An Integrated Notion of "Law"

1 Introduction
2 What are laws in general?
3 Synchronous view
   3.1. About dynamical and statistical laws
   3.2 Integrated notion of law
      3.2.1 Integrated notion of law for a system and its elements
      3.2.2 Necessity and chance in the integrated law
      3.2.3 Integrated Law in Physics
            3.2.3.1 Newtonian mechanics – dynamical view *
            3.2.3.2 Newtonian mechanics – statistical view *
            3.2.3.4 Statistical physics
            3.2.3.5 Microworld
   3.3 The Integrated Law
4 Diachronic view
   4.1 Stable Self-reproduction
   4.2 Emergence of New in the bifurcation-points
   4.3 Historicity and lawfulness
1 Introduction
 If we speak about laws of nature and society we are in a confused situation. On the one hand we speak about scientific propositions with a special structure, called "laws of science" – and on the other hand we speak about the world to which the propositions refer. We see more or less essential relations in the world - and we describe them with language and mathematics. There are many ways to describe them – but there is only one world. Sometimes this world looks like it is determined (maybe by connections, which we can call "laws"); sometimes it looks like it is indetermined. What is the applicable view? It depends...

We often disregard the hierarchical structure of our world when we talk about determinism or indeterminism. Hierarchical structure means that all things are composed of parts and that they are parts of other, larger things. That does not mean, that the "greater" thing must reign over the others – its only a structural reality. Because we are aware of the association of all things in the world we have to consider that there are differences in the world, too. There are differences at each level – and there are different levels of structures, from elementary particles across atoms and bodies to cells, organism and social structures.
If we ask what is determined or not fully determined, we have to consider the nature of our system, its elements, and its environment. I think, necessity and chance are objective-real categories - in their relativity to ontological system or element. But in our view categories necessity and chance are dependent on what system and elements we assume (see the principle of observability in the Paper of Arshinov and Budanov about principles of synergetic, Arshinov, Budanov 2002).  

2 What are laws in general?

We don’t speak about laws in the legal sense here, although the concept of laws in nature and society was derived from laws in jurisprudence. Here I'm interested in understanding the nature of laws in the sciences of nature and society – and their correspondence to nature and society. I don’t follow the analytical philosophy, which assumes that laws are merely statements about everything in a given topic.
There is no clear notion of a law. I think, the only common ground is that laws deal with some general and universal characteristics. Hempel said that laws must have a general form because of their function in scientific explanations (Hempel 1965, p. 343). But not all general or universal statements are (expressions of) laws (Ayer 1976, S. 192ff.).
Popper uses the term "natural necessity" to distinguish between mere generalization of facts and generalization of laws (Popper 1989, S. 382).
But Ayer (1976, S. 192) rejects this, because he thinks that the determination of necessity uses the notion of lawfulness and this would be circular. Popper derived the natural necessity from other considerations.
Röseberg called laws : "universal-necessary connections" and declared that "universal-necessary" means that the connections are due to a certain class of objects with necessity. (Röseberg 1975, p.9). The behaviour of such objects will show that under the same essential conditions the same event will occur. Hörz emphasizes this reproducibility (Hörz 2001).
It is not usual, but helpful, to understand laws as universal-necessary and/or "essential connections". Modern philosophers of science mostly refuse such "metaphysical" terms like "essence". But a dialectical approach can understand it in a useful way. The simplest understanding of essentiality of laws is: The essence determines the characteristics of the connection, which determine the difference to other systems (Röseberg 1975, S. 9). The determinations of "system", "essence" and "law" are connected in a dialectic way.
 
 3 The Synchronous View
3.1 About Dynamical and Statistical Laws
 Max Planck distinguished dynamical and statistical laws. Dynamical laws unequivocally connect present states with states in future. Statistical laws connect them only by probability.

In classical mechanics the physical states are usually connected in a dynamical way . This view presupposes a classical view of motion. In this view we assume, that
  • all quantities of motion can be exactly measured and

  • the calculated trajectory corresponds to the real path of the body.


We can assume the second Newtonian law [ d/dt ( mv) = F ] as a dynamical law: The equation describes an infinite set of possible trajectories. If we add specific initial conditions to this we'll get one possible trajectory for the bodies, which will be realized exactly. Chances are only sources of irritation.

