A Socio-physical Ethical Research Program

International Conference on SocioPhysics, Bielefeld, June 6 – 9, 2002

Hermann H. Rampacher


There still is no academic discipline called ethics being able to prove only the existence of categorical imperative rules, further to explain the origin of ethical conflicts and to solve them precisely without metaphysical arguments. A new scientific ethical theory including an detailed empirical ethical research program is proposed explaining ethical norms, ethical system variables and ethical conflicts. The ethical theory is based on the principle of risk minimisation, the fundamental physical concept of interaction and the measurement of ethical system variables as justice, solidarity, freedom and sustainability, the respective values of those may be observed for every existing civilisation and every existing nation. The theory can derive ethical norms as categorical imperative rules and the research program solves traditional as well as new ethical conflicts that result from scientific, technical and economic evolution. Any human interaction, universally done or undone, that destabilise each system, in which the interaction can occur, may be called ethical, every system being stabilised or destabilised by an ethical interaction may be called ethical. Technical change brings out a rapidly growing number of ethical interactions, called non-elementary, because they can be performed only by means of science and engineering. An ethical interaction may be associated with both a risk factor and a ranked ethical rule of behaviour. The rule’s rank is proportional to the assigned risk factor. Ethical risk factors can be calculated for specific ethical systems, including social systems, using relevant statistical data. It is assumed that a specific final set of both done and undone high-ranking ethical interactions may stabilise a pre-set ethical system. Then the set of associated ethical rules minimises linearly the decay probability of the system and equally the ethical risks belonging to the particular rules, provided the rules are respected simultaneously (ethics of risk prevention). For that reason we identify final sets of high-ranking ethical rules of behaviour, stabilising the global society in the biosphere with sets of ranked ethical norms. Globally accepted moral and legal standards (e.g. human rights) are compatible with subsets of elementary ranked ethical norms. Prevention fails as soon as only one ethical norm is broken. For the interaction assigned to the broken norm activates correlative interactions, not all ethical norms can be observed any more simultaneously and hence an ethical conflict arises as an non-linear effect in one ethical system or even in more afflicted ethical systems. If an intervention favours higher-ranking ethical norms at the expense of lower-ranking norms harmful consequences of the conflict are limited (ethics of intervention). Non-elementary ethical norms, ethical risk factors, and demonstrable and reproducible correlation must be discovered by dedicated interdisciplinary ethical research projects as a part of a whole ethical research program. Provided this ethical research work is done, ethics as social physics is able to solve ethical problems using mathematical methods – e.g. statistics, non-linear dynamics, game theory and self-organisation – and as well methods of computer science including system simulation. Some important applications: Penal law (death penalty is prohibited) and penal justice (punishment has to be replaced by best possible compensation), peace-keeping interventions, conflicts in energy production (nuclear versus fossil combustion), medical research in human embryology. Furthermore the stability of nations can be investigated by means of simulation models using peace, justice, solidarity, sustainability and freedom as ethical system variables with actual and ideal values.


  1. Ethics – Discovering Norms to be Globally Applied
  2. Ethics Reflecting Reality: Interactions and Norms
  3. Prevention is better than Intervention (Linear Ethics)
  4. Intervention is better than Toleration (Non-linear Ethics)
  5. Outlook to further Ethical Research Work
  6. Some first Conclusions
  7. References
1. Ethics – Discovering Norms to be Globally Applied
Ethics deals with norms and values, physics with natural laws. Both disciplines need an empirical basis to be applied.
We know: There are natural laws reflecting facts in space and time, they allow at least on the planet correct forecasts and the construction of technical systems which globally applied are able to clearly expand or alternatively destroy everybody’ s real freedoms.
We feel: Only if civilisations are based on moral standards and states founded on the rule of law our living together is going to be peaceful, just, shows solidarity and the individual will enjoy liberty [e.g. Mill, Liberty]. But do we really know which particular behavioural norms are necessary to enable societies to survive and as well individuals to cope with their lives?
Aristotle was the founder of both physics [Weizsäcker, Physiker] and ethics [Aristotle]. But since the end of the middle ages physics has become a science and hence has shown a remarkable growth of knowledge. Ethics however still is considered to be a branch of philosophy showing no growth of knowledge: “From the dawn of philosophy, the question concerning the summum bonum, or, what is the same thing, concerning the foundation of morality, has been accounted the main problem in speculative thought, has occupied the most gifted intellects, and divided them into sects and schools, carrying on a continuous warfare against one another. An d after more than two thousand years the same discussions continue, …” [Mill 98, Utilitarianism, p. 131].
We know from experience, that nature seems to obey natural laws, individuals and social groups, however, frequently break the rules of law and morality. But every conflict over moral or legal standards breaks down society and clearly harms individuals directly involved in the particular conflict. Hence cases of conflicting obligation “are the real difficulties, the knotty points both in the theory of ethics and in the conscientious guidance of personal conduct.” [Mill 98, Utilitarianism, p. 158].
Primarily two main problems have to be solved by a philosophical or a scientific ethical theory:
  1. How to discover rules of society – ethical norms – which clearly benefit both, the individual and the society, and can be applied globally

