"Operational Closure"の和訳について
Varela以降自律性（autonomy）の概念の定義（またはその一部）としてしばしば用いられている"operational closure"の概念を日本語に訳す際、僕自身は以前は特に深く考えずに「操作的閉包」と訳していたのだけれど、ある原稿の執筆時に編集者の一人から指摘が入ったので改めて色々読み直した結果、今ではとりあえず「作動的閉包」と訳す派になった。
ちなみに定訳も「作動的」。
まずDi Paoloら (2017) は、彼らのいう"operational"が実験心理学（や物理学）における「操作的定義」などのそれとは異なっていると述べている（以下、下線は引用者による）：
Throughout this book, the term operational is used in two senses, neither of which corresponds exactly to the meaning given to this term in experimental psychology. The latter is merely a synonym of measurable. In our case, one meaning of the term refers to the possibility of a noncircular grounding for a given concept (this is almost contrary to some misuses of the term in psychology, which can sometimes be circular as in, e.g., intelligence is what is measured by intelligence tests). Typically, an operational definition is one that is grounded naturalistically (i.e., it involves a description of the multiple elements that constitute a particular concept, and these elements are themselves grounded operationally). A consequence of having a naturalistic grounding is that in principle at least, an operationally defined concept will also lead to ways of measuring a particular phenomenon, though not necessarily straightforwardly. A different sense of operationality, used in some of the following chapters, is applied to processes, whose unravelling over a course of time is described as their operation. The two different senses should be clear from the context.
Di Paolo, E. A., Buhrmann, T., & Barandiaran, X. E. (2017). Sensorimotor Life: An Enactive Proposal. Oxford University Press. (p. 24, footnote 6)
そして、"operational closure"におけるoperationalは後者の意味で用いられている：
An autonomous system is defined as an operationally closed and precarious system. This means that among the conditions enabling the operation of any constituent process in the system (a black circle in the figure) there will always be one or more processes that also belong to the system. In addition, every process in the system is an enabling condition for at least one other constituent process, thus forming a closed network of enabling relations (black arrows) (Di Paolo 2009).
Di Paolo, E. A., Cuffari, E. C., & De Jaegher, H. (2018). Linguistic Bodies: The Continuity between Life and Language. MIT Press.
https://scrapbox.io/files/65a4c9e9f5a67f0024a18a6b.png
The enactive view seeks to explain such seemingly mysterious processes of self-individuation by reference to the properties of certain systems that actively conserve their own organization (see, also, Jonas 1968). A fundamental concept in understanding the material and energetic conditions under which initially undifferentiated processes organize and through their operation lead to the individuation of a well-defined unit is that of operational closure. The term originates in the mathematical concept of closure, which defines a set as being closed under certain operations if the application of those operations to elements of the set only produces other elements of the same set (the integers, e.g., are closed under the operations of addition and subtraction, but not division). Closure in this formal sense is sometimes called organizational. The enactive concept of operational closure is similar but the term “operational” highlights that closure is achieved through the actual work and transformations done by processes in time (i.e., we are not merely talking about closure in a formal, mathematical sense). The concept then refers to a network of processes whose activity produces and sustains the very elements that constitute the network.
Di Paolo, E. A., Buhrmann, T., & Barandiaran, X. E. (2017). Sensorimotor Life: An Enactive Proposal. Oxford University Press.(p. 112)
これに従うなら、プロセスの継続的な「作動（operation）」が問題になっているということで、心理学や物理学における操作主義との混同を避けるためにも、ひとまず「作動的」と訳すのが良さそうである。
※ここからは少々ややこしいので、より詳しく知りたい人向け
ちなみに、Varela自身は以下のように述べている（上の引用にも同様の言及が含まれているが）：
Hypothesis 1 (Closure Thesis):
Every autonomous system is operationally closed.
The notion of closure here is intended in its algebraic sense : a domain K has closure if all operations defined in it remain within the same domain. The operation of a system has therefore closure, if the results of its action remain within the system itself. This notion of closure has nothing in common with the idea of a closed system or closedness, which means an incapacity to interact. Obviously we are interested in interacting systems; ...
Bourgine, P., & Varela, F. J. (1992). Towards a practice of autonomous systems. In P. Bourgine & F. J. Varela (Eds.), Proceedings of the First European Conference on Artificial Life (pp. xi–xvii). MIT Press. (p. xii)
これを読む限り、もともと"operational closure"という語は"operationally closed"という語の名詞形であり、かつそれは、他のものとの関係から隔絶されているという意味での閉鎖性（closedness）と区別するために"operationally"という副詞がつけられているにすぎない。
つまり、この段階での「operational closure」は実は数学的な意味での「closure」と同義であると考えられる。
... Notice how operational closure and viability domain are closely linked although not equivalent. The first refers to the algebraic closure of the system on the basis of its previous state and its coupling; the second to the fact that it remains within bounds so that its operation may continue and hence within the viability domain.