Laws in their dynamical form can be defined the following way:
A law is a "universal-necessary connection, in the sense that there is, depending on the initial conditions, only one possibility which necessarily realises itself " (Hörz 1974, p. 465).

This form of a law contains the possibility of behaviour at one level of structures and not the connections between such levels. If there are influences from other levels, they are seen as mere contingencies.
But if the influence of these contingencies becomes greater and greater – the behaviour of the body seems to be unlawful, indeterminate.
In thermodynamics and quantum theory we have to use statistical laws.
It’s interesting that Max Born showed that classical mechanics can be written as a theory using only statistical laws too (Born 1961/1963). Schrödinger quoted Exner, who assumed that "it is possible that the laws of nature have a statistical character" (Schrödinger 1922, p.16). With respect to Darwin and Boltzmann Schrödinger wrote: "It involved a new outlook on the nature of the laws of Nature; namely, that they are not rigorous laws at all, but "only" statistical regularities, based on the law of great numbers" (Schrödinger 1944/1984).

3.2 An Integrated Notion of Law
3.2.1 Integrated Notion of Law for a System and its Elements
 These two approaches, the dynamical and the statistical, are different but not unrelated. We don’t have to decide between them.
The form of laws depends on the form of motion. We know dynamical and statistical motions and dynamical and statistical forms of laws. Is there mere an inseparable difference between dynamical and statistical forms?
Sometimes, if we can presuppose the dynamic view of motion (we can see only the motion at one level and take the influences from other levels as unessential chances), then we can use the dynamical view of law (like Newtonian Laws and Lagrange- and Hamiltonian equations) or the statistical (like Max Born did). We have learned that in thermodynamics and quantum theory we can´t presuppose the dynamic view of motion; the phenomena of the marcoscopic level are not separable from the "lower" level and therefore here we have to consider the essential connections between the macro- and the microlevel and we must use another form of laws.

In the 1970s Herbert Hörz integrated the two views into one notion of law. He called it the "statistical notion of law", because the statistical view can include the dynamical view. But I suggest using the term "integrated notion of Law" in order to avoid a confusion with the "pure" statistical notion of law and in order to interpret other forms of lawfulness (see below) like the "singular particular".

For that integration we suppose, that there is a system that is built from elements. Each element can be a system itself and each system may be an element in a "higher" system. But if we speak about laws of a special system, we hold one system and its elements in our glance. This view we call the "synchronous view" (later we will discuss the diachronous view).

Now we can say:
  1. At the level of the system we focus our glance on the self-identity (and self-reproduction) of the system itself. If it would have another form of existence or self-reproduction, it would be another system. Therefore the system at this level has only one (essential) possibility for existence, self-reproduction and motion (the unessential characteristics may change). If a thing has more than one essential possibility, it is built of several systems. (Now we have a definition of such a system: it is an entity, which has at this level of structure one possibility of behaviour only). For the system as a whole we get a dynamical lawful behaviour – it will move according to a determined tendency. For example, a classical mechanical law contains a set of all possible paths. The determined tendency of the system as a whole shows us the "dynamical aspect" of the Integrated Law.


  2. At the level of the elements there is a degree of "freedom". Elements are not only "smaller things" – we assume measurements, trajectories, or other phenomena to be the elements of a system in physics. These elements are not fully determined by the dynamics of the system. They have a set of possible behaviour, statistical behaviours (with respect to the system – if we regard them as systems themselves, they will have dynamical behaviour too). There is a "distribution of probabilities" for the behaviour of the elements. We get probabilities to measure special quantities. Only in trivial cases we will get a probability of 0 or 1. This aspect is called the "stochastic aspect" of Integrated Law.


  3. Now we look at a single phenomena. For each phenomenon there is a probability of transition from one state to another. This is called the "probabilistic aspect" (for a discussion of some details cf. Schlemm 1996, p. 213 ff).