  2. How to explain and to solve conflicts over ethical norms
Putting through ethical norms generally is the business of morality, law and politics, but not of ethics. To achieve growth of knowledge ethics should become a science. Ethical norms, universally applied, should provable enlarge the degree of real freedoms everyone enjoys world-wide and as well should enable the global society to survive. To become a science, ethics needs a dedicated empirical research program. But as far as we know there is no empirical research program without a basic hypothetical principle constituting the program.
As we know the physical research program discovering natural laws which enable us to construct working and operatively sound technical systems is constituted by the causality principle. The ethical research program discovering ethical norms however may be constituted by the principle of ethical risk limitation. By definition ethical risks are going along with particular done or undone interactions living beings are exposed to. Interactions increasing an ethical risks by definition are ethically forbidden whereas interactions decreasing ethical risks by definition are ethically commanded by a particular ethical norm. The program is correct, if we are able to test its results empirically by observation.

2. Ethics Reflecting Reality: Interactions and Norms
From Aristotle [Aristotle, p. 5] to Bentham [Bentham, p. 8-89] or Rawls philosophical ethics empirically has been based only on prevalent convictions. For example the utilitarian philosophy assumes the pursuit of happiness or later Rawls [Rawls] supposes the idea of justice as fairness would optimal reflect prevalent convictions of individuals living together. However to establish a scientific ethical research program safeguarding our future provable we need a constitutional principle which reflects reality as physics does. The principle should be based on facts in space and time and should allow to derive ethical norms as mathematically categorical imperative rules of behaviour which can be applied globally to protect the individual. In particular we should be able to show, that sets of moral standards belonging to the common heritage of mankind, henceforth called moral norms, are compatible with sets of elementary ethical norms.
Already Plato has taught us how to decide whether an act is right or wrong [Plato, p. 85-92 ]: Any act risking the stability of the state, if all citizens would perform the act, is prohibited.

Plato did not forget the statement, that there exists no complaint against the existing laws of say Athens, hence the laws as particular norms of behaviour seem to be just.

Plato’s criterion seems to be in some respect equivalent to the far more famous Kantian maxim: “So act, that the maxim of your will could always hold at the same time as a principle in a giving of universal law.” [Kant, p. 164]. The categorical imperative and equally Plato’ s principle of stabilisation both show, that the consequence of their global adoption would be such as no one would choose to incur. But only Plato’s proposal can be smoothly transformed into the language of mathematical systems theory.
In our age of “global neighbourhood” [Carlsson] a necessary – but not sufficient – condition to decrease risks, every human being is exposed to and hence directly and indirectly increase the degree of real freedoms everyone enjoys world-wide [e.g. Sen, p. 5-11 ]is the global balance of nature and society.
Any globally and regularly done or undone interaction j which contributes either to stabilise or to destabilise the global balance of nature and society and as well all the systems in which j occurs is defined to be an ethical interaction. Every system to be either destabilised or stabilised by a particular ethical interaction by definition is an ethical system. The smallest existing subsystem contributing to a stable global balance of society seems to be the family, larger subsystems seem to be enterprises, cities, nations or in our age technical subsystems like the global transportation or global information network.
Any acting individual or social group henceforth may be subsumed under the ethical model of an agent.
Say a is an element of the set A of all agents, g an element of the global system G of nature and society exposed to a particular ethical interaction j(a, g). Regularly but randomly either done or undone by all agents who are skilled enough j(a, g) either stabilises or destabilises all ethical systems, in which j is defined. If g is in particular an element of the subset V of living beings the particular v by definition is called a victim.
We further assume that a monotonous ordered set ethical interactions is necessary and sufficient to stabilise as an interactive basis j = [j(1),…, j(µ),…, j(k)] every ethical system S. The higher the complexity of s, the larger k, the dimension of the basis. The component j(1) may go along with the highest, j(k) with the lowest contribution to stability. How to find the contribution to stability, the so-called rank of j(µ) we shall see below.
We now assume the particular component j(µ) done by all agents being able to perform j(µ), contributes to stabilise G and consequently those remaining ethical systems, in which j(µ) is defined; then j(µ) is commanded by the active ethical norm n[j(µ)]. Further we assume j(µ’ ), done by all agents being able to perform j(µ’ ) contributes to destabilise G and equally the remaining ethical systems, in which j(µ’ ) is defined; then j(µ’ ) is forbidden by the passive ethical norm n[j(µ’)]. A normative basis of system G may be described by a vector base n = {n[j(1)], n[j(2)],..,n[j(µ)].., n[j(k)]}. By definition j(1) and as well n[j(1)] is going with the highest and j(k) and equally n[j(k)] with the lowest rank.
If we are able to identify a particular ethical interaction j(a, v), whereas v is an element of V, and the associated norm n(j) by thought experiments only, j(a, v) and n(j) may be called elementary; otherwise j and n(j) are called non-elementary. We shall see below, that philosophical ethics deals primarily with universal norms of behaviour going along with elementary ethical interactions.
We should keep in mind: If there is any doubt, whether a particular interaction j(a, g) either does or does not contribute to the stability of all the ethical systems in which j is defined, than n[j(a, g)] must not be chosen as an element of a normative basis.

