~ Foundation Encyclopedia Dialectica

QmtL'nO of 0wra lion:Stars' End, New YorkTenninious.. CahhnU.a

Webmaster. www.diaJectics.org

August 01, 2008 C.E. I S.U.E.

Subject: ~. D. Briefs #2 - Meta-Monadology: The Universality Of The «Au/heben... Process.

Dear www.dialectics.orgWebmastec,

Greetings to you from F.~..Q.!

Enclosed with this cover letter please find--

• g. D. Briefs #2 - Meta-MonlldDlogy: The Universality Of The «AujhEbeM Process, Parts l. &!!.

This cover letter conveys a new text, the second contribution to your new "g. D. Briefs" page, whichhas been contributed, not by a member of the Foundation, but by a reader OfyOUI site.

We could do no better than to present Lhe following excerpt from the author's letter, by which heconveyed lhis text to the F.gq. General Council:

"...What this text addresses, in toto, is the "'psycho-historicar", cognitive revolution that F.E.D. isoffering. It's deeper title, th~ should be-

Announcing Q Cognitive Revolution, N~cesSQry Precursor to Mankind's Liberutory Transfrmno.lion of theCapitJlI-Rew.fion as Predominant Social Relation of Production OfModem Society.

As I state at the outset of Part II. of this text, I believe that experience wilh compact; explicitdialectical models; with the 'algorithmic dialectics' and the 'dialectiCtlI algoritllmics' of, e.g., the Qcategorial ideography, can help to catalyze, in the 'experiencer', a cognitive revolution. It can help tocatapult that experiencer [deeper] into "'the dialectical operations stage of adult human cognitivedevelopment'''. That, at lea!'iit, has been my experience.

I also hold that such a reoolution in cognition, diffusing in widening waves, rippling throughout theglobal populace, is prerequisite to a successful, liberatory transition to the higher polity - to thepolitical-economic denwcracy - of 'democratic-communist' society, i.e., to the 'externality-equitiesbased economic democracy that F.~.D. advocates [for more on this, see www.eguitism.org F.£.D.l.-

The rest of the content of Part II. is a specimen of the positive fruition of a Marxian, immanent critiqueof the core of Modem Science - i.e., of an evocation of a detenllinate [self-]negation of the capitalepoch's science of arithmetic, resulting in the discovery and presentation of an arithmetic for Marxiandialectics.

The 'cognitive revolution' created by the assimilation of the resulting -new «organon»- for science iscatalyzed and facilitated by the new, partially-algorithmic, partially intensional/intuitional; andinterpretive/connotative, Dialectical Heuri.'itic of F.E.Do's new, and Trans-Leibnizian, Di/dectical«Characteristica Uniuerslllis».

This Mathematics of Dialectics, fruit of the Historical Dialectic of Mathematics, and of thedialectical, Immanent Critique ofModern Mathematics, provides, at last, the precision ground.work ofa non-reductionist, non-atomistic paradigm for a 'Trans-Modem Science' - for acomprehensive Scientific and Mathematical Altenlative to Reductionism.

The communication strategy applied in Part II. may be of interest to the F.E,.Q. General Council.

It essays to illustrate the !Elfamiliar - in this case, both Systematic Dialectics, and the compact,mnemonic Modeling thereof in the language of F.E,.Q:s new dialectical algebra -- via a partialredudion 0/ !E!.lamiliarity. It seeks to convey both of these "e§.otenc" topiCS via their illustration inthe context of a topic which is C:!oteric to the readers of the www.dialectics.org and of thewww.adventures.in-dialectics.orgwebsites;well-known to them simply by virtue of their literacy.

The text of Part II. illustrates the narrative -method of presentation- [Marx} of systemaHc dialectics,and the compact modeling thereof via the new Dialectical ldeography, for the familiar case ofPhonetic Writing Systems.

In this process, Part II. moves beyond insubstantial and external, undialectical critiques of ModernScience, to immanent critique. It locates the foundation of its critique in the very heart of the object ofcriticism, in this casc, in the 'sel[.duality' of ordinary arithmetic. By then developing that immanentground of critique, i.e., of the self-critical, determinate self-negation of standard arithmetic - f!i. 'it­self !!y. 'it-self -- Part II. achieves a positive development that both supersedes and criticallyconserves the content of that object of criticism - Modem Mathematics -- in the «aufheben», cUalecticalmanner.

