Schelling Concept of Self Organization

8/12/2019 Schelling Concept of Self Organization

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Schelling's Concept of Self-OrganizationM. L. Heuser KeBlerPhilosophisches Institut der Heinrich-Heine-Universitiit Dusseldorf,Universitiitsstr. 1, W-4000 Dusseldorf 1, Fed. Rep. of Germany

Abstract: In the early 19th century the classical Naturphilosophie of P.WJ.Schelling (1775-1854) had many repercussions in the sphere of science. The termself-organization was originally introduced by I Kant to characterize processesof organic nature. Schelling was the first to extend the concept to inorganic nature, for he applied it to the complete evolution of the universe, from theprimordial beginnings of matter up to the origin of life and human mind.Schelling attempted to go beyond the contemporary mechanistic theory of natureby designing a program for science that would focus on the self-creation oforganizations . Of course he could not fall back upon elaborate scientific theories of self-organization, and at his time even empirical phenomena of self-organization were scarcely known. So Schelling created a speculative physics whichwas based on philosophical principles and intended to yield a systematic explanation of the history of nature. This paper will deal especially with the origin ofSchelling's concept of self-organization, the specific meaning of this concept inthe context of his work, and his method of construction. Apart from that it will beshown how the reception of Schelling's ideas in 19th century science led to firstattempts at mathematical theories for a non-mechanistic concept of nature, especially concentrating on the works of Bernhard Riemann.

1. IntroductionSchelling's works on Naturphilosophie - especially those of the early phase:Ideen zu einer Philosophie der Natur (1797), Von der Weltseele, eineHypothese der hoeheren Physik zur Erklaerung des allgemeinen Organismus(1798), Erster Entwurf eines Systems der Naturphilosophie (1799), AllgemeineDeduktion des dynamischen Prozesses oder der Kategorien der Physik (1800),but also those of the later period: Die Weltalter (1811/1813), Darstellung desNaturprozesses (1843/44) - represent a first extensive attempt to establish atheoretical basis for a scientific treatment of the history of nature and of the selforganizing character of the inorganic, organic, and cognitive spheres. Hisobjective is to find the universal principles of the productivity of nature , whichcan explain on an evolutionary basis the underlying unity of organic andinorganic nature, but also the unity of the external, visible nature with ourinternal, invisible nature.Springer Proceedings in Physics, Vol. 69Evolutlon of Dynamical Structures in Complex SystemsEditors: R. Friedrich A. Wunderlin SpringerVerlag Berlin, Heidelberg 1992


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396Schelling believed that the creative productivity of man - which is responsiblefor the fact that human beings have a history - is intimately connected with theprocess of nature as a whole. As a consequence the innovative faculties peculiarto human beings do not separate or distinguish them from nature. On thecontrary, it is the core of nature which is reflected in human creativity. Incontrast to the transcendental philosophies of Kant and Fichte, which are concerned with the productive powers of the spirit, Schelling proceeds from the pre

sumption that - apart from man's faculty to build up a world in theory - natureitself must have created the diversity of organizations in reality. In his ErsterEntwurf eines Systems der Naturphilosophie of 1799 Schelling stated thefollowing as a first principle: .. nature takes its reality out of itself - it is its ownproduct - a self-organizing and self-organized whole. /'13, i l l p.17/ For Schellingthis means that nature has unconditional reality , that it does not depend onexternal conditions, but is self-creative, and he assumes that there must be alsoempirical evidence for this process of self-organization. The Unconditional - aterm that has often been misconstrued - is nothing other than the originalproductivity which produces each level of development in a non-mechanisticmanner, i.e. without external determination.

On the basis of this fundamental principle of self-organization Schellingcriticizes the empiricism as well as the mechanicism of his age. Empiricism - sohe argues - takes the objects of nature as given and then proceeds to observation,analysis and description of the relations pertaining between them. Thereconstruction of the origin and genesis of natural objects - according to him theprimary task of a future science - is left out of account. Schelling writes: Thedifference between empiricism and science is based on the fact that empiricistsconsider their object as something complete and as a product, whereas scienceobserves the object in the process of emerging and as something that has yet tobe brought about. /23, III p.283/ Schelling's intention was not to advocate ascience without empirical methods. But it was important for him to construe theobjects of experience as products (natura naturata) of an original generative process (natura naturans). This process can only be understood by an unbedingterEmpirismus , i.e an empiricism with respect to the self-construction of nature.The mechanistic theories of nature were criticized by Schelling for limiting theirexplanation to external causation, an approach which excludes a self-organizingprocess of nature right from the start.I. Kant had shown that there are at least two areas which cannot beadequately described in mechanistic terms: the area of living things and the areaof practical reason that is based on freedom. In his Critique of Judgment hehad analysed in detail that organisms are not susceptible to mechanisticexplanation. He was the ftrst to introduce the term self-organization in order tocharacterize the dynamic process of the organic sphere as opposed to themechanic sphere of physics. Kant puts it this way: An organized being is,therefore, not a mere machine. For a machine has solely motive power, whereasan organized being possesses inherent formative power, and such, moreover, asit can impart to material devoid of it - material which it organizes. This,


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397therefore, is a self-propagating formative power, which cannot be explained bythe capacitiy of movement alone, that is to say, by mechanism. - We do not sayhalf enough of nature and her capacity in organized products when we speak ofthis capacity as being the analogue of art. For what is here present to our mindsis an artist - a rational being - working from without. But nature, on the contrary,organizes itself, and does so in each species of its organized products - followinga single pattern, certainly, as to general features, but nevertheless admittingdeviations calculated to secure self-preservation under particular circumstances. /16, p.557/ In an organized being every part is thought of as owing itspresence to the agency of all the remaining parts, and also as existing for the sakeof the others and of the whole. Every part is an organ producing the other parts.Therefore Kant writes: Only under these conditions and upon these terms cansuch a product be an organized and self-organized being, and as such, be called aphysical end. /16, p.557/One can in particular deduce from Kant's choice of examples that his interpretation of the term self-organization differs from modem usage. He doesnot refer to the origin of organization, but to the reproduction of existing organized beings, especially those of organisms. Kant excluded the evolutionary perspective as a daring venture on the part of reason /16, p.579/ and refrainedfrom taking up the topic of the emergence of life from the inorganic sphere,which would have led him to questioning his mechanistic concept of physics. Hedeclared Newton's physics to have unrestrictedly validity. To him a physics ofself-organization was unthinkable. Therefore he only accepted the concept ofself-organization in biology as a merely regulatory but not as a constitutive principle. The limitations of Kant's concept were fully realized by Schelling. He extended the concept of self-organization as an emergent process to the whole ofnature and to the coming about of new forms of organization as opposed to thereproduction of existing ones. Schelling writes: The whole of nature, not only apart of it, should be like an ever-becoming product. All of nature must be thus inperpetual formation, and everything must be included in this process. /23, mp.33/ The history of nature is thus for Schelling a progressive Potenzierungsproze6 which goes from the simplest to the highest and the most complex. /23,IVs.89/Before one can draw a parallel between Schelling's idea of self-organizationand the modern one /8/, we have to take into account that he developed thisidea as a philosopher and not as a scientist. As a consequence of his interest inNaturphilosophie he succeeded, however, in making himself familiar with thestate of the art in contemporary science, and his philosophical reflections arecertainly on the level of the scientific knowledge of his period. At that time therewas no such thing as a physics of self-organization, not even an accepted theoryof evolution in biology. Lamarck published his work Philosophie Zoologiqueonly in 1809, and Darwin his Origin of Species in 1859. Not even empirical phenomena of self-organization in the sphere of physics were known. The Laser,Benard cells, the Belousov-Zhabotinsky-reaction were all completely unknown atthe time. The only processes in physics which Schelling could point to were