An example of a high-ranking elementary ethical norm is the prohibition of abortion: If a foetus would be killed by intervention, the global society would collapse as well as if every born baby would be killed. Equally every nation or every family would collapse, if abortion would become the rule.
An example of a high-ranking non-elementary active ethical norm is contraception by the pill or other methods of modern science: If every act of sexual intercourse would be done without contraception the global population clearly would explode and hence nature would lost its global balance.
A simple example of a high-ranking non-elementary passive ethical norm is the prohibition of smoking. If every person would be a heavy smoker, in a statistical sense more then half of the global population would die, as well smaller social systems would collapse either. Hence smoking is forbidden by a non-elementary ethical norm, because we need epidemiological research work to identify the actual degree of destabilisation by smoking.
An important class of non-elementary ethical norms is represented by norms going along with mental interactions, because elements of this particular class can be understood only by interdisciplinary empirical projects of behavioural research. Further classes of non-elementary ethical norms forbid interactions which increase the greenhouse effect in our atmosphere or command interactions, which increase the production of wind energy or interactions to cure aids.

Every agent is able to observe every passive ethical norm; hence in particular the relevant authorities are able to put through passive norms by the rule of law. To perform an active ethical norm, however, particular skills are necessary. But even an agent with high skills may fail sometimes to perform an active ethical interaction. Active ethical norms can be observed only more or less frequently. Hence ethics reflecting reality necessarily is a statistical theory.
An agent observing autonomously and simultaneously all the elementary passive components of a particular normative basis n of G by definition acts justly. The more frequent an agent acts justly, the higher by definition the agent’s autonomy. Hence the degree of autonomy determines the degree of predictability of a particular agent.
The more frequent an agent observes all the elementary active components of n simultaneously, the agent is able to perform, the more the agent by definition shows solidarity. And the more frequent an agent observes all the active components of n simultaneously, the agent is able to perform, the more the agent by definition shows reason. Hence ethics contributes to “reason in human affairs” [Simon].
Every pre-set ethical interaction j(a, g) defines two classes: the agents’ competence class and the objects’ class. If j is a passive interaction, elements of the first class are all agents, if j’ is a particular active interaction, the elements of the particular class represent the set of competent agents, agents who are able to perform j(a, g) successfully with high probability.
As well all objects g which are influenced by a pre-set j(a, g) are elements of the objects’ class of j(a, g). The nature and as well the number of different interactions, a particular g is exposed to, defines a pre-set object g ethically.

In human beings as particular victims v suffer from classes of interactions which generally consist of larger numbers of different elements than the classes of interactions other living beings are exposed to. All living beings v suffering from a pre-set subclass of ethical interactions j are ethical equivalent with respect to the particular j. The statement says nothing of the rank of an ethical norm n(j) protecting the particular v.

