14) Extending Multiple Form Logic™ to other Boundary Logic Systems

It seems to me sometimes a “trivial task”, but (in practice) ominous in volume, to start translating some other “Boundary Logic Systems” into Multiple Form Logic™. What I mean by “translation” is (1) firstly to devise appropriate additional definitions, with structure and properties that are derived from these other Boundary Logics, and (2) secondly to work out derivations within Multiple Form Logic™ that take into consideration the additional definitions, to get similar or identical results. The beauty of Multiple Form Logic™ is that it allows such tasks to be accomplished, without discarding the validity of the three axioms, and –usually- without needing to replace these axioms, or to use new symbols.

There is a reason for this simplicity: Multiple Forms are (by nature)… Multiple! ;)

In other words, you don’t need any extra symbols (such as “special forms of parentheses”) to denote your “special boundaries”. You can use ordinary symbols, such as «Ψ», for any “special distinctions”. Then, after adding the definitions of these new distinctions to Multiple Form Logic^™, let it boil and simmer… E.g. Jeffrey James’s Calculus of Number Based on Spacial Forms, a Boundary Logic with three axioms:

Invollution ( [ A ] ) = A = [ ( A ) ]

Distribution ( A [ B C ] ) = ( A [ C ] ) ( A [ C ] )

Inversion A < A > = .

If we define the distinctions Ψ, φ and Δ for “[]”, “()”, “<>” (respectively), and also drop the symbol “#” (XOR) by assuming that it’s valid by default, then the above system becomes, in Multiple Form Logic™:

Involution A Ψ φ = A = A φ Ψ

Distribution (A , (B + C)Ψ)φ = ( Α , ΒΨ )φ + (Α , CΨ )φ

Inversion A + AΔ = void

(I am working on this one). However, we can define Arithmetic in other ways, within Multiple Form Logic™. The easiest way I found -so far- is to introduce “+”, an arithmetic operator which stands for the “sum”, or “accumulation” of “forms in space”, and then assert an additional “Law of accumulative distributivity”:

( A + B ) # C = ((A # C) + (A # C))

What I found most challenging and fascinating, is Ben Groetzel’s use of truly different kinds of boundaries, e.g. which either allow or disallow the process of internalisation (=to bring a form inside the interior of another form). I think this is -just about- the only Boundary Logic which may need to modify or discard the “Axiom of Perception”, for certain types of Distinctions. Most other Distinction Systems I’ve seen (notably Bricken’s) can be re-written into Multiple Form Logic™ in a more-or-less straightforward way, probably without any significant difficulties. Underneath all this, the philosophical approach followed by Multiple Form Logic™ is the same as all for all the other esteemed Brownian systems. The community of Boundary Logic researchers is bound ;-) to grow and grow, and I have no illusion of having found the “Holy Grail”™ which “puts out of business every other guy’s Boundary Logic Grail”. The basic principles of Multiple Form Logic™ are childishly simple and understandable by kids, at primary school perhaps!

My mother (the late Iphigenia Stathis, Maths teacher for High School students) and I were discussing for a number of years, the possibility of introducing some basic ideas of Boundary Logic (and my own Multiple Form Logic™) to experimental lessons given to school-children, before they learn other Algebraic Systems, or the Boolean Logic of computers. Can you imagine what it would be like, if Boundary Logic was (today) a mainstream theory for educational purposes, too, i.e. for teaching Boolean Algebra and the basics of Maths to students? I believe that Multiple Form Logic™ is one particularly useful system for such a purpose, but it’s one among several such systems. However, my mother died (in 1998) before we could find the time and the means to begin such an over-ambitious project. Perhaps the most important educational project which was accomplished, was the one which changed our selves, our own ways of thinking and contemplating: E.g. I stopped believing in Determinism and Mechanism. The universe was suddenly revealed a “Magic Place”, where every human is a secret “Harry Potter” at heart, and anything (well, almost anything!) is possible!

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