Part 07: Seldon's Series on
‘‘‘Dialectical Categorial Progressions’’’.
CARDINAL
FEATURES
of
Their
‘Content-
Structure’.
Dear Reader,
It
is my pleasure,
and my honor, as an elected member
of the Foundation Encyclopedia Dialectica [F.E.D.]
General Council, and
as a voting member of F.E.D., to share, with you, from time to time, as they are approved for public release by the F.E.D. General Council, Seldon’s commentaries on key Encyclopedia
Dialectica concepts of Seldonian Theory.
This 7th text in
this new such
series is posted herewith, together with
supporting text-images and diagrams
[Some E.D.
standard edits have been applied, in the version presented below, by the editors
of the F.E.D. Special Council for the Encyclopedia,
to the direct transcript of our co-founder’s
discourse].
Seldon
–
“The special
‘dialectogram’ diagram, posted above, atop the other images also posted above, is
what I want to use to address some salient and cardinal aspects of the
‘content-structure’ of dialectical categorial progressions, especially those
generated using the Encyclopedia Dialectica ‘dyadic dialectical function’.”
“The
categorial progression example illustrated in that special ‘dialectogram’ is
that for our ‘dialectic of nature meta-model meta-equation’,
starting from a ‘‘‘Dark Energy’’’ – from our ‘Regenerist’
hypothesized ‘spandetron’ – «arché»-category; for our, highest-content,
known ‘cosmo-ontological’ categories’ ‘Dialectical Theory of Everything’
master equation, which can stand in for myriad other dialectical categorial
progression ‘meta-models’ for the myriad dialectics going on ‘inside’ these
high-level categories, at ‘qualo-fractal’ scales scaled-down from that highest
scale.”
“Note:
The last three, bottom-most category-symbols in the ‘dialectogram’ at top,
represent our predictions, or ‘symbolic ontological
pre-constructions’, of the future of the dialectic of nature, at least in our
planetary vicinity. Even the category
denoted h,
for ‘humanitys’,
stands for, in particular, planetary ‘humanitys’ that have
achieved their, predicted by us, higher destinies,
each unit a
‘political-ECONOMIC-DEMOCRATIC’ ‘planetary polis’, made up out of a
heterogeneous multiplicity of globally-federated sovereign nation-state units
as its sub-units.”
“Consequently,
the next ‘self-hybrid’ category, denoted by y in that
‘dialectogram’, stands for the category for ‘meta-humanity’ units, each such unit being an «aufheben»
‘meta-unit-ization’ of two or more such ‘planetary polis’ units, forming, as its ‘meta-units’,
an, also ‘political-ECONOMIC-DEMOCRATIC’, interplanetary
federation, but still within a single stellar/planetary system, each one made up out of a
heterogeneous multiplicity of ‘planetary
polis’ units
as its
sub-units.”
“Again,
consequently, the still-next ‘self-hybrid’ category in this,
cosmological, dialectic of nature categorial progression – the category denoted
by z
in that ‘dialectogram’ – stands for an «arithmos» of ‘meta-meta-humanity’ units, or ‘meta2-humanity’ units, each such unit being an «aufheben»
‘meta-unit-ization’ of two or more
such inter-planetary federation
units,
each within a
distinct, single stellar/planetary system, forming, as ‘meta-units’, an, also
‘political-ECONOMIC-DEMOCRATIC’, multiple stellar/-planetary
systems interplanetary federation, i.e., an inter-stellar/planetary
systems unit,
each one made
up out of a heterogeneous multiplicity of single
stellar/planetary system interplanetary federation units.”
“One
can, of course, imagine beyond category z, envisioning galaxy-wide meta3-human social formations, and on to inter-galactic social
formations – such as might even possibly already exist elsewhere in our
universe. But let us, for present
purposes, confine ourselves to the ‘Star Trek Hypothesis’, or to the ‘Star Wars
Hypothesis’, or to the ‘Star Gate Hypothesis’, and stop our ‘pre-constructions’
at the – already fabulously
ambitious – multiple stellar/planetary systems interplanetary
federations ‘qualo-fractal’ scale of meta-human social
formation. The ‘social self-force of
human-societal expanded self-re-production’ is, at present, too limited to give
such further extrapolations of this universal categorial progression much ‘thought-concreteness’.”
“Now,
let’s get to noticing the cardinal ‘content-structure’ features of this,
ultimate, dialectical categorial progression, that might be general features,
applicable to the whole category of ‘dyadic dialectical function’-generated dialectical
categorial progressions.”
“First
off, please note that the ‘“epochs”’ being defined here, so as to showcase the
cardinal, quantitative features of NQ, ‘dyadic- dialectical-function-generated’ progressions, series or [non-amalgamating]
‘‘‘sums’’’ of heterogeneous, qualitatively distinct category-symbols, are not
the standard ‘“epochs’’’ of which we usually speak and write, in
this, categorial progressions’ context.
The epochs addressed herein are ‘real subsumption
[cf. Marx] epochs, or ‘rs-epochs’ for short.”
“The
‘real subsumption epochs’ differ significantly from
our standard concept of ‘dyadic dialectical function’,
dialectical categorial progression epochality.