 
The unity of all aspects can give us an integrated notion of law:
A law is a "universal-necessary connection, which
  • determines one possibility for the behaviour of the system, which will realize nessecarly (dynamic aspect),

  • in which exists an objective field of possibilities for the behaviour of the elements, from which one possibility will be realized by chance (stochastic aspect) and

  • this possibility has a certain probability (probabilistic aspect). (Hörz 1974, p. 365/366)

"The philosophical conception of the statistical law regards laws (systems of laws) as general, necessary, and essential connections between objects and processes in a system, where, under the conditions of the system, a possibility is necessarily realized (dynamic aspect), but where there is a field of possibilities for the elements. A probability distribution exists for the random realization of this field (stochastic aspect) and the transition from one state into another is conditionally realized by chance with a certain degree of probability (probabilistic aspect)."
Herbert Hörz (1982): Dialectical Contradictions in Physics. In: Dialectical Contradictions: Contemporary Marxist Discussions. Minneapolis: Marxist Educational Pr. Studies in Marxism Vol. 10. (ed. by Erwin Marquit, Philip Moran, Willis H. Truitt). p. 201-222.p. 215
The connection of two neighbouring levels at least is very relevant for all approaches of worldview. The German physicist and philosopher Ulrich Röseberg wrote:
"The philosophical interest of attempts to establish the statistical physics is grounded on this, that in this theory the connection between two objectively separated material levels of structure (atoms, molecules and macro objects) is given in a particular science which is important with respect to analogous questions for more complex systems (living beings, societies)." (Röseberg 1975, p.107).
 
3.2.2 Necessity and Chance in the Integrated Notion of Law
 There is a unity of necessary tendency of the system and the accidental behaviour of the elements (in relation to this system) in an integrated law. We are not allowed to forget that being system and elements are relative: Systems may be elements in other relations and elements can be systems too. Necessity and chance are relative to being a system or an element.

Because it depends on our point of view, we might think, that there is no real difference. But in reality there is: There are really connections which determine a dynamic tendency for a unity at one level (the system) and behaviour by chance for its elements.

For each system there exists a totality of conditions. This totality of conditions (for the system it is only given in an analytical view, never in reality) determines the necessity of the behaviour of the system. Seen from this level, the behaviour of the elements is only determined by partial wholeness of conditions, i.e. the behaviour is determined/conditioned by chance.
The connection of system- and element behaviour is given by the constitution of the possibility of the system by the possible behaviours of the elements. And at the same time the behaviour of the elements is not fully but partially determined by the system. Ernst Bloch said: "Even the vacant is not arbitrary... the can-be is lawful, too." (Bloch, p. 172)
 

3.2.3 Integrated Law in Physics
3.2.3.1 The Dynamical View of Newtonian mechanics
The system in Newtonian mechanics will be a set of measurements (maybe of planets) – the several measurements are the elements of the system. We are presupposing that the body will at each time be at one certain location and that these points can be measured with any required exactness. Then and only then we can reduce the integrated law to its dynamical aspect because we have now eliminated all accidents in the behaviour of the elements (measurements).
We’ll get our "reduced" integrated law in the form:

Dynamic aspect Stochastic aspect Probabilistic aspect

We can determine the behaviour of an mechanically moving body in an unambiguous way with given initial conditions, mass and influencing forces.
The set of possibilities is reduced to one determined unambiguous measurement.
Each measurement will give us the same result (with a probability of 1).

In classical mechanics we are not interested in the inner structure of the moving body. And its motion is characterized by unambiguous trajectories whose diversity can be calculated with equations and conditions. We’ll get a single path, if we use concrete intitial conditions, which are not determined in the law. The law contains an infinitive set of paths (of mathematical possible paths) and the conditions will select the (one) real possible path. This real possible path is the "necessarily realizing" mathematical possibility (even if the behaviour is not computable).

Classical mechanics as a prototype of science
Classical mechanics with its reduction of the dynamic aspect became the prototype of science.
But what premises do we have to take into account?
Its method is grounded in the elimination of dialectical contradictions. The real dialectical contradictions (i.e. the contradiction of movement, like Zeno showed us) are reduced in this way:

We determine such quantities, in which the opposite moments are distributed. We don´t use the place of a moving body at one time and the place at another time, because there is the Zenonian contradiction of movement. We use the place and the first derivative of a space-coordinate (velocity) in our equations as quantities. Now noncontradictionary mathematics is possible (see Ruben 1977, p. 115).