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398hydrodynamic whirls, crystallization, chemical and physiological processes.Nevertheless Schelling adopted the far-reaching hypothesis of a universal self-organization of nature as the central principle of his Naturphilosophie andfurthermore attempted to establish a preliminary theoretical basis for a futureresearch program of a science of self-organization. There was no chance for thisprogram in the 19th century, because neither the necessary instruments of empirical research nor the mathematical theories were available. So the advocates ofa mechanistic theory of nature won their case as opponents of the Schellingschool in a polemic disqualifying dynamic Naturphilosophie as speculative pipedreams . As a consequence Naturphilosophie as a discipline almost fell into oblivion.Schelling himself was quite aware of the fact that his project could not bemore than a preliminary stage. He was primarily concerned with stating the factthat nature is not a static and mechanistic system, but a progressive genesisproceeding from the origin of inorganic systems up to the emergence of humanconsciousness /23, X p.229/. He compares the intention of philosophy to explainthe fact of the world with the role of experiment in science and writes: Nothingseems easier than naming the fact that philosophy has to explain. But think of allthe work and efforts which are necessary in science to arrive at a single true factconcerning a simple phenomenon. People will say: philosophy is supposed to explain the fact of the world. But what about this world is the fact? /23, X p.2'lJ3/The genesis of nature could be considered as a hypothesis and submitted to experimental treatment only after certain experiences with respect to the self-organization and history of mankind were made resulting in a new self-image of mankind, which were formulated by the philosophers of the Enlightenment (moreabout this in the next section).Schelling regretted greatly the limitations of contemporary experimentalscience: The more we describe the sphere of investigation, the more we see howscanty and defective the relevant experience is, and few will feel this imperfectionmore deeply and vividly than the investigator himself. /23, II p.351/ Schellingthought that still he deserved credit for at least having dared anything at all inthis science, so that others may be in a position to practice their wit by detectingand refuting the errors. /23, II s.351/His courage in formulating new hypotheses was rewarded. Though Schelling'sNaturphilosophie was criticized by scientists and philosophers of empiricist andmechanistic standing, it was received favourably in mathematical physics, and itseems to have survived there in covert and transformed shape the attacks of 19thcentury science. Schelling's Naturphilosophie can be shown to have served as anorientation and guideline for a whole generation of theoretical physicists, whocreated an abstract science of physics working with mathematical-theoreticalmodels besides the concrete science of physics with its strong empirical bias.(viz. Caneva who shows this for the context of electromagnetism, /1/). Someexamples of this can be also drawn from the work of a research project that isunder way at Duesseldorf University. Unfortunately this project is still in its early


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399stages so that results cannot be fully stated as yet. One of its objectives is to explore the historical continuity of Schelling's philosophy of self-organization intopresent-day physics of self-organization. Apart from that the project intends toexamine the chances to maintain Schelling's concepts under present conditions inthe light of certain mathematical considerations which were made in the 19thcentury. This would require a detailed analysis of the particular mechanjsms conceived by Schelling in his speculative physics and an analysis of the works ofthose mathematicians, who were influenced by Schelling's philosophy, but thisanalysis is still under work, and so only the general ideas can be presented.One of the mathematicians influenced by the philosophy of Schelling isHermann Grassmann, who in his Ausdehnungslehre of 1844 developed a vector calculus for multidimensional space in order to formulate better explanationsfor morphogenetic processes. He applied his new mathematics especially to theprocess of crystallization and tried to find a more adequate mathematical basisfor the dynamic principle of Schelling's philosophy. It is interesting to see howclosely his abstract conception of multidimensional power space is connectedwith Schelling's concept of space as developed in Allgemeine Deduktion des dynamischen Prozesses oder der Kategorien der Physik (1800). According toSchelling, space is not the empty Euclidean space or a Kantian form of pure intuition, but constituted by means of magnetism, electricity, and chemical process.The three dimensions of space are not an absolute fact but attributable to particular physical conditions / also see 17/.Schelling's ideas had a great impact on those theories of crystallization in theearly 19th century which were based on dynamic principles. In the visible shapeof crystals they saw the c;xpression of an invisible system of production principles,and they were the first to introduce point symmetries and description in terms ofvectors to the theory of crystals. Prominent in this sphere were Christian SamuelWeiss and Justus Guenther Grassmann, the father of Hermann Grassmann./27/Bernhard iemann was also familiar - by way of. Herbart and Fechner - withSchelling's Naturphilosophie , as we can learn from his posthumous writings,which have not all been published yet. He laid the foundations for mehrfachausgedehnte Mannigfaltigkeiten (multiply extended manifolds) with differentmetrical systems and for non-Euclidean geometry, which at first sight seemed tocontradict empirical evidence. Before he wrote his thesis for habilitation Uberdie Hypothesen, welche der Geometrie zugrundeliegen (1854) he was - to followhis own words - almost exclusively occupied with Naturphilosophie with the intention to establish a novel conception of nature that would go beyond mechanistic theories and be based upon an integration of magnetism, electricity, lightand gravity. The relation between Schelling and Riemann will be elaborated later. What concerns us here is that Schelling's speculative method was adoptedespecially by those mathematical physicists who undertook a (field-theoretical)construction of material phenomena on the basis of abstract mathematical consi-derations and whose overall objective was to find the dynamical organizing principles of nature. These principles cannot be extracted from the data, but are supposed to be the synthetic-constructive generation of the phenomena.


