The problem is “I,” the shortest self-referential loop. When speaking about oneself, using “I,” Magic is performed. One creates oneself by creating oneself. “I” is the Operator who is the result of the operation. -- Heinz von Foerster ⇒ The Ethical Imperative ⇒ Child (as in a self-fulfilling prophecy) gains an Address and with it the possibility of establishing self-reference.
To complete an operational description of round- and Square-Brackets, we will need an axiom that specifies how the two boundaries interact in configurations more complex than the double nesting of Inversion. Here is the James axiom of Arrangement. The axiom specifies an invariant structure across frames.
DOT FROM lambda-browsing