Part II. follows F.s.D:s lead, essaying to aid the reader's discernment of this immanent ground of thecritique of arithmetic also via the "'erternar", 'psycho-historical' eTJidence of 'psycho-archaeology'. Itdocs so, in this case, by resurrecting some terminology and concepts - in particular, that of«arithrnos» and that of «monad», or, respectively, that of "nu.mber" [of qualitative units} and that of[qualitative) u.nit - from Ancient Mediterranean humanity's development of mathematics, up to thestart of the last Occidental -Dark Ages-. As we show, these Ancient developments partially survive,to this day, in vestigial and col,rnate forms within modem mathematical terminology and conception.

'Psycho-historical analysiS' of the Ancient theory of arithmetic - as elaborated also in Jacob Klein'sbook entitled "Greek Matllem.tltical Thought and the Origin of Algebra", as well as elsewhere - revealsa more sensuous and qualitative scientific and mathematical «me:ntaliti» among our Ancientancestors, versus that of Modern Occidental humanity. It reveals that Ancient «mentalite,.~ to be,precisely, one not yet as pervasively impacted by the incessant experiences of exchange~valutexchangeas was the mathematico-scientific «men-tulile» Lhat had emerged by Lhe time of the EuropeanRenaissance, closing the Occidental -Daxk Ages". The later «men-Laliti ... gave birth, at length, toModern Science.

Humanity's pervasive and intensive diffusion, and incessant daily practice, of commodity exchange­even of barter, bUl, especially, of money-mediated exchange of commodities, and of money-price­consciousness - has subliminally introduced a fundamental confusion regarding the dispensability 01the IflUIlitative, and about the reductive 'equatablity' of the heterogeneous, into humanity's«mentalite». This was evident already in Marx's analysis of the very «arclre» form of exchange-value,the ..elementary or accidental form of [commodity·}value", in his Capital, vol. I, Chapter 1., Section 3. A.

1bis Ancient mathematico-scientiJic «metltalite.> can thus be leveraged to outwardl" 'co-illuminate'the ground of the innermost of the immanent critiques of Modem Science, thaL of Modem Arithmetic:the ...archi» of all of the ideology, as also of much of the social-reproductive efficacy, of ModernScience.

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The Modem «mentalit€lf is content with the purely-qlUlntitative abstraction of '2 + 2.4'.

The Ancients' was not.

As evinced in the Ancient Alexandrian «Aritlrmitike» -- or '«Aritlrmos·ltike»' - of Diophantus, circa250 CE., in which the earliest known emergence of [proto-]ideographic-symbolic algebra wasrecorded, the Ancients required expressions of the form 'MlJ'p,' La. M&", wherein the Greek letter-beta- is used to represent the number we denote today by '2', the Greek letter "delta" to representwhat we today denote by '4', the abbreviation 'La.' to represent ·equals· or '.', and the abbreviation'M' to represent the Greek word ~(Mova~,or «Monad», which translates to the word ·unit" in ModemEnglish. Note that, in the Ancient expression. the qualifier, not the quantifier, comes first!

Yes, the Ancients abstracted, but they did not abstract only generic '''quantifiers1tl, such as the '2's and

the '4' in the example above. 'lhey also abstracted a generic, symbolic qualifier, M., denoting thegeneric qlUllitative Imit - ontological or metrical - with which every '"well-formed''' abstractquantifier must be paired.

The «monad» symbol, or unit symbol. M, could stand for a cabbage, for a cannibal, or for a king - forwhatever the context of the given expression required - indifferently and 'chameleonical1y'. This"syncopated" symbol, M, stood for the generic «Monad» of Plato's «.ArithmoiMonadikoilf.

It denoted, proto-ideographically, an abstracted metrical unit [e.g., a unit of conventional measure,like a «stadium»], or and abstracted ontological unit [e.g., for an individual unit of some kind ofbeing, such as a "'philosopher"'] QUALIFTER. This usage vanished in the post-Dark Ages rebirth ofOccidental mathematics and science. It was eclipsed in their adoption of a more fully ideographicallysymbolic [Hindu-Arabic} arithmetic and algebraic notation of abstract quantity, until now - untilF.g.D.