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400As historians of science have very well pointed out the pioneers of field theoryin physics were mostly advocates of Schelling's philosophy (for further literaturesee /8/): i.e. Oersted, who was encouraged by Schelling's ideas to look for experimental evidence of the connection between electricity and magnetism. Thanksto Naturphilosophie he was in a position to give a coherent interpretation to hisobservation of the fact that a magnetic needle is deflected by electricity. Withoutthe particular theoretical guideline the special significance of this observationwould have escaped him. Faraday, whose mentor Humphry Davy was an admirer

of the ideas of Coleridge, an intimate connoisseur of Schelling's works, discovered that the relation works the other way as well: magnets can induce electriccurrent. (The macroscopic standpoint of coherence in Haken's theories was likewise induced by field physics. The enslavement of the particular motions of electrons is due to the amplitudes of the light field, even i f conversely the amplitudesare generated by motions of the electrons.)Last but not least William Rowan Hamilton, to whom we owe an abstractformulation of mechanics, was a follower - via Coleridge - of the dynamicalconcept of nature created by Schelling and Kant. /4/

2. How Did Schelling Conceive the Idea of Self-Organization?In the introduction of his first work concerning Naturphilosophie , i.e. Ideen zueiner Philosophie der Natur , Schelling remarks: We are still pressed by thesame failure to understand how mind and matter can be connected. One can tryto conceal the harshness of the contrast by all kinds of illusions, we can insertmore and finer intermediate stages between matter and mind, but still we fmallyget to the point, where matter and mind must either unite or the great leap wewanted to avoid all the time becomes inevitable, and this is the same in all theories ( ..) We leave man behind as the visible and walking problem of philosophy./13, II 53sqq.j In order to solve this problem, Schelling formulated as a preliminary integrative objective the following postulate: Nature shall be visible mindand mind shall be invisible nature. /13, II p.54/How are these formulae of identity philosophy to be interpreted? At firstsight we could be persuaded to assume that Schelling is expressing an epistemological relation, because human mind recognizes nature or at least tries to do so,and by the process of cognition pervades natural mechanisms and thus transforms them into something spiritual. Of course the sciences are not themselvesnature, but at least they are implicitly based on the assumption that nature issusceptible to cognition. It can be expressed theoretically and thus spiritualized.On the other hand our mind must be in some way related to nature, becauseotherwise the mind wouldn't be able to recognize the nature.

But Schelling wants more than this epistemological relation between mindand nature. According to Schelling we not only expose an epistemic attitude towards an existing world. We are creative beings, and to that extent we have a hi-


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401story. Human beings are not inherently limited to a particular biological programof behaviour. This recognition was the deciding factor of the Enlightenment ,which was taken up by Schelling. Accordingly we differ from animals in our faculty to liberate ourselves from existing conditions and circumstances. In a waywe can separate ourselves from immediate experience and abstract from empirical data. This faculty of abstraction is the prerequisite for our ability to set asideall particulars and situational elements in order to reflect the whole fundamentally and with respect to its principles (= philosophy). With our criticalassessment of the fundamentals of a given situation we can invent alternatives,improvements and new circumstances, in the sphere of science as well as insociety.The invention of new systems is an expression of the creative nature of mankind, which is not exhausted in one particular system or satisfied with oneproduct. We fmd in ourselves an infinite tendency to self-organization, thatpervades all formations without ever completely realizing itself. Schelling's earlyhypothesis (1796/1797) is the following: In our mind we find an infinite strivingfor self-organization, and something like this must also reveal itself in theexternal world as a general tendency towards organization. And it is really so.The system of the world is a kind of organization extending from a commoncentre. The powers of chemical matter are already beyond the limitations of themerely mechanical. Even raw matters settling out of their medium form regularfigures (i.e. crystallization M.H.). /23, I p.386/

This is the background for Schelling's postulate that nature be visible mindand mind invisible nature . It means that the productivity of human mind, whichis responsible for our having a history, is not a point of separation or distinctionbetween man and nature. On the contrary, productivity is at the core of nature.Nature produces out of itself the whole diversity of natural products, includingourselves. This unconscious activity of nature is basically identical with what wedo consciously. Thus productive nature is visible mind with respect to reality, andproductive mind is invisible nature with respect to ideality. Schelling's philosophyis essentially a philosophy of productivity. The transcendental part of Schellings'sphilosophy takes care of epistemology. It explains the reality of visible natureideally, i.e. theoretically, whereas philosophy of nature explains the ideal on thebasis of the real. With his Naturphilosophie Schelling is seeking a physical explanation of idealism , i.e. an explanation for the question how we could erupt atthe borderline of nature the way we did. f self-organizing mind is a product ofnature, then nature cannot be a merely mechanical system. It must at least havemade freedom possible.

3. Schelling's Method of Construction and MathematicsSchelling derived his concept of construction from Kant's philosophy of mathematics, as described in The Critique of Pure Reason . In Kant's view, only mathematics is able to construct objects by non-empirical intuition and to make a


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402priori synthetic judgements, so that mathematics is the only science which presents the most brilliant example of the extension of the sphere of pure reasonwithout the aid of experience /15, p.211/. For Kant, creativity which goesbeyond experience and constructs new objects not learned from experience, isonly possible in mathematics. Kant argues as follows: When for example thegeometrician conceives a triangle, he makes not a specific, empirical triangle, butthe, general, invariant triangle form, which includes all possible triangles, whatever their size, position or special shape. He constructs the general in the particular , meaning the general conception of the triangle form, which is still a specific general conception in contrast to other geometrical figures, such as the circle.According to Kant: The construction of a conception is the presentation apriori of the intuition which corresponds to the conception. For this purpose anon-empirical intuition is requisite, which, as an intuition, is an individual object;while, as the construction of a conception (a general representation), it must beseen to be universally valid for all the possible intuitions which rank under thatconception. /15, p.211/According to Kant, only the mathematician can construct objects independentof sensory experience and develop new insights because he constructs in the formof pure intuition of space. The geometrical figures are each specific limitations ofspace and concern the form of reality, not the matter. Accordingly, only sizes canbe constructed, i.e. shown a priori in the intuition, whilst qualities can only beregistered a posteriori. Therefore natural scientists, like philosophers, can onlylearn things by experience. Natural scientists structure these experiences underthe category of causality; philosophers sub-classify individual experiences undergeneral conceptions discursively.Schelling disputes Kant's view. According to him, creativity is also possible inother fields besides mathematics. In particular, it must be possible forspeculative physics to construct natural objects in terms of both form andmatter if one wishes to go beyond the mere surface of phenomena and reveal theinternal drive system of nature s self-construction (also see /12/, /13/). Asnature itself produces things by means of an original process of generation, itmust also be possible to apprehend nature s self-construction in theoretical termsif there is to be a science of nature that not only describes these manifestationsphenomenologically, but also aims to explain them. The natural objects and phenomena we perceive can only be a provisional starting point and must be thestarting point, for, according to Schelling: 'We do not know only this or thatthrough experience; rather, we originally know nothing at all except throughexperience and by means of experience, and, in this respect, our entireknowledge consists of sets of experiences. /23, III p.278/ But - and, according toSchelling, this is the starting point for science - these sets of experiences must betransformed into sets a priori by recognizing their inherent necessity. We gainsuch insight into their inner necessity, and thereby certainty about nature, whenwe penetrate the inner constructional and evolutionary principles of nature itself,from which individual natural phenomena can then be explained as products.