Bourgine and Varela (1992, p. xiv)
ここでの「operation」とは数学的な「操作」（「演算」）のことであり、その意味では「操作的」と訳す方が適切かもしれない（その場合でも、その操作・演算の「実行」「作動」が重要なんじゃいとは言えるが）。
Di Paoloらは、ここでの単なる数学的・形式的な意味を超えたニュアンスを"operational"という語に担わせて"organizational"と区別していると言えるだろう。
Di Paolo and Thompson (2014) では（これが彼らの定義の最も重要な点ともいえるのだが）、operational closureは「状態変化のプロセスに関して閉じた状態の集合」ではなく「可能化関係 (enabling relation）に関して閉じたプロセスの集合」として定義されている。
この定義に従うなら、その閉包を規定している（上の引用の意味での）"operation"＝「操作」とは「可能化関係（をたどること）」あるいは（そのような形式的・静的な「関係」ではなく）あるプロセスによる別のプロセスの「可能化」である。
ちなみに、同じく自律性をなんらかの関係や操作に関する「閉包」として定義する試みとしては他にMossio, Moreno, Montevilなどによる「制約の閉包（closure of constraints）」に基づく定義があるが、彼らもまた、自律性を定義する閉包は〈状態と、それらの間の遷移プロセスのレベル〉ではなく〈プロセスと、それらの間の依存性（あるいは因果性 causation）のレベル〉で考える必要がある（そしてVarelaによる元々の定義は良い線行ってるのだがその点において失敗している）と言っている：
Despite its qualities, however, we would underscore what we take to be the fundamental weakness of Varela’s account of closure. The characterisation described above refers to the processes as the relevant constituents of the system that, when organised in a network, must realise mutual dependence and closure. It seems only fair to point out that, for Varela, closure is understood as closure of processes. And here, in our view, is where the problem lies. Formulated in these terms, closure can in principle be used to describe not only the constitutive organisation of biological systems – which are by hypothesis the prototypical example of autonomous systems – but also a number of physical and chemical systems such as, for instance, the famous hydrologic cycle.
...
Our diagnosis concerning Varela’s account of closure is that, although it points in the right direction by emphasising the fact that the organisation of autonomous systems somehow involves a mutual dependence between its components, it fails to locate closure at the relevant level of causation.
なので、あえて混乱するような言い方をするならば、Di Paoloに代表される現在のEnactive Approachにおけるoperational closureとは、それに属するプロセスたちが「プロセスAがプロセスBを可能化する」というある種の「操作（operation）」に関して閉じていることによってそれらのプロセスが継続的に「作動（operation）」し続けるような性質であるといえるかもしれない。
あるいは、Di PaoloらはMaturanaとVarelaが強調する「構造（structure）」と「組織（organization）」の間の区別（あるいは"constitutive domain"と"relational domain"の間の"non-intersection"）のような立場を批判している（Di Paolo, 2009; Barandiaran, 2017など参照）が、ここでも二つの意味での"operation"が二元論的に相互に独立なものとして区別されるのではなくお互いに絡まり合い両者にまたがっていることを強調している、ともいえるかもしれない。
組織とは、あるシステムがある特定のクラスのメンバーとなるために、そのシステムの構成諸要素相互のあいだに存在しなくてはならない諸関係のことだ。構造とは、ある特定の単体をじっさいに構成しその組織を現実のものとしている、構成要素と関係の全体をさす。
『知恵の樹』p. 58
Di Paolo, E. A. (2009). Extended life. Topoi. An International Review of Philosophy, 28(1), 9–21.
Barandiaran, X. E. (2017). Autonomy and Enactivism: Towards a Theory of Sensorimotor Autonomous Agency. Topoi. An International Review of Philosophy, 36(3), 409–430.
For Maturana and Varela, autopoiesis is not a property of the ‘‘structure’’ of the machine, the actual relations obtaining in its physical space, but of its ‘‘organization,’’ the relations defining it as an entity belonging to a certain class (autopoietic or allopoietic). The tautological character of this definition is readily apparent: autopoiesis is that property of the organization of a system that makes it belong to the class of autopoietic systems. More importantly, however, its clean separation from structure renders autopoietic organization an abstraction removed from the domain of real interactions and actual components.
実際、あるプロセスが起こる（＝作動する）ことと、それが他のプロセス（計測機器に生じる変化なども含む）を可能化することとは切り離せないだろう（他のプロセスに一切影響しないプロセスは果たして「生じている」と言えるだろうか）。
やや我田引水すると、これはまさに圏論的な見方であるといえる： Hirota, R., Saigo, H., & Taguchi, S. (2023). Reformalizing the notion of autonomy as closure through category theory as an arrow-first mathematics. ALIFE 2023: Ghost in the Machine: Proceedings of the 2023 Artificial Life Conference. https://doi.org/10.1162/isal_a_00627