What the resulting new, precision «orgallon» of dialectics offers - what the new, DialecticalcCl,araderistica U"iversalis.,. bequeathed. to humanity by F.gD. offers - is, 1 think, not the blindinglight of a formless, indeterminate and indulgent effulgence. The dawning of such a light, becauseblinding, is also, still, '''that dark night in which all cows are black" [Hegel}. It provides no visiblenavigational specificity, either as a -method of discoveryN IMarx], or as a "method of presentationN

[Marx], post-discovery. Nor does Q offer a rigid dichotomization - e.g., of ultra-dense, impenetrable"atoms ll versus vacuous void, providing a total void of creative freedom; no scope for novelexploration, nor for intuitive imagination. It is raU,er, a complex unity of some aspects of the two,and, precisely, a dialectiCtlI complex unity thereof, which constitutes, as a whole, an 'AlgorithmicHeuristic' .

I have encountered numerous abstract negations, of late, regarding the Capital-relation-shapedideology in Modem Science, among self-professedly "Marxian" circles. Given the tenor of those[pseudo-l"critiques", I felt that the highest priority - for the moment - resides elsewhere than in adirect critique of such extremely altti-Marxian ideologies. AU of these pseudo-Marxian, anti-scienceideologies bear the markings of the 'huma" anti-humanism' of the ruling faction of the present rulingclass. They demonstrate the potential lethality of the 'anti-psychohistory' of that faction's massiveideology-engineering operations. Those operations are aimed to vitiate, eviscerate, and immobilize anyopposition. informed by actual Marxian theory, to that faction's 'humanocidar plans.

The priority is, IMHO, not a mere critical negation of those negations, but a 'pos-i-tion': positingspecimens of the FRwnON of the dialectical, or immJment, critique ofModern Science.

Most of "critiques" of Modem Science I cited above amount to nothing more than an "externaf"critique of Modem Science. They lead to an "'abstract negation'" of Modern Science - to "throwing thebaby out with the bathwater".

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The pseudo-Marxian critics who purvey them say that there is liD ~aby" in Modem Science. They saythat Modem Science contains nothing whatsoever that is a product of "universal labor" [Marx];nothing of universal use-value; nothing "this-~;ded", no practical truth (Marx, Theses on Feuerbach];no historically-generic social-reproductive efficacy. They say that nothing of these beneficial featuresexists al all in the Science which the human species has so protractedly created, in co-evolution withour creation. and world-historical elaboration, of the Capital-relation.

Their fundamentally nihilistic critiques of Modem Science seek to extert/ally "egate ModernScience, on 'Naturist' and 'A"imalist' groWlds, leaving only an indeterminate "Nothingness".

'Relrojecting' the upshot of such 'extemalist' critique into the past finds the following simile. It wouldbe as if Marx had succumbed to such sub-dialectical, reductionist tendencies, and had simply written,in place of the ..Grundri..<;.<;e~, and of the fOUT volumes of ..Das Kapital», etc., etc., the single sentence:·Bourgeois Political Economy is not IJ science; it is nothing but iJhology.·, and left it at that. I feelsure that there were also whole legions of 'sub-dialecticals' in Marx's time, and before, who did,essentially, just that. We do not know their names. Deservedly so. For, in regard to any actualcritique of Modem Science, they conlributed, essentially, ·Nolhi"g· to humanity: -indeterminateNothin~ess·.

The chief virtue of dialectical, or immanerat, critique is its "'radicalism"'.

Dialectical critique, immanent critique, locates the deepest root of the indictments lodged by both theexternal and the internal dissent from a given, ideology-afflicted science - or from Modem Science asa totality - in the innennost core, the very heart of that object of critique itself.

It locates that root in the most fundamental, ..archb category, or concept, residing at the veryfoundation of that object of critique, from which that ideological science flows/has developed; the·cell fonn n [Marx] of its totality. It locates that root in an 'intra-duality' - in a 'self-duality' - of thatvery root category, or concept, itseU.

That 'internal duality' partially vitiates the theoretical and practical grasp of the totality - here ofNature itsclf, as maximal totality - that this ideological science aims and claims La comprehend.