To illustrate his notion of construction, Schelling cites the example of anengineer. The person who really knows a machine is not the one who perceives it


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403through his senses and merely describes its outward appearance and names theparts, and it is also not the one who analytically dismantles it, then reassemblesthe parts, and, in this way seeks to unravel its functions (although this methodwill reveal considerably more than a mere description), but it is the engineer whoinvented and built it. Not only does the inventor know how each part relates tothe other parts, but also how the machine itself and above all its total complexityand coherence originally came into being. He knows the idea of the machine byhaving conceptualized the ftrst prototype. Schelling's method of construction isessentially orientated to the paradigm of the inventor and artist, not to thearistotelean paradigm of the craftman, who normally works from the traditionalprototypes and does not create his own.Schelling's idea, then, is that it is not just the inventor who creates qualitatively new entities in the form of prototypes, but that nature does this as well byway of a process of self-organization - but in this instance not ideally, but reallyby means of natural powers. For example, with the construction of the fIrst livingcreature, a prototyP' of organismicity is produced that is a specifIc general forminsofar as it is a new l ype of natural object that essentially differs from inorganicobjects. Thus, the ftrst living creature is an identity of the particular and thegeneral, the lasting invariant of which - in contrast to Kant's example of thetriangle - is not to be found in the mere outer form, but in a specifIc productiondynamism. By deducing this prototype of production dynamism from principlesof self-organization, the natural scientist proceeds just as constructively as amathematician. Unlike Kant's geometrician, who constructs invariants of specifIcgeometrical objects, according to Schelling, the natural scientist should seek toconstruct invariants of process types, from which the entire multiplicity of aspeciftc sphere can be derived.Another important difference to Kant's example is that the geometricianconstructs his objects as limitations of space, while in Schelling's example, thephysicist constructs the speciftc spheres as limitations of natural activity byapplying a principle of inhibition. Like space, which is not a single object andtherefore cannot be grasped through empirical but only through non-empiricalintuition, the original activity of nature also can only be perceived by nonempirical intuition. Only the objects of nature and their changes can beempirically experienced, but not their original construction. (Note 1) Because ofthe possibility of conceiving the original productivity of nature by means of nonempirical intuition, it follows that speculative physics also can apply theconstructive method.Schelling endows the basic invariants of all Being with a certain dynamism.Not the atoms in absolute space and absolute time and the forces interacting withthem are the basic invariants, but the process of self-construction in its unlimiteddeftnition. For Schelling Being in itself = activity (more about this in the nextsection). In his Allgemeine Deduktion des dynamischen Prozesses oder derKategorien der Physik Schelling tried to demonstrate this fteld-theoretically interms of magnetic, electrical, and chemical processes. Further research would beneeded to determine whether or not he succeeded. Schelling also postulated that


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404the process of self-construction is in some way linked to a unification of the geometrical continuum and arithmetical discontinuum. /13, V 125 sqq./The limiting conditions, i.e. inhibitions, of unlimited natural activity each determine certain spheres (transformation groups) of nature, which can be characterised by specific forms of production. For Schelling evolution is not a chainof product stages but a chain of productivity. According to Schelling: To date ithas been claimed that every organisation corresponds to a certain developmentstage. I can now claim the reverse: the diversity of the stages alone accounts forthe diversity of organisations. /13, III p.54/ The different stages of developmentare not designated by objects and their invariants, but by production and their invariants. Invariants of specific types of production result from restrictions of unrestricted activity by the inhibition principle. Schelling writes: Each stage of development thus has its own character. At each stage of development, nature isrestricted to a certain only one possible Gestalt, in respect of this Gestalt sheis completely tied, in the production of this Gestalt she shows no freedom. /13,III p.43/ The fIXation of development at a certain development stage is not thesame as nature being entrenched at this stage. For in Schelling's words ondynamic systems: That the product is inhibited at a certain development stagedoes not mean that it ceases to be active, but that it is restricted in itsproductions, i.e. it can reproduce ad infinitum nothing but itself'. /13, III p.59/If, like Schelling, one postulates a history of nature that has successively produced different evolutionary stages and successively created the levels of inorganic, organic and cognitive nature as various Potenzierungsstufen'., the construction of inorganic matter must then be the most basic work of the naturalsciences, from which all other stages must derive. Schelling does in fact representa certain physicalistic standpoint. He is of the opinion that the theory of the selfconstruction of matter is the basis for the theory of the origin of life and the biological evolutionary process. Schelling rejects the vitalistic point of view.According to him, life must be explainable in physical terms, otherwise it is impossible to comprehend its origin from inorganic matter. /9/ For Schelling, evolution is selfsimiliar because of the recurrent self-construction of matter at various stages . The theory of the history of nature is therefore equivalent to thetheory of the self-construction of matter. /13, VI p.4/According to Schelling: The only task of the natural sciences is: to constructmatter. This exercise can be solved, although the application derived from thisgeneral solution is one that is never complete. f t were the intention of a generaltheory of nature to reach a consciousness of the infinite multiplicity and depth ofphenomena, which are unconsciously produced in nature, it would have to beconsidered an impossibility. /13, IV p.3/ To penetrate the endless variations ofnature's products in detail would be an exercise far beyond all our finite powers.Schelling therefore takes the view: Our entire effort can only be dedicated toresearching the general principles of all nature's productions - their application,however, which extends in all dimensions into infinity, must be regarded as anunending exercise. /13, IV 3 sq./