We distribute the whole process in an analytical way and we get two forms of the process:
  1. The process of maintaining the identity of the state of motion of the body (self-maintaining-first law of Newton), and the

  2. changing of the state of motion as a result of forces from outside (second law of Newton).


Dynamics deals with "searching these determining factors, which are an expression of the maintainance of the system within the interactions of its elements" (Ruben 1977, p.115). This shows: If we reduce the integrated law to the dynamical aspect that we, we'll be focused to the aspect of self-maintaining. We can see only the way determined with tendency of the whole system.
 

3.2.3.2 The statistical View of Newtonian mechanics
Max Born showed that the classical mechanics can be interpreted in a statistical way. He takes statistical distributions for the binitial values and the quantities become probabilities, not exact coordinates. In the dynamical view we took the disturbing influences as unspecific. Now these influences will become specific conditions of the effect. The state is not determined by exact coordinates, but by a probability distribution. We will get single measuring-quantities from a series of measurements (of one state).
Now we’ll get our integrated law in the following form:
Dynamic aspect Stochastic aspect Probabilistic aspect

There is one possibility, which is realized necessarily, for the distribution of probabilities.
There is a set of possibilities for the separated measured quantities. In each single measuring one of the possibilities will be encountered by (partially conditioned) chance.
Each of these quantities has a certain probability.
 
3.2.3.4 Statistical physics
Statistical thermodynamics connects two levels of structure. The macroscopic motion of particles is considered as a result of the motion of the molecules at the micro level. The macroscopic area is characterized by physical quantities like temperature and entropy. These are functions or functionals of microscopic quantities (i.e. velocities of particles).

The function of distribution is the necessary realizing possibility of the system. The microscopic quantities fluctuate. Fluctuations become immediately constituting elements of theory.
"Fluctuations belong to the essential characteristics of the macro physical state (Necessity asserts itself through individual fluctuations – therefore by chance – "law of fluctuation")" (Röseberg 1975, p. 120).

Here the elements really are the objects of a deeper level (not only measurements or something similar). Here the wholeness is a "sum of relatively isolated separated objects which are interacting, but the interaction has accidental character" (Hörz 1964, p. 164). This is a difference from quantum theory.

Now we can consider the integrated law for statistical thermodynamics:

Dynamic aspect
Stochastic aspect
Probabilistic aspect

Distribution-function (for velocities of particles) is the necessary realizing possibility for the system.
The set of possibilities contains the individual fluctuations of velocity.
Each particle has a concrete velocity and for this velocity there is a probability.
 

3.2.3.5 Microworld
 Quantum Mechanics
In quantum mechanics we can’t assume isolated "smallest bodies", which can be found at a certain time at a certain space. The classical-mechanics-motion-view fails.

Even in classical mechanics we don’t speak about bodies in reality – we speak about their "mass points" and idealized paths (because the classical view of motion is an idealization). Now we use other idealizations and constructions. We speak about operators in a Hilbert space and construct new measuring-quantities, called observables. These observables can’t all be measured simultaneously. The objects of quantum mechanics are states which are superpositions of eigenstates.

Before measuring we have only information about the discrete spectrum of eigenvalues of observables, i.e. an statistical proposition as information about the state. (The statistics belongs to repeated measurements, not an ensemble of particles!)

If we measure, then we act in a materialistic way with our technical devices. The quantum-objects and the device become one system, they are no longer independent from each other. The wave function is not a product of the wave function of the object and the wave function of the device (Meier, Zimdahl 1986). Now a projection happens into one eigenstate which is determined only statistically and we can´t know it before measuring. This is often called "reduction of wavefunction" – but we can get more precise information now. In our measurement we have interrupted the whole quantum process, we have neglected certain aspects of motion (Hörz 1964, p. 135).

