take unmarked states, or empty places, though being indeterminate or unknown, into account nevertheless.

Georg Simmel, in his digression on the question of how society is possible, already has a keen eye on that necessity of empty, yet to be determined places, for the synthesis of the society, in that he describes modern society as providing a place (*eine Stelle*) for the unpredictable individual, and as defining a kind of being socialized which is determined, or at least partially determined, as he says, by a kind of not being socialized. That is of course just another formulation of the century-old discovery that individuals in their thinking, wishing, and feeling are opaque to outside observers (and to themselves, indeed), thus forcing society, on the one hand, to account for the unpredictable by means of communication that are sufficiently attractive for individuals to participate in, and to provide for structures, on the other hand, which are able to socialize the individual into such a kind of being unpredictable, thus telling it how to deal with its necessity to be free, as Hegel used to say.

Network synthesis comes with reference, self-reference, and the form of any distinction including an unmarked state as a way to account for network. To synthesize a network means to indicate, to self-include, and to account for the indeterminate. We take it that accounting for the indeterminate is only possible within the distinction of reference and self-reference, thus ending up with a self-similar structure which repeats itself by having to take into account ever new unmarked states.

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