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1 Ferury 2004 LIFE AS POLY-CONTEXTURALITY *) y Gotthrd Günther Kein Leendiges ist ein Eins, Immer ist's ein Vieles. (Goethe) Prt I : The Concept of Contexture A gret epoch of scientific trdition is out to end. It hs lsted lmost two-nd--hlf millenni nd philosophers nd scientists egin to cll it the clssicl period of science. However, there is not yet cler conception of wht siclly chrcterizes the pst scientific trdition nd wht distinguishes it from the er we re out to enter nd which might rightly e clled the ge of trns-clssicl science. We shll strt our reflections with short nlysis of the fundmentl difference etween the two. It is possile to trce the distinction etween the clssicl nd the trns-clssicl ck to deeply hidden metphysicl ssumptions out the nture of this Universe. Everyody knows tht the Greeks were the cretors of the clssic concept of science, nd tht this concept ws first clerly formulted y Aristotle. The dominting intent of the philosophy of Aristotle is, s he himself insisted, purely methodologicl. He strts from the shrp Pltonic distinction etween Being nd Thought or etween oject nd suject, nd poses the question: How cn Thought ever know Being in rigorous nd communicle wy? The method is ccording to the Aristotelin logic found to e in the deduction of the prticulr from the generl. The generl, however, is something which ridges the cleft etween the ojectivity of Being nd the sujectivity of Thought. Despite their infinite vriety the prticulr things tht exist in this Universe hve something in common tht links them ontologiclly together nd tht is their ultimte essence: Being, mnifesting itself s ojective existence. The relness of the ojects is lwys the sme t the ottom, lthough it ppers in infinitely differentited properties. In short: Being is n undifferentited ll-pervding universlity nd the mny things nd ppernces in this world re only the more or less prticulr mnifesttions of n underlying generl sustnce or essence, which is the sme in everything tht exists in this world. If we re looking for distinctions we hve to move into the relm of the prticulr. Being-in-generl shows no distinctions. On the other hnd, s Aristotle points out, when we think we lso try to del with the reltion etween the generl nd the prticulr y either deducing the prticulr from the generl or y inductively scending from the prticulr, to the generl. Thus Greek philosophy discovered common link etween sujective Thought nd ojective Relity. It is the generl or s it is etter clled in its ontologicl spect the universl. The generl is, qu Being, the ultimte sustrtum of Relity on which *) erstmls veröffentlicht in: H. Fhrench (Hrsg.), Wirklichkeit und Reflexion, Festschrift für Wlter Schulz, Pfullingen 1973, Adruck in: Gotthrd Günther, "Beiträge zur Grundlegung einer opertionsfähigen Dilektik", Bnd 2, Meiner Verlg, Hmurg, 1979, p

2 Gotthrd Günther Life s Polycontexturlity everything rests, ut t the sme time it is the supreme Ide from which ll prticulr thoughts derive. It follows tht we re in possession of something which Leiniz much lter clled pre-stilized hrmony etween our thoughts nd Relity. On the one side the generl qu Being is the cuse of the things nd events in this physicl world; on the other side the generl is the reson from which our ides nd concepts logiclly follow. The Tle I elow illustrtes this dulism which emerges from the peculir miguity of the generl: Tle I It follows, ccording to Aristotle, tht logicl necessity s conceived in the mind of the Universl or Generl scientist is the exct imge of the ojective connection which links Being in generl to the Being Thought prticulr things in this world nd their Cuslity Reson properties. In other words: Thinking fultlessly Thing Concept will lwys descrie ojective Relity in n Positive Negtive dequte wy. This implies tht y following the lws of reson we my ccurtely postulte the existence of things in this world efore we hve empiriclly discovered them. An exmple in modem physics is the postultion of the existence of elementry prticles long efore the experimentl mens re ville to demonstrte their relity in physics l. In view of its mzing success in the history of western science, we do not see the slightest reson to qurrel with the Aristotelin theory of epistemology, t lest s fr s it goes. But this theory solid s it is within in its own confines hs certin limittions. It hs hppened gin nd gin in the development of clssicl science tht the ltter ws confronted with certin phenomen occurring in this world where the nswer of the investigting thinker lwys hd to et tht the phenomenon in question could not e explined ecuse of its irrtionl chrcter. Thus the question rose whether the world we live in is perhps composed of two ntipodl components, one eing rtionl nd ccurtely descrile nd one irrtionl nd not conceivle y rigorous logicl mens. It is the chrcteristic feture of ll clssic science tht the nswer to the ove question hs een emphticlly ffirmtive. Moreover, the source of this irrtionlity ws identified s the suject of cogniznce itself. It ws pointed out with some justifiction tht ojectivity could not possily e the source of the irrtionl; which left only the suject. And since the Aristotelin epistemology required cler cut distinction within sujectivity etween the suject s the crrier or producer of thoughts nd the thoughts themselves, it ws resoned tht the suject of cogniznce could hve rtionl thoughts without eing rtionl entity itself. To seek the source of irrtionlity on the side of the suject ws quite plusile, ecuse sujects cn err nd sin ut noody in his right mind would insist tht mere ojects re cple of sin or error. They just re. In the course of clssic trdition the two terms "ojective" nd "rtionl" hve ecome prcticlly synonymous. It is the mrk of distinction etween the period of clssic science nd present ttempts to estlish concept of trns-clssic science tht we re nowdys forced to question the theorem of the irrtionl chrcter of the suject of cogniznce. Since Knt s Critique of Pure Reson we know, t lest logiclly, tht certin fetures of sujectivity 2

