Seldon Speaks: ‘Elision and Re-Emergence of the Arithmetical Qualifiers’.

Full Title -- Seldon Speaks:   

‘The Elision and Re-Emergence of the Arithmetical Qualifiers 

and Marx’s «arché», “The Elementary Form of Value” ’.

Dear Readers,

It is my pleasure to share with you, from time to time, selections from the seminal sayings, shared by him among we of F.E.D., that are regularly spoken forth by F.E.D.’s co-founder, Karl Seldon, once the transcripts of such are released, by the F.E.D. General Council, for public sharing.  The text reproduced below is a case in point.  The standard E.D. editors’ edits have been applied to this text.  In this case, I have also appended some key Encyclopedia Dialectica diagrammatic modules, which may help to illustrate Seldon’s account, below.

Regards,

Miguel

P.S.  As of today, 23FEB2016, I have received special dispensation, from the F.E.D. General Council, and from the F.E.D. Special Council of Psychohistorians, in joint session, to publicly release additional portions of the transcripts of Seldon’s remarks on this topic, now added in below, and including some new edits by Seldon himself.

“ . . . [proto-]human civilization, science, mathematics did not simply pick-up again, at the end of, or as the end of, the [northern] Mediterranean/European Dark Ages, at exactly the point where they had left off, at the point of their zenith development by the time of the catastrophic fall of the ancient Mediterranean Civilizations, that culminated in the Roman/Hellenistic civilization, prior to that catastrophic fall.”

“There were collective-cognitive ‘psychohistorical hystereses’.”

“Psychohistorical changes, changes in the Mediterranean/western European ‘‘‘memes-pool’’’, ‘human phenome’, or ‘human memenome’ -- changes in collective human «mentalité» -- had continued to accumulate throughout these [regional] Dark Ages -- especially, and at a slowly accelerating pace, during the socio-politico-economic ‘upsurgence’ & the ‘re-burgeoning’ of mercantile commerce, that drove the prelude to the European Renaissance -- as adumbrated in the groundbreaking 1997 C.E. book The Measure of Reality:  Quantification and Western Society, 1250-1600, by Alfred W. Crosby.”

“This cumulative shift in occidental ‘human-societal self-reproductive praxis’, and, consequently, in the occidental ‘human phenome’, manifested itself, “even” in the rarefied ‘‘‘superstructural’’’ realm of re-emergent theoretical mathematics, including in the form of the Renaissance elision of the ancient Mediterranean, circa 250 C.E., diophantine ‘onto-metrical arithmetical qualifier’, M^o.” 

“That “syncopated” symbol was psychohistorically rooted in the even more ancient, circa 3000 B.C.E., Mesopotamian ‘‘‘incised/impressed-token-image’’’ ‘proto-arithmetical’ ontological and metrical ‘qualifier’ ‘‘‘proto-symbols’’’, as described by Dr. Denise Schmandt-Besserat in her 1992 C.E. breakthrough book Before Writing:  From Counting to Cuneiform.”

“Diophantus’s M^o, was excluded from this re-awakening western European arithmetic and algebra, and, in cases like that of Simon Stevin, this elision was greeted with considerable explicit -- & favorable -- awareness.”

“The mystery that Alfred Crosby failed to solve in his . . . Quantification and Western Society. . . -- the mystery of the massive psychohistorical shift in the Western European branch of the ‘human phenome’, that he documents so richly therein -- was already solved, long ago, as early as 1867 C.E., or even earlier, by Karl Marx, in his monumental discernment of what he called the “Elementary or Accidental Form of Value”. 

“This “Elementary Form of Value” is not only the starting point, the «arché» -- within our contemporary global capitalist system, the ever-present origin and foundation, and also the past [psycho]historical foundation -- for Marx’s entire treatise, for his entire four+ volume systematic[-dialectical] presentation of the content characterizing “Modern Society”, i.e., for his theoretical explanation of the ‘Capitals-System’; for his entire dialectical, immanent critique of the ‘ideologized’ science of ‘‘‘capitalist political-economics’’’.”

