The book in question:
http://www.siese.org/modulos/biblioteca/b/G-Spencer-Brown-Laws-of-Form.pdf
Another influence on these musings is the "Tree of Life" that back in the first half to three-quarters of the 20th century was widely treated as fundamental to "Western" occultism; in particular Aleister Crowley's writing thereupon.
I have been pondering LoF's "first distinction" as the distinction between nothing and something, which leads me to wonder what the second distinction might be.
In LoF any number of the first distinction scattered willy-nilly all over a page of otherwise nothing only counts as something, not as a number of that something nor as a number of somethings; which harks me back to my own labelling of the Sephiroth of the Tree of Life as IS, MEANS, SO, CAN, DO, I, WILL, WOULD, GET and THAT.
Basically the first distinction is that there IS something rather than nothing.
In my own long-ago words again "there is nothing; so there is nothing to prevent there being something, thus there can be something", which is basically how I expressed the so called three veils of nothingness, the 000, 00 and 0, Crowley shows the Tree of Life emanating or arising from.
Since number is conspicuously missing from LoF's "boolean arithmetic", I was led to wonder if number might be a candidate for a/the second distinction, which brought to mind Crowley's Supernals, and geometric dimensions, and ultimately to think the second distinction is between something and something else.
One is one and all alone, a dimensionless point possibly, but if a second something distinct from the first something - a second distinction - existed then even if it itself was also a dimensionless point two distinct (separate, distinguishable) points introduces directionality; for each of the two there is something outside itself different from the nothingness that exists in all other parts portions or directions of outside-itself.
It cannot even intelligibly rotate or spin or, indeed, move, until there is something "relative to which" it does so.
Two points also, of course, in geometry defines a line, so if there are two distinctions distinct from one-another a one-dimensional line becomes imaginable, maybe a "virtual" line maybe an "implied" or "implicit" line, maybe line is implied by direction and direction by a line.
Continuing along Crowley's lines if there were a third distinction distinct from the first two distinctions, even if it too is just a dimensionless point three points "defines" a circle, it "creates" or "implies" a circle, if only a "virtual" (in some sense) circle.
I keep putting the word "virtual" in here because to me part of what makes quarks and gluons so hard to think distinctly and clearly about is the whole "gluons cause horrible messes of virtual particles conjured into existence all around them" stuff so I am hoping these musings might eventually help clear up the whole "virtual particles" idea at some point. :)
So per Crowley IS MEANS and SO (as I like to label Sephiroth 1 2 and 3) have brought us to the idea of a geometric plane, which to we who live in a seemingly 3-dimensional geometry is kind of "supernal". It is not until we admit a fourth distinct distinction (I like to call it CAN in honour of tin cans, because its planet is Jupiter whose metal is tin) that even if it too is a dimensionless point CAN, if not on the same geometric plane as the previous three, define a three-dimensional space, Buckminster Fuller's fundamentality of the tetrahedron maybe?
The label MEANS arises partly because the fact that there is a second MEANS there IS already a first.
SO maybe there CAN be more?
DO please follow the thread I am hoping this post will be the start of... :)
-MarkM- ( aka knotwork as in for example https://MakeMoney.Knotwork.com/ )
NOTE: Sequel post is @knotwork/lets-not-forget-synergetics-r-buckminster-fuller