The possibility for the behaviour of the system is given by the motion-equation (Schrödinger-equation) for the state-vector Y and the possibilities which are realizing by chance are the wholeness of simultaneous measurable observables, whose expectation-values can be determined.
Now for quantum mechanics we have: the theory records possibilities of behaviour of the quantum objects and one of them will be realized conditioned by concrete conditions of experiment.
Dynamic aspect Stochastic aspect Probabilistic aspect

I. Copenhagen Interpretation (+ von Neumann)
The possibility of behaviour of the system is given by the equation for Y in the Hilbertspace.
The field of possibilities contains the discrete spectrum of eigenvalues of the observables. This field/set refers to repeated measurements, not an ensemble of particles. Even after a measurement the object and the measurement instrument will stay correlated, we don´t know an exact measuring value.
There is a projection to one eigenstate in each single measuring – called "reduction of wavefunction". This is not included in the Schrödinger equation.
The projection is caused by interuption of the movement, by neglecting of certain aspects of movement ... (Hörz 1964, S. 135)

The state Y can change in two ways. It can change continuously, if we consider an isolated system without interaction or measuring according of Schrödinger´s equation. But if we take into consideration interaction of a nonisolated system, we get a discontinuously change, according to probability laws.
The Copenhagen interpretation concentrates on the interaction between quantum object and measurement system. It was shown by Bohr that we can speak about a "phenomenon" only if we look at the whole process with its conclusion: the registration ("irreversible amplification effect") (Bohr 1958/1985, p. 96). Therefore in quantum mechanics all knowledge about quantum objects contains the interaction of quantum objects and classical objects, of objects and the practice of subjects. This brings the statistical character into the quantum mechanics. Grete Hermann showed that such a statistical view doesn't deny causality " (Hermann 1935: 721). Quantum Mechanics expects a lawful explanation also for events, which are not predictable in advance.

The new decoherence-interpretation, based on Zeh 1970, assumes that there has to bee a dynamical cause for the non-occurence of observed superpositions in macroworld. Zeh analysed the dynamical decoupling of components following Everett (1957/1983). For macroscopically different states he recognised that "the significantly different interaction of their components with their environment" (Zeh 1970, p. 348) destroys their superpositions. Decoherence describes the fleeting interactions between an object and its environment, which allow the object to select on concrete state from a lot of simultaneous possibilities (Hergett, p. 6). By means of this decoherence we can calculate that systems with a big mass and chaotic systems have a very short coherence-time and from this coherence-time one can derive that the classical world has no quantum behaviour. The decisive innovation of the decoherence-conception is the consideration of the influence of the environment and the consideration of the object and the measuring instrument as open systems (see Müller 2003).

Dynamic aspect Stochastic aspect Probabilistic aspect
II. Coherence-Interpretation
Correlation of object, measuring instrument and environment. Description by a mixed density matrix. 		Environment-induced decoherence destroys the coherent superposition. All possible results of measuring are elements of the reduced density matrix. Transition to one measure-value (not described yet - see Müller, p.6).

I think, this view corresponds to the assumption of Wheeler, who said that "each of the laws of physics [is] at bottom statistical in character" (Wheeler 1980/1983, p. 203).

We see that a view that assumes that the quantum-objects are separable "things", fails (only some properties are stable like mass, charge, spin). There are always interactions. Quantum theory shows that only if we consider the openness of real (quantum-)systems, we can explain the stochastic and probabilistic aspect. If we look at "deeper" levels, some of the "stable" properties will demonstrate their instable character too.

Elementary Particles
In Quantum Mechanics we speake about states like |Y> in a Hilbert space, not about "little objects". When we speak about "little objects in micro world" we mostly speak about elementary particles. Modern physics tells us that these particles seem to have no intrinsic characteristics - only interactions give them their characteristics. Without concrete interactions - in a symmetric state - i.e. electrons and neutrinos would have no differences, they would be the same thing. Only the interaction with (not yet observed) Higgs-particles gives the electrons their mass - Higgs-particles for a neutrino-mass don't exist in our concrete world (Smolin 2002, p. 67). In such a way differences emerge through concrete interactions in the world. This is called symmetry-breaking. "Each elementary particle possesses a set of several potential characteristics, but only one is realised in a stable universe" (Smolin 2002, p. 69). The theory (the dynamic aspect of law) is symmetric, it can't determine the concrete stable configuration. Only the concrete system "will decide". We can say now:
Dynamic aspect Stochastic aspect Probabilistic aspect

In the theory of elementary particles (i.e. Weinberg-Salam-model) there is a unity of particles (without concrete interactions or before concrete conditions emerged in the very early cosmos).