“That “Value-Form” -- as the past [psycho]historical, and as the ever-present meme-seed, throughout the capitalist epoch, of all forms of [the exchange-]value -- is also the foundation, both ever-present and past [psycho]historical, of ‘the Modern «Mentalité»’ itself; of [not just “The German Ideology”, but, as well, of] ‘The MODERN Ideology’ entire.”

“The “Elementary Form of Value” is the cognitive, ideological basis of “Modern Society”, of ‘“Modernity”’ -- i.e., of capitalist civilization -- as a whole; the most radical root of the Capital “Value-Form”[Marx] itself, and of the Capital-[value-]relation as predominant “social relation of production”.”  

“That “Elementary Form of Value” is, in its essence, the incessant contemporary equating -- implicit in and permeating the inveterate «praxis» of our daily lives, globally, today, in and by the “exchange of equivalents”, e.g., the exchange, for Money, of two qualitatively different Commodities -- let’s call them, generically, C₁ & C₂ -- that are incommensurable in their qualitative, use-value core, but that are apparently, superficially, equated by “pure” quantity alone, i.e., by “[proto-] price”, in a «praxis» which continually, uncritically inculcates in us a semi-conscious paradigm of the habitual reduction of the qualitative to the “purely” quantitative. [Note:  arithmetical qualifier ideograms are distinguished from arithmetical quantifier ideograms, herein, by underscoring/underlining].”

“In the exchange-equation (c₁)C₁ = (c₂)C₂, in which c₁ denotes the count of units of commodity C₁ that have the same price as c₂ units of commodity C₂, or, in --

(c₁/c₁)C₁ = (1)C₁ = (c₂/c₁)C₂

-- in which (c₂/c₁) represents the C₂ “price” of one unit of commodity C₁ -- the indicated mere quantifiers, though applied to qualitatively heterogeneous commodities, seem to render them qualitatively homogeneous; proverbial “apples” versus “oranges”, made ‘equatable’, as if by some kind of mystic magic.” 

“However, in reality, to deeper psychohistorical discernment, such as that achieved by Karl Marx, this ‘exchange-equating’, this ‘‘‘homogenization’’’, is rendered possible -- is rendered ‘sustainedly practic[e]able’ long-term -- only by way of a common quality, invisibly uniting C₁ & C₂, but whose ‘arithmetical unit qualifier symbol’, representing that quality-in-common, is absent, is elided, in both of the equations above.”

“This syntactical absence represents -- symbolizes -- a substantive absence, from common capitalist consciousness, from the common mind of the capitalist epoch, from the predominant «mentalité» of capitalist humanity -- from the ‘human phenome’ of the capitalist interval of human-historical time, i.e., from the capitalist ‘historical «species»’ of humanity [cf. Marx on “historical specificity”] -- of this common quality, which is unknown to that mind; whose meme is missing from that stage of the developing ‘human phenome’.”  

“This common quality is created and sustained -- continually reproduced -- by an unconscious alchemy of our own «praxis» of capitalist competition -- e.g., of price competition -- itself, i.e., by an unconscious and unintended aspect of our own social agency; of our own social-reproductive ‘‘‘subject-ivity’’’; of our own daily activity.”

“This common quality, and the ‘arithmetical unit qualifier’ that can represent it, becomes known, to such agents, only if they scientifically theorize, or become acquainted with other agents’ scientific theorizations, of the phenomenon of exchange-value within a[ny] capital-centered, capital-dominated society.”

“This common quality -- of capitalist commodities, of capital-produced commodities; of “commodity-capital” [Marx] -- becomes known to such agents only, albeit only partially, only distortedly, via the labor-time value theories of, for example, Adam Smith, Benjamin Franklin, David Ricardo, etc.”

“This common quality becomes known more fully, more scientifically, via the “law” of value theory -- via the ‘price-attractor of a commodity = abstract-labor-time-presently-socially-necessary-to-reproduce a unit of that commodity’ theory -- via the breakthrough psychohistorical theory of Karl Marx himself.”

