Paradox and Self-Reference

Descartes employed radical doubt until he reached the point where he could doubt the fact that he was doubting. This was the paradox that stopped him in his tracks, or rather it gave him a secure point of origin for thinking. From there, he chose one side of the distinction and began his cognitive operations. His “Cogito, ergo sum” was this starting place. If he was thinking, then he he surely existed. There can be no thinking without a thinker.

This is from The Dream of Reality: Heinz von Foerster’s Constructivism by Lynn Segal (1986).

A paradox is a statement that is false when it is true and true when it is false. Paradox can occur whenever statements are self-referential. For instance: 1) This statement is false. 2) I am lying. 3) Please ignore this notice. 4) It is forbidden to forbid.

A paradoxical assertion is indeterminable or undecidable, which means a theorem or proposition cannot be proved or disproved. The paradox “it is forbidden to forbid” cannot be established as true or false; therefore, it is useless cognitively; it doesn’t lead anywhere. A thinker must choose one side of the two-sided form. As Luhmann put it, “If one tries to observe both sides of the distinction one uses at the same time, one sees a paradox—that is to say, an entity without connective value. The different is the same, the same is different. So what?” (Theories of Distinction, p. 101).

Segal continues:

Each statement comments on itself. . . . Why do logicians object to paradox? . . . Logicians work with declarative statements called propositions. . . . Aristotle taught that if a proposition makes sense it must be either true or false. . . Paradox renders a proposition’s truth value indeterminable. Paradoxical statements or propositions are neither true nor false.

Autopoietic systems are self-referential systems. There is a re-entry of a distinction (the system/environment distinction) into the system that allows the system to observe itself.

The elements (or operations) of the system can only connect with elements of the same system (which also have to be the same kind of elements); the system produces its own elements. It produces itself; it is not produced by anything outside of itself. It is a causa sui. This means that when a system observes itself it has no beginning and no end. As far the system is concerned, it has always existed and will always exist. It cannot conceive of its own ending because each operation presupposes a subsequent operation. Nor can it conceive of its own beginning because every operation presupposes a previous operation. Thus a human being cannot imagine her/his own death. There always has to be something coming next. Beginning and end can only be observed from outside the system.

Similarly, if we want to talk about language, then we need a meta-language. This is how we dissolve a paradox. But this is really a fiction because a metalanguage is still just language and it is still just talking about itself. A new distinction must be made, which implies that a new paradox must be ignored. In order for the discussion of language to carry on, we need to ignore the fact that we’re using language to talk about language. That is to say, we have to ignore the distinction (language/metalanguage) that we are using. If, in this case, we can’t put our use of this distinction in a blind spot, we will tie ourselves up in knots. When we use language to observe (discuss, think about) language, we move to second-order observation.

Russell’s paradox:

Russell’s paradox has to do with logical classes and the logical elements the classes may contain. A class is a logical collection of objects that share a defined property. If one defines a class of books–all books past, present, and future–one can logically separate all objects in the universe into two classes: those that have class membership and those that don’t. If we allow a self-referential statement by asking if the class is a book, no paradox occurs. The class of books is not a book. (Segal )

So, the class of books does not contain itself. But what if we progress to a set of all sets that do not contain themselves as an element? The only way to dissolve this paradox is to move to a higher level. Yet, on this “ higher level” we need another distinction.


  1. Sorry for placing this comment here, but your original post (where you replied to my initial comment) is somehow not available anymore. You asked if I was working on organizations. Not directly — I’m interested in the change of society by computers (what Dirk Baecker calls “computer society” or “next society”), and my approach started with individuals and ended up with social systems.

    (In a very small nutshell: In my PhD thesis I modelled computer users as systems and computers as environment, and then observed both (partly in lab situations, partly in real-world situations). I looked for traces of reproduction of the “user system” while disturbed from unexpected environmental events. It got esp. interesting when these “user systems” were not observable as “user systems” anymore. In these cases, the same individuals became observable as part of “social systems” (for example when the computer user has to call for help, because there is some problem the user can’t solve). Unfortunately all of that is published in German, otherwise I’d simply send you a copy.)


    1. I see that your earlier comment was on the “The blistering demon of normality post.” I don’t know why that wasn’t available anymore. Your PhD research does sound interesting, although from the “very small nutshell” I don’t think I really know what you mean by “user system.” Is there a structurally coupling between the human user and the technology?


      1. Strange. Today I can open the “blistering demon” post again. I don’t know why last time WordPress gave me a “post not found” error. Anyway …

        In my model, the coupling was between human user and software, although the key here was the definition of “user”. The same human being is of course much more than a user. Also, using software is related to certain user goals which go beyond being just a user. Being a user in the model refers to just one of several “Sinnfunktionen”. The term “Sinnfunktion” comes from Dirk Baecker and maybe can be translated as “functions for making sense”. Baecker suggested several of these functions, namely the very basic “System” function. But there are several more related to it (like “Person”, “Design”, “Control”, etc.), which I took into account. Baecker expressed these functions using the Laws of Form, and I adopted this approach, partly to put Baecker’s “Sinnfunktionen” to a test (a test of their practicability for structured empiric research).

        For example, when I use WordPress, I do this not just for the sake of using WordPress. Instead, I’m trying to achieve some goal (publishing a text, reflecting on my thoughts, …), and this may also be embedded in some social context (communication with others, getting endorsement, …). While I’m observable as using the WordPress user interface (clicking links, uploading pictures, typing text, …), one can model this observation as system function “software usage” where a “user” (Mario) is coupled with the “software” (WordPress). This, in itself, is nearly trivial, but it’s the basis for further observations, esp. when this “software usage” is not reproduced anymore. When the WordPress site crashes, or the Internet connection fails, or when I can’t find your “blistering demon” post anymore :), what do I do then? Is the individual still observable as a user in these situations, i.e. is it still able to reproduce? Or is the individual suddenly observable as a person instead (e.g. utterances that show emotion, helplessness, …)? Does this person get part of a social system (e.g. by contacting the WordPress support, the ISP’s service hotline, …)? Does the social system “help” to re-instate system function again? And so on. These and other kinds of relations I tried to observe and describe.

        Sorry, it’s a bit difficult for me to express all this rather spontaneously in English. The defence of my thesis was three years ago, and there was a lot of theory attached to my work before the empirical part started (not just systems theory, but also ethnomethodology, some linguistics and a bit of philosophy of science and technology philosophy).

        And sorry again if my comment feels too long; I don’t want to spam your blog. But this motivates me to write a proper English summary of the basic approach and findings, probably in my blog. I’ll let you know when it’s available 🙂


      2. I had accidentally changed that post to draft status. No need to apologize for the long reply. I’ll say more later.


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