Part 12: Seldon Presents Series -- ‘ ‘Oppositional Products’ and ‘‘‘Products of Oppositions’’’, Boolean vs. ‘Contra-Boolean’. ’

Part 12:  Seldon Presents Series --

  

‘ ‘Oppositional Products’ and ‘‘‘Products of Oppositions’’’, Boolean vs. ‘Contra-Boolean’. ’

Dear Reader,

It is my pleasure, and my honor, as an officer of the Foundation Encyclopedia Dialectica [F.E.D.] Office of Public Liaison, to share with you, from time to time, as they are approved for public release by the F.E.D. General Council, key excerpts from the internal writings, and from the internal sayings, of our co-founder, Karl Seldon.

The twelfth such release in this new series is entered below [Some E.D. standard edits have been applied, in the version presented below, to the direct transcript of our co-founder’s discourse].

For more information regarding, and for [further] instantiations of, these Seldonian insights, please see --

www.dialectics.info

ENJOY!

Regards,

Miguel Detonacciones,

Member, Foundation Encyclopedia Dialectica [F.E.D.],

Participant, F.E.D. Special Council for Public Liaison,

Officer, F.E.D. Office of Public Liaison.

“...Perhaps the starkest way to portray the difference -- even the ‘opposite-ness’ -- of the original Boolean algebra in relation to our ‘contra-Boolean’ algebra, is this:

“(1)  In Boolean logic, the generic, algebraic representation for physical opposites [“primary propositions”] or for propositional opposites [“secondary propositions”] is the following:   

(x)  vs.  (1 – x).”

“In Boolean logic, there is no reconciliation of specific opposites, or of opposition-in-general. “

“The product of two opposites produces precisely NOTHING, 0 -- a ‘‘‘lose-lose situation’’’ in which both “sides” are lost --

(x)  x  (1 – x)  =  0,

which is also the Boolean expression of Aristotle’s ‘‘‘Law of NON-Contradiction’’’;

This expression also algebraically implies that --

x - x²  =  0,

which further algebraically implies --

x  =  x²

-- which is algebraically equivalent to --

x²  =  x

-- which is Boole’s “Fundamental Law of Thought”, or “Law of Duality”.  It

implies that logical NON-linearity reduces immediately to absolute linearity.

There is no ‘expanded reproduction of ideas/memes’ modeled here.

For Boolean logic, there is only the ‘‘‘simple reproduction’’’ of ideas/categories        /classes

[‘Boolean ‘‘‘self-(s)election’’’ is gainless’].”

“(2)  In the Foundation’s ‘contra-Boolean, dialectical Logic’, on the contrary,

  

x²  =  x + Delta x,  

modeling a qualitatively expanding reproduction of [ideo-]ontological categories, via the second term on this equation’s Right-Hand Side, Delta x, as well as conserving the Boolean moment via the recurrence of the x variable as the first term, also on the Right-Hand Side of this equation.  The product of categorial opposites always possibly yields, again, yes, the ‘‘‘simple reproduction’’’ of those opposite categories as free-standing, unreconciled opposites, but also, plus [+], a possible reconciliation, a ‘‘‘synthesis’’’, or ‘‘‘complex unity’’’, of the two thus become one, a <<tertium quid>> category-unit named --

q       _{Delta x; x}.   

Using the ‘meta-genealogical evolute product rule’ axiom, we have --

x x Delta x   =   x + Delta x + q            _{Delta x; x} .”