[Aside:  “Of course, Marx’s “law” of value is his analytical abstraction, to enable the theorization of the capitalist system.  It is an ‘‘‘homeomorphic’’’ short-cut or proxy that allows the dialectical derivation and prediction of the long-term tendencies of that system, in abstraction from a witheringly-detailed micro-analysis of the actual historical course of the competitions of individual capital[ist enterprise]s.  Actual, ‘‘‘socially-necessary-abstract-labor-time values’’’ are actually ever-changing, and empirical prices are ever-deviating from, and “hunting” for, those [changing] values, and therefore are continually fluctuating above and below those values, driven by the market competition of capitals.” 

“The ‘‘‘abstract-labor-time value’’’ of any capitalist commodity only appears, empirically -- as its price -- momentaneously, and, even then, only as modified by other conditions immanent to the capitals-system, such as the process of the competition of capitals that produces the equalization of the rate of profit, or the formation of a general rate of profit, across the social expanse of the differing technical compositions/productivities of productive industrial capitals.” 

“That ‘‘‘abstract-labor-time value’’’ is like a [ “strange”] attractor of an asymptotically aperiodic nonlinear dynamical system, and of a nonlinear dynamical system that is also continually “bifurcated” by causes external to that system proper, and is also continually ‘self-bifurcated’ by causes internal to that system proper, e.g., by the growth of productivity, or of the “productive force”, of industrialized capitals’ commodity-production.” 

“Indeed, so ‘fluctuatory’, so oscillatory, are the phenomenologies of ‘price-attractors’ within the capitals-system, that one might [mis]take those phenomenologies to be “pure”, “random” fluctuation only, without even any transient central tendencies of any kind.”].”

“Let us denote, by L(.), a function/operator that returns, when applied to a symbol that represents a given «species» of commodity, the quantity of hours of generic, “abstract” [Marx] human labor typically needed to reproduce a single unit of that commodity under the presently, momentaneously prevailing conditions of the competitive capitalist market for that commodity, including the labor-productivity of the most advanced fixed capital technology presently being applied to its already marketed production.” 

“Let us denote, by l, the ‘arithmetical unit qualifier’ for a single unit, say a single hour, of that generic, “abstract” human labor time.  Let l₁ denote the quantity of “abstract” or generic human labor hours presently needed to reproduce a unit of commodity C₁, and l₂ the quantity of “abstract” human labor hours presently needed to reproduce a unit of commodity C₂.”

“Then:  What must be going on, therefore, per such deeper discernment, can be reflected, explicitly, symbolically, by inserting, into those ‘exchange equations’, on both sides of each such equation, this ‘arithmetical ontological* qualifier’ operator/function, L(.), to stand for the “abstract” human labor time kind of thing/common quality shared by all capital-produced commodities, thereby achieving a ‘‘‘re-qualification’’’ of  those equations, with a symbolic provision for/representative of that common quality, viz. --

[(c₁)C₁ = (c₂)C₂]  ==>  [(c₁)L(C₁) = (c₂)L(C₂)]  ==>   

[(c₁)(l₁)l = (c₂)(l₂)l]

-- or --

(l₁)l  =  (c₂/c₁)(l₂)l

-- where we restore the heretofore elided ‘arithmetical unit qualifier’, so as to make the exchange equations make sense -- that is, so as to make the exchange equations address the same kind of thing, the same common quality, the same ‘arithmetical unit qualifier’, l, on both the left hand side and the right hand side of these exchange equations, rather than, as before, equating “apples & oranges”.”

“Let us next “decode” the generic algebra above into a specific, hypothetical case example, so as to obtain a more direct, more specific -- i.e., an arithmetical -- “feel” for what the generic algebra above really means.”

“Suppose that we imagine a moment of human-social time in which it typically takes 30 “abstract” human labor hours to produce each single bed, and 10 generic human labor hours to produce each single chair, and in which a generic human labor hour [for both] costs $10.”

