COMMENTARIES: The E.D. 'Unified Theory of Universal Dialectics' -- 'Vertical Dialectics', 'Horizontal Dialectics', and Their UNITY -- 'Bi-Axial Dialectics'.

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-à-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.