# Axioms

## AXIOM 1: Oneness (“All is One”)

1 , A = 1

Union of Anything with “ALL”  = “ALL” (where “ALL” is “One”).

In Boolean Algebra:  1 OR A = 1

If “1” stands for “everything that can (ever) be distinguished”, then any other thing (different than “1”) is by definition already included inside “1”.

Here is a “proto-proof” of this Axiom, in a three-step “Primordial Contemplation“:

1. Suppose something is outside “Everything”.
2. Then, it does not exist, since “Everything” already contains it.
3. Therefore, it was not outside Everything in the first place. -QED

Primordial Verification: If “everything” does not contain something, then how can it be “everything” (in the first place)?
Primordial Corollary: There is no Existence outside “All Existence”, or: There is nothing, which is not contained in “Everything”.

NOTE 1: (for Sages, Seers and Mystics, mostly 😉 ): This Axiom arises spontaneously, by itself, out of the Unfathomable Void, by “Primordial Reasoning of the deepest depth”, at a level of Mind where imagination and reality are still One. At this level, all Gods and all Religions are still possible, since (at this stage, which is poetic, luminously contemplative and totally spiritual), no “cancellation of the objects of perception” has taken place yet (according to Axiom 3) and (well)… even if such objectification did take place, it is still totally reversible (by Axiom 3), so that the Primordial Purity of this Mind-State can still be restored, in its entirety.

NOTE 2: (for skeptics, pessimists, jokers, materialist critics, et. al): Despite the pompous quasi-religiosity of the previous paragraph (NOTE 1), you could also (if you wish) re-interpret this first axiom differently, since the most typical known physical entity which absorbs anything outside itself, inside itself, is a… Black Hole. Stating this intuitive discovery more elegantly:

Primordial Isomorphism 1:
(please bear in mind with care that…)
The statement “ALL is ONE”

is indistinguishable from “ALL is a BLACK HOLE”

## AXIOM 2: (self-) Reflection (is void)

A # X # X = A

To distinguish (the very same fact) that we are distinguishing, is the same as not distinguishing (it). I.e. a finger pointing to itself, does not point to anything. Hence (by “Primordial Reasoning” of the Deepest Depth):

-To distinguish (the fact) that we distinguish “A”, is the same as “A” itself.

In Boolean Algebra:  A xor X xor X = A

## AXIOM 3: Perception is (reversible)internalisation

A , X # ( A, B)   =   A , X # B

In a (self-) Boundary of Perception X, any-thing A that exists outside the boundary, can also be brought inside the boundary. Conversely, any-thing A that exists inside a boundary of perception X can also be cancelled out iff (if and only if) it (or a “copy of itself”) also exists outside the boundary X.

I.e. Any-thing (we see) outside ourselves, we may (also) assume (or imagine) inside ourselves. Any-thing we assume (or see) inside ourselves, we need not assume (or imagine it), iff we can also see it (as a “fact”) outside ourselves.

### In Boolean Algebra:A or  ( X xor (A or B) ) = A or (X xor B)

-To pursue further the “metaphysical” or “psychological” essence of Axiom 3, it is note-worthy that variable “B” (the blue human, in the above figure) represents an “Inner Reality” which does not exist in the “Outer World” (represented by “A”, or the picture of the church).

Hence (or otherwise) the “strictly esoteric reality Bcannot be “cancelled out”, inside the (self-) boundary represented by “X” (it is esoteric, iff it doesn’t exist outside ourselves).

Anything that “exists outside us” is unreliable, since (at any moment) it might be cancelled out (one way, or another).  The Truth(tm) is Inner, and there exists no “Inner Truth” in the Outer World. However, there is “Inner” Truth inside Other Minds (as well)!

NOTE 3: (for skeptics, pessimists, jokers, materialist critics, et. al): Despite the pompous quasi-religiosity of the previous paragraph, you could also (if you wish) re-interpret this third axiom differently:
Primordial Isomorphism 2:
(Please bear in mind with care that…)
The statement “There is an Inner World, not existing outside ourselves” is indistinguishable from the statement:
“We cannot perceive everything that exists outside ourselves”

Informal “Proof” of “primordial isomorphism 2”:

1. To “perceive something” (say X) means that it exists outside our boundary of perception
2. Suppose we can perceive “everything” that exists
3. Then, let there be (any-thing) “X”, inside our boundary of perception.
4. Since “we can perceive everything“, we can also perceive X.
5. if we can “perceive X”, then it also exists outside our boundary by (1),
6. Therefore X was NOT (only) “inside our boundary” (in the first place)…
7. By induction, NOTHING can exist inside our boundary of perception (which cannot be cancelled out)!  – Q.E.D.

