COMMENTARIES: The Encyclopedia Dialectica ‘Unified Theory of Universal Dialectics’ – ‘Vertical Dialectics’, ‘Horizontal Dialectics’, and Their COMPLEX UNITY –
‘Bi-Axial Dialectics’.
Dear Reader,
We hereby offer, for your consideration, the following commentaries on the Encyclopedia
Dialectica ‘Unified Theory of Universal Dialectics’ – of ‘Vertical Dialectics’, versus ‘Horizontal Dialectics’, and of Their UNITY – which we name ‘Bi-Axial Dialectics’.
COMMENTARY. “First-off, here I’ll be writing about, not
“genus” and “species” as restricted to merely biological “Taxa”, but «genos»
and «species» as, since ancient times, applying to the
long-sought ‘Universal Taxonomy of All Ontology’ – of “all things”, both
biological “things” and non-biological “things”, alike.
In the latter context, RELATIVE to one another, «genos»
categories are the more abstract, more ‘gene-ral’, less “determinate”
categories, their implicit ‘“internal”’ units exhibiting fewer “determinations”
or ‘speci-fications’. «Species»
categories are the less ‘gene-ral’, more ‘speci-fic’,
more “determinate” categories, i.e., which integrate more “determinations” –
more attributes, features, predicates, epithets, facets, talifications, dimensions
– to their implicit, ‘internal’’’ units, than are attributed to their proximate
«genos» category, to which their implicit, ‘‘‘internal’’’ units
all belong, for all of the «species» “of”/implicit in
that «genos».
There are, on first perception, TWO «species»
of dialectic depicted in the ‘dialectogram’ diagram, the first diagram image above.
BTW, this diagram is in ‘Platonian format’, not in
‘Marxian format’. That is, in the
vertical direction of that, Platonian, ‘dialectogram’, the three ovals, «species»-category-unit
below, are shown as transitioning vertically upward, into the single «genos»-category-unit,
with its color-coded-yellowish boundary, placed immediately above the level of
the three «species»-category-units.
Thus, the more general and abstract category-unit single
oval is placed above the three more ‘thought-concrete’, more specific,
more determinate category-units’ ovals, below it.
In a ‘Marxian format dialectogram’, based upon Marx’s
methodological commentary on pages 100-101 of the Grundrisse,
the more ‘thought-concrete’, more specific category-symbol units/ovals
are placed above the more abstract, more general
category-symbol unit(s)/oval(s).
The unit/«species»-category of ‘Vertical
Dialectic’ in this ‘dialectogram’ is represented by the «aufheben» ‘meta-unit-ization’ transition of the
three «species» category-unit ovals up into the one «genos»
category-unit oval.
The unit of ‘Horizontal Dialectic’ in this ‘dialectogram’ diagram
is represented by the color-coded inner-edge boundary-lines of the three «species»-category-units’
ovals, immediately below the color-coded yellowish boundary-line/border of the «genos»-scale/«genos»-level
oval.
The left-to-right transition, indicated by the ‘---)’ sign, i.e., the self-interaction-generated self-movement, from the left-most
«species»-category-unit-representing oval, with its inner-border
color-coded reddish, to itself again plus the ‘middle-most’, inner-border
color-coded orange «species»-category-unit-representing
oval, and then on [‘---)’] from there, by the interaction of the
first two «species»-units-representing ovals, to
themselves again plus the right-most, inner-border color-coded yellowish «species»-category-unit-representing
oval, represents the ‘Horizontal-Dialectical’ self-movement in
this ‘dialectogram’: ‘dialectical speci-ation’, from «arché»-«species»
to that again plus ‘first contra-«species»’,
to those again plus ‘first uni-«species»’.
