'''Formal Subsumption''' and '''Real Subsumption''' in the Context of the Categorial-Dialectical Calculus.

Dear Reader,

Marx addresses a special case of «aufheben»-conservation/subsumption processes in the [unpublished] so-called “6th Chapter” of «Das Kapital», in the context of the self-development of the [incarnated and ‘agented’ and reproduced by humans] capitals-system -- from an early ‘ascendance phase’ of that system, characterized by the ‘“[merely] formal subsumption of the labor-process under capital”’, toward a zenith, and then toward a ‘descendance phase’, of that system, increasingly characterized by the ‘“real subsumption of the labor process under capital”’.

In this blog entry, I focus on a more general case of dialectical, categorial subsumption, where -- and recurrently so -- a ‘‘‘formal subsumption’’’ of one or more priorly-irrupted or priorly-evoked ontological categor(y)(ies), by a most-recently-irrupted or most-recently-evoked ontological category, is succeeded by a ‘‘‘real subsumption’’’ of that/those earlier-irrupted or earlier-evoked ontological categories, by that most-recently-irrupted, or most-recently-evoked -- and therefore ‘‘‘meristemal’’’/ ‘‘‘vanguard’’’ -- ontological category.

An example of this progression from ‘‘‘formal’’’ to ‘‘‘real’’’ subsumption, in the context of systematic dialectics, is that for the simplest categorial-calculus dialectical ‘meta-model’ of Marx’s «Das Kapital» --

for step 2, )-|-(₂  =  (⁾ C ⁽)^{2^2}  =  C⁴  =   C  +  M  +  q_MC   +  K;

for step 3, )-|-(₃  =  (⁾ C ⁽)^{2^3}  =  C⁸  =  

C  +  M  +  q_MC   +  K  +  q_KC  + q_KM  + q_KMC + q_KK.

-- wherein this ‘meta-model’ exhibits, in its step 2, a ‘‘‘formal subsumption’’’ of the earlier-evoked categories of exchange-value/social relations of production -- Commodities and Monies -- by the ‘‘‘Kapitals’’’/wage-labors, exchange-value/social relation of production category. 

Formally, at step 2 of its presentation, its ‘‘‘Kapitals’’’ category already «aufheben»-subsumes its Commodities, Monies, and Money-mediated Circulations of Commodities [q_MC] categories, by its mere, “additive” [‘+’], presence in this step, because K has become the new leading category, surpassing, hence subordinating and demoting, all previously-presented categories, in complexity, in thought-concreteness -- in determinateness -- and in aptness for the Domain [‘kapitalist society’] being presented, systematically, in «Das Kapital».

And yet, thereby, it has not yet presented the forms/categories which express the incorporation and integration of those three pre-evoked categories in[to] a self-reproducing system of [especially industrial] ‘‘‘Kapitals’’’. 

So far, in presentation step 2, K connotes mainly the still present descendants of the early, pre-capitalism, “antediluvian species of capital” -- primarily mercantile capital -- which are confined to the Monies/Commodities Circulations-processes of social reproduction, but which do not directly re-organize and dominate its ‘productions-processes’ as well.

It is in step 3 of this ‘meta-model[ed]’ presentation that the ‘‘‘real subsumption’’’, by the ‘‘‘Kapitals’’’ category, of all of its earlier-evoked categories, arrives explicitly, in the form of the superposition [‘+’] of the categories ‘‘‘Commodity-Kapitals’’’ [q_KC], ‘‘‘Money-Kapitals’’’ [q_KM], and ‘‘‘Circulations of the Total Social Capital’’’ [q_KMC].

The latter category, q_KMC, connotes the [partial] take-over, subsumption, or appropriation, by the ‘‘‘Kapitals’’’ category, K or q_K, of the earlier-evoked  category of the simple Circulations-of-Commodities-by-Monies processes [q_MC], a take-over which evokes the existing category of the realization of surplus-value profits via the social circulations of ‘‘‘Commodity-Kapitals’’’ [q_KC] and of ‘‘‘Money-Kapitals’’’ [q_KM], i.e., of ‘‘‘Kapitals’’’ as a whole, in their alternating, “metamorphosizing” forms of ‘‘‘Commodity-Kapitals’’’ [q_KC] and ‘‘‘Money-Kapitals’’’ [q_KM], by which Kapital takes full command of both the circulations-processes and the productions-processes of human-societal self-reproduction.