It was Schelling's basic idea that it must be possible to construct the objects ofnature from a few underlying, physical production principles. His aim was a


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405unified theory of the history of nature. Given the limited knowledge of thenatural sciences and mathematics at that time, this demanding researchprogramme could not be carried out in Schelling's day. However, it encouraged anumber of scientists to look for nature's basic process invariants, for exampleRobert Mayer, an admirer of Schelling, who formulated the principle of energyconservation.By attempting to establish the construction method which Kant wanted toreserve for mathematics in the realm of physics as well, Schelling philosophicallyupgraded theoretical physics. Schelling was thus fascinated by Le Sage's theoretical mechanics because they deduced the whole structure of this science from afew basic principles. Schelling merely thought that the principles of mechanicsshould be supplemented by dynamic self-organisation principles. By the sametoken, there were a number of theoretical physicists who appreciated Schelling'smethodical approach. Hamilton can be cited as representative of many: ''Thereare, or may be imagined, two dynamical sciences: one subjective, a priori,metaphysical, deducible from mediation on our ideas of power, space, time; theother objective, a posteriori, physical, discoverable by observation as a generalization of facts and phenomena. /4, p.179/

It was also Schelling who realized early on that a theory of natural history instrict terms of a priori-constructions is problematic. In an interesting workentitled Is a Philosophy of History possible'l (1797/1798) he stated: whateverhas to be calculated a priori or happens according to necessary laws, is not theobject of history; and in reverse, whatever the object of history is, does not needto be calculated. /23, I p.467/ Calculable processes, according to Schelling,include all periodically recurring events. Consequently, history cannot happen inperiodical cycles, but must be progressive . However, this progress, if historical,can only be based on freedom which enables specified boundaries, or spheres, tobe exceeded. In this essay, Schelling therefore concludes that an a priori scienceof history is not possible, for such a science would have to show the necessity ofevents which would effectively exclude freedom. In his subsequent writings heattempts to solve this problem by assuming a law of freedom , in which necessityand freedom are not opposed and which occurs in the transition from one sphereto another. Schelling's definition of freedom should not be confused withcoincidence or mere arbitrariness. In the case of mere arbitrariness we wouldonly be infinitesimally different from Buridan's mule, who could not decidebetween two haystacks of the same size and composition at the same distancefrom each other. Truly free are those who can transcend causal connections andshape them autonomously. Here, again, as already mentioned at the outset,abstract thjnkjng is required to lead us to a higher plane. According to Schelling,nature's freedom is not demonstrated so much in incidental fluctuations, but inthe production of higher levels of multiplicity or Potenzierungsstufen , whicheach determine a higher hierarchy level.


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4064. Schelling's Speculative Physics of Self-OrganizationSchelling published several drafts on the physics of self-organization. TheIdeen einer Philosophie der Natur (1797) is still strongly influenced by Kant'sproblem of self-reproduction of the biological sphere. In his subsequent workDie Weltseele (1798) he explores for the ftrst time in detail the question of theorigin of life from the inorganic sphere and, since he considers both physiological chemism and the vitalistic position as inadequate, he is driven to the problemof outlining a physics of self-organization. In his paper Erster Entwurf einesSystems der Naturphilosophie (1799) he explores the idea of a systematic natural history which attempts to deduce all evolution from basic principles of selfconstruction of matter. This idea, that only a theory of the original genesis ofmatter and its organization can provide a basis for an evolution theory, is taken a

stage further in the Allgemeine Deduktion des dynamischen Prozesses oder derKategorien der Physik (1800), in which Schelling seeks to derive spatial dimensions and matter from magnetism, electricity and chemism. For the ftrst timehere, Schelling no longer regarded magnetism and electricity as speclftc characteristics of certain types of matter, but defines these as constituents of all matterand as such as categories of physics, because they supply the schemata for theirself-construction . This was a very courageous hypothesis, for in Schelling's day,most physicists regarded magnetic and electrical phenomena as the effects ofcertain fluids, but not as a universal constituent of matter itself. In the following,I should like to focus on Schelling's Erster Entwurf eines Systems derNaturphilosophie .As Schelling's question concerns the origin and genesis of nature which refersto the entirety of real and possible objects, he cannot begin his construction witha single given object or a set of objects. This seems to be one of the major differences between the philosophy of self-organization and the natural science ofself-organization. Schelling's philosophy explores the universal, basic conditionsfor objectivization, i.e. it asks how it is possible for isolated, limited forms toemerge at all. In contrast, the self-organization theories of the various branchesof science begin with a prescribed system of parts. Furthermore, the externalboundaries of the systems to be investigated are demarcated by means of an experimental arrangement. In the self-organization theories of natural sciences,open systems with limitations are prerequisites which allow the flow of energyor material induced from outside. /10/ Schelling's approach is different. Hewrites: Originally there is for us in nature no one single Being (as one that hasemerged), for otherwise our approach is not philosophical, but empirical. - Wemust see the object in its fIrst origin. Initially, everything in nature, and nature asthe quintessence of Being, does not exist for us. To philosophize about nature isto create nature. /23, III p.13/ Self-organization in this case is therefore nottaken as an attribute of prescribed systems, but ontologically as their geneticground.

But how should we make a start with our construction i f not with an object ora number of objects? In the Erster Entwurt Schelling begins with pureconstructing as such or purely productive activity which, as a basic principle of


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407everything that is objective, is itself not an object and which has no corporealmaterial substrate as its carrier. Individual things are only isolated restrictions ofthis activity; Being itself is meant as productivity in its unrestricted sense. (Note2) - How then from unrestricted, constructive activity can individual, final products now come into being? To explain this, Schelling lists a series of conditionsor restrictions.Firstly he states that unrestricted activity is manifested not by a finite but onlyby an infinite product, namely by infinite becoming ( das unendlich Werdende ).This statement expresses the fact that universal productivity is not exhausted in asingle product, for then evolution would already have come to an end. Infinitebecoming would, however, manifest itself empirically as a becoming with infinitespeed that produces nothing determinable if, apart from the productionprinciple, there were no inhibiting principle, which, for its part, would collapseeverything into a point if able to manifest itself unrestrictedly. Pure productivityonly becomes empirical becoming through the inhibiting principle: The trueconcept of empirical inftnity is the concept of an action which is inhibited intoinfinity. /23, III p.16/ But at each point of the line it is still infinite. In thiscontext Schelling takes recourse to mathematics: The original, infinite series, ofwhich all speciftc series (in mathematics) are only imitations, does not come intobeing by addition, but by evolution, by the evolution of One size already infinitein its origin, which flows through the entire series; in this one size is originallyconcentrated the entire infinity, the successions in the series are but themanifestations of the speciftc inhibitions (through reflection, i.e. self-reflexivityM. H.), which continually set limits to the expansion of that size in an infiniteseries (infinite space), which otherwise would occur with infinite speed allowingno real intuition. /23, III p.lS/

From this construction of infinite becoming, Schelling concludes that eachproduct of nature only appears fixed to our intuition, whilst in reality it isconstantly undergoing change. The apparent fixation is brought about by naturalproducts being reproduced, like a whirl in currents which, by constantreproduction, appears constant, whilst in reality it is in constant flux. The process,however, does not stop at reproduction, but contains further developmentpotential.