Via this double -- these two -- nested/concentric color-coded
edges/borders/boundaries of each of the three [relative] «species»
category-units’ oval symbols, the ‘Vertical Dialectic’ and ‘Horizontal
Dialectic’ units depicted by this ‘dialectogram’ are integrated/-interwoven,
into their own dual ‘uni-«species»’/‘uni-thesis’ symbol,
represented by both that diagram as a whole, and by the third «species»-level/«species»-scale
category-unit-symbol oval, the rightmost oval, within/inside that ‘dialectogram’
diagram as a whole.
In summary –
‘Vertical Dialectic’ in the upward vertical direction,
depicted as moving from the «species»-scale/-level up
to the «genos»- scale/-level, of this ‘dialectogram’
diagram, represents a process/movement of ‘gene-ralization’,
i.e., of abstraction, and of simplification in the sense of a partial ‘de-determination’,
the shedding or revocation-into-‘implicitude’, of some determinations of
the «species»-level – of those determinations that constitute
the «differentia specifica», i.e., which tell the different «species»
of the «genos», below, apart.
‘Vertical Dialectic’ in the downward vertical
direction, from the «genos»-scale/-level down to the «species»-scale/-level,
represents a process/movement of ‘speci-fication’, of accretion/evocation-into-‘explicitude’,
of additional determinations, inhering in the implicit, ‘“internal”’ [sub-]units
of each «species» category-unit, i.e., of those «differentia specifica»
which separate out, from the relatively ‘‘‘color-less’’’,
singular and apparently monolithic «genos» category-unit symbol,
the full spectrum of its multiple «species» [sub-]category-unit
symbols, suggesting the ‘‘‘multi-chromaticity’’’ of their, qualitatively-differing,
implicit, more-specific ‘‘‘internal’’’ units.
‘Horizontal Dialectic’, in the rightward horizontal direction of
this ‘dialectogram’ diagram, and confined to its «species»-scale/-level,
represents ‘«aufheben» speci-ation’, or ‘dialectical
speciation’, one «species» category-symbol giving rise
to its next «species» category-symbol to its right.
This depicted rightward motion represents that which is caused – alternatingly – either by the ‘self-combination’ of the implicit units represented by a single «species» category-symbol oval with itself [‘«auto-aufheben»’], or by the implicit mere combination of the implicit units of one «species» category-symbol oval, with those represented by other, also already extant, «species»-category-symbol ovals [‘«allo-aufheben»’], i.e., via [partial] categorial dialectical syntheses, with new determinations – new qualities – arising from the combinations of the determinations of the implicit units within/inside/‘‘‘internal to’’’ older, earlier ‘extantized’ «species» categories, in either case, in both cases, whether by ‘«auto-aufheben-izations»’ or ‘«allo-aufheben-izations»’.
“This ‘dialectogram’ diagram features just three «species» category-symbol ovals – a single triad of dialectical-«species» category-symbol ovals – beneath/implicitly ‘‘‘within’’’ its single «genos» category-symbol oval.
However, many of the dialectics that We have modeled feature hundreds, even more than a thousand, «species»-category-symbols, e.g., our ‘dialectic of nature’, ‘Nature-history’, ‘cosmos-history’ ‘meta-model’.
In greater detail –
We call these «species» of
dialectics ‘Vertical Dialectic’ and ‘Horizontal Dialectic’, because the «aufheben» processes/-relations depicted in our ‘dialectograms’ happen in both their
vertical, upward direction and in their, perpendicular, horizontal, rightward direction.
There’s a passage on pp. 100-101 in the [Nicolaus English translation of the] «Grundrisse» – in the most detailed methodological passage by Marx of which I know -- where Marx identifies the vertical upward direction as the direction of increasing specificity, determinateness, and ‘thought-concreteness’, contrary to Plato and Platonian idealism/mysticism in general.
But the ‘dialectogram’ at issue here uses the ‘Platonian format’, not the ‘Marxian format’, in accord with the more typical of the prevailing intuitions. We plan to offer a ‘Marxian format’ version of this ‘dialectogram’ in another venue.