An example of this progression from ‘‘‘formal’’’ to ‘‘‘real’’’ subsumption, in the context of [psycho]historical dialectics, is that for the hypothesis of Dr. Denise Schmandt-Besserat, regarding the first genesis of written language, in ancient Mesopotamia.

Early-on, per this hypothesis, temple dues contributions, as well as debts, were recorded via fired clay token ‘micro-icons’, that represented individual units of specific kinds of goods donated/owed, tokens which were kept together, late in the ‘meta-evolution’ of this accounting praxis, by depositing them into hollowed-out wet clay envelopes, envelopes that were later fired. 

Because these clay envelopes were opaque, auditing a debt, or a tithe, required breaking open the envelope containing the record thereof, and, thereafter, also required the labor of creating a new envelope to re-house the tokens representing that record. 

At some point, accountant-scribes began to press the hard, fired clay tokens, that were to be put inside a clay envelope, into the wet clay of the outer surface of that clay envelope, before depositing those clay tokens inside that clay envelope, and firing that envelope, thus leaving “2-dimensional” impressions of the tokens inside, on the outside of the envelope, thereby making auditing less laborious. 

Thus was born a new ‘meme of representation’ -- of 3-dimensional objects [e.g., the fired clay tokens] by “2-dimensional” marks in clay. 

For a long time, a dual, redundant representation system persisted -- token-marks on the outside of the clay envelopes, tokens full-blown inside those same clay envelopes. 

This dual, redundant representation phase represents the ‘‘‘formal subsumption’’’ phase, of the 3-D ‘tokenology’ meme, by the “2-D” ‘tokenography’ meme. 

However, at a certain critical point, scribe-accountants stopped hollowing out wet clay slabs, to form them into clay envelopes, and, instead, molded those wet clay slabs into solid wet-clay tablets, upon which “2-D” marks were made by impression, and by ‘“incision”’. 

This clay tablets stage instantiates the ‘‘‘real subsumption’’’ of the 3-D ‘micro-iconic’ representation meme, by the meme of “2-D” representation, and leads on to the full cuneiform system of writing.

In general, in _NQ dialectical-algebraic terms, ‘‘‘formal subsumption’’’  is ‘sum-subsumption’, ‘additive [‘+’] subsumption’, or ‘superpositional subsumption’, by the content represented by the ‘‘‘meristemal’’’ category, for a given stage in, e.g., a Dyadic Seldon Function dialectical ‘meta-model’, of all of the earlier-‘extantized’ ontological-categorial content of that ‘meta-model’, via the ‘qualitative superposition’ processes signified by the _NQ versions of the “plus sign” -- non-amalgamative, momentary/stroboscopic non-interaction-operation ‘separator symbols’, that sign the momentaneous formation of the ‘cumulum’ of ontologies present for that stage, just prior to the inception of the category-interactions/-multiplications that generate the successor stage/‘cumulum’ representation.

 In general, in _NQ dialectical-algebraic terms, ‘‘‘real subsumption’’’  is ‘multiplicative subsumption’, or ‘product subsumption’, and ‘[allo-]hybridization subsumption’, by the content represented by the ‘‘‘meristemal’’’ category-symbol, for a given stage in, e.g., a Dyadic Seldon Function dialectical ‘meta-model’, when it generates its incremental symbols for the next-stage ontology representation, via that ‘‘‘meristemal’’’ category-symbol ‘ontologically-multiplying’ itself against/interacting with, the category-symbols representing all of the content of the earlier-‘extantized’, and still-[possibly-]extant, ontological-categorial content of that ‘meta-model’ that is represented in the given stage’s ‘cumulum’.

Regards,

Miguel