## NOTES (Connections with William Bricken’s Logic, etc.):

William Bricken used three axioms in his system. His first two axioms are said to “parallel the laws of arithmetic” and his third axiom represents the Law of the Excluded Middle. These axioms were called “Dominion”, “Involution” and “Pervasion”:
 1) Dominion A ( ) = () 2) Involution ( ( A ) ) = A 3) Pervasion A ( A, B ) = A ( B )

Multiple Form Logic also has three axioms, which are similar, but much more generalised. Here they are:

 1) Oneness 1 , X = 1 2) Reflection A # X # X = A 3) Perception A , X # ( A , B) = A , X # B

-where the operator “#is effectively identical to the Boolean Exclusive-OR (XOR) and “,” (comma) is logical “OR”.

The important difference is this: The variable “X”, in these axioms, is not a constant operator or parenthesis (as in Bricken’s axioms), or a “syntactic sugar glue symbol”, but a (variable) Form, i.e. a “citizen of equal status” to all other variables in these expressions, where each variable can also be another Form, i.e. another entire expression.

In another section (“More Theorems of Multiple Form Logic”) there is a formal proof that William Bricken’s system is in fact a restricted version or a subset of Multiple Form Logic. The formal proof is followed by informative graphic representations (elucidating what is going on, even for people with no training in Formal Logic).

To elucidate these Three Axioms a bit further, and to see that they are non-trivial generalisations of Bricken’s System (which had not yet been invented -by the way- when Multiple Form Logic™ was first created back in 1983/1984, in the typewritten version given to Professor Jones) …please bear in mind:

1.      In Multiple Form Logic™, all Forms are “relative” except logical “One”, which is the “Universal Form”. This unique Universal Form “1” is defined as the Union of all Forms in the Universe (which is “The All”). So, Axiom 1 of Multiple Form Logic™ becomes a naturally recursive representation of the (self-evident, for many people) Universal Truth: The union of any-thing with “the All” is (still) the All, and All is One.

• At this point, if you’re finding all this… a bit too heavy, here is a relevant joke to cheer you up: What did the hungry Buddhist say to the Hindu hot dog vendor? “Make me one with everything“!

2.      In Multiple Form Logic™ there exist only two fundamental operators or relationships between “forms”: “or” and “xor”. They are almost identical in meaning to the (well-known) Boolean operators “OR” and “XOR”; “almost” identical but not “completely identical”, because Multiple Forms are not necessarily Zero or One: By nature they are multiple and multi-valued. Furthermore, countless “forms” can co-exist peacefully side-by-side, in a relation we can treat formally as “logical OR”. Only when such forms are the same, do they reduce to only one. However, such (OR-) cancellation (X or X = X) is not an axiom, but a consequence (theorem T2) of the “Law of Perception” (Axiom 3).

3.      The meaning of “XOR” is changed: it is now a “cancellation effect” of identical distinctions, expressing an intuition that states “to distinguish the fact that we are distinguishing is the same as no distinction“. However, whenever different distinctions distinguish each other, they do NOT cancel out; they can co-exist peacefully instead. However, within any structure of Forms or Distinctions distinguishing each other (XOR-wise), every pair of identical distinctions cancels out. (This is an intuitive explanation of Axiom 2, above).

4.      The operation “XOR”, within any expression, is valid “by default”, i.e. “XY” means “X xor Y”, “ABC” means “A xor B xor C”, etc. This is the notation used for many years (submitted to the university of Manchester). However, while developing Theorem Proving software for this calculus, I decided to use the symbol ‘#’ for XOR, hoping for an improvement in readability (for machines, as well as humans). Furthermore, the “OR”-operation is denoted by a comma between (Multiple) Forms. E.g. the expression “X,Y” expresses the (Boolean) “X or Y”; “A,B,C” expresses the (Boolean) “A or B or C”; “X Y (A,B,C)” means “X xor Y xor (A or B or C)”, and so on.

5.      Multiple Form Logic™ does not con-fuse the presence of parentheses as “glue symbols”, within expressions, with the existence of Forms or Distinctions. I.e. parentheses are mere representational tools, without “inherent essence”. Some people discussing Brown’s work occasionally used parentheses to represent Distinctions, so –unfortunately- many Brownians -ever since- inherited a strange confusion about the meaning of parentheses, in the last 3-4 decades.

 However, “metaphysical contemplation” is beyond the scope of practical work, or the crux of this matter computationally, which is:faster and more efficient Logic deductions!

(under construction)