Thus, it is the vertical, upward direction in which the three, “lower-down”,
«species» category-units, as units in their own right -- albeit also
having other units, non-categorial ‘‘‘sub-units’’’,
individuals of the specific ‘“kind”’ that they represent, implicitly
and connotatively ‘‘‘inside’’’ them – are joined together/intersect in the
bottom vertex of their “higher”, more abstract «genos» category-unit,
i.e., in a vertex which is the ‘‘‘vanishing point’’’ of their “«differentia specifica»”.
Thus, the «species» category-units do not lose
their identities in their «genos» unit, any more than any other
kind(s) of units lose their identities in/to the category in which they inhere.
Their «genos» category-unit merely summarizes
its «species» category-units, collectively, by being more
abstract/more ‘gene-ral’ than they are, and by retaining explicitly
only the qualities that they, its «species» category-units,
all share/have in common, rendering their “«differentia specifica»” only
implicit/‘“invisible”’ at its scale, at their «genos»
scale.
Thus, their «genos» category-unit epitomizes/synopsizes
the ontological content of its «species» category-units by
leaving out of its ‘explicitude’ – by abstracting from – its
«species» category-units’ “«differentia specifica»”.
The upward-vertical dialectic in such ‘dialectograms’ thus constitutes a vertical, upward ‘meta-unit-ization’, i.e., a vertical/upward «aufheben» negation/-elevation/conservation of its multiple «species» category-units to the, ‘de-explicitized’, ‘implicitized’ ‘‘‘inside’’’ of their single «genos» category-unit, above them.
Now to what we call the ‘Horizontal Dialectics’
dimension of such ‘dialectograms’.
‘Horizontal Dialectics’ are no longer the, primarily cognitive, «aufheben» determinate-negation/-elevation/conservation of the more “specific”, «species» category-units up into the next-“higher”/more-abstract/-more-‘gene-ral’ [single] «genos» category-unit.
‘Horizontal Dialectics’, as we define them, happen entirely within the single,
relatively more-specific/less-abstract/less-‘gene-ral’
ontological-taxonomic level, and ‘qualo-fractal’ scale, of
the multiple «species» category-units in these ‘dialectogram’
diagrams.
‘Horizontal Dialectics’ do not involve any transition from one ‘dialectogramic’ diagrammatic scale or level to a different consecutive level/scale, e.g., from a more-specific level, up, or, vice versa, down, to the next-higher, more-‘gene-ral’ level, or, vice versa, down, to the next-lower, less-abstract, less-‘gene-ral’, more-specific [e.g., sub-«species»] level.
A ‘Horizontal Dialectic’ stays within a single “vertical” level/scale of determinateness, e.g., within the most-specific, lowest[-‘visible-ized’] “vertical” level of such a diagram [if a ‘Platonian format dialectogram’].
‘Horizontal Dialectic’ represents a dialectical – or ‘«aufheben»-istic’ – movement from an ‘«arché-species»’
category, to a ‘first contra-«species»’ category,
or ‘first antithesis-«species»’ category, e.g., by
means of a ‘‘‘self-interaction’’’ of the ‘«arché-species»’
category ‘‘‘within’’’ itself, leading to an «aufheben» ‘meta-unit-ization’ of the units ‘‘‘internal
to’’’ the ‘«arché-species»’ category, or ‘thesis-«species»’
category, itself.
That first «aufheben»
movement is then followed by a second «aufheben» movement – that of the interaction between the units ‘‘‘within’’’
the ‘thesis-«species»’ category and the units ‘‘‘within’’’
the ‘antithesis-«species»’ category.
That interaction typically reproduces more of both of the units
of these first two «species» categories, but also typically
yields ‘hybrid units’, ‘‘‘hybridizations’’’ of the qualitatively different
units of the first two «species»-categories.
The irruption of these ‘hybrid units’ define the existence, for
human cognition, observing these movement/processes, of a third «species»-category,
a «tertium quid» [‘“third thing(s)”’] category, which we call the ‘first uni-category’, or ‘first
uni-«species» category’ – the ‘first-synthesis’ category.