Only an agent being an elements of the competence class of j can take responsibility for j(a, g). The higher the rank of an ethical interaction, the higher the responsibility of an agent who is able to perform the particular interaction and the smaller the number of competent agents. Hence the degree of responsibility can be measured.

The larger the set of active ethical interactions an individual is able to perform and as well the larger the set of ethical interactions the particular individual is suffering from, the larger by definition the degree of the individual’ s individuality.

3. Prevention is better than Intervention (Linear Ethics)
Not every agent is acting at least justly. And even if an agent strictly intends to perform all the active ethical interactions within the limits of the agent’ s competence, the agent may fail to perform the particular interaction successfully: Even a bright surgeon may fail to operate on somebody’ s lung.
To identify fundamental ethical risks as measurable statistical quantities any element g of G is exposed to, every component of an interactive basis j or as well of a normative basis n of G by definition is linked with two different individual ethical risk factor R and r describing the macro-ethical respectively the micro-ethical status of an ethical system

j = [j(1),….,j(µ),….,j(k)]

n = {n[j(1)],…,n[j(µ),…,n[j(k)]}

R = {R[j(1)],…,R[j(µ)],…, R[j(k)]

r = {r[j(1),.., r[j(µ)],…, r[j(k)]}

Every living being is exposed to the individual ethical risk factor r[j(µ)] and every ethical system S as a whole – therefore macro-ethical state – is exposed to the ethical Risk factor R[j(µ)]. The vectors r and R describe the two versions of a risk basis and – as well as j and n – they represent state vectors of G.
Ethical risk factors R and as well individual risk factors r quantify the concept of ethical ranking in an interactive basis j, in a normative basis n of G or any other ethical system.

Examples of elementary individual risks factors children or adults are exposed to are illiteracy, risk factors going along with the elementary ethical interactions of deception or arson. If for instance all homes in the global society would be destroyed by arson, then the risk factor R equals the expense to restore all buildings and movables; the individual risk factor r is describing the particular expense divided by the number of individuals.
Examples of a non-elementary ethical risk factors are the risk factors every individual is exposed to due to smoking tobacco, missing health care, missing energy supply, mobility or computer illiteracy.

If r is associated with a passive norm n(j), then r measures the expense to restore the status of the living being before n(j) was violated; if the expense is infinite, violation of n(j) is related to an irreversible process.
If r’ is going along with an active norm n(j’ ), then r’ measures the foreseeable expense, which would have been emerged pro living being, provided all agents would have done their duty.
Generally an individual ethical risk is defined as the product of the individual risk factor r(j) and the probability the interaction j is regularly either done or undone.

The values of individual risks are varying from ethical system to system; generally the individual risks depend on space and time and perhaps on additional system parameters measuring the actual behaviour of responsible individuals or social groups in a pre-set society..

In case the size of a particular individual risk factor r is infinite, r will be replaced with the probability that the event leading to an infinite individual risk factor will occur. An individual ethical risk factor r is infinite if a human being as an object of the highest potential or actual degree of individuality is killed.
The individual risk factors going along with passive interactions or norms we call zero risk factors, the specific risk factors associated with active interactions or norms we describe as non-zero individual risk factors. Of course this does not mean, that any risk factor itself equals zero, but the risks associated with zero risk factors can principally become zero, whereas the risks linked with non-zero risk factors can never become zero.
Every human victim in the global society described by j , n, or r is exposed to a resulting individual ethical risk at point x and time t
r(x, t) = p(1, x, t)x r(1) + p(2, x, t)x r(2) + …. + p(k, x, t)x r(k),
In the so-called ground state of the global society the resulting ethical risk is minimal. Hence everybody’s real freedoms are optimal. For the individual ethical risks p°(µ, x, t) going along with the individual zero risk factors r(µ) are zero and further the individual risks p°(µ’, x, t) going along with the individual non-zero risk factors r(µ’) still have finite but small values:

r°(x, t) = p°(µ’, x , t) x r(µ’) + p°(µ’’, x , t) x r(µ’’) + … + p°(k-k’, x , t) x r(k-k’),
whereas the r(µ’) are the individual non-zero risk factors and the p°(µ’, x , t) the probability going along with the r(µ’).
The higher the skills of the agents performing the high-ranking active interactions of a particular interactive basis, the smaller the p°(µ’, x, t). Generally the interactions j and as well the associated individual risk r(j) are correlated. Therefore there are always finite transition probabilities. But the transition probabilities are activated only, if at least one ethical norm is violated, say n(µ). Hence p°(µ, x, t) has to be replaced by a higher occupation probability of state n[j(µ)] with p(µ, x , t) > p°(µ, x , t). Then we have

