I would say that the first-order Cybernetics (as exemplified IMO in Ashby's book) is all about symbolic formalism for "circular loops in causality", and that Second-Order Cybernetics is a species of mysticism (I hasten to add that I don't mean that in a derogatory way. I'm a Mystic myself.)
You could imagine a spectrum from logic to cybernetics to philosophy to mysticism. It's all fine, just I believe that it's important to be clear where on the spectrum you're working. If you want to build machines that do things use Cybernetics and feedback/control theory, if you want to grok reality and self eat a mushroom and read "Gödel, Escher, Bach" or Tao Te Ching.
In re: "Laws of Form", yeah, he identifies the boundary or distinction between the mystic realm (non-form, non-distinct, non-dual) and symbolic logic, and then builds a lovely binary Boolean logic directly off of that. It's a tour de force.
The really interesting thing is that George Spencer-Brown figured out how to deal with circular logical systems by introducing the concept of imaginary Boolean values.
It's a formal system for symbolic logic, and you can indeed build a lovely and efficient SAT solver with it using Bricken's Basis. E.g.:
https://ariadne.systems/pub/~sforman/Thun/notebooks/Correcet...
(For reference, here's the LoF/Bricken formalism)
Arithmetic
(()) =
()() = ()
Calculus
A((B)) = AB
A() = ()
A(AB) = A(B)
(That third rule in the calculus, discovered by Bricken, is the kicker!)
cf. "The Markable Mark" George Burnett-Stuart
http://www.markability.net/
GBS (not GSB, they're two different people) has managed to extend the system to Predicate Logic as well!
William Bricken's home page:
https://wbricken.com/
His Iconic Math Page (a wonderland!)
https://iconicmath.com/
To sum up, we need symbolic formalism to communicate and build machines, otherwise we're just sort of reading poetry to each other, which can still be helpful, but in a different way than building machines. (And when I say machines in the context of Cybernetics I mean to include those made out of people! "Human use of Human Beings", eh?)
As an aside, there is a fascinating talk and book "My Stroke of Insight: A Brain Scientistʼs Personal Journey" by Dr. Jill Bolte Taylor:
> In it, she tells of her experience in 1996 of having a stroke in her left hemisphere and how the human brain creates our perception of reality and includes tips about how Dr. Taylor rebuilt her own brain from the inside out.
https://en.wikipedia.org/wiki/My_Stroke_of_Insight
https://youtu.be/UyyjU8fzEYU (TED Talk)
When "Laws of Form" talks about the beginning of logic from the pre-logical non-distinct or non-distinguished realm, the "mark" that divides the world into A and Not-A, it turns out to be quite literal, purely biological: the brain does it. When the part of her brain that "does logic" was rendered inoperative due to the stoke she was having, she reports an inability to tell herself from the world around her accompanied by oceanic bliss...
Mysticism is real, you just can't talk about it. The very first chapter of the Tao Te Ching says it right off: the Tao that can be talked about is not the Tao.