In the context of Historical Dialectics, or ‘Diachronic
Dialectics’, this left-to-right movement as depicted in the ‘dialectogram’ -- all
within the «species» level/scale of that ‘qualo-fractal’ diagram –
represents an historical movement.
In the context of Systematic Dialectics – ‘»Synchronic Dialectics’ -- , this left-to-right, horizontal movement, as depicted in the ‘dialectogram’, may represent simply the movement of presentees’ attentions, guided by the discourse of the presenter, whose presentation may be, typically, of an overall duration of only, say, an hour “of history” – i.e., a ‘‘‘micro-historical’’’, micro-temporal process, describing present, enduring, dialectical/-«aufheben» RELATIONS, not extended-duration dialectical/«aufheben» PROCESSES; RELATIONS that manifest within a PRESENT ontological Domain, or ‘‘‘sub-totality’’’ of Nature – of our cosmos, as ‘THE TOTALITY’.
That is, a systematic dialectic may be a presentation of “systematic”
– classificatory – taxonomic ontological categories, not a model
reconstruction of the past “longitudinal”, long-duration, historical
progression of a lineage/‘meta-genealogy’ of ontological
categories, all belonging to the same , taxonomic, ontological Domain, and all sharing
the same ‘«arché-species»’ category, or ‘first thesis-«species»’
category.
Also, contrary to what is the case with ‘Vertical Dialectics’,
the units of the three «species» of a minimal – triadic,
single-triad – ‘Horizontal Dialectic’ are not
typically themselves also sub-categories-as-units in their own
right.
The represented units of/‘‘‘inside’’’ the «species»
categories are either tangible, physical unit[ie]s, or abstract, intangible,
“purely”-ideational/mental unit[ie]s, or even unit[ie]s that are
hybrids of those former two kinds of unit[y] – ‘ideo-physio-ontological’
unit[ie]s.
For examples, (a.) the H2O units of the category of water molecules would exemplify mainly ‘physio-ontological units’, albeit with some cognitive content admixed; (b.) the category of abstract, “purely”-quantitative “Natural” number units, each denoted ‘1’, would exemplify mainly ‘ideo-ontological units’, and (c.) a ‘psychohistorical material’, such as metallic monetary coins, exemplify the “Kind” of “physical”, tangible objects onto which contemporary human psyches project -- collectively, culturally, ‘phenomically’ – ideal, mind-resident, aphysical attributes and qualities, e.g., economic value.
The economic value attributed to goods as commodities is “the very opposite of the coarse materiality of their substance” such that “not an atom of matter enters into its composition.” [Marx, Capital I, New World, p. 47].
Other “physical” examples of the units ‘‘‘inside’’’
«species» categories include “Big Bang Nucleosynthesis”-produced,
or ‘cosmological nucleosynthesis’-produced, Helium nuclei [total-]ions,
or even non-ionic, ‘electro-neutral’ Helium atoms, which
form a, relative, sub-«species» sub-category
of the «species»-category of atom units in general [named ‘‘‘atoms’’’].
Such atom units form a ‘first contra-«species»’
category to the relative ‘«arché-species»’ category of sub-atomic
“particle” units [named ‘‘‘sub-atomic particles’’’], such as the following “particle” sub-categories
units -- the units of the “naked protons” sub-category [named ‘‘‘protons’’’], the units of the neutrons sub-category
[named ‘‘‘neutrons’’’], and the units of the electrons sub-category
[named ‘‘‘electrons’’’].
The units of the atoms ‘first contra-«species»’
category are ‘Horizontal Dialectic’ «aufheben»
‘meta-units’ to units of the ‘«arché-species»’
category of sub-atomic particles, because each atom unit is made up out
of a heterogeneous multiplicity of sub-atomic “particle” «species»
units, e.g., electron sub-«species» units, proton sub-«species»
units, and neutron sub-«species» units. All of these categories inhere in the Domain
of ‘cosmological dialectic’, or of ‘the Dialectic of Nature as a Whole’.