In this unity there are many possibilities to become particles (or interactions) with several different characteristics.
When symmetry-breaking happens the several particles get certain characteristics.

Theories of Everything?
There is yet no successful "Theory of Everything" - a theory of the foundation of the world, of the final unification of the fundamental forces in the world. For a long time many scientists trusted in the string- or superstringtheory. But in the theory there would be 9 dimensions, which is 6 dimensions too many. It is possible to explain these extra dimensions as rolled up, and thus not detectable. But there are many, many possibilities to roll them up and these possibilities produce too many new parameters (Smolin 2002, p. 83). The conclusion of such a Theory of Everything would be: "Everything is unified, but there are ten thousands of possibilities for the configuration of the universe." (p. 88).

Based on Roger Penrose´s suggestion to view physical laws as combinatory principles, some physicists developed another fundamental theory, the loop-theory. Each quantum state can be considered as loops of space - or better: spin networks. The mostly amazing characteristic of such spinnetworks is that also space and time turned out to be only a possibility of being of the network of relations (Smolin 2002, p. 336, Smolin 1995 and Zimmermann 1991).  

 

3.3 The Integrated Law

The Integrated Law combines the necessity of whole systems (the motion of the system is tendencially determinated with necessity) and the conditional-probable behaviour of the elements of the system, and in this way, the system with its outer conditions (which influence the symmetry-breaking). Because each system is an element in a "comprising" system and each element is a system itself (hierarchical structure), we get a concept in which necessity and conditional-chance are connected. The elements are not fully determined by the system. The law has an necessary tendency – but its elements have a "field of possibilities", which depends on really given (and changing) conditions. Each thing is a system and an element likewise. Furthermore the law has an inner structure. This structure is the prerequisite that symmetry-breaking occurs in temporal changes. Then the influence of the outer conditions can no longer be neglected.

This concept is an approximation to a concept of possibilities in a lawful world. It works in the sphere of abstract system-thinking and uses the dialectic "essence" to determine which connections are laws (unessential connections are not laws, see above).

It is not concrete enough to determine the particular character of the elements. It has the tendency to assume the elements are homogeneous, and to ignore the essence of human being: the individuality, the special quality of each individual. Refer to human society, we have to add that humans are equal only in that sense that each of them has their own individual special quality. Here the abstract notion of law cannot grasp the special concrete (!) quality of human being.

4 Diachronic view
 In the diachronic view we are interested in the temporal development of the behaviour of systems and elements, not only their structure. We have to consider two possibilities:

  1. The elements are smaller objects like molecules, atoms, cells or so on for the whole system.

  2. The elements are qualitative determined moments, factors or so on and not only "smaller things".

The systems and their elements are not eternal phenomena, they are changing in time. And they are changing in several specific ways. There is not only chaotic change in the world: for a while we can regard a system as relatively stable (see 4.1) and in other times there are (more or less) important changes (see 4.2).
 
 4.1 Stable Self-reproduction
 If we speak about systems, we mostly speak about their identical self-reproduction. In this relatively stable phase, a complex system maintains its identity by self-reproduction of its elements. We can say that a living being maintains itself by changing its biochemical processes and renewing its parts. With respect to A) we can see that a society may be stable although its members are born, live and die. And with respect to B) we can say that e.g. the economic process reproduces itself by changing its interacting moments: production, consumption, distribution and exchange.

Now we have the situation of the synchronic view - seen as a circular process: The elements build up the system and the system gives the constraints and the possibilities for the elements to do that.


Role of Fluctuations of Elements
 There are fluctuations on the level of the elements at all times. These fluctuations were suppressed (physical solid bodies) in some systems, other systems consist of regular fluctuations (thermodynamic macroscopic quantities).

In society there is another "degree of freedom" for the individuals: They don’t have the function of constituting the society – the society exists to enable individuals to human freedom! (c.f. the specific connection of possibilities for human beings in the Critical Psychology of Klaus Holzkamp).