“To arrive at the simplest, uttermost root -- the “economic cell-form” «arché» -- of capital[ist][ exchange]-value, Marx abstracted out, e.g., the Money[-price] mediation of typical, present-day exchanges in capitalist society, driving that mediation back into implicitude.” 

“For clarity, we shall now put that Money[-price] mediation back, explicitly, into these ‘Elementary Form of Value’ exchange equations, moving to the more ‘thought-concrete’ presentation-step of explicitude for the “Money-Form” of value, and for its ‘‘‘money-mediated circulation of commodities’’’ [generically ‘algebraicized’, by Karl Marx, as, e.g., C-M-C’, such that commodity C is qualitatively unequal to commodity C’].  Let us, therefore, for familiarity’s sake, now relax that abstraction, and explicitly posit symbolization for the Money medium into our thus revised, & case example concretized, exchange equations --

(6)chairs = (2)beds;

(6)chairs = (600)dollars = (2)beds, instantiating Marx’s “C-M-C’”;

  

(6/6)chairs  = (600/6)dollars, ==>

(1)chair(s)  = (100)dollars, the unit price for chairs is $100;

(2)beds  = (600)dollars, ==>

(2/2)beds  = (600/2)dollars, ==>

(1)bed(s)  = (300)dollars, the unit price for beds is $300.”

“Now, let us make the exchange equations “commensurable”, by re-expressing them in terms of the “abstract” or generic human labor hours presently needed to reproduce a unit of the commodity “beds”, and of the commodity “chairs”, as of the hypothetical present moment of our example --

(6)L(chairs) = (2)L(beds); 

(6×10)l = (2×30)l;  

(60)l = (60)l;  

(6)(10)/(60)l = (60/60)l  = (600/60)dollars, ==> (1)l  = (10)dollars;

the unit-price for the “abstract” or generic human labor power commodity is $10 per hour.”

“Thus, if a critical theory of capitalism -- of our capital-«praxis» -- is in place, i.e., if Marx’s “law” of value is in the minds of the human personifications/agents of the “social relations of production” that are incorporated into, and intrinsic to, that «praxis» -- “social relations of production” named, per their Marxian names, as the “Commodity-relation”, the “Money-relation”, and the “«Kapital»-relation” itself -- then the “common quality” of capitalist exchange-values can be restored to those agents’ awarenesses of capitalism’s exchange-relations.  The ‘arithmetical ontological* qualifier’ labor-hour unit, l, for the “abstract” or generic human labor hours presently socially necessary for the reproduction of given Commodities, can then be represented explicitly in the exchange equations.  Under this immanent critique, those equations transform as follows --

(c₁)C₁ = (c₂)C₂ becomes (c₁)(l₁)l = (c₂)(l₂)l;

(c₁)C₁ = (m)M = (c₂)C₂ becomes (c₁)(l₁)l  = (m)$ = (c₂)(l₂)l;

(6)chairs = (2)beds becomes (6)(10)l = (2)(30)l, and;

(6)chairs = (600)dollars = (2)beds becomes

(6)(10)l   =  (60)(10)$  =  (2)(30)l.”

“However, for those personifications of these social relations who remain unaware of the critical theory of capitalism, and of its psychohistorical “law” of value, which names a pattern inadvertently created and continually reproduced by their own activities, of price-competition, etc., and by the similar activities of other such human agents, these exchange relations/equations remain opaque.”

“Seemingly unqualified -- qualifier-elided in fact -- and heterogeneous, qualitatively different commodities appear to be exchange-equated, made homogeneous, made commensurable, as if by “pure” monetary quantity alone, i.e., by monetary units [e.g., $s] quantities, “prices”, whose true units, whose ‘arithmetical ontological* qualifier unit’, l, remains obscure.”

