Part 12:
Seldon’s Insights
Series -- The
Core of the ‘CONTRA-Boolean’
Dialectical Principle: ‘‘‘When a Something Becomes
‘OF Itself’, It also becomes Something Else, Something
Other, Something More
-- Something Qualitatively, Ontologically DIFFERENT!’’’
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 and final 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,
see --
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.
“... The key insight that the NQ_ ‘contra-Boolean
arithmetic’ -- our ‘first dialectical arithmetic’ -- was engineered to capture can also be stated as follows -- ‘When an arithmos of monads becomes ‘OF Itself’, It also becomes somethings else, somethings other, somethings new and unprecedented [if this is the first occasion of its becoming ‘OF
Itself’]; somethings
more -- somethings Qualitatively, ontologically DIFFERENT!’.
“At
first, I did not grasp the mathematical modeling efficacy of the ‘‘‘evoluteness’’’ products-principles. At first,
I explored ‘‘‘convolute’’’ product-rules and product axioms, not the ‘double-conservation
«aufheben»
evolute product rule’, not the ‘meta-catalysis’ evolute product rule’, not the ‘triple-conservation
‘meta-genealogical’
evolute product rule’.”
“Therefore,
my first formulations of
the ‘contra-Boolean
dialectical principle’ took the form
--
x x x = delta-x
-- such that delta-x ~=
x & delta-x ~>
x & delta-x ~<
x.”
“Thus,
delta-x was non-quantitatively
unequal to x, and therefore must be qualitatively, ontologically unequal to x, while also being still ‘meta-genealogically’
related
to the
x «arithmos» and, thus, to its
«monads».”
“This contrasts
sharply with
the Boolean “fundamental law”, given by Boole as --
x x x = x, or x2 = x, which works for an x in the solution-set {0,1}
-- and
which Boole “factored-out” into --
x x (1 - x) = 0, and interpreted as an assertion of formal logic’s core non-contradiction
principle:
‘“x
and not-x is nothing”’.
”
“Nonetheless, the idea all along was that the interaction of an «arithmos», i.e., of a ‘‘‘number’’’ [of «monads» or of units of a given kind, i.e., of a given category], WITH ITSELF, ‘x x x’, or ‘x2’, its
‘self-product’,
interpreted
by us
as representing
the ‘intra-action’
of the constituent
«monads»
that it
implicitly represents, produces another, higher ‘‘‘number’’’, interpreted by us as constituting a new «arithmos», a ‘cumulum’ of ‘‘‘higher’’’ «monads», of «monads» of a new, ‘‘‘higher’’’ kind.”
“This
idea was expressed analytical-geometrically
by representing
this arithmetic
and its algebra by an abstract space in which the self-multiplication of any one of the ‘meta-numbers’
already constituting this space gives rise to a new axis, perpendicular to all of the previous axes extant for this abstract space.”
“That is, any
self-multiplication
of a ‘meta-number’
already in this space gives rise to a new ‘meta-number’, as a new dimension; “adds” a new orthogonal direction [in]to that space, so that the space expands, as a result, not just quantitatively
but dimensionally. We interpret this as defining a space that grows qualitatively; ontologically, that breaks, and breaks out of -- transcends -- its “closure”, with every new such arithmetical operation.”
“Such self-multiplication
was to be used
to model actualities in
which the ‘‘‘singularity’’’
resulting from the crossing of a critical density[/‘‘‘temperature’’’] threshold by and within a ‘cumulum’ of «monads» of a given «arithmos»/kind/«genos» is seen to give rise to a new «arithmos», of a new kind of units.”
“If
we interpret ‘x x x’ after the manner of classical function notation, then ‘x x x’ or ‘x2’ becomes --
x(x)
-- which can
be read-off, per
that function notation, as ‘x OF x’, or as ‘x OF itself’. Thus, per
our ‘‘‘convolute’’’ version of our ‘contra-Boolean’
fundamental ‘‘‘law’’’: x OF itself yields ‘delta-x’: which
we interpret as representing a new «arithmos» of «monads» that are, precisely -- ‘somethings else, somethings
other, somethings new and unprecedented [if this is the first occasion of its becoming ‘OF Itself’]; somethings more
-- somethings Qualitatively, ontologically DIFFERENT!’’ -- ‘something ontologically REVOLUTIONARY.”
“If one
looks for examples of ‘xs OF xs’ in ‘the dialectic of Nature’,
one finds such as the following --
‘...[sub-atomic]
particles
of particles -- which
are no longer [sub-atomic]
particles,
but atomic nuclei.’
‘...atoms
of atoms -- which are
no longer atoms,
but molecules.’
‘...molecules
of molecules -- which
are no longer molecules,
but [polymeric “macromolecules” and
pre-eukaryotic,
or prokaryotic,] cells.’
‘...[prokaryotic]
cells of cells -- which are no
longer [prokaryotic] cells, but eukaryotic cells.’
‘...[eukaryotic]
cells of cells -- which are
no longer [eukaryotic]
cells,
but “multi-cellular organisms”.’ ”
“Of course, a key insight
along this way
was to see
how typically
it was the case that each
of the new units of this new «arithmos» thus produced were some kind of ‘‘‘aggregate’’’ of certain
of the units
formerly inhering in the “old” «arithmos»; to see that each of the new units was a ‘self-involution’, a ‘self-internalization’, a ‘self-meta-unit-ization’,
or a ‘self-meta-holon-ization’ of some definite ‘sub-«arithmos»’ of the thus now former units of the “old” «arithmos» -- and seeing
that all of these descriptions of such processes were, in
their unity, descriptions of an «aufheben» annulment/elevation/conservation process, and, hence, of a ‘gene-ric’ dialectic.”