3 Gotthrd Günther Life s Polycontexturlity cn e interpreted in rtionl terms. And more recently, especilly since the dvent of cyernetics, it hs een demonstrted tht certin dt tht the clssic trdition judged to e "spiritul" or "trnscendentl" cn e unmsked s mechnisms. In other words: they re cple of ojectivtion nd technicl repliction so they cnnot hve n irrtionl root. However, since we insist tht the Aristotelin epistemology is vlid s fr s it goes, the only wy open to us is to sk ourselves whether this sis of knowledge might not e rodened. In order to do so let us go ck to the originl metphysicl ssumption from which Aristotle strts: Everything there is in the Universe shres in the generl ctegory of Being. And Being is identiclly the sme in ll ppernces nd vrieties of existence. As much s ny two things might differ in the predictes or properties tht elong to them, they re identicl qu Being. Being is the underlying sustrtum which crries everything nd which pervdes ll there is in exctly the sme wy. This mens: Being per se is s noted ove in itself totlly undifferentited. It is "symmetricl" hving no different properties in different prts of the Universe. The only distinction tht cn e ttriuted to it is tht it is distinguishle from Nihility or Nothingness. Nothingness nd Being re relted to ech other in such wy tht their mutul ontologicl position is defined y the logicl principle of the Tertium Non Dtur (TND). Something is or it is not; tht is ll there is to it in ontology. It is ovious tht the lterntive etween Being nd Nothingness is the solute widest tht our thinking my conceive nd we shll cll, from now on, domin which is chrcterized y n solutely uniform ckground nd whose limits re determined y n solutely generlized TND n ontologicl contexture or contexturlity. The role tht the TND plys with regrd to the concept of contexture indictes tht the structure of such domin cn e exhustively descried y two-vlued logic. At this junction it is importnt to rememer tht the TND which encompsses the domin must e the most generl tht is conceivle ecuse two-vlued logic implies n infinity of TND s involving prtil negtions. If we e.g. pose the lterntive "the defendnt is guilty or not guilty", then we encounter lso TND of sorts. But the rnge of terms is rther limited ecuse it extends only to juridicl concepts, nd it should e pointed out tht such TND does not constitute genuine contexturlity. We mke shrp distinction etween the fmilir term "context" nd "contexture". If we spek in every dy lnguge of context we do not imply universl TND the generlity of which cnnot e surpssed ut we mke this very impliction when we spek of contexture or contexturlity. We re now redy to see the deep ontologicl ssumption which lies ehind the epistemology of Aristotle. It cn e formulted s follows: the Universe is, logiclly speking, "mono-contexturl". Everything there is elongs to the universl contexture of ojective Being. And wht does not elong to it is just Nothingness. From ll this follows tht every logicl opertion we cn perform is confined to the contexturlity in which it origintes. It is trivil to dd tht no logicl opertion cn strt in Nothingness or continue there. But lso, if we count numers this process of counting, i.e., the sequence of numers, is confined to the contexturlity in which it origintes. You cnnot cross the orderline etween Being nd Nothingness nd still continue your process of counting. Such rguments re ovious. However, wht is y no mens self-evident is tht we hve to consider Nihility or Nothingness lso s n "ontologicl" contexture. The difficulty is 3

