Here’s the story.

During 1665-1666 -- while Newton was discovering the
integro-differential calculus [his “Method of Fluxions”] -- Leibniz, who was
later to

*independently*[re-]discover that calculus, was discovering something else: the mathematics of formal logic; the ability of an arithmetic limited to the values**0**and**1**to model key characteristics of Aristotelian, syllogistic formal logic.
For Leibniz, this discovery constituted a starting point for
his lifelong quest to find and to found a <<

**>> -- a “universal character-language”, that is,***characteristica universalis***,***a*__universal____algebra__**to facilitate both a scientific method of discovery and a scientific method of presentation of scientific discoveries.***a universal ideography*
But Leibniz’s voluminous manuscripts on the algebra of
formal logic, and on the larger <<

**>> beyond it, were never published in Leibniz's lifetime.***characteristica universalis*
Sometime before 1847, when he published

Boole found, and then publicly founded, “Boolean Algebra”, the algebra of formal logic, that was to serve also the algebra of later electronic digital computer logic.

**, George Boole, with no knowledge of Leibniz's unpublished manuscripts on the algebra of formal logic, also [re-]discovered Leibniz’s discovery: the capacity of a**__The Mathematical Analysis of Logic__**{0**,**1}**arithmetic to mimic much of formal logic.Boole found, and then publicly founded, “Boolean Algebra”, the algebra of formal logic, that was to serve also the algebra of later electronic digital computer logic.

**What do**

*¿***0**, which Boole took to model the “Nothing” category, and

**1**, which Boole took to model the extreme opposite category of the “Nothing” category, namely, the Everything category -- or “Universe” as Boole called it -- have in common

*?*
Multiplicatively, they are “idempotent”: their self-multiplication produces only
themselves again as their only product --

**0 x 0 = 0**

**1 x 1 = 1**

-- ‘Nothing times
Noting equals Nothing’; ‘Everything times Everything equals Everything’: identical in form, maximally different in
meaning.

Boole took an algebraic equation, universally true in an arithmetic limited to

**{0**,

**1}**, as his “fundamental law of thought”, or “law of duality” --

**X x X = X**.

For Boole, this equation meant that when a category
interacts with itself, nothing new results:
such self-interaction

**the category itself, without any conceptual or intellectual gain [or loss].***simply reproduces*
Such a “law” describes an eternally statical conceptual
universe, an intellectually stagnant universe of thought.

On April 7th, 1996, Karl Seldon -- who later, in 1999,
became a co-founder of

**Foundation****[**__Encyclopedia Dialectica__**F**.**.**__E__**.] -- discovered an “ ontologically dynamical ”, “contra-Boolean”**__D__**, an algebra of qualitatively, ontologically***algebra of*__dialectical__logic**, after a nearly 40-year search, triggered by a childhood dream, in which he saw an “Equation of Universal Evolution”.***expanding reproduction*
The “fundamental “law” of

__dialectical__thought*”*which Seldon formulated, using this new “contra-Boolean algebra” is a**, <<**__dialectical__**>> negation of Boole’s “fundamental law of [formal-logical] thought”: Seldon’s law conserves, and elevates, and transforms Boole’s “fundamental law” --***aufheben*

__X__x__X__**[**

*is qualitatively**ontologically*]

__un__equal to**;**

__X__

__un__equal to**in**

__X__**[**

__kind__**in quantity]**

__not__
-- and, more specifically --

__X__x__X__**=**

__X__+

__DX__
-- where

**denotes a new category, for a different**__DX__**of things than the**__kind__**of things category**__kind__**denotes, but such that the**__X__**new**__DX__**“grows out of” the**__kind__**old**__X__**.**__kind__
The first term on the right-hand-side of the equation above,

**, is the “Boolean” term: the self-interaction of**__X__**reproduces**__X__**again.**__X__
The second term on the right-hand-side of the equation,

**, is the “contra-Boolean” term: the self-interaction of**__DX__**also produces something new.**__X__**Can Seldon’s “contra-Boolean algebra” model aspects of experienced, empirical reality that Boole’s algebra cannot, reconstructing the historical**

*¿*

__past__?
Consider the history of the “ meta-evolution ” [ http://www.dialectics.org/dialectics/Glossary_files/F.E.D._Definitions,EVOLUTION_vs._%27META-EVOLUTION%27,19DEC2012.jpg ] of the Marxian “social relations of
production”.

