Women's studies must be able to take the difference between man and woman (to put it in the conventional order) as a basis.
Its theoretical possibilities depend on how this difference is conceived, how it is brought into the Form of a Distinction.
Apart from all natural distinctions, which assume that there is a corresponding difference, and which thus always take over quite a lot of definition into the theory unseen (one would then have to follow up and ask what men or women actually are), the logic of Spencer Brown opens the access to research with an instruction: draw a distinction! Make a distinction!
Who commands here? A man? And what happens?
The introduction of a distinction is first of all the introduction of a Form. A form is the distinction of an inside (of the distinguished) from an outside (of the thing). So the introduction of any distinction is itself a distinction.
And who distinguishes this distinction? All beginning begins with already having begun, that is, with a paradox (Glanville/Varela 1981). Spencer Brown shows, however, that this does not hinder the development of a calculus and can be cleared up later, when the calculus is complex enough.
Equally: without execution of this instruction no observation is possible. Observation (finally self-observation, for example of the woman as a woman) can be defined as gaining and transformation of Information with the help of a distinction. With the help of a distinction it must be ascertainable what is excluded by an information, and in the case of being a woman this is understandably being a man.
Of course, this also applies when a secondary interest arises to blur the distinction again or to make it unrecognizable. Or if one needs for certain operations a rejection value in the sense of Gotthard Günther, which neutralizes the distinction for the moment without abolishing the distinction itself. Cf. Günther (1976 and 1976a).
However, it is not at all obvious what could be gained or lost by starting information acquisition and processing with a distinction – for instance that of man and woman or any other. It is at this point that Spencer Brown provides the crucial insight. Spencer Brown summarizes two different functions in one operator, namely distinction and indication. A distinction as such is incomplete, operatively imperfect, if it does not at the same time designate the one side that is being distinguished. Accordingly, designating has Meaning only within the framework of a distinction, while the latter can only have the sense of preparing a designation.
See Meaning (Sinn).
The other side is kept accessible, it is reachable by a "crossing". But, as can easily be seen, this is only true because of the asymmetry already created in the initial operation. The asymmetry is then expressed in the two fundamental axioms (and further ones are not necessary). The repetition of the operation condenses the signified, but adds nothing (The value of the call made again is the value of the call). The opposite is true for the repetition of the crossing (The value of the crossing made again is not the value of the crossing). The result is an enrichment of form, a reflection on the basis of the boundary, and finally a re-entry of the distinction into the space in which it distinguishes something.
The fact that there is only this one basic operation also has the consequence that it makes history. Once it is set, it cannot be erased again, because there is no operation of its own available for it. There is no way back to the "unmarked space". The beginning is fatal. If one wants to change something, then only with operations that always already perform distinctions and designations, separations and asymmetrisations in one. That is why also the consequential problems in the system structure occur temporalized. For example, there is no simultaneous yes and no, i.e. no contradictions, but only an oscillation between both possibilities, which may appear as a contradiction to an observer who abstracts from time relations in the system. So the question, with which distinction (e.g. that of man and woman?) one starts, is rationally undecidable, but momentous.
We will not pursue the calculus thus formed, but only clarify some implications of the approach:
Distinctions cannot distinguish themselves. Nevertheless, an observer can distinguish distinctions, for example, according to whether they construct a universe with the help of the additional axiom of the excluded third or whether they function as mere duals. The former possibilities could also be called totalizing distinctions. Classical (nowadays disputed) logic is perhaps the most famous case. It has led to paradoxes which had to be excluded; and finally to a "re-entry" of the distinction into that which is distinguished by it, so that one accepts as true only what is "true and not untrue".
Is the distinction between women and men meant as a totalizing distinction, and if so, how are the then due additional provisions handled? Or is this question already the trap that a male logic sets up to put women's studies on a slippery slope right from the start?
Distinctions are made arbitrarily. But this means nothing more than that they are not given independently of observation. They do not result from the thing itself, in the case of men and women, for example, not from a basic anthropological fact. They are constructions of a reality that could also be constructed in a completely different way, starting from completely different distinctions. This does not exclude that their use (as an observer can see) is motivated and can be justified; and of course "postrationalizations" (Glanville 1984) remain possible at any time. Therefore, the initial instruction is rightly: make a distinction (otherwise nothing works). But is this already the trap? And should one consequently advise women: make no distinction?
Finally, it should be noted that connectable distinctions require an asymmetrization (however minimal, however reversible). The one (and not the other) side is designated. It is obvious that the distinction would be at the same time beginning and end of operating, if it did not carry a designation with it. One would then have no clue on which side the operation could be continued (and be it as crossing). The machine would stop. As in Aristotelian physics the equilibrium is a deficient state, because it prevents the movement to seek its natural place, so the pure distinction is inconclusive. True, one might object that the choice of designation could be left to the situation – sometimes the man, sometimes the woman according to a fair equality, and so on. But this would be a fallacy at this level of theory construction; for then the order of situations would be superior to logic, it would dominate the operations, one would in fact have a hierarchy in which the operation only carries out what the situation demands (and as a sociologist one could add: one knows that this correlates with power relations, stratification, etc.).
So not like that! Apparently there are reasons not to handle distinctions completely side-neutral, but to mark them by a slight preference for one side. One thinks of famous cases like: subject/object, figure/ground, sign/designated, text/context, system/environment, master/servant. This does not deny that each side has meaning only in relation to the other, nor that a transition from one to the other is possible at any time. But it must be prevented that the operation gets stuck in an undecidability like Buridan's donkey between the haystacks; and it must also be prevented that the situation alone indicates the way out and thus overrides the structure, because then no more expectations can be formed. So it could have its justified reason to build a slight asymmetrization as a perfection feature into the basic operation. We suppose: already in it is the decision of this logic for the man. But is it to be avoided?
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LUHMANN, Niklas, 1988. Frauen, Männer und George Spencer Brown. Zeitschrift für Soziologie. Online. 1 February 1988. Vol. 17, no. 1, p. 47–71. [Accessed 24 October 2022]. DOI 10.1515/zfsoz-1988-0104, p. 48–50.