Independence of purpose. The purpose/goal does not depend on the object (system) as it is determined not by the given object or its needs, but by the need of other object in something (is dictated by the external medium or other system). But the notion of “system” in relation to the given object depends on the purpose, i.e. on the adequacy of possibilities of the given object to execute the goal set. The goal is set from the outside and the object is tailored to comply with it, but not other way round. Only in this case the object presents a system. Note should be taken again of the singularity of the first consequence: the system’s purpose/goal is determined by a need for something for some other object (external medium or other system). Common sense suggests that supposedly survivability is the need of the given organism (the given system). But it follows from the first consequence that the need to survive proceeds not from the given organism, but is set to it by another system external with respect to it, for example, the nature, and the organism tries to fulfill this objective.

Specialization of the system’s functions. In response to certain (specific) external influence the system always produces certain (specific) result of action. Specialization means purposefulness. Any system is specialized (purposeful) and follows from the axiom. There are no systems in abstracto, there are systems that are concrete. Therefore, any system has its specific purpose/goal. Executive elements (executive SFU) of some systems may be homotypic (identical, non-differentiated from each other). If executive elements differ from each other (are multitype), the given system consists of differentiated elements.

System integrity. The system exerts itself as a unitary and integral object. It follows from the unity of purpose which is inherent only in the system as a whole, but not in its separate elements in particular. The purpose consolidates the system’s elements in a comprehensive whole.

Limited discrecity of system. Nothing is indivisible and any system may be divided into parts. At the same time, any system consists of finite number of elements (parts): executive elements (subsystems, elements, SFU) and management elements (control block).

Hierarchy of system. The elements of a system relate to each other in varying ways and the place of each of them is the place on the hierarchic scale of the system. Hierarchy of systems is stipulated by hierarchy of purposes. Any system has a purpose. And to achieve this purpose it is necessary to achieve a number of smaller sub-goals for which the large system contains a number of subsystems of various degree of complexity, from minimum (SFU) up to maximum possible complexity. Hierarchy is the difference between the purposes of the system and the purposes of its elements (subsystems) which are the sub-goals in respect to it. At that, the systems of higher order set the goals before the systems of lower order. So, the purpose of the highest order is subdivided into a number of sub-goals (the purposes of lower order). The hierarchy of purposes determines the hierarchy of systems. To achieve each of the sub-goals specific element is required (it follows from the conservation law). Management/control in a hierarchic scale is performed in accordance with the law “the vassal of my vassal is not my vassal”. In other words, direct control is only possible at the level “system - own subsystem”, and the control by super system of the subsystem of its system is impossible. The tsar, should