4 Gotthrd Günther Life s Polycontexturlity tht, if we insist on descriing Nothingness s contexture, we hve to orrow our terms from Being, nd doing so we discover we hve only repeted our description of the contexturlity of Being [1]. Nevertheless, the domin of Nothingness hs proved extremely useful in the history of humn thought. Whenever it ws ssumed tht Relity hrored rtionl s well s n irrtionl component the contexture of Nothingness served s the ontologicl loction for everything tht did not seem to e rtionlly conceivle. It lso served s the ontologicl locus into which the oserver of the world could e plced ecuse it ecme very soon evident in the history of logic nd of epistemology tht the clssic pttern of thinking with its concomitnt mono-contexturl ontology offered no plce for the oserver of the world or the thinking suject ecuse it would hve een surd to ssume tht the suject of cognizing elonged in the contexture of tht which ws cognized. On the other hnd, since tht which ws cognizle on principle constituted the possile rnge of world experience, there ws no plce for the suject inside the world. Thus humn thought unvoidly projected trnscendent domin eyond ll Being, nd Nihility served s very convenient vehicle for such projection. The most outstnding historicl exmple of such projection is the "negtive theology" of Dionysius Areopgit. The ontologicl domin of Being i.e. our first contexturlity hd its rnge of ojects generted y the TND (in the field of prtil negtions) nd if there ever existed ny greement in the history of logic, then it ws this: tht such logicl principle could not generte the ontologicl conditions for the existence of thinking suject. The reltion of the cognizing suject to its rnge of ojects is lwys one of discontexturlity [2]. Of course, this rgument should lso hve een vlid for the contexturlity of Nothingness, ut y trnsposing this contexture into supernturl Beyond, the mysterious Nihility ws exempted from such rigorous demnds. The first thinkers who roke consistently with the Aristotelin ssumption of the mono-contexturlity of this world were the trnscendentl-specultive idelists Knt, Fichte, Hegel nd Schelling. It ws especilly Hegel who pointed out (lthough in different terminology) tht Relity must hve poly-contexturl structure; nd tht it is impossile to ring two different contexturlities into n immedite confronttion. This lies ehind the provoking sttement in the first prt of his "Science of Logic" (Wissenschft der Logik) tht Being is Nothingness nd Nothingness is Being, nd tht they cnnot e distinguished in their immedicy (Unmittelrkeit) [3]. He then continued to demonstrte tht there is one sic ctegory which cnnot e hrored either in the contexture of Being (which represents sttic IS) or in the contexture of Nothingness. This is the ctegory of Process or Becoming (Werden). By showing how Becoming hs component of Being s well s Nihility, he unwittingly lid ground to theory of "poly-contexturlity". Becuse, if we wnt to estlish such theory, we should not ssume tht ll contexturlities cn e linked together in the wy geogrphicl mp shows one country ordering on the next in two-dimensionl order. If the contexturlity of Becoming overlps, so to spek, the contexture of Being s well s of Nothingness, nd the contexture of Becoming in its turn my e overlpped y fourth contexture which extends eyond the confines of the first three, we will otin multi-leveled structure of extreme logicl complexity. 4

5 Gotthrd Günther Life s Polycontexturlity Hegel s logic further shows tht if Tle II plurlity of contextures is introduced one cnnot stop with three. In fct, one hs to postulte potentil infinity of them. If one elieves Hegel nd there re most convincing rguments tht one should then ech world dtum in the contexturlity of Being should e considered n intersection of n unlimited numer of contextures. Tle II with its seeming chos of stright lines crossing ech other t ll possile ngles my illustrte wht is ment. Ech contexture is logiclly finite insofr s its structure is confined to two vlues. But their respective rnges re infinite ecuse one cn generte, within the respective domin, potentil infinity of nturl numers. We hve indicted the logicl finiteness of the different contextures y hving them represented y lines no longer thn 2 inches. In Tle II our contextures re ritrrily chosen nd wht they represent seems to e rther chotic jungle. However, we insist tht there is no such thing s chos in Relity. In fct, we my sy tht Relity nd Order re synonymous terms. If something is, it must hve order nd if it ppers s chos it only mens tht we hve not yet found the code which unrvels the seeming chos nd shows us the hidden order in the imroglio. There is no dout tht this Universe we live in displys n enormous mount of contextures in ewildering rrngement. Since we hve defined contexture, y reference to the TND, s domin the oundries of which cnnot e crossed y processes tking plce within the rnge of the domin, we re forced to ssume tht ll psychic spces of living orgnisms constitute closed contextures. It is self-evident tht the process of thinking tking plce within one person cnnot e continued into the psychic spce of second person. My thoughts, s mentl events, re only mine nd noody else s. A second person my produce the very sme thoughts; ut they re his nd cn never e mine. The concept of contexturlity illustrtes the ge-old logicl distinction etween identity nd smeness. If I count 1, 2, 3, 4, nd so does my neighor, then the numers we oth count re the sme. However, insofr s these numers hve their existence only in the counting process, they re not identicl ecuse the two counting procedures cn e clerly distinguished s hving different origins in two seprte orgnic systems. In other words: in the sitution descried ove the sequence 1, 2, 3, 4, turns up in two seprte contextures. And no mtter how fr I count there is no numer high enough to permit me to cross over to the psychic spce of my neighor. But wht we sy out ourselves nd our neighors is eqully vlid for every niml s fr s it hs consciousness, nd this lone shows tht the numer of closed contexturlities which crisscross this Universe is enormous. On the other hnd, if we spek out the Universe s whole, the very term uni-verse suggest tht ll contexturlities somehow form unit, the unit of contexturl existence 5