P (µ’, µ; t + dt*) = w(µ’,µ)dt, µ not equal µ’,
whereas P(µ’,µ; t + dt) is the probability that the particular ethical system at time t is leaving state µ and is going to be in state µ’ at time t + dt and is called transition probability. The term w(µ’,µ) is defined as transition probability per unit of time. The stronger j(µ’ ) and j(µ) are correlated the greater w(µ’,µ); the particular value must be investigated by observation of the pre-set ethical system. The transition probability pro time is describing behavioural patterns of individuals involved. If transitions are activated an ethical conflict arises (see section 4).
We now have got an alternative formulation for the fundamental stabilisation principle constituting ethics: The ethical risk limitation principle.
Risk limitation can be realised in two steps. First step: the linear risk minimisation. The process necessarily is linear, because a non-linear approximation generally cannot guarantee that real freedoms of every human being and the over-all stability of the global society is optimised simultaneously. Second step: risk limitation by intervention (see next section).
The aim of linear risk minimisation in a pre-set ethical system is achieved, if all ethical norms are conserved in the particular system and hence no transition probability w(µ’, µ) per unit of time actually is activated. There is a standard quotation ‘prevention is better than cure’ which can be transformed into ‘prevention is better than intervention’.

Consequently the ethical norms linked with ethical interactions necessarily are universal binding rules of behaviour or – as philosophers say – categorical imperative rules of behaviour.

Hence we have shown that in the ethical systems theory there exist final sets of categorical imperative rules of behaviour without any reference to prevalent convictions or metaphysical arguments.

For better understanding of the general theory lets give a very simple example. The stability of the global society may be described by only four different elementary ethical interactions j(1), j(2), j(3) and j(4). j(1) may be the passive interaction of physical violence, j(2) the active interaction of help for human beings in need of help, j(3) the passive interaction of deception and j(4) the passive interaction to damage or take away other people’s property. Provided j(2) is universally and regularly done and as well the remaining j(µ) are regularly and universally undone then the global society as a whole is stabilised and equally every human being is protected against attacks or inactivity of responsible individuals or social groups.

This simple example give us two firm insights. First: Well-known moral standards are nothing else than elementary ethical norms, norms going along with elementary ethical interactions j(a, v) human or other living beings (physical violence, help for living beings in need of help) are exposed to. Second: Only if at least all passive norms are observed autonomously, the society is able to concentrate all its skills to show a higher degree of solidarity and the society does not need any effort to control the behaviour of unwilling agents. As well simple thought experiments show us: Fundamental human rights as declared by the United Nations in 1948 are equally going along with elementary ethical interactions. In particular human dignity is optimised for every human being, if all components on n are observed autonomously and simultaneously.

Within the scope of the ethical risk limitation theory the existence of finites sets of universal binding rules of behaviour is a consequence of the minimisation process: The conservation of a finite number of ethical norms is a necessary and sufficient mathematical condition for linear minimisation and hence the optimisation of the degree of real freedoms the individual enjoys world-wide.

This does not mean that the real freedom of every citizen is equal. The higher the skill of an agent the higher the agent’ s real freedom; otherwise the agent cannot perform in particular high-ranking active ethical norms. Consequently equality is incompatible with the optimisation of opportunities in life or real freedoms for everybody. Hence the theory of ethical risk limitation is a theory being only in parts egalitarian.
The importance of this fact cannot be over-estimated. With respect to active interactions there are extreme inequalities. The more difficult an interaction, the smaller the number of agents to be in a position to perform the particular interaction successfully.
A difficult problem of democracy is the fundamental right: one person – one vote. The complicated problems to be politically solved adequately in modern democracies are baffling for a growing number of citizens. Even educated voters often are unwilling to inform themselves sufficiently. So results of elections are becoming more and more random. But omissions of governments in office often cannot be compensated in the future. Due to the actual behaviour of an increasing number of voters the future of nations and as well the future of the global society is becoming more and more risky.
The fundamental values of the French Revolution has been liberty, equality and fraternity. At least the principle of equality before the law is either a trivial tautology or it is an absolute empty demand [e.g. Kelsen, p. 35-40].
Another difficult ethical problem is, that the human rights can be observed optimally only in a society, in which there are enough skilled agents. Hence developing countries generally are not able to protect every citizen optimally without help from outside.