The production and inhibiting principle can elucidate an evolution with finitespeed, but not the emergence of different qualities. Thus Schelling adds aninfinite multiplicity of original inhibiting, selfreflexive points which serve as adevice for conceptualizing a dynamic atomic theory . The evolutionary continuum is to a certain degree broken down into singularities, which are conceivedas original productivities (now already in the inhibited sense). In this he observes that the most difficult problem of his Naturphilosophie is to explain how thisinfinite multiplicity of original actions could come about. (In his subsequent pa-per he explains this as points of indifference at which the duality of the production and inhibiting principle is overcome, thereby producing new differences.)These original actions, which Schelling also compares with Leibnitz' Monads ,demonstrate a common tendency to ftll space from the inside out. Filled space is


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408only the phenomenon of an aspiration, the principle of which is not in spaceitself. Schelling fIrst considers this common filling of space as a completely cbaotic mix in which, down to the smallest part, all tendencies are to be found. As aresult, matter is not only infInitely separable like homogeneous space, but is really infInitely separated, differentiated and heterogenous. The first product of thechaotic mix is the amorphous in which each action is restricted and disturbed byall other actions. This dynamic equilibrium of actions can be disturbed by theslightest change . How can order arise from this chaos?As an answer, Schelling introduces the principle of subordination , whichrestricts the degree of freedom of each action, thereby imposing an organizationand design: accordingly, no matter can leave the amorphous state without someaction becoming predominant. However, no action can become predominantwithout suppressing or destroying another. /23, III p.37/ He explains this asfollows: Since each action is highly individual, and as each strives to producewhat it has to produce according to its nature, this generates the drama of conflict in which no force wins or loses completely. The egoism of each individualaction will have to bow to that of all the others; whatever happens is the productof subordination of all to one and one to all, i.e. completely mutual subordination. /23, III p.4l/Should a certain macroscopic organization of elementary actions come aboutby subordination, a certain proportion of actions to one another can be observed.The difference in the various organizations is then the result of each of the different proportions of the actions to one another. As many variations in the proportions of these actions as are possible, so many variations of different formsand development stages. /23, III p.43/The transition from one form to another is enabled by cancelling the equilibrium of the actions, which manifests itself by a certain proportionality. Themore independent actions become from each other, the more the equilibriumwithin a certain natural sphere, which they defme, will be disturbed. I f they arriveat the apex of mutual independence, they reach the highest moment of disturbedequilibrium. But in Nature the highest moment of disturbed equilibrium is oneand the same as the restoration of (a new, M.H.) equilibrium. Between the two,no time passes. /23, III p.50/Schelling also defmes the term organization as the common expression for amultiplicity of actions, which mutually confIne one another to a certain sphere.The sphere is that which has emerged in conflict, so to speak the monument ofthose intermeshing activities or the lawfulness of the product itself' /23, IIIp.65/. This strange term spbere , which appears to be Schelling's own creation,does not mean the same as the mere sum of single activities, but contains a synthetic, macroscopic quality: and that is the lawfulness of the product itself. In hiswork Weltseele , Schelling had already stated: The perennial would then not bethe phenomena within this sphere (for they would in this case also emerge anddisappear, disappear and emerge again), but the perennial would be the sphereitself, within which each phenomenon is contained: the sphere itself could not bejust a mere phenomenon, for it would be that which has emerged in the conflict


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409of those phenomena, the product, so to speak, the concept (the enduring) ofthose phenomena. 123 II p.5161 Accordingly, the sphere does indeed consist ofcomponents and individual processes, but only the integration of these factorsinto an indivisible , coherent whole gives rise to the sphere itself. This is nowgoverned by laws which can only be explained in terms of this cooperative whole,the product itself, but not in terms of individual components and their characteristics.

5. Schelling and RiemannRiemann came into contact with Schelling's philosophy by means of Herbart.Herbart was Riemann's colleague at the university of Goettingen, where hetaught philosophy. From the unpublished posthumous writings of Riemann in themanuscript collection at Goettingen university we can conclude that Riemannhad acquainted himself with Schelling's philosophy. Moreover Riemann verymuch appreciated Fechner's philosophy of nature that included many ofSchelling's points, especially the idea of nature as an organized whole. The notesRiemann made of Herbart's writings show that Riemann was primarily interested in questions of genesis and the development of nature. Here we can onlymention a few instances of agreement between Schelling and Riemann's conceptof nature and epistemology. A detailed comparison is still in preparation:

1) Riemann's method differed from that of the empirically oriented scientistsof the 19th century. But at the same time he avoids an a priori mathematical approach. According to Riemann science proceeds by improving the traditionalconceptual systems. By virtue of new concepts we do not only add new perceptions each moment, but also classify future perceptions as necessary or - if theconceptual system is incomplete - as probable. 122 p.5211 On the other hand,unexpected perceptions can lead to changes in the conceptual system. By thisprocess our understanding of nature is improving continously and at the sametime going further back behind the surface of phenomena.(my emphasis, M.H.)Iloc.cit.1 Science should not content itself with the observation and calculation ofthe outside of nature, but aim at the inside of nature . In his own theorybuilding work Riemann relies on an inner perception , a non-empirical intuition122 p.52BI. The difference between the external perceptible objective side ofnature and its internal workings was Schelling's main argument against theempirically oriented scientists of his time, and he intended to establish a scienceof nature which seeks to decipher the internal productive processes of nature.2) Riemann shared Schelling's persuasion that the internal workings of naturecannot be purely mechanical. Therefore he aimed at a new concept of nature:My main efforts concern a new conception of the well-known laws of nature - anexpression in different basic terms -, and this enabled me to use experimentaldata on the interaction between heat, light, magnetism and electricity for an investigation of the connection between them. 122 p.507I Riemann intended to develop a concept of nature beyond the foundations of astronomy and physics laid