Fully-ionized, electron-less Helium nuclei units too are made up
out of a heterogeneous multiplicity of sub-atomic “particle” units – of proton
units [two each], and of other sub-atomic “particle” units, e.g., of neutron
units [also two each]. Helium nuclei units
thus also form another sub-«species» of the «aufheben» ‘meta-units’ to the «species»
category of sub-atomic “particle” mere units.
So, we have such “particles” as ‘«arché-species»’ category units, Helium ion units as among their ‘first contra-«species»’
category’s units.
What are the ‘‘‘hybrid units’’’ of the ‘first uni-«species»’
category for this example, of the “particles” ‘«arché-species»’
category, and the atoms [atomic nuclei] ‘first contra-«species»’
category, both categories of ‘micro-cosmic object-units/‘eventity-units’?
Perhaps surprisingly, no less than "first generation", “main sequence” STAR
units – decidedly ‘macro-cosmic’ units, which have a lot of Helium
units along with Hydrogen units in their initially-cooler outer envelopes/layers, and “naked
proton” units [fully-ionized Hydrogen atom units] in their hot – plasmic -- central
cores, i.e., in their ‘zeroth envelope/layer’.
Such star units are thus hybrids of “particle” units [proton
units] and atomic units [Helium units].
Such stars-category
units are inherently conducting processes of “stellar nucleosynthesis” in
their, protonic, cores -- converting proton units into[, e.g., “diproton”
units, and thence into] Helium nuclei atomic units.
Without this -- explosive -- stellar-core
process of the “stellar nucleosynthesis” «aufheben» ‘meta-unit-ization’ of proton “particle” units up into their Helium
atomic [meta-]units, these stars-category ‘‘‘hybrid units’’’ would momentaneously implode,
collapsing due to their gigantic forces of “self-gravitation”, thus immediately
ceasing to exist as star units.
For another example, this time a ‘human-Nature-al’, hence ‘psychio-physio-ontological’
example, by hypothesis, consider the earliest known human-social forms –
hunter-gatherer-scavenger, quasi-familial “bands”, as the ‘«arché»
thesis’, ‘«arché-species»’ category of the human social
forms Domain.
With growth of the number of such “bands”, via the gradual
growth of their ‘societal self-reproductive self-force’ – i.e., the growth of their
sustained rate of “bands” self-reproduction, hence their ‘meta-Darwinian fitness’ – via gains in their hunting/gathering/-scavenging
[self-]productivity, by means of innovative advancements in their
hunting/gathering/scavenging tools/weapons, new ‘psychio-physio-ontology’,
new ‘human socio-ontology’, begins to emerge.
The emergence of this new “human-social relations of production”
‘socio-ontology’ is driven by the growing number of “band” units, and by their
increasing local density, or physical-spatial concentration,
hence by their increasing frequency of ‘inter-mutual’ encounter and
confrontation, all the result of their acceleratedly growing “human-social forces of [self-re-]production”,
‘self-[re-]productivity’, or ‘societal self-reproductive self-force’, hence of their ‘meta-Darwinian fitness’.
Multiple “bands” begin to, at first sporadically/-seasonally and transiently, coalesce into [e.g., multi-familial] units that are qualitatively different, dynamically-different ‘meta-units’ in relation to mere ‘band’ units, and their dynamics.
These ‘meta-units’ are today,
in the English anthropological literature, typically called “camp” units.
Each typical single “camp” unit consists of a heterogeneous
multiplicity of [typically increasingly-former] “band” units, and thus
constitutes an «aufheben» ‘self-meta-unit-ization’
of/by those “band” units.
The resulting “camp” human-social form units are multi-familial, multi-band ‘[ev]entity’ units.
They form[ed], in contemporaneous as well as in subsequent human minds – human psyches – the then radically new, unprecedented ‘human socio-ontological’ category, whose name(s) refer(s) to these “camp” units.