6 Gotthrd Günther Life s Polycontexturlity nd co-existence. We shll cll such unit compound-contexturlity. In other words: the confusing lines of Tle II must form, in their reltions to ech other, n order which constitutes unity. Prt II of our nlysis shll show how such n order or unity cn e detected. Prt II : Contexture nd Proto-Structure We hve insisted tht contexturlity is logicl domin of strictly two-vlued structure nd its rnge is determined y using the TND s n opertor such tht the generlity of the lterntive which the TND produces cnnot e surpssed. In other words: if we consider the Universe s compound-contexture it must e composed of n innumerle numer of two-vlued structurl regions which prtly prllel ech other or prtly penetrte ech other since, s we pointed out, ech oservle entity in this Universe must e considered n intersection of n unlimited numer of two-vlued contextures. This suggests the following ide: If we consider such point of intersection s elonging only to one contexture, the point cn only e occupied (consecutively) y two vlues. If we consider it s elonging to two contextures, the point will still only e le to e occupied y two vlues ut they my now elong to two different contextures. This mens: one vlue my elong to one nd the other vlue to the other contexture provided the contextures intersect t the plce which is occupied y the vlue. In Prt I we introduced the distinction etween smeness nd identity. The two-vluedness in ech contexture is the sme s the two-vluedness in ny other contexture. But this does not men tht let us sy the positive vlue in contexture A is identicl with the positive vlue in contexture B. But s the identity of the "sme" vlue chnges with reference to different contextures, we my lthough we insist tht our Universe displys in ech contexture strictly two-vlued structure introduce system of mny-vluedness with regrd to the identity prolem. Such system of mny-vluedness will not constitute mny-vlued logic which we my use s vehicle for our thinking. It will not descrie the Lws of Thought s produced y humn consciousness. It cnnot e done ecuse, ccording to wht we hve previously sid, the psychic spce in which thought processes evolve constitutes closed contexturlity nd is, s such, strictly two-vlued. But the projected system of mny-vluedness will form wht we shll cll n ontologicl grid which determines the reltions of the vrious contextures to ech other. It will e our next tsk to construct the most elementry form of such grid. We must strt, of course, with one-vlued system nd there is little to sy out it ecuse it cn only e represented y single symol nd no opertor is s yet ville to mnipulte it. Moreover, if y some mirculous method we could mnipulte it, this would entil trnsforming our symol into different one ut since no second symol is ville the only mnipultion which might e conceivle would mke our symol dispper. In order to otin system cple of positive mnipultion, we must turn to two-vlued system, which trivil to sy requires two vlues nd two plces to put them in. This leds to 2 2 = 4 possile comintions of the ville vlues, s shown elow: T F T F T F F T 6

7 Gotthrd Günther Life s Polycontexturlity where T mens, in clssic logic, "true" nd F "flse." However, since we insist on distinguishing plces from vlues which cn e put into plces we hve mens to tell re structure from the vlue configurtions which my occupy it. We shll use for empty plce structures the smll letters of the lphet nd it is ovious tht the letter sequence represents T T s well s F F nd tht stnds for F T nd lso for T F. If we proceed to three-vlued-system which mens, of course, dding one more vlue nd one dditionl plce we otin 3 3 = 27 vlue configurtions which shll e reduced in the sme mnner. Thus we otin the following plce structure: c So fr, so good. But since we re intent on reducing our structures to the rest possile minimum, we shll now stipulte stipultion not yet necessry in the cse of two-vlued logic tht the position of plce symol in given symol sequence shll e irrelevnt. This enles us to reduce the 5 verticl sequences ove to 3. So we get the following result: c We shll, for convenience s ske, lwys strt with the letter on top nd introduce only fter our store of s is exhusted. And c will follow when there re no more s ville to put them ove it, nd so on. Our next step leds us to system with four vlues nd four plces. Here the numer of comprle vlue configurtions increses to 4 4 = 256. In order to reduce this mount to size comprle to the previous plce structures, we dd nother stipulton which ws necessry neither in the cse of the two nor the three-vlued system. We shll mke the condition tht, in ddition to the former restrictions, only the symol for the first plce () my e repeted in single verticl column. This leds to the following drstic reduction. First step: c c c c c c c c d If we then ignore tht the position of our letters is relevnt, we otin (s second step) the further reduction to c c d However, since we will permit only one plce symol to e iterted, we hve to eliminte the centrl verticl column nd we otin s the finl result 7

