Logic of Forms and lambda calculus

Loet Leydesdorff wrote (in the Luhmann mailing list):

"Beyond Varela, it has been Louis Kauffman who has taken lambda calculus to its consequences. The lambda calculus was developed in a series of papers with Goguen. Kauffman coauthored with Varela a paper entitled "Form dynamics" in the Journal of Social and Biological Structures (1984). There is a follow-up in 1987 with a paper entitled "Self-reference and recursive forms" in the same journal. Recently, Kauffman returned to the issues in "The Mathematics of Charles Sander Pierce," Cybernetics & Human Knowledge 8 (2002), 79-110."

That is not the first time, that Loet contributed on the subject ([1], [2]). In August 2005 he wrote (see [1]):

"Spencer Brown's specification of an observer is part of a mathematical discourse. It is a logic (static) and not a calculus (dynamic). Varela has tried to extend it to his so-called lambda calculus from a biological perspective, but that project has failed. In my opinion, we have a calculus available in Shannon's information theory, but the latter needs then to be extended to communication systems (instead of communication channels) and a theory of meaning. Elements are to be found (and have been found) in Maturana's theory of autopoiesis. Furthermore, there is beautiful work in biology about systems evolution and probabilistic entropy (e.g., Brooks & Wiley) and the theory of anticipatory systems is relevant."

If you google for <"Form dynamics" in the Journal of Social and Biological Structures (1984)> you will come across Louis' paper "Time, Imaginary Value, Paradox, Sign and Space" (see [3]).


[1] LUHMANN Archives — August 2005 (#83)

[2] LUHMANN Archives — October 2005 (#296)

[3] http://www.math.uic.edu/~kauffman/TimeParadox.pdf


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