Multiple Form Logic: Home Page
  Multiple Form Logic TM

is consistent with the
Ancient Buddhist Logic
of Nagarjuna 
(a more-or-less rigorous proof)
by George Alexander Stathis © 2007
Original Date of publication: 10/08/2000
Revision 1.01 (minor corrections): 26/2/2007

The following is a (more-or-less) rigorous proof that Nagarjuna's Ancient Buddhist Logic is completely compatible with Multiple Form Logic

DEFINITION: "Holy Spirit" = (logically) Unmarked State = Voidness (full of Light) or "Nirvana".

As explained elsewhere, "egos" or "selves" arise out of boundaries drawn within Voidness. The most elementary such boundary acts like a circle separating a plane surface into an inside and an outside.

George Spencer Brown (who invented this theory) remarked that Logical Truth or Form or Distinction can be identified with the Christian Trinity's "Father". Then the "space" inside the boundary can be identified with the Christian Holy Ghost and the space outside the boundary can be identified with Christ the Son, also identified with the Outer World!

However, under certain extensions to Brownian Logic provided by Multiple Form Logic, Brown's theology is wrong:

There is no single and unique Form; there is only the sum total of all possible forms, which is (in reality) "Logical One". And this is an infinite set; not a single "thing". Indeed, traditionally, God has been identified with the Infinite.

Well, God is Logical Infinity, but only as a construct; NOT as a "thing"-in-itself ! Under this new interpretation, it appears that the only common ground of theologically universal status which can be found, is the Absence of Form (or Void). And this signifies a State of Mind which is Raw Sensation, which does not distinguish inner from outer, and which is also en-lightened, i.e. full of light, rather than (mechanistically or nihilistically) "empty".

This is the ultimate nature of our own minds, as Lama Yeshe said, but it is also the "Holy Spirit" of Jesus and "the transcendent quality of God's nature".
i.e. God is a construct:

Now Tang Huyen (a well-known Vietnamese Buddhist scholar) is probably going to start mumbling something again :-) about Buddhist Voidness or Emptiness being the "absence of mentation" (rather than a "Brahmanist myth") but he might also heed the fact we have defined "God" or the Experience of the Divine State, as being no more and no less than the sum total of all possible mentations, in our own minds, and in all other minds, within all possible universes! And  we have defined Pure Reason, or Form, no longer as the mere "one and only" (jealous?) God, but instead as the sum total of all possible Gods, Mentations, Egos, Selves, Beings, or even Spooks or Ghosts(!) within the entire universe.

This logic works!  Its two axioms are sufficient to derive formally all the Logic theorems of the Propositional Calculus, and more.

In Multiple Form Logic (which is an extension of Brown's "Laws of Form") these two axioms are revealled to be (nothing but) a method for re-writing Boolean Algebra using only two "logic operators":

Logic Operator 1:
Exclusive Or  (distinction, or perfect continence, which corresponds to "ego")
Logic Operator 2:
Logic Or (or "lumping together", which corresponds to "peaceful coexistence")

Now, go find me a buddhist refutation of this logic, and I will... pierce my nose to wear a ring through it! :-)

There is simply no buddhist refutation, because this Logic is perfectly compatible with Buddhism and with Nagarjuna's Logic - revisited in our time.
Literally so; not metaphorically! Everything else is soap-bubbles. Actually, Nagarjuna's logic WAS the same as the above, since (for example) he says:

( in URL: http://www.bahai-library.org/personal/jw/other.pubs/nagarjuna/nagarjuna.06.html )

Well, if we abolish "true" and false" and if we accept A and B to signify distinct truth values, then the above paragraph by Nagarjuna is satisfied totally!

Proof:

1)  (a prerequisite) The equation "A = B" in Multiple Form Logic is (re-)written: "A xor B xor 1".

NOTE:  This happens because "Equality" is the Negation of Distinction (or of Difference), and because logical "negation of" some-thing (or of any-thing) is (no more and no less than) the formation of a "Universal Boundary" around "that thing"; where the "universal boundary" is "God" or "Logical One" and the (logical) relationship between this Universal Boundary and "the thing" itself is"Distinction" or "Perfect Continence", expressed formally by Exclusive OR in traditional Logic and Boolean Algebra. So, if Equality is just the negation of Exclusive-OR and the negation of X is "X exlusively ORed with One", it follows that Equality between A and B is the negation of A, exclusively ORed with B;  the latter is an exclusive-OR between Universal Form and [A excl.ORed with B].