8 Gotthrd Günther Life s Polycontexturlity c c d If we proceed to five-vlue system no further reductionl stipultions re necessry to otin the re minimum structure; nd this goes too for ll further increses in vlues nd plces. Thus we otin kind of pyrmid with single plce on top nd n ever rodening se t the ottom. For every vlue dded the se increses its width y one verticl column s shown in Tle III. This tle displys the most elementry structurl configurtion for plces corresponding up to 6 vlues. We hve connected y continuous lines the verticl columns of ever incresing length ccording to rule which shll e explined further on. We hve lso drwn dotted lines which seprte the letter sequences t the extreme left nd the extreme right from wht there is etween them. These vlue sequences, where on the left side the plce symol never chnges nd on the right side no letter is ever repeted in given verticl sequence, hve logicl chrcteristics which set the commonly prt from ll the other sequences. The letter rrngement in Tle III ws, in former pulictions of the uthor, clled "proto-structure" nd we shll use this term from now on. The proto-structure gives the ppernce of rther trivil structurl chrcteristics. But it contins, s we shll soon see, t lest one essentil feture which is nything ut trivil. We shll descrie it in contrst to nother pyrmid which stems from the dys of Plto nd which descries the reltion etween the genus proximum nd the differentie specifice in clssic two-vlued logic. This pyrmid strts t the top with the most generl term (the Pltonic Ide) nd Tle III c c c d c c d c d e c c d c d e c d e f Tle IV 8

9 Gotthrd Günther Life s Polycontexturlity reches down from there to the more nd more prticulr nd would hve, t the ottom, the set of ll irreducile individuls logicl gol which, of course, cn never e otined since the pyrmid is s ottomless s the one of proto-structure. Tle IV shows this pyrmid nd we see t once tht it illustrtes fmous metphysicl principle s pronounced in ntiquity. It is contined in the terse Pltonic sttement (the wy up nd down is one). If we wnt to trce the trck from one single point elow to the top of the Pltonic pyrmid, we notice tht there is one nd only one wy to do it. And if we wnt to return from the top to the very sme prticulr point, there is no other rod ut to retrce our originl steps. Wht this pyrmid depicts is the structurl pttern of n solute hierrchy where ll elements re linked y common mesure. This ssumption tht the universl dominntes the prticulr nd tht the reltion etween the two is totlly non-miguous hs governed ll ontologicl reflections s well s specific mthemticl nd logicl endevours for more thn two millenni. We my dd now, fter wht ws sid in Prt I, tht this order will lwys e vlid nd unimpechle, provided we restrict ourselves to closed contexturlity. If we now compre the Pltonic pyrmid with the pyrmid of proto-structure in Tle III, we re in for considerle surprise. We shll notice tht the ncient metphysicl thesis, tht the wy up nd the wy down re identicl, holds only for the symol sequences on the extreme left nd the extreme right, locted outside the dotted lines. In oth of these cses there is only one wy to go from the ottom to the top nd the very sme wy to descend from the top to the ottom. For ll the other sequences, however, this principle is invlid. We shll illustrte this with the wy the sequence issues from the sequences nd. We hve n equl right to sy tht our three-plce sequence is derived from y dding to it; ut we might s well sy tht emerges from y repeting the. This mens tht for ll the symol sequences inside the dotted lines there re vrious wys from the ottom to the top nd vice vers. And going down to the very sme plce we hve the choice of tking the sme wy we cme up ut we might s well, within the given limits of the structure, choose different route. This is the mening of the connecting lines etween the letter columns. They indicte the possile choices for scending or descending etween the top nd se of the pyrmid. This possiility of choice is very significnt ecuse it shows tht we my lso use the pyrmid of proto-structure s Pltonic pyrmid. It goes without sying tht y doing so we forfeit theoreticl possiilities which might e otherwise ville. Here we come to n importnt point in the theory of trns-clssic contextures. Since the dvent of the so-clled mny-vlued logics, conservtive logicins hve insisted gin nd gin tht there is no need to go eyond two-vlued logic nd tht every spect of the Universe wherever we look displys two-vlued structure [5]. This is perfectly true nd we re the lst to deny it. But the rgument misses the point. Wherever we extricte ny two dt from this world, we will find tht they shre in common contexture nd tht their reltions cn e descried y two-vlued logic. This test will never fil us. But since we pointed out tht every ontologicl dtum of the world must e considered n intersection of n infinite numer of contextures, the fct tht ny two dt we choose to descrie in their common two-vlued reltions elong to one contexture does not exclude tht the very sme dt my lso prt from the 9