As the “social forces of production” -- as the “productivity of labor” -- grows, the social relations of production category of barterable

As the “social forces of production” -- as the “productivity of labor” -- grows, the social relations of production category of barterable

**ommodities, the interactions of the rising,**__C__*population and density of commodities and of barter-activities, gives rise to a “singularity” in human social relations, with irreversible changes in human activity and mentality: the irruption into existence of monies and of the “***expandedly**-**reproduced****onies” category:**__M__

__C__--->__C__x__C__=__C__**+**.

__D____C__=__C__+__M__Or, consider the history of the “meta-evolution” of pre-human ontological categories.

When the rise in the populations and local ‘densifications’ / ‘concentrations’ of

**toms, i.e., the**

__a__*of atoms -- e.g., in the original proto-stellar ‘atomic clouds’ -- crosses a critical threshold, the first “*

**expanded reproduction****olecules” are born, and “atomic clouds” become “molecular clouds”:**

__m__

__a__--->__a__x__a__=__a__**+**.

__D____a__=__a__+__m__This “fundamental law of

__dialectical__

*thought**”*also applies to the realm of mathematical ideation, including to the case at hand.

If we take

**to denote the category of**

__B__**oolean Algebras, and**

__B__**to denote the category of Seldonian**

__C__**ontra-Boolean algebras, we can present the following progression of categories of the algebras of logic, beginning with the**

__C__**of**

__dialectical__antithesis**and**

__B__**--**

__C__

__B__--->__B__x__B__=__B__^2 =__B__+

__DB__=__B__+__C__
-- which, by going one step further, by multiplying again by

**, yields --**__B__

__B__x (__B__+__C__) =__B__+__C__+__q__

_{CB}
-- all of which we can summarize as “the negation of the
negation

*of***,**__B__*by***, i.e.,**__B__
by

**~~**--__B__=__BBB__=__B__x (__B__x__B__)

__B__^3 =__B__x (__B__x__B__) =__B__x (__B__+__C__) =__B__+__C__+

__q__

_{CB}

_{}
-- wherein

__q__**signifies a**_{CB}**of**__dialectical__synthesis**with**__C__**, i.e., here the**__B__**by itself signifies any kind of logical algebra category, and**__q____q___{CB}**signifies a kind of logical algebra that combines the**_{}**kind with the**__C__**kind.**__B__
In the

**F**.**.**__E__**. rendering, the**__D____q__**algebra of logic is an**_{CB}*“*, whereas**logic”**__actualization__**is a**__B__*“***certainty***logic”*, and**is a**__C__*“*.**possibility**logic”
The

The

**algebra tells you what is**__B__*about categories, or “classes”, by virtue of their form alone, ignoring their content.***certainly true**The

**algebra tells you what ontological categories are**__C__*populated in a given epoch, versus which are***possibly**__[yet]__**not***to be populated in that epoch.***possible**The

__q__

_{CB}**algebra allows you to tell whether a category**

_{}__manifested in a given past epoch or not, because it combines__

**actually****type coefficients with**

__B__**type ontological categories:**

__C__**b**

_{c}(**t) x**.

__c__
If

If

**b**_{c}(**t)****= 1**, then category**was**__c____manifest / populated / instanced in epoch__**actually****t**.If

**b**_{c}(**t)****= 0**, then category**was**__c____extant / existent in epoch__**not****t**.**Can Seldon's "**

*¿*__ontra-Boolean algebra" of dialectical logic predict -- or "pre-construct, symbolically" -- possible__

**C**__historical developments__

**future**

*?*A dramatic possible instance of such dialectical prediction is Seldon's hypothesis that the ontological category of "

**umanity",**

__h__**, if it continues to grow and "densify", will give rise to a new cosmological ontological category, which he calls "meta-humanit**

__h__**" --**

__y__

__h__--->__h__x__h__=__h__+__Dh__=__h__+__y__-- which, in terms of individual "meta-human" body-types, will develop three species, a "thesis" species category, a "contra-thesis" species category, and a "uni-thesis" species category --

__g__--->__g__^3 =__g__x (__x__**g**__) =__**g**__g__x (__g__+__r__) =__g__+__r__+__q__rg-- such that --

__g__**=**bodies resulting from human-

**enome self-re-engineering;**

__g__

__r__**=**bodies resulting from android

**obotics [http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/AndroidRobotics/AndroidRobotics.htm], and;**

__r__**bodies built by the combination of**

__q__rg =__c__=**with**

__r__**--**

__g__**yborg prosthetics / bionics [ http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/CyborgProstheticsBionics/CyborgProstheticsBionics.htm ].**

__c__Regards,

Miguel

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