ISOMORPHISMS OF SPENCER-BROWN'S LAWS OF FORM AND VARELA'S CALCULUS FOR SELF-REFERENCE†
Daniel G. Schwartz · International Journal of General Systems · 1981
Exact isomorphisms with formal systems which employ the standard linguistic notations are established for Spencer-Brown's primary algebra and F. J. Varela's calculus for self-reference. The primary algebra is “essentially isomorphic” with classical propositional calculus, and the calculus for self-reference translates isomorphically into an axiomatization of S. C. Kleene's three-valued logic of partial recursion. This correlates Varela's “autonomy” with “total recursive undecidabilily,” and it suggests the use of Kleene-Varela type systems for discussing “mechanically unknowable” or empirically untestable system properties.