10 Gotthrd Günther Life s Polycontexturlity contexturlity chosen for our description elong seprtely to dditionl nd different contexturlities. Our first dtum my, e.g., e n intersection of the contexturlities α, β, γ, λ nd the second my e intersected y the contextures β, δ, κ, π it. Wht we insist on, however, is tht ny two world dt we choose to compre hve t lest one contexture in common. They my shre in more ut it is impossile tht there is no contexturl linkge etween them t ll. If tht were the cse then one of the two dt would e "not of this world ". Another wy to put it is tht for ny two dt which shre given contexture there will lwys e third dtum tht is excluded from it. This is the mening of Hegel's insistence in the fce of the TND tht there is Third. When we compre the Pltonic pyrmid of the reltions of the genus proximum, nd the differentie specifice with Tle III, our comprison will not e complete unless we drw ttention to second difference prt from the violtion of the tenet y proto-structure etween the two pyrmids. In the Pltonic order of concepts only the very first ifurction of the pyrmidl structure my e interpreted s totl negtion etween positive nd negtive in generl. Since the numer of vlues represent simple dulity ll the wy down to the ottom of the pyrmid, ll susequent ifurctions led to prtil negtions. This is why logic sed on the principle of vlue dulity hs to sty within single contexture nd cnnot cross its oundries. The pyrmid of proto-structure, on the other hnd, does not del with prtil negtions t ll. Its ever widening scope is produced y the cquisition of new vlues nd consequently dds new contextures in ddition to the first on top which it shres with clssic logic, if we just mke generl comprison. However, since ny vlue (nd its totl negtion) my e chosen s n ontologicl deprting point for two-vlued system, we my consider the pyrmid of protostructure s n ontologicl grid which descries the mutul positions of single contextures. Furthermore: since clssic logic recognizes only single contexture the reltion of concepts to numers remins, notwithstnding the work of Kurt Gödel, rther undefined. Wht Gödel hs demonstrted is tht logic is cple of rithmetiztion. But his rithmetiztion concerns only the extensionl domin of logic nd ypsses those intensionl reltions where dilecticl principles come into ply. However, if we proceed from single contexture to poly-contexturl structures y incresing the numer of totl negtions, much closer connection etween concept nd numer is estlished. We shll tke the first step in this direction y ttching numers to our proto-structurl grid. This will give us the opportunity to discuss in Prt III some of the spects of poly-contexturl ontology nd its logicl consequences. Prt III : Pltonic Hierrchy nd Contexturl Heterrchy When we developed pyrmid of proto-structure we did so y dding with every step down one new plce for vlue occupncy. This ws done in twofold wy: we either repeted the originl symol or we dded new symol. We shll from now on cll the first method of increse "itertion" nd the second "ccretion." The symol sequences outside the dotted lines re, s Tle III shows, fully itertive on the left side nd on the right side fully ccretive. Wht is inside the dotted lines, is prtly itertive nd prtly ccretive with chnging rtios etween itertion nd ccretion. It is now very simple to ttch numericl vlues to ech of these symol sequences y counting the numer of 10

11 Gotthrd Günther Life s Polycontexturlity symols tht mke up the length of sequence nd y counting the numer of ccretions it contins. Our first symol "" will e counted s the first ccretion, nd y putting the numer for the length of the sequence first nd for the degree of ccretion second, nd seprting oth numers y colon, we otin for the numericl expression 2:1 nd for consequently 2:2. 2 : 1 Tle V 1 : 1 2 : 2 Peno : 1 3 : 2 3 : : 1 4 : 2 4 : 3 4 : : 1 5 : 2 5 : 3 5 :4 5 : : 1 6 : 2 6 : 3 6 : 4 6 : 5 6 : : 1 7 : 2 7 : 3 7 : 4 7 : 5 7 : 6 7 : : 1 8 : 2 8 : 3 8 : 4 8 : 5 8 : 6 8 : 7 8 : : 1 9 : 2 9 : 3 9 : 4 9 : 5 9 : 6 9 : 7 9 : 8 9 : : 1 10 : Tle V shows this numericl pttern up to 10 plces. On the right side we hve written the fmilir sequence of nturl numers s defined y the xioms of Peno nd which represent the ntique tenet tht the wy of counting up nd counting down is one nd the sme. Within the pyrmid we hve gin seprted the numericl sequences t the extreme right nd the extreme left y dotted lines from wht is inside the pyrmid. There is only one wy to go from 1:1 to 10:1 nd ck. There is lso only one wy to do this etween 1:1 nd 10:10 However, if we wnt to count from 1:1 to let us sy 10:5, there re lredy 126 wys to choose from. These choices increse very rpidly nd, if we would proceed to the numer Of 20:11, the wys we could count from 1:1 on would mount to different sequences. The increse of choices for ny n : m cn e derived from the formul n = m n! ( n m )! m! In other words: we cn red them off the tle of inomil coefficients. 11

12 Gotthrd Günther Life s Polycontexturlity In order to use proto-structure s n ontologicl grid for Tle VI contextures we shll project the Pltonic pyrmid in vrious wys onto proto- structure, s will e demonstrted y the following 3 Tles. In Tle VI we hve superimposed the Pltonic pyrmid in such wy onto proto-structure tht the pex of the two-vlued pyrmid coincides with 1:1 Proto-structure is indicted y dotted lines nd we notice tht the dichotomies of clssic logic only strt from certin intersections of the protostructurl grid which re seprted y incresing intervls determined y the squres of nturl numers. It seems tht this reltion etween logicl dichotomy nd the squres of nturl numers ws lredy discovered in the Pltonic cdemy nd some scholrs scrie it to Plto himself. On the next Tle VII we hve moved the pex of the Pltonic pyrmid one step down, nd we hve tken the left side of the ifurction t the top so tht the pex is now locted t point 2:1 of our proto-structurl grid. But we hve lso put into the sme grid second Pltonic pyrmid strting t 15:11 to illustrte our point further tht this grid encompsses n infinite vriety of two-vlued contextures. 15:11 is, of course, quite ritrry s strting point, nd we might s well hve used ny other intersection of the dotted lines. Tle VII Tle VIII Tle VIII finlly, ws drwn to remove the prejudice tht Pltonic pyrmid, if projected ginst the ckground of protostructure, must necessrily hve symmetricl 12