Maybe in stable phases of development ot the system there are other forms of elements (emerged by fluctuations)that are not the main quality of them. But they are not important, not specific, not essential for the system and therefore they will be suppressed.

But the system will come into a phase, in which the fluctuations,i.e. the other possible qualities will become important. Such systems come to such a phase, because their self-maintaining-processes exhaust their own conditions (Schlemm 1996).

In our further explanations we will speak about complex systems with a non-linear behaviour and an entropy-export.

If the system reaches a point in which it can’t proceed further in its previous way, then new possibilities will emerge. Some of the fluctuations of the previous set of possibilities for the elements can become essential. And a new field of possibilities emerges as well....

It is typical for all complex systems to reach a "critical point" in this phase. A new way to exist must emerge in this point – but it is not determined by the previous process: a specific new quality comes into being. Because the path of development has more than one possibility we speak about "bifurcation" at the "bifurcation-point". Such a form of development is essential to the conception of self-organization.

4.2 Emergence of Novelty in the Bifurcation Points
 In the approaches to self-organization the probabilistic aspect becomes very important. Here, changes of qualitative states are the topic of science. We sometimes speak about a paradigm-shift from the classical, dynamical view to the new self-organization-view. We know the metaphors about symmetry-breaking, about "sensible phases" and so on. Chance is here the "constituting moment of building of structures" (Hörz 1990, p. 37).

Uwe Niedersen even suggests considering that "singular individuals" transcend the "fixed fields of possibilities"(Niedersen 1990, p. 79, see also Niedersen 1988).Yuri Melkow (2002, p.3) suggests assuming spontaneity as the correct term for a "third kind" of determination.
We mentioned that the fields of possibilities will change at bifurcation-points, too. We have to take into account that there are not only "old possibilities" of the "old system". The old system can vanish – a new system can emerge, a system with it’s own new possibilities.
But the old and the new system are not unconnected. They are connected by (spatially and/or temporally) larger connections. We get – in a like manner we got a hierarchy of systems – a hierarchy of laws.
There are transitions: In our synchronous view we get transitions between several levels of structure and in the diachronous view we get transition between temporally states of systems.

The Hegelian view emphasises the dialectical transitions in a form like steps between the states – without a possibility of ramifying. This view works, when we ask how a given stage emerged from its predecessors (if we look from present time to the past). But if we are standing in our present time and we are looking forward into future, we can’t use this view only. Now we use the knowledge about the openness of future, the different possibilities, what can happen, the possibility of ramifying similar bifurcations. (Later we will see a step-like way with a backward view, too).

In a transition between stages or states with essential qualitative differences we will transcend the range of a law. Because there is a hierarchy of systems (synchronous and diachronous) we don’t reach a range without laws at all. Each system is in the domain of particular laws and each system is a part of a (spatially or temporally) larger system in which the transition happens. Then we speak about "laws of development" ("Entwicklungsgesetze", Hörz, Wessel 1983, p. 98ff.). They include the dialectic of the elementary level and the system level too, and therefore the "laws of development" include the "degree of freedom" of the elements.
We can see cycles of evolution with a directed tendency in the Hegelian view. (It is not a question here if the direction can be characterized towards "higher" levels).

We saw even in our dynamic view of laws, that there are an infinite set of possibilities, in which conditions select the "necessarily realizing" one in the equations. In our evolutionary view we see, that all "essential processes in nature are non-linear, determined chaotic and therefore ramifying" (Zimmermann 1990, p. 58).

Dynamic aspect Stochastic aspect Probabilistic aspect

If we analyse the past, we'll we can see a not interrupted, but sometimes "bended" way from the past to our present state. Each state has a particular predecessor, from which several maybe (in this past time) accidental conditions lead to the present state. There is a dynamic connection from past to our present time. Our present state is the "necessarily realized" of the formerly existing possibilities.
In each present-time there is the possibility of different futures, depending on the conditions and the behaviour of the elements of our system. We can be in one of several states:

a) present at a "stable phase" (at an attractor), in which deviations are depressed;

b) present at a "bifurcation-point", in which deviations can become new essential characteristics of the new emerged systems.
For each element/deviation is a possibility to become essential, which is different in several phases of the process.
 
