Boolean Contradictions as Latter-Day Seed-Forms for Dialectics.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

Boolean Contradictions

 

as

 

Latter-Day

 

Seed-Forms

 

for

 

Dialectics.

 

 

 

 

 

 

 

 

 

 

 

Dear Reader,

 

We wrote about the Boole’s ‘time during which true’ interpretation of original-Boolean-algebra equations when used to model propositions, rather than existential assertions, in a recent entry to this blog –

 

F.E.D. Dialectics: The Fatal, VIOLENT Unrealism of Aristotelian-Boolean “Logic” in Human Affairs.  

 

 

In a “purely-qualitative”, classes or “sets” interpretation of the Boolean-algebraic equation –

 

x  =  (1 – x)

 

i.e.,

 

x  =  not-x,

 

or

 

“x  =  anything in the Universe [denoted by 1] other than x

 

 

– this equating of x to not-x makes no existential sense.

 

But in Boole’s original, ‘quasi-quantitative’, “temporal” or “durational” interpretation of his equations, when interpreted as modeling formal-logical propositions, this equation means that the modeled proposition is true for the same number of units of time as is its, formally contradictory, opposite – as is its Boolean negation – albeit during distinct stretches of time:

 

t  =  (1 – t);

 

\ t + t  =  1 – t + t;

 

\ 2t  =  1;

 

\ t = 1/2

 

\ also (1 – t) = 1 – (1/2)  =  1/2

 

– that is, one proposition is true “half” of the time, and the other, contrary proposition is true the other “half” of the time, somewhat like the propositions “It is daytime.” and “It is not daytime.”, or “It is nighttime.”. 

 

Neither proposition is true “eternally” – “t = 1”, or true never, “t = 0”. 

Each is “half-true”; each is also “half-false”. 

 

Boole did not intend for such equations to model anything more meaningful than formal contradictions.  But the oscillatory meaning of such equations is latent – immanent – in Boole’s algebraic models of propositions nonetheless. 

 

The resulting immanent critique of original Boolean algebraic-logic identifies a seed form that points toward an algebraic-logic capable of modeling dialectical logic itself.

 

 

 

 

 

 

 

 

 

 

 

For more information regarding these Seldonian insights, and to read and/or download, free of charge, PDFs and/or JPGs of Foundation books, other texts, and images, please see:

 

www.dialectics.info

 

 

and

 

 

https://independent.academia.edu/KarlSeldon

 

 

 

 

 

 

 

 

 

 

 

 

For partially pictographical, ‘poster-ized’ visualizations of many of these Seldonian insights -- specimens of ‘dialectical art’ – as well as dialectically-illustrated books published by the F.E.D. Press, see –

 

https://www.etsy.com/shop/DialecticsMATH

 

 

 

 

 

 

 

 

 

 

 

¡ENJOY!

 

 

 

 

 

 

 

 

 

 

 

Regards,

 

 

 

Miguel Detonacciones,

 

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

Elected Member, F.E.D. General Council;

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

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

 

 

 

 

 

 

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