“Therefore, every continually repeated daily act of monetary purchase, of the exchange of quantities of given commodity units for quantities of money units, incessantly engaged and practiced by all of we agents, inculcates and reinforces, in our minds, both unconsciously and semi-consciously, its seeming reduction of all qualities to “pure” quantity; its qualifier-elided, use-value qualities-elided, ‘qualitativity’-elided, “pure” ‘‘‘quant’’’ paradigm, and «mentalité»; the typical «mentalité» of modern, capitalist humanity.”   

“All this is reflected, psychohistorically, in the modern “standard”, ‘contra-ancient’ arithmetics, of “pure”, ‘unqualified quantifiers’, starting with the so-called “Natural” numbers, i.e., with the elements of the set N = {1, 2, 3, ...}, and continuing on into those of the sets, or spaces, W, Z, Q, and R.”

“Karl Marx identifies the root issue of this whole matter as follows -- 

“In order to discover how the elementary expression of the value of a commodity lies hidden in the value-relation of two commodities, we must, in the first place, consider the latter entirely apart from its quantitative aspect.  The usual mode of procedure is generally the reverse, and in the value-relation nothing is seen but the proportion between definite quantities of two different sorts of commodities that are considered equal to each other.  It is apt to be forgotten that the magnitudes of different things can be compared quantitatively, only when those magnitudes are expressed in terms of the same unit.  It is only as expressions of such a unit that they are of the same denomination, and therefore commensurable.  Whether 20 yards of linen = 1 coat or = 20 coats or = x coats -- that is, whether a given quantity of linen is worth few or many coats, every such statement implies that linen and coats, as magnitudes of value, are expressions of the same unit, things of the same kind.  Linen = coats is the basis of the equation.  But the two commodities whose identity of quality is thus assumed, do not play the same part. ... .”

[Karl Marx; Capital; volume I; Chapter I., Commodities.; Section 3., The Form of Value or Exchange-Value; A. Elementary or Accidental Form of Value; 2. The Relative Form of Value; International Publishers [New York: 1967], pp. 49-50, emphases added by F.E.D.].”

“The ‘Elementary Form of [Commodity[-Capital-]]Value’, or --  

{ (c_j)C_j  = (c_k)C_k }, for all j ~= k in N 

-- is Marx’s name for the epoch-making cognitive ‘psycho-mutation’ in the ‘human phenome’ that makes the capitalist system collectively-cognitively, culturally possible, & that, via the daily human experiences of capital-dominated society, expandedly reproduces that ‘psycho-mutation’ throughout the capitalist epoch, spreading out over the face of the earth with the “world market”.”

“In the epoch of the ancient Mesopotamian civilizations, and even so late as that of the ancient Mediterranean Hellenistic civilization, the prevailing ‘human phenome’, the prevailing individual human «mentalité», was not yet quite so permeated by the unconscious/semi-conscious paradigm of the social practices of exchange-value exchange, let alone by that of capital-value, as has been our post-Renaissance epoch, so that their early arithmetics still featured ‘arithmetical qualifiers’.” 

“Only pre-capitalist forms of the Commodity-[barter-]relation, and of the Money-relation, and only the “antediluvian” forms of capital -- usurer’s capital, mercantile capital, and slave-labor-based [not yet wage-labor-based] latifundial agricultural productive capital, were as yet extant in the ancient epoch. 

“The attained levels of the human-societal self-force of human-societal self-reproduction, of the ‘meta-Darwinian’ self-reproductive force of the human species, throughout the ancient epoch, were insufficient to even episodically induce, let alone to sustain, the full development of “the capital-relation”:  industrial capitalism.”  

“The human «praxis» of exchange-value exchange achieved even greater social practice ‘‘‘density’’’, or ‘‘‘concentration’’’, than ever before, in the ‘social singularity nucleation zones’ of proto-Renaissance Europe, e.g., in what was to become Italy, where, e.g., double-entry accounting for capitalist enterprises first spread, & where western acceptance of Indo-Arabic numeration first surged.”