4. Intervention is better than Toleration (Non-linear Ethics)
4. 1 Micro-Ethics

Moral norms and legal standards are violated more or less frequently: Individuals and social groups are frequently unfair to their neighbours and act at the expense of others if nobody would discover their wrong behaviour or agents are to powerful to put them in their place.
The history of the last century [e.g. Hobsbawm, Courtois] has showed the deep conflicts going along with the frequent violation of moral norms compatible with high-ranking ethical norms by political and military leaders and as well whole nations like Russia and Germany.
If only one moral or legal standard equal to an high-ranking elementary ethical norm is broken, due to the generally mutual correlated ethical interactions it becomes impossible to observe the remaining ethical norms simultaneously: An ethical conflict arises.

If, for example, a man is trying to rape a woman, a witness having the physical strength and agility to actually help the woman under threat must use violence. Thus the helper himself necessarily is breaking high-ranking ethical norms to minimise ethical risks, the victim is exposed to.

There is a first micro-ethical intervention rule, called the rule of ‘Intervention and toleration’ [Rampacher 98] that helps to solve principally an actual ethical conflict, replacing linear risk minimisation by risk limitation:

An agent has to intervene putting through higher-ranking ethical norms at the expense of lower-ranking norms.

To enable agents to actually limit risks we need a second intervention rule:

If a pre-set ranked ethical norm protects both the victim and the culprit, the rank of the norm protecting the culprit is decreased compared with the rank of the norm protecting the victim.

Culprit by definition is the responsible individual or social group violating an ethical norm first.
Both ethical intervention rules have already guided judges as empirical “ad-hoc rules” since there exist legal systems. The ranks of particular legal norms, however, have reflected only prevalent convictions of those in power, but not facts related to risk factors to be discovered by dedicated empirical research projects.

In our micro-ethical example above the ranks of the norms protecting the culprit are decreased compared with the same ethical norms protecting the young woman.
If a nation – optimising only the nation’s own interest – attacks another nation the norms protecting the soldiers of the aggressive nation are diminished compared with the same ethical norms protecting the soldiers of the self-defending nation. Since generally the soldiers on both sides are not responsible for the out-break of the war, the number of soldiers to be killed or wounded must be as small as possible. To harm the civil population of both nations outside the front-line is ethically forbidden as well.
An actual example reflecting the evolution of life sciences: What is more important: To cure in near future individuals incurably ill or to protect surplus frozen embryos already produced by reproduction medicine?
We do not know yet ranks of involved norms, because there exists no dedicated ethical research program investigating. But we are able to draw conclusions in analogy to problems we have already solved. In the process of self-defence even living individuals, young soldiers, are sacrificed to win the war. Existing embryonic stem cells are no human beings, hence the norms protecting the stem cells are lower than the norms protecting living individuals incurably ill. But even the ranks of not implanted embryos, who represent a preliminary stage of human beings are clearly lower than the norms protecting living ill individuals, since only implanted embryos have the full potentiality to become adult human beings.

4.2 Macro-Ethics
The status and as well the dynamic development of ethical and in particular social macro-systems – democratic or totalitarian nations, central or federal states, states founded on the rule of law or ignoring laws frequently – in the end cannot be described correctly without mathematical modelling. Relevant mathematical methods to describe the dynamic development and as well the dynamic stability of social systems are already known [e.g. Weidlich]. These methods may help to solve stability problems of ethical systems, too.
Provided we are going to give priority to the over-all stability of civilisations and nations rather than to increase real freedoms of single individuals we have to place special emphasis on the macro-ethical aspect of our ethical systems theory. Therefore we have to emphasise on the state vector R and on collective system variables like justice, solidarity, liberty and sustainability.
As we already know the state vectors j, n and R describe the system variable liberty of the global society. As well we should be able to define state vectors describing peace, justice, solidarity and sustainability.
If the components of j describing any interaction of violence would be conserved in G, the global society would be peaceful, hence the actual value of the system variable peace would be equal to the smallest, the ideal value.
If the components of j describing all passive elementary interactions would be conserved in G, the global society would be just or fair, hence the actual value of the system variable justice would be equal to the ideal value.
If the components of j describing all active elementary interactions would be conserved in G, the global society would show optimal solidarity.
If the passive and active components of j contributing to the balance of nature – the particular components we know only, provided we have got already stable results of dedicated ecological research projects – the global system G would be organised on condition that sustainability is linearly optimised.
The time-dependent occupation probabilities p(µ,t) of the state described by the particular state vector R may be described as

[p(1,t), p(2,t),…,p(µ,t),…, p(k, t)].
p(µ,t) is the time-depended probability describing that the risk factor R[j(µ)] is switched on and that the ethical risk p(µ,t) x R[j(µ)] the particular ethical system is exposed to is going with the particular risk factor R[j(µ,t)].