2) Now let's take the equality "A = B" literally.  I.e. Suppose A is identical to B. Then "A = B"  is really translatable to the Logical Form "A xor A xor 1" which simplifies to "1". (by following blindly the formal rules of rewriting traditional logic in XOR/OR notation, and then noticing that "A xor A" cancels out, leaving only "1" at the end).

INTERPRETATION:  (since A and B are arbitrary symbols)

i.e. to assert that [for all A,and for all B] "A=B", is like saying... "Hallelujah". ;-)
And this (in itself) means... nothing (pun intended here); i.e. ...everything!

3) Now let's take the non-equality "A = not(B)". This is algebraically the same as "not [A=B]". Since we already know (step 2, above) that "A=B" can be written as "(A xor B) xor 1", and since "not X" is equivalent to "X xor 1", we can now translate immediately the inequality "A = not(B)", together with the substitution "A <- B" (since we assumed any forms A, B are "the same" in this universe) to the following new form: 

((B xor 1) xor B) xor 1   (a translation of "A is not equal to B", while A=B)
But then one can apply the First Axiom (of "Cancellation", "X xor X = void") to cancel out all the B's and all the 1's, reducing the above equation to VOID:
 
((B xor 1) xor B) xor 1 (a translation of "B is not equal to B")
((B xor 1) xor B) xor 1 (cancelling out 1, since 1 xor 1 = void)
((B .........) xor B) ......... (So now we are left with "B xor B"...)
((B.........) xor B) ......... (cancelling out B, since B xor B = void)
(( -.........) xor  - ) ......... =>  VOID !

This shows that "in a universe where any form (A) is the negation of any (other) Form (B), there can be nothing - but - Void(ness), which is simply the Absence of Form. In other words, any (hypothetical) universe where "everything negates everything else", is of necessity, and quite simply... an Empty Universe !   ( Moral: Be positive! :-) hehe! )

Of course we could have avoided all this work, if we asked the question (from the beginning) "What is the logic value of the assertion "B=not(B)". However, in this logic, we cannot take certain assumptions for granted. Remember that we are reasoning at a lever much deeper than "Boolean". Boolean Logic follows as a consequence in this system, it is NOT assumed to be true a priori. So one has to painfully "translate" everything, at a primordial level which can be said to "pre-exist" Boolean Algebra and the Propositional Calculus. If you disagree, this is fine. The same result holds if you skip the labourious "translation" above.

4) Hence, or otherwise, Nagarjuna's dialectics are correct - in stating that the Logical Forms A and B, are NEITHER "the same" NOR "different" (in Truth Values). A and B are quite simply distinct forms, or distinct boundaries, which cannot be reduced any further, i.e. they can neither be "identical" (leading to... everything!) nor "different" (equal to nothing!). Steps 2 and 3 (above) illustrate the latter cases of "identity" and of "difference" in a formal way.
- What Nagarjuna was saying, in other words, is that... Forms (or Distinctions) are (1) MULTIPLE, and (2) NEITHER Zero nor One!
Because (corollary) if Forms are the same (not multiple) or forms are different (not the same) then in both cases the result is VOID!

(and Boolean Algebra always reduces forms to either absolute sameness = 1, or absolute difference = 0)

To summarize, we now have the following:

1) A "universe" of an infinite number of truth values or forms or minds.

2) The union (OR-wise) of all possible forms (or distinctions or minds) as "Logical One" or "God" or "Universal Form" 1 (where "1 OR X = 1").

3) The "absence of form" as logical Zero or Void / Emptiness.

4) Three axioms, including (2) above (expounded elsewhere).

5) The Multiple forms or truth values in this universe (which are more Nagarjunean than "Boolean") with two "fundamental logic operators": "XOR" (exclusive or; "neither-nor") and "Logical OR".

I.e. Toothpaste! :-) Lots and lots and lots of... Logic Toothpaste.. ;-)  Also known as "Void-gate toothpaste" (to clean up both Samsara and Nirvana)...


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