“The stage was thereby prepared for the formation of the ‘Elementary Form of Value’ as the unrecognized cognitive core of modern society, for the eventual irruption of industrial capitalism -- of capitalism proper -- and for the elision of the ‘arithmetical qualifiers’, as a ‘‘‘superstructural’’’ psychohistorical reflection of that formation.”

“This Foundation is designed to be a harbinger of the higher global civilization; of the first planet-wide -- Terra-wide -- Renaissance; of the supplementarily-opposite system, the higher successor-system, to the present, capitals-system.  By this, we mean the higher successor-system whose foundation is generalized equity, as the successor predominant “social relation of production” to capital as predominant “social relation of production”; the ‘‘‘equitist’’’ society, of Political-Economic Democracy, that is to come, if this planetary human species “passes” its looming ‘Meta-Darwinian Planetary Selection Test’ global crisis of humanity.”

“It is fitting, therefore, that the [dialectical] arithmetics, discovered, wielded, and propagated by this Foundation, as cognitive-psychohistorical harbingers of a society no longer obsessively centered upon “the exchange-value” [Marx], but, on the contrary, centered upon that higher form of individual, personal, local use-value which is social, collective, nonlinear use-value; which is ‘meta-Darwinian human-species-fitness-advancing’ human-societal self-reproductive use-value; which is human-societal self-reproductive self-force itself, are dialectical ideographies which -- helically, spirally, in a higher form -- restore the ‘arithmetical qualifiers’ of old, of the ‘human phenome’ before its formation of the ‘money-mind’ -- i.e., of the ‘capital-mind’ -- of the ‘exchange-value mind’; of the ‘‘‘quant’’’ mind, one-sidedly, “purely” quantitative in its [thus] mal-appreciation of reality -- of the human experience entire.” 

“Again, we should emphasize, this return of the ‘arithmetical qualifiers’, and of the ‘qualitative aspect of arithmetical ideography’; this [psycho]historical re-emergence and restoration of the ‘arithmetical qualifiers’, is no merely cyclical, circular return.  It is, on the contrary, a “return with development”.” 

“This return, too, exhibits a collective-cognitive ‘psychohistorical hysteresis’, a psychohistorical gain -- by this time, so long after the last Dark Ages -- relative to the development of ‘arithmetical qualification’ as it stood even at its zenith development before those Dark Ages.”  

“This revelation will not be immediately accessible to most of those most afflicted with the “Elementary Form of Value” cognitive deformation.  Those whose minds are, mostly unconsciously, pervaded and permeated by this one-sided “Elementary Form of Value” paradigm will not be quickly or easily able to detect its impact upon their thought and feeling -- to discern how this paradigm possesses their cognition; how pervasively it appropriates and molds their entire awareness.”

“Assimilation of this revelation requires time, reflection, thorough self-inspection, deep introspection and meditation -- to which the Foundation’s “cloistered” conditions are conducive -- even to discern it, let alone to transcend it; let alone for modern humans to free themselves from that cognitive deficit.”

“We have found that the learning of the F.E.D. dialectical ideographies -- the F.E.D. systems of qual[o-quant]itative arithmetic/algebra -- and their application to the ‘meta-modeling’ of the our universe, and of its sub-universes, can serve as a powerful psychohistorical therapeutic practice, for amending, and helping to heal, the cognitive diseases of the contemporary ‘human phenome’, and for preparing the way to the higher ‘human phenome’ to come.”

*[Our ‘arithmetical qualifier’ herein, l, is actually a ‘compound qualifier’, the product of a ‘metrical qualifier unit’ [mu^o1] for the time dimension, e.g., for hours, with an ‘ontological qualifier unit’ for that Marxian-discerned “kind of being” which is industrial-capital-immanent “abstract human labor” [m₁], such that, in the 7th, _Rm_ system of dialectical arithmetic in the F.E.D. [meta-]systematic dialectical presentation of the dialectical progression of the F.E.D. dialectical arithmetics, l would be more richly re-expressed as --

m₁  x  m_u^o1   =   m_{1 + u}^o1 ].