13 Gotthrd Günther Life s Polycontexturlity shpe. In Tle VIII we hve moved the pex of the two-vlued pyrmid ck to 1:1 And for the first two steps down we hve repeted the previous pttern. For the next step down (from 8:1 to 8:8) we hve still dhered to symmetry ut mde the lines of the dichotomies cross ech other. From the eighth level of proto-structure down to level 16 we hve ndoned the principle of symmetry nd drwn our isecting lines indicting two-vlued dichotomies in quite n irregulr mnner. This ws done to show tht wht is logiclly relevnt in the Pltonic pyrmid prt from the principle of dulity is only the tenet. Since one cn go only from one hevy dot to the next on the levels 1, 2, 8, 16 nd cnnot chnge stright lines t ny intersection in etween, the principle tht the wy up nd the wy down is one is still preserved, nd tht is ll tht mtters. Our configurtion of the hevy continuous lines still represents the Pltonic pyrmid lthough the eye my hve difficulties recognizing it s such. Our nonsymmetricl Pltonic pyrmid still constitutes n solute hierrchy in world where everything hs common ontic mesure. But hving common ontic mesure is only different expression for sying tht everything elongs to the sme contexture. Since we hve demonstrted the origin of proto-structure we know tht our grid determines only the reltive positions of individul contextures to ech other in Universe where only one ontologicl dtum (or one symol) is permitted to e iterted. In cse we discover tht this does not yield sufficient numer of contextures, we my proceed to more elorte grid y stipulting tht second, third, fourth nd finlly ny symol my e iterted. If we still stick to the requirement tht the plcement of the symol is irrelevnt, we otin configurtion which we hve clled (in different puliction) deutero-structure [6]. By gin projecting contextures ut this time onto deutero-structure we otin richer reltions etween the single contexturl domins nd, of course, even more contextures. However, since Science is instile in its demnd for precision in detils, in the next step we my require tht even the plcement of single symol in n individul sequence my e relevnt with regrd to the reltive positions of contextures to ech other. This leds to third nd ultimte grid which the uthor hs formerly clled trito-structure. So fr we hve delt with rdiclly formlistic techniques. But since our explortion of the world will lwys fce the prolem of the opposition etween pure form nd mtter in the sense of content of the form, we cn del with this prolem in the following wy: First let us rememer tht we otined proto-, deutero-, nd trito-structure y deling only with empty plces from which vlue occupncy hd een removed. The letters c d in Tle III signify nothing ut empty plces which cn e rrnged ccording to certin rules. This remins so in deutero- nd trito-structure. But fter hving reched this mximum of structurl configurtions, we my reintroduce vlues into these configurtions of empty plces s their contents. Reltive to the empty plce the ctul vlue which is inserted is something entirely contingent. In other words: the reltion etween plce nd occupying vlue corresponds to the distinction etween form nd mtter. However, this essy is not the proper plce to follow this trend of thought ny further. In fct, it cnnot e fully discussed unless the reltion etween pure form nd numer is further developed. According to Plto, numers occupy n intermedite plce etween the empyren relm of Ides nd the empiricl world of our sense. If this doctrine is true nd so fr it hs not een refuted then it is impossile to pply trns-clssic 13