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410by Galilei and Newton /22, p.52PJ/ that would be in accordance with continuumtheory. The atomistic and mechanistic hypothesis, according to which naturalphenomena can be explained by reduction to elementary particles and their mechanistic interaction in an empty Euclidean space, seemed insufficient to him.Riemann's ideas aimed at a general field theory, although he assumed - liketraditional continuum theory - the existence of ether /Scholz, 24, p.99/. He imagined cosmic space as filled with an incompressible, homogeneous fluid withoutinertia, i.e. he did not support a mechanistic hypothesis of ether. Riemann, quitelike Einstein, speaks of a physical space whose forms of motion are supposedto explain the forms of motion of light and gravitation. Riemann's work on nonEuclidean geometry originates from a period, during which he was almost exclusively occupied with Naturphilosophie /18, p.547/ and much concerned withfmding a unifying concept for electricity, galvanism, light, and gravitation(loc.cit.). The same idea was central for Schelling, and had inspired Oersted certainly, and perhaps Faraday, in their attempts at unification /8/. Furthermore,and this is the really surprising point with respect to Riemann, Schelling had already arrived at a concept of space quite beyond the Kantian. For Schelling spacewas not an absolute intuition, given a priori by the organization of our mind, inwhich material interaction can be localized. He considered the dimensions ofspace as generated by the physical processes of magnetism, electricity and thechemical processes /23, IV p.1-78/. For Schelling space was not a Euclideancontainer for physical processes, but - like Riemann - he saw its structure asgenerated by the self-construction of matter /23, IV p.4/.3) Furthermore Riemann tried to combine his continuum concept with particle physics. The fact that he considered the continuum to be a kind of fluid(without properties of inertia) suggested a treatment of the problem in the context of hydrodynamics. In his 1860 paper Ueber die Fortpfianzung ebenerLuftwellen von endlicher Schwingungsweite Riemann developed a processtheoretical approach to the problem of continuity and discontinuity. In this paperhe dealt with the emergence of shock waves, i.e. stable, definite entities withparticle properties. Riemann found out that differential equations of plane airwaves expose a discontinuity, a singular instability at exactly the point wheresudden compression of waves produce shocks of compression /21, 164 ff./.Riemann sees the reason for this discontinuity in a salient change of thephysical parameters (essentially in density and speed) which make a lineardescription impossible. According to Riemann the differential equations losetheir validity at the point where the shock waves originate. They cannot serve tocalculate the process of emergence, because some of the terms assume the valueof infinite at the singulary point. Quite in accordance with contemporarybifurcation theory Riemann comes to the conclusion that spontaneous, dynamicstructure-building processes exhibit a non-differentiable quality in a critical point,a fact which points out a non-deterministic and non-mechanistic process ofphysical nature. Instead of introducing - like modem theories of self-organization- accidental fluctuations by way of stochastic methods, Riemann looks out forcharacteristic invariants in order to decipher the dynamics of shock waves in the


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411point of origin. He is looking for non-mechanistic laws of nature, or - in terms ofSchelling - for a law of freedom, for Riemann was convinced that freedom isvery well compatible with strict lawfulness of the course of nature. /22, p.519/

Schelling also tried to deduce discontinuity from the continuum, but incontrast to Riemann he interpreted the continuum as an absolute productivitywhich become discontinous by the agency of the selfreflexive inhibitions. In thiscontext Schelling was also interested in hydrodynamic processes. As he did notknow shock waves, he often used the formation of whirls as an example. / e.g. 23,mp.289/.4) The fact that Riemann was influenced in his reflections on the self-organization of nature by Schelling's philosophy is supported by a remark he makeson the origin of life /22, p.514/. There he assumes - using the same words asSchelling - an organizing principle in order to explain the emergence of thefirst organisms on earth out of the inorganic. According to Riemann thisorganizing principle has to be interpreted as analogous to the process of thinkingSchelling was one of the first to reflect upon the origin of life from inorganicmatter, and in his reflections was led to an organizing principle that is verysimilar to present-day ideas of self-organization /8/, /9/. Furthermore Schellingsaw the self-organizing principle as a principle that is at work in human mind aswell as in nature. Obviously Riemann agrees with this identity philosophy ,because he identifies the organizing principle with mental activity. Mentalprocess takes place not only in us, but is analogous at the same time to a processon the inside of ponderable matter , for the impossibility to explain mentalactivities by way of material motions in space can easily be affirmed by anyonewho tries to analyse his own inner perceptions; but still we can concede theabstract possibility here. /22, p.516/ Thus Riemann -like Schelling - assumed anidentity of the internal principle of matter and the principle of mental activity.5) Like Schelling Riemann is not merely an advocate of biosophy. For him theprimary ontological reality is not the organism, but the organizing principle,which is the basis of the emergence of life from the inorganic sphere and of itsevolution and therefore cannot be construed as an inherent principle of the organisms itself. The organizing principle always leads from existing formations tomore perfect formations: In the course of its life (the earth's, M.H.) always newand more perfect organisms appear. So we must look for the reason in a mentalprocess which is proceeding to higher stages. /22, p.517/ Riemann was obviouslyinterested in the progressive moment of development towards higher levels, theemergence of new stages of diversity ( Mannigfaltigkeitsstufen ), which he saw inanalogy to the progessive, creative process of thinking. This seems to me to bethe strongest evidence for Schelling's influence, for the later so-calledRomantische Naturphilosophie placed much more emphasis on the metaphorof the organism, a metaphor that belongs to the context of hylozoism, i.e. atheory that Schelling rejected. /11/ This has to be taken into account especiallyfor an assessment of the influence of Fechner, to whom Riemann refers repeatedly.


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412(6) Riemann refers to Herbart and Fechner as philosophical sources. /22, 507ff./ /Scholz 25/ Riemann could follow Herbart in his epistemology and psychology, but not in his philosophy of nature, which was conceived as a programm

opposing the Schelling School. Herbart was one of the acutest critics of the wellknown doctrine of Naturphilosophie , namely absolute identity, which iscontrary to experience which shows us a multiplicity of things in accidentalconnection and separation. /7, VII p.13O/ Instead of conceiving the invariants ofproductivity a future philosophy of nature should rely on the chemical elementsas invariants. Our chemistry leads us to the opposite conclusion, namely to elements which maintain their inherent nature through all their changes of state inaccidental mixtures .. /7, V p.134/Riemann obviously could not agree with this chemical atomism. At this pointhe favoured Fechner /2/, /3j. Fechner - via Oken - was influenced by Schelling'sphilosophy /5/, /6/ but deviates from Schelling in certain points. As a matter offact, Riemann returns to Schelling's position in exactly these points. Inagreement with Fechner Riemann was convinced that earth is an animatedbeing , for the well-organized expediency of the biosphere suggests an animatednature. In contrast to Fechner Riemann did not consider inorganic matter a laterproduct of evolution, but agrees with Schelling in the conviction that organicmatter emerges from inorganic by virtue of an organizing principle.