The ethical risk L(t) the society as a whole is exposed to at time t reads:

L(t) = p(1,t)x R[j(1)] + p(2,t)x R[j(2)] + …+ p(µ,t)x R[j(µ)] + ….+p(k, t)x R[j(k)]

The ethical risk L(t) measure the actual value of the system variable liberty describing the over-all status of the global society.
The probability vector of the most stable state, the ground state of the global society, reads:

[p°(1,t), p°(2,t),….,p°(µ,t),….,p°(k, t)].
Now we are able to redefine the vague moral law by means of particular ethical systems variables. The state vector describing peace in the global society reads:

R’ = {R[j’ (1)],…,R[j’ (µ’)],…,R[j’ (k’)]},
the j’ (µ’) are the passive elementary interactions which prohibit all varieties of physical or psychical violence, the state vector describing justice

R’’ = {R[[j’’ (1)],…,R[j’’(µ’’)],…,R[j’’ (k’’)]},
the j’’ (µ’’) are describing all the passive elementary interactions. The state vector in the global society which shows solidarity reads:

R’’’ = {R[j’’’(1),…,R[j’’’(µ’’’]],…,R[j’’’(k’’’)]}.
The ethical risks going along with the particular ethical risk factors associated with the system variable peace, justice and solidarity can now be calculated analogous to the above formula for L(t), provided the probabilities associated with the particular risk factors are known by dedicated ethical research projects.
In the ground state the particular risks describing the global society and which are associated with the variables peace, justice and solidarity are minimal.
If only the smallest risk factor – say the factor which describes theft of pockets – R’’(k) is switched on due to correlation there is only a small but finite probability that there will arise a transition from sub-state k to the neighbouring sub-state k-1:

p(k-1,k; t + dt) = w(k-1,k)xdt
But if for instance the ethical risk of arson is non-zero, according to strong correlation the ethical risks going along with cases of physical violence, theft or deception will increase strongly due to the greater particular transition probabilities w(µ’, µ) per unit of time involved in the interaction of arson.
Transition probabilities per unit of time describe the actual behavioural patterns of both agents and victims. Therefore this quantitative terms must be investigated statistically by systematic and regularly observation.
The most dangerous situation with respect to peace or justice for example will arise, if the zero risk factor R (1) is not switched off. Then the numerical greatest transition probabilities per time unit w(k,k-1), w(k,k-2),…. will be activated by the misbehaviour of a high number of agents.

5. Outlook to further Ethical Research Work
The connection of morality and ethical systems theory now seems to be quite clear. The connection of ethical systems theory and say theological ethics (Protestant Churches) or moral theology (Catholic Church) as well as the connection of ethical systems theory and the Islamic ethics or law has to be investigated in more detail.
The perhaps most important micro-ethical application would be the reform of the penal law of western democracies. The particular penal law using still atavistic concepts like guilt and atonement should be reformed completely. In particular punishment should be replaced by the best possible compensation of harm or damage caused by the autonomous violation of legal standards which are compatible with ethical norms.
Important political applications are peace-keeping military interventions as already mentioned above, ethical norms stabilising the systems of national economies and – even more important – the global economical or ecological system: If ethical norms are broken frequently, economical or ecological systems will become in-stable or will even collapse.
Hence we need in particular a new version of economics integrating ethical norms as precondition of regional and global economic stability. The global logic of ethics is much more comprehensive than the global logic of economy [e.g. Weizsäcker, Globalisierung].
There are qualitative analyses of social conflicts [e.g. Dahrendorf] and a lot of qualitative investigations of the political and economic development of nations and ideologies [e.g. Furet, Hobsbawm; Kennedy; Kissinger]. These analyses give a rather unsophisticated approach to political, social and economic development, because the dynamic development of correlated ethical risks cannot be described adequately by qualitative modelling of ethical complexity.
But any application of the outlined ethical systems theory in micro-ethics and as well in macro-ethics is only possible if we alt least know ranked ethical norms for all social systems, which are destabilised by actual ethical conflicts. A numerical investigation of the dynamic stability of the global system G is only possible, if the particular transition probabilities per time unit are measured by observation. A first and rather comprehensive attempt to measure human welfare in the field of ecological systems has been made by Lomborg [Lomborg].
Hence to apply the new ethical systems theory world-wide a detailed ethical research program is necessary investigating ranked ethical interactions, the ethical risk factors associated with ethical interactions and ethical norms and the transition probabilities per time unit into sub-states described by the components of the state vectors of the involved states.
If an interactive or a normative basis of a pre-set ethical system is known including the associated ethical risk factors and transition probabilities than for instance the stability of the particular social system in its environment may be estimated macro-ethically by non-linear system modelling or by means of the master equation [e.g. Weidlich]. Micro-ethical problems may be solved using methods of game theory. Game theory mainly deals with problems of intelligent but only rarely with problems of responsible behaviour.