Then, this immanent critique unfolds outward from that innermost heart of its object, reconstructingthat object as it goes, until the totality of that object has been transformed "'from bottom to topm;"'from inside to outside"'; from core to surface; from root to branch to leave.

In that process, whatremains 'use-valuable' in what was already explicit within that object, prior tothis critique, is preseroed, and elevated into a new and '"higher''' - ie., into a more-inclusive - context,where vast treasures of new 'ideo-ontology', of new conceptual advances, that had been locked andblocked by the old object, prc-critique, are evoked, and burgeon into explicitude.

The result is, not an "abstract llegatio,,", wasting all, and leaving nothing, but a "'determinatenegation"', rich in its manifold of new and old determinatenesses.

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A specimen of the fruition of such an immanent criLique of Modem Science is what I have sought toprovide in the enclosed text, entitled -

Meta-MonadolofY: The Universality Of The II.Aufheben» Process.

To synopsize the substance of this text. some of its key, core content is called-out below.

1. Applic.Jtion of the -N.Jtur.Jl DiaJectors- Arithmetic to Genente Key. Core Content of Mux's .DlIs Kapitlll••

The specimen includes a demonstration of how the tt.arche» category of Marx's 4(Das Kapital», thatof the Commodity, or, more specifically, that of the Elementary Commodity Value-Form, cangenerate the 'Table of Content' for a Marxian Critique of Political Economy, as a 'SystematicDialuticaf presentation, or «auJheben»-cumulative catcgorial progresSion, via the 'self-iteration',or 'iterated categorial 'self-subsumption/self-intemalization', i.e., by means of the 'self~rc.flexive·

self-confrontation of that category as an tt.aufhebe1l» operator, under the rules of the F.~.Q.'s Qdialectical arithmetic, as contra "Natural" Arithmetic.

2. The Self-Duality of the so-called "Natural" Arithmetic of the so-caned "Natural" Numbers, N - {1, 2, 3 ....}.The ·Natural Numbers", the -ultimate cell-form" of all of the mathematical systems of ModemScience, is a one-sided construct. If, in the phrase "3 pounds Iofl potatoes·, we described '3' asUlquanti/ier'''. 'pounds' as 'metrical qualifier, and 'potatoes' as 'ontologiad qualifier', it is dear that

'3' alone, as in N - {1, 2, 3, ...}, is an 'u!YIUQlified quantifier. The suppressed 'intra-dual' tothat one-sided interpretation of the root category of ·Natural" Arithmetic is an Arithmetic of'u~uantifiableontological qualifiers'. Such a system is 'contra-thesis' to the '«arche»-thesis' of the'u~ualified quantifiers' system of arithmetic. 11tis 'contra-thesL'i' constitutes a "Non·Standard­arithmetic, a system of 'meta-"Natural" meta-numbers'. Upon examination, after 'de-suppression',it is found that this F.gD.-discovered 'counter-arithmetic' fits. and quite spontaneously so, thedescription of a 'de-Parmenidcanized', dynamical and 'meta-dynamical', revolutionized versionof Plato's ancient and, until now, mysterious 4Carilhmoi eidetikoilJ, the _arithmoi» of his4Cdialektik.i». Not surprisingly. it also fits the description of a 'contra-Boolean algebra', of adialecti.cal logic, as 'contra-thesis' to the •4Carchi»-thesis' of Boote's arithmetic and algebra forformal logic. This opposite, 'contra-thesis' of a 'dialectical symbolic logic' flows from a deepnegation of the axiom that Boole called" the ftmdamentallaw of [linear] thought".

It is also found that these new "qualitative numbers" conform to the same four, "first order"axioms, or "Peano Postulates", as do the "Natural" Numbers, although with a completely contrarysense - as F.gD. has already argued in its extant expOSitions. Indeed, it is also found that thesefirst four axioms are so universal that both the "categorial progressions" of "systematic dialectiC',and the 'syste~progressions' of historical dialectic are also described by them; are also 'Pean;c'.

This result was foreseen,. in so far as the 'DianoeLic' tools of «Verstand» reasoning. and of the 20thCentury burgeoning of -Mathematical Logic-, can encompass them, via some of the deepesttheorems of Modern Mathematics. They are (1) the GOde1 Incompleteness Theorem [in conjunctionwith the COdel Completeness Theorem, co-applied at the "first order" level], and (2) the LowenheimSkolem Theorem. Each of these theorems by itself predicted, "non-constructively", thelconstructability' of "Non-Standard Models" of the "Natural" Numbers.