Our standard such epochs, after the zeroth epoch, each end
with the latest new ‘self-hybrid’ category-symbol, or latest ‘contra-category’
symbol; they end with the latest new ‘antithesis category’ symbol. They thus represent the ‘“formal subsumption’’’ [cf. Marx] of all priorly-arisen category-symbols by that latest category-symbol, but not their ‘“real subsumption’’’. The sub-progression of the real
subsumptions of all of the previously-posited category-symbols by
that latest ‘self-hybrid’ category-symbol are all allocated to the consecutive next
standard epoch.”
“On
the contrary, the ‘real subsumption epochs’ – again,
after their zeroth rs-epoch – all begin with that
latest, ‘self-hybrid’, ‘contra-category’, ‘antithesis category’
symbol. They then continue with all
of the previously-posited category symbols that have now, all thus being now
more-advanced ‘allo-hybrid’ category-symbols, in the given, new rs-epoch,
achieved partial dialectical synthesis with – or, finally, full dialectical
synthesis with – that latest ‘antithesis category-symbol’, that has thus
subsumed, or coalesced with, all of those previously-posited category-symbols. The given rs-epoch’s categorial sub-progression
ends with that epoch’s maximal, and ‘‘‘culminant’’’ ‘allo-hybrid’
category-symbol, whose subscripts include the subscript for that latest ‘antithesis
category-symbol’, together with all of the earlier-arisen, category-describing
subscripts.”
“That
‘‘‘culminant’’’ ‘allo-hybrid’ category-symbol is the ‘full-synthesis
category-symbol’, the fullest dialectical synthesis
category-symbol that is possible for the given rs-epoch, and for that
epoch’s beginning ‘antithesis category-symbol’; the highest-in complexity-scale
category-symbol in the ‘qualo-fractal’ scales-progression of that series of rs-epochs;
the topmost of the ‘qualo-fractal’ levels of that category-symbols’ series
up to that rs-epoch.
“In
the example at hand, our first three standard epochs are –
á x ñ à á x <+> c ñ à á x <+> c <+> qcx <+> r ñ.
–
whereas, for rs-epochs, those three are –
á x ñ à á x <+> c <+> qcx ñ à
á x <+> c <+> qcx <+> r <+> qrx <+> qrc <+> qrcxñ.”
“Please
observe, via the images posted at the top of this blog-entry, that –
1. Consecutive ordinal powers of the dyad, 2 – starting with/from
the zeroth power, 20, as embedded in the function (2(t+1)) - 1, applied to the first rs-epoch, t = 0 – tell you the total count of distinct,
qualitatively-different ‘cosmo-ontological’ category-symbols in the rs-epoch
representation generated by that power-of-two function, when the «arché»-category symbol,
herein x,
for the ‘cosmo-ontological category’ of/for our hypothetical “Dark Matter”/‘spandetron’ units, is raised to that power of two,
i.e., ‘self-involutes’ to that, (2(t+1)) - 1, degree;
2. Each “rs-epoch” begins with a new, unprecedented
‘self-hybrid’ category symbol, and then continues with a non-amalgamating
sum of also new,
unprecedented ‘allo-hybrid’ category-symbols. Each of the latter has the subscript
representing that new
‘self-hybrid’ category-symbol explicitly constituting the
leading, left-most epithet of its multi-epithet, or hybrid, subscript, thereby asserting
that the united meaning of all of its right-more subscripted epithets
has been subsumed by the meaning of that left-most, new, latest
subscripted epithet;
3. For rs-epoch of ordinal number t = n, there are (2(t+1)) - 1 qualitatively-distinct
‘cosmo-ontological’ category-symbols in that rs-epoch’s categorial
progression as a whole. All of those
distinct category-symbols are syntactically and combinatorically possible. Each epochal category-symbols’
non-amalgamating ‘‘‘sum’’’ marks a ‘possibility space’,
with each category occupying a different dimension of that space, so that the ‘dyadic
function’, as t increases, forms
an ‘‘‘analytical-geometric’’’ space that is [self-]expanding in dimensionality
with every successive squaring of that category-symbols-sum, as each t succeeds/exceeds itself to its t + 1. But that mere syntactic and combinatoric ‘possibilisticity’ does not
mean that all of these category-symbols will ever be actual, instantiated, viable, semantically meaningful, in the Domain whose ontological-categorial realities the
categorial progression is intended to model.
Some category-symbols may represent null categories, always-empty
categories, for the given Domain. Others, “populated”
in one+ rs-epoch(s),
may later go extinct, from within a later epoch, & remaining extinct thereafter;
4. For each rs-epoch ordinal number, n, denoted generically by this ordinal variable within N, there will be 2n – 1 brand new ‘allo-hybrid’ category-symbols, summed together with their one new ‘self-hybrid’, leading category-symbol, in rs-epoch t = n;
5. All of the category-symbols, from
epoch t = n = 1 on, are generated by the self-iterated
‘‘‘self-involutions’’’ of the «arché»-category-symbol, x, or qx, i.e., via, in this example, x2t, as t = n increases, monotonically and consecutively,
recurrently, from each t to its t + 1.”
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:
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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