6. Some First Conclusions
  1. Moral norms are elementary ethical norms reflecting reality.

  2. Moral norms are able to increase peace, justice, solidarity and liberty globally and as well protect the individual.

  3. Ethical norms, observed simultaneously, stabilise nature and society globally and optimise the individual’ s real freedoms.

  4. An ethical conflict arises, if only one ethical norm is violated. Negative consequences – risking the global balance of nature and society and harming directly human and other living beings – can be limited by interventions which advance higher-ranking norms at the expense of lower-ranking norms.

To sum up, one can say:

The system theory based on ethical interactions sets objective standards but does not put them through. The actual ethical research program is the alternative program of every kind of social Darwinism or any other social ideology. Ranked ethical norms derived from the theory improve piece by piece the protection of the human being world-wide and the global stability of nature and society.

7. References
  • Aristotle: The Nicomachean Ethics; Oxford 1998
  • Bentham, Jeremy: An Introduction to the Principles of Moral and Legislation, p. 65-111, in: Utilitarianism and other Essays (ed. A. Ryan); London 1987
  • Carlsson, Ingvar and Ramphal, Shridath: Global Neighbourhood; Oxford (UK) 1995
  • Dahrendorf: The Modern Social Conflict; 1988
  • Furet, Francois: Le passé d’ une illusion ; Paris 1995
  • Hobsbawm, Eric: Age of Extremes. The Short Twentieth Century 1914-1991; London 1994
  • Hume, David: Enquiry concerning the Principles of Moral; Oxford 1902
  • Kant, Immanuel: Practical Philosophy (ed. J.M. Gregor); Cambridge 1999
  • Kelsen, Hans: Was ist Gerechtigkeit? Stuttgart 2000
  • Kennedy, Paul: The Rise and Fall of the Great Powers; New York 1987
  • Kissinger, Henry A.: Diplomacy; New York 1994
  • Kohlberg, Lawrence: Moral Development; International Encyclopedia of the Social Sciences; New York 1968
  • Landes, David: The Wealth and Poverty of Nations; New York 1998
  • Lomborg, Bjorn: The Sceptical Environmentalist – Measuring the Real State of the World; Cambridge 2001
  • Mill, John Stuart: On Liberty, p. 5-128, in On Liberty and other Essays (ed. J. Gray); Oxford (UK) 1998
  • Mill, John Stuart: Utilitarianism, p. 131-167 in: On Liberty and other Essays (ed. J. Gray); Oxford (UK) 1998
  • Plato: The Last Days of Socrates; London 1993
  • Popper, Karl
  • Roemer, John E.: Theories of Distributive Justice; Cambridge (US) 1998
  • Rampacher, Hermann: What may we do? Section Theoretical Ethics; Twentieth World Congress of Philosophy, Boston, 10-16 August 1998
  • Rawls, John: A Theory of Justice; Boston 1971
  • Sen, Amartya Sen: Development as Freedom; Oxford (UK) 1999
  • Simon, Herbert: Reason in Human Affairs; Stanford (US) 1983
  • Smith, Adam: An Inquiry into the Nature and Causes of the Wealth of Nations; Oxford (UK) 1998
  • Weidlich, Wolfgang: Sociodynamics – A systematic Approach to Mathematical Modelling in Social Sciences; 2000
  • Weizsäcker, Carl Christian von: Logik der Globalisierung; Göttingen 1999
  • Weizsäcker, Carl Friedrich: Große Physiker; München 1999