The N plus the contra-N systems of arithmetic go on to find a "'complex unity"', or 'ulli-thesis'; a'~-qUQntitative' third category and system in their own Q-modelable categorial-progression 1­sys~-progression.

Thatcategory is the category of a system of 'quantifiabl~ontologiad qu.alifiers arithmetic', called U.

F.~.D.'s dialectic of tl.e dialectical arithmetics, modelable by themselves as such, then burgeonsforth from there.

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This immanent negation of the exchange-value-inculcated, ideological one-sidedness that infectscontemporary "'capitalist arithmetic''' brings something positive to light. It brings to posit'ivefruition an 'ideo-ontologically' expanded, «aujheben»-expanded, qualitatively revolutionizedconception of arithmetic, and an expanded, 'qualo-quantitative' transformation of mathematics ingeneral, in the form of !!. general theory Qf. «arithmoi"..

By UUs phrase, I take it that F_E-D. means a universal theory of those assemblages, «ensembles»,"sets", or "populations" of (qualitative, heterogeneous] «monads», i.e., of the [qualitative]'" units''', '"parts'u, .11particulars"', '''clements''', "'members''', 'uconstituents"', or '''individuals''',the 'little unities', the 'little wholes' that we encounter, so ubiquitously, at every level, and scale, ofour experience and cognition of this «kosmos»,

3_ The "'Set OfAll Sets'" and the Immanent Critique of "'NaturaJnt Set Theory. Set Theory is still oftconsidered to provide the foundational theory for all of Modem Mathematics. The '"Set Of AllSus'· is the set-theoretical, -extensional- definition of the "Set" idea itself. The [finitaryj "'Set OfAllSets'" should therefore be: the fundamental [idea-jobjecl of a Set Theory that should also, itself, be:"'realistic", or finitary and "'co'15tructivist!". Instead, the "'Set Of All Sets'" has been deniedand exiled from Set ·lbeory, because of the "contradictions- - "lonnal", "propositional- and also'contental', 'ideo-ontological - which the admission of this [idea-Jobject entails for ""dialectical,'dianoetic' Set Theory. The immanent critique within this specimen reveals lhat this set turns out tobe: (i.) not a static, noun-like 'idea-objecf, but a 'self-eonstructing idea-process', an idea(l[ized)llIlprocess-object''', a 'menial evenliW whose very essence - the essence of the Set concept itself - isself-transformation; (ii.) a Modem. trans-Platonic '{ideo]-«auto-1cinesi.'i»', and (iii.) a set-theoreticalmodel of the generic dialeetU: itself. The [rc-]admission of the "'Set Of All Sets'" into Set theoryleads to a deductive «reductio ad absurdum»; to a formal-logical self-refutation of 'dianoetic'''''Natural''' Set Theory', by way of the negation of its impljdt, formally unstated tparmenideanPostulate', asserting universal 'ideo-ollto-«stasis»'. ,.."

We recommend the deployment of this text as follows, as an addition underneath the existing, firstBrief on your Briefs Page --

ElIlyclopulhl Oilll«tica: Briefs

E. Q. §rid#1 - The g, (IT Pu r~ Quu1itlltiu~, DialecLical Algebra as«Olllrad~ri5HcaUllivusalis>>: A Step-by-5tep Guide on How Tv Use it as an«Orgalloll» for Discovery. By Aoristos Dyosphainlhosto) The g Dialectical Idoography as an lleurisl:ic. Intentional/intuitional 'Calculus

for Discovery': Generallnsfruch'ons.

(1) Example. Historical Dialectic - 'The DiaJectic of ature [The selI-<<4lJljhdlm»Sell-Progression of Natural Systems)_

(2) EXillrnple. Metil-System-atic DiaJectic - The Dia1ect:ic: of The Rules-Systrms ofArithmetics/ Algebra!' of Logie..