These “camp” units are the units of the ‘first contra-«species»’
ontological category in this ‘Dialectic of human-Nature’ episode within the ‘Dialectic
of Nature as a Whole’ -- which comprises both ‘‘‘human-Nature’’’ and ‘exo-human
Nature’ alike.
What, then, are the ‘first uni-«species»’
category’s units, if any, in this ‘Horizontal-Dialectical’, ‘Historical-Dialectical’,
relative-«species»-level dialectic?
The ‘hybrid-«species» process-units’ that combine –
that result from the interactions of – “camp” «species»-units
with remaining, continuing, independent “band” «species»-units, we see as follows.
Some “camp” units interact with still-extant “band” units in ways
which convert themselves into larger “camp” units, by assimilating into
themselves those “band” units, converting – enlisting, recruiting, or coercing –
those “band” units into themselves, achieving the subsumption of those
[thus-former] “band” units by such “camp” units, e.g., due to the perceived advantages
of “camp” units vis-Ã -vis isolated “band” units.
Other groups of “band” units are ‘‘‘catalyzed’’’ into forming their own “camp” units by ‘emulation dynamics’, e.g., by a ‘“band-wagon-effect”’ copying of nearby “camp” units, or by being provoked, defensively, into forming their own [e.g., competing] “camp” formation(s).
Now, I’ll just cap-off this account of «species»
ontological categories, and of their associated «genos»
ontological categories, as follows –
The dialectical synthesis of the «species» 1 category of ‘Vertical Dialectics’, and
of/with its opposing «species» 2 category, of ‘Horizontal Dialectics’,
both in/for the Domain of ‘dialectogramic dialectical diagrams’, is the «species»
3
category, which we name the «species» category of ‘Bi-Axial
Dialectics’, the ‘‘‘complex unity’’’ [cf. Hegel] of ‘Horizontal Dialectics’
and/with ‘Vertical Dialectics’.
This ‘Bi-Axial Dialectics’, dialectical synthesis, ‘first uni-«species»’
category is, in fact, PRECISELY what that ‘dialectogram’ diagram
depicts/represents AS A WHOLE.
That ‘dialectogram’ diagram depicts a hybrid unit of
dialectic. Each such hybrid unit is made
up out of a heterogeneous multiplicity of exactly two units of dialectic, one unit from each of two qualitatively different «species»
of dialectic: one unit of ‘vertical dialectic’, and one unit of ‘horizontal
dialectic’, integrally fused together into a single unit of ‘bi-axial dialectic’.
The unit of ‘vertical dialectic’ in that diagram consists of the
outer, all color-coded-orange
edges of the three, oval, «species»-category units depicted below the single
«genos» category unit oval, which is color-coded yellowish, with the three «species»
category unit ovals depicted as transitioning upward and merging into that single, yellow-edged, «genos» category unit.
The unit of ‘horizontal dialectic’ in this ‘dialectogram’ diagram
is represented by the inner edges of the three «species»
category units’ ovals, color-coded, from left to right, reddish, orange,
and yellowish.
Via this double -- these two -- nested/concentric color-coded
edges/borders/boundaries of each of the three [relative] «species»
category-units’ oval symbols, the ‘Vertical Dialectic’ and ‘Horizontal
Dialectic’ category units depicted by this ‘dialectogram’s’ ovals are
integrated/interwoven, into their own dual ‘uni-«species»’/‘uni-thesis’
symbol, represented by both that diagram as a whole, and
by the third «species»-level/«species»-scale
category-unit-symbol oval, the rightmost, color-coded-yellowish oval, within/inside that ‘dialectogram’
diagram as a whole.
The, depicted, upward, cognitive movement, of dialectical, or «aufheben», ‘meta-unit-ization’, from «species» to «genos», and the depicted rightward, observational movement, of ‘dialectical speciation’ -- first of dialectical, ‘auto-«aufheben», self-meta-unit-ization’, followed by ‘allo-«aufheben», hybrid unit-ization’ -- are thereby combined into a unity, a unified representation of dialectic as a whole.”
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¡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.