14 Gotthrd Günther Life s Polycontexturlity (mny-vlued) logic directly to our physicl world. It cn only e done through the medition of numers. Epilogue Wht remins to e discussed is the significnce of the concept of contexturlity to the phenomenon of Life. It hs een n ncient elief tht Life, Soul or Sujectivity re phenomen which hve no ontologicl grounding in our physicl Universe. If we re to elieve Socrtes in the Dilogue "Phidon" the Soul stems from trnscendent world nd hs stryed into this mundne world only to return fter deth into the unfthomle Beyond. If we divest this ide of its mythologicl connottions, there remins n strct pttern of thinking which, properly modified, will hve to e recognized s vlid. We shll formulte it s follows: Between the innimte phenomen of this Universe nd the phenomenon of Life or Sujectivity there exists logicl rek of contexture. If we spek of Life, Consciousness, Soul, Thought or Will we refer to n s yet unexplored property of the Universe which we shll cll its discontexturlity. Wht clssic science hs investigted so fr is sujectless Universe; nd sujectless Universe presents us with rigorously mono-contexturl structure. The property of discontexturlity hs no plce in it. But when erly Mn discovered tht this Universe lso hrored the phenomenon of nimted mtter there ws no other wy to explin it ut to sy tht Mn hd not only to del with the forces of this World ut in ddition with trns-cosmic powers tht roke into this World from n unpprochle Beyond. When the world religions spek of Heven, or Hell they refer, in fct, to the phenomenon of discontexturlity. But since every higher religion is coupled with the unshkele elief tht this erthly relm is mono-contexturl, discontexturlity utomticlly ssumed the function of the orderline etween physicl relity nd spiritul Beyond. On the other hnd, the turn from clssic to trns-clssic thinking mens tht the mono-contexturl concept of Relity is ndoned nd replced y poly-contexturl theory of Existence which mkes room for the phenomenon of Life within this Universe. In poly-contexturl Universe we do not hve to consider Life s n element totlly lien to innimte mtter, ecuse mtter in itself lredy contins the seeds of Life in its dilecticl contrposition of Being nd Nihility. It is, of course, still vlid up to point to consider the "mteril" sustrtum of this world s mono-contexturl (nive mterilism). But it will e necessry to consider ll living orgnism s poly-contexturl structures. For the clssic trdition there is complete rek etween Life nd Deth. It is theoreticlly, lthough not prcticlly, possile to fix the moment of Deth s the time when the Soul deprts from the ody. From the poly-contexturl spect of living ody this is on principle impossile, ecuse Deth mens only grdul decrese of the discontexturlity of Mtter. We re eginning to lern tht the discontexturlity of humn ody, e.g., is enormous; the numers of contextures tht re involved re superstronomicl. And since the phenomenon of discontexturlity lso involves the reltion of n orgnic system to its environment it is quite legitimte to sy tht something my e live reltive to one environment nd ded reltive to nother n ssumption tht would e surd if we 14

15 Gotthrd Günther Life s Polycontexturlity defined Deth s the deprture of unit Soul from inert mtter it hd previously nimted ut hs cesed to inhit. One finl word regrding the "seculriztion" inherent in the concept of discontexturlity: when we sy tht the immnence of erthly existence is seprted y metphysicl yss from the trnscendence of Heven nd Eternity we imply, first, tht "Being" in our physicl world is not the sme s the "Being" of Heven or Hell. In other words: there is n ontologicl difference etween the two, s ll gret world religions hve insisted. Second, we postulte tht ll our sujective stirrings s perception, feeling, willing, nd thinking will rek down t the rrier etween the Here nd There. The Beyond is only conceivle s mysterium of which we my know only y divine Reveltion. It should e kept in mind tht, if we postulte polycontexturl Universe, the rriers of discontexturlity which now cut through this empiricl world, hve lost nothing of their intrnsigency y eing multiplied. But just the sme the sitution is different. Since the clssic trdition permits only one discontexturlity, i.e., tht etween the so-clled physicl nd the so-clled spiritul there cn e no such thing s linking two elementry contextures into compound contexture, for this would require minimum of three contextures. One of the three would hve to medite etween the other two. In other words: we would e provided with contexture descriing the phenomenon of discontexturlity. This is the point where dilectic logic strts. The point is reflected in theology in the sttement tht the lmighty God rules Heven nd Erth. In order to give credence to this clim theologins hve dogmtized tht the Divine hs to e understood s Trinity dogm which gin is cple of seculriztion. However, s soon s we dmit the possiility of trinitrin compound structure, the gtes re open for the cceptnce of compound contexturlities emodying n infinite sequence of higher complexities. Notes nd References 1. In order to clrify the mutul positions of Being nd Nothingness it might e sid tht they re distinguishle s domins ut indistinguishle with regrd to their rnge. 2. See G. Günther, "Cyernetic, Ontology nd Trnsjunctionl Opertions" in Self-Orgnizing Systems 1962, M. C. Yovits, G. T. Jcoi, nd G. Goldstein (eds.), Sprtn Books, Wshington, D. C, p There the discontexturlity of vlue is estlished y its hving rejection function. 3. Hegel, Cf. "Wissenschft der Logik", WWIII, Meiner (ed.), 66-67, G. Günther, G. "Nturl Numers in Trns-clssic Systems", BCL Report No. 3-4, AFOSR , AFOSR , Deprtment of Electricl Engineering, Engineering Experiment Sttion, University of Illinois, Urn, 42 pp. (1970) 5. It is significnt tht such recent hndook of Logic like Normn L. Thoms "Modern Logic", first pulished in 1966, refers to mny-vlued logic only in footnote (P. 92) Of two (!) lines. (Pul. Dmes & Noel, New York, fifth printing, 1970) 6. See gin BCL Report No. 3.4 (Nov. :1, 197o) nd G. Günther, "Time, Timeless Logic nd Self-Referentil Systems" in Annls of the New York Acdemy of Sciences, 138, p , (1967) Copyright 2004 This mteril my e freely copied nd reused, provided the uthor nd sources re cited printle version my e otined from 15


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