 4.3 Historicity and Lawfulness

We sometimes speak about laws as "stable connections" between changing phenomena. Then we get a contrast. Stability, connected with laws, and changing of the phenomena may be a contradiction.
But here is a better view:
Laws are not connections between things ore phenomena that forbid changes. Laws are the "rules of change" beneath the level of phenomena. The laws are the expression of the possibilities of behaviour and change in a different way for the systems and the elements – in their connectedness.

In our synchronous view we can distinguish between one possibility (the directed tendency) for the behaviour of the system and the set of possibilities for the elements.

In the diachronous view we have another aspect, the aspect of time. Laws depend on conditions and these conditions can change in time. The conditions can change in such a way that the system can’t exist in its essential quality any longer. Then the system vanishes and its elements vanish too, or they became elements of other systems or they change themselves in such a manner that a new system (with new essential qualities) can emerge.
Here we have to consider our well known phases of self-organized processes.

Because of the changing of the systems the laws will change too.
"Therefore possible laws of nature can be identified as such only bit by bit, namely between the critical points of evolution, because the structure building fluctuations dominate at the critical points." (Zimmermann 1991, p. 61). ). Biologists usually speak about "evolution of evolution-mechanisms" (see Schlemm 1996, p. 59 and p.206). This seems to be very hard to grasp for cosmologists. When I wrote my first book in 1994 to 1995, in which I take the self organization of the universe for granted (Schlemm 1996, p. 28) and suggested searching evolutionary feedbacks in cosmology (p. 186), Lee Smolin wrote his historical book about the historicity of cosmological laws in a "Darwinian cosmos" (I would doubt his concrete mechanisms, but the idea of evolution of conditions and laws seems to be all right).

We know - beneath such essential qualitative changes - that even in laws the fields of possibility can change. Hörz and Wessel distinguished between modification I, in which the stochastic distribution changes and the essential characteristics do not change and modification II, in which the field of possibilities changes, but the dynamic aspect remains (Hörz, Wessel 1983, p. 134). Another view differs between two types of possible "innovation", described by R.E. Zimmermann (2001, p. 5). One type is based on "internal potential" ("sleeping variables") and the other type is based on "external potential" (new derivates are being spontaneously included in the system).

The relation of lawfulness and evolution with essentially qualitative changes can be characterised int the following way (see Schlemm 1998):
Self-organized evolution follows laws and doesn’t follow laws:

  • Evolution is not lawful, because the laws of the old system don’t determine the further evolution.

  • Evolution is lawful, because the system is kept in a larger system with its own laws and the new system will create its own new laws.


The historicity of laws is i.e. for Lee Smolin (2002, p. 23) an amazing quality of laws – but dialecticians knew it all the time.
Maybe we can use a new type of mathematics (Negator Algebra, see Zimmermann 2001) to describe temporal processes in future. Then it will be essential, if there are only internal potentials (like Kauffmann assumed, see Zimmermann 2001, p.6) and the field of possibilities would be determined all the time (out of all time, like Schelling said); or if real novelty can emerge, i.e. something is not pregiven "out of all time".
But in both cases we can’t find out what will happen in future. I prefer the second view: that there is the possibility of emerging new states, which are not pregiven in the eternal "substance". But even if one assumes that there is such a substance from what the space-temporal world emerged/s, we – as a being in space and time – can’t find out what will and what shall happen on principle.

Science as knowledge of laws can’t determine in advance what we have to do, because there is no "one, right" way.
If science has the real, changeable conditions of possibilities as its topic, it can be a critical one. Science has two possibilities: Science can recognize the conditions of all connections and tell us: "if this.. then that". This enables instrumental acting. The conditions are accepted as given conditions.
But if the conditions are grasped as changeable, then our thinking is not only interpreting, but becomes comprehending (this difference - "Deuten - Begreifen" - see also Holzkamp 1985) and "critical".
 
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This paper is published in: Arshinov, Vladimir; Fuchs, Christian (Eds.) (2003): Causality, Emergence, Self-Organisation. NIA-Priroda. Moscow 2003, p. 56-75.
See also http://www.self-organization.org/results/book/EmergenceCausalitySelf-Organisation.pdf

 





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