6. Final RemarksIn 1832 Schelling held a public lecture before the Bayerische Akademie derWissenschaften about Faradays neueste Entdeckung /23, IX p.439-452/, an invention which, although scarcely publicly known, he praised enthusiastically. Thisspeech testifies to the keen interest Schelling the philosopher took in major research advances of the natural sciences. I f Schelling were able to experience thediscoveries being made today about the self-organization of nature, he wouldcertainly be very pleased, not only because they confirm his fundamental hypothesis that self-organization also extends to physical nature.I am glad to have had the opportunity, on the occasion of Hermann Haken's65th birthday, to give you an account of some of Schelling's ideas, albeit allowingfor the fact that Schelling's thinking was far more profound than I am able toconvey here. Today of course we can only look back on Schelling's work and readthat which our minds comprehend today. But nevertheless it is astonishing to fIndso much in this work, written some 200 years ago, that is relevant to us today. Infact, for many it was an amazing revelation to frod that the idea of nature's selforganization, which has revolutionized our view of nature since the 1960's and1970's, had already been elevated to a comprehensive research programme by aNaturphilosoph in 1800, and had even inspired a number of scientists and mathematicians in the 19th century in their attempts to develop a non-mechanistic,dynamic theory of nature.


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Heuser-KeSler, Marie-Loise, Die Produktivitat der Natur. SchellingsNaturphilosophie und das neue Paradigma der Selbstorganisation in denNaturwissenschaften, Duncker&Humblot-Verlag, Berlin 1986Heuser, Marie-Loise, Schellings Organismusbegriff und seine Kritik desMechanismus und Vitalismus, in: Allgemeine Zeitschrift fUr Philosophie,14 (1989) 2, pp. 17-36Heuser, Marie-Luise, Zur Kritik gegenwartiger Selbstorganisationstheorien, in: Philosophy of the Natural Sciences, ProceediDgs of the13. International Wittgenstein-Symposium, Kirchberg am W e c h s e ~Austria 1988, Wien, pp. 246-249Heuser, Marie-Loise, Wissenschaft und Metaphysik. Uberlegungen zu einer allgemeinen Selbstorganisationstheorie, in: Wolfgang Krohn, GUnterKlippers (ed.), Selbstorganisation. Aspekte einer wissenschaftlichenRevolution, Vieweg-Verlag, Baunschweig/Wiesbaden 1990, pp. 39-66.Heuser-KeBler, Marie-Loise, Maximum und Minimum. Zu BrunosGrundlegung der Geometrie in den Articuli adversus mathematicos undihrer weiterfiihrenden Anwendung in Keplers Schrift Neujahrsgabe oderYom sechseckigen Schnee, in: Klaus Heipcke, Wolfgang Neuser, ErhardWicke (ed.), Die Frankfurter Schriften Giordano Brunos und ihreVoraussetzungen, Weinheim 1991, pp.181-197.Heuser-KeBler, Marie-Loise, Keplers Theorie der Selbststrukturierungvon Schneeflocken vor dem Hintergrund neuplatonischer Philosophie derMathematik, in: Selbstorganisation. Jahrbuch fUr Komplexitat in denNatur-, Sozial- und Geisteswissenschaften, Berlin 1991, S. 43-62.Hogrebe, Wolfram, Pradikation und Genesis. Metaphysik a1sFundamentalheuristik im Ausgang von Schellings Die Weltalter ,Suhrkamp-Verlag, Frankfurt a. M.1989Kant, I m m a n u e ~ The Critique of Pure Reason (1781), translated by J. M.D. Meiklejohn, in: Great Books of the Western World, ed. by RobertMaynard Hutchins, Bd. 42: Kant, Chicago/London/Toronto/Geneva1952, pp.1-252Kant, I m m a n u e ~ The Critique of Judgement (1790), translated by JamesCreed Meredith, in: Great books of the Western World, ed. by RobertMaynard Hutchins, Bd. 42: Kant, Chicago/LondonjToronto/Geneva1952, pp. 461-613Poincare e n r ~ Why Space has Three Dimensions?, in: Mathematics andScience: Last Essays, Dover Publications, New York 1963Noether, M./ W. Wirtinger, Bernhard Riemann's Lebenslauf, in: B.Riemann, Gesammelte Werke, hg. v. e. Zermelo, Berlin 1932, pp. 539-538.Otte, Michael, the Ideas of Hermann Grassmann in the Context of theMathematical and Philosophical Tradition since Leibniz, in: HistoriaMathematica 16 (1989), pp. 1-35Riemann, Bernhard, Gesammelte Werke, hg. v. E. Zermelo, Berlin 1932Riemann, Bernhard (1860), Uber die Fortpflanzung ebener Luftwellenvon endlicher Schwingungsweite, in: B. Riemann, Gesammelte Werke, hg.v. E. Zermelo, Berlin 1932, pp.157-175.


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415(22) Riemann, Bernhard, Fragmente pbilosophischen Inhalts, in: B. Riemann,Gesammelte Werke, hg. v. E. Zermelo, Berlin 1932, pp. 507-538.(23) Schelling, Friedrich Wilhelm Joseph, Sammtliche Werke, hg. v. KFA.

Schelling, Stuttgart 1856-1861.(24) Scholz, Erhard, Geschichte des Mannigfaltigkeitsbegriffs von Riemann bisPoincare, Birkhiiuser-Verlag, Boston/Basel/Stuttgart 1980(25) Scholz, Erhard, Herbarts Influence on Bernhard Riemann, in: HistoriaMathematica, 9 (1982), pp. 413-440(26) Scholz, Erhard, Riemanns frUbe Notizen zum Mannigfaltigkeitsbegriffund zu den Grundlagen der Geometrie, in: Archive for History of ExactSciences, 27 (1982), pp. 213-232(27) Scholz, Erhard, Symmetrie, Gruppe, Dualitiit, Birkhiiuser-Verlag,Basel/Boston/Berlin 1989

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Schelling Concept of Self Organization