(3) I:!xample. Metil.-Sysfern-alic: Dialectic - The Dialectic: of The Rules-Systrms ofDiall!Cticnlldeograplly Itself,

£_ Q. Brid#2 - Mefa-Mollttdolorr Thf' Univeru..lity Of The «Alljht'bm» Proc65.. by AI/onymous

1. Part I.: The «A.ujheb"", MebI-:\1ooadolo&Y olPlatonk. cA.rirhmoi Eiddilui» Diakrtic:s.A.D.

2. Part II.: A Model ror Sutrmatic DitlkchC6.A.

E

3. Part III.: Thrtt Models in Hj.WriCGIDiJlltclics. lnol )'tllJ'anSJnmcdl.

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We plan to transmit to you Part III. of Brief#2 in due time.

Dialogically yours,

Hermes de Nemores

Secretary, General CouncilFoundation Encyclopedia Dlalectica

Enclosed herewith -~. D. Brie(#2 - Meta-MonadolofY: The Universality Of The «Aujheben'lt Process.­Part I.: The «Auflleben» Meta·Monadology of Platonic ...Arilhmoi Ewelilw;'" Dialecti~.

Part II.: A Model for Systemalic Dialectics.

Forthcominr, -

Appendices Lo g D. Brief#1 - The Q. OT Pure-Qualitative, Dialectical Algebra as .Charllctzrisfi.al.UniWTSlllis»: A Step-By-Step Guidt on How To Ust' It as a1l «Organon» for DisanJoy;

g. D. Brief#2 - Meta.Monadology: The Universality Of The «Aufh£ben» Process­Part III.: Three Models in Historical Dialectics.

g. D. Brief#3 - A [Brief] Definition of Dialectics;

~. D. Brief#4 - Dialec;l.ical Meta-Ariomqtics: A Methodology/or Marxian, Dialectical Science;

Concluding sub2-sections of D/a/ectJcalldeographv. Part I.: Part I. e., Briefings on 1!!-A A A

• Britfing on the Q3

- ~ • ~ • .u arithmetic for 'quantifilOlbk ontological, or'ontic, qualifiers';

A A A

• Brnfing all the Q7 - !.QN. !wU. ~ [«mu») arithmetic for 'ontically &: mdTically qualifitd

quantifiers' [for'qllalllo-qualitativt' statNJariableS/cotdrol-parameters];

A A• Bmfing Qn the DiS - gAM:u. coil [«1l1phll-mu»] arithmetic Cor fmela-]dynamiclll-[superO-ISYstems;

A A

• Briefing on Q31

- DBAMU • 1kJ!. ,I, [«bdll.mun], for (melll-)dynllmiclll-{supt',.:t-]systmrs;

A A

• Briefingon g63 - ArBAWu • lJo~· l~ If(gamma-mu»], for [melQ-]dynllmical.[supa2.Jsystems.

Parts II. and III. of Supplement B. to the F.g.D.lntroductory LeHer;Revised version of Supplement A.; Parts I., II., and III.; "'rc-sync'd. tII with revised Supplement B.;

Dia/ecticalldeoqraphv. Glossary of Neologia, section for words beginning with the letter 'e';

F.~.D. Vi~nett£s, #1, A Universe that Adds New Classes Lo ItselfContra-Variations on a Theme 0/ George Boolt;

F.gg Fractment #2, TI,e Grand Interconnexion: Nonlinearity, Self-Reflexivity,«Autokinesis», the 'Ontological Self-Conversion Meta-Dynarnic'l andDifferetltial Equation Singularity.

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P. S. Work on Parts II. and III. of Supplement B. is on hold. Work on Vig1lette #1, A Universe tlultAdds New Classes to Itself: Contra.Variatiolls 011 a Theme of George Boole is also on hold, as is workon F.gO. Fradmt'nt #2, The Gra-utl lntercotutexion~ Nonlinearity, Self-Reflexivity, «Autokinesis ..,iN 'Ontological Self-Conversion Meta-Dynamic', and Differential Equation Singularity. We plan tosend these texts to you, along with the other forthcoming items, as circumstances permit.

We also plan to send you further sub-sections of the Clossary and 'Precursors' portions of thePostscripts to Dialectical Jdeoqraphy. as well as additional F.g.D. 'Fractments' and Vignettes.

Work is accelerating toward initial distributions of Part II. and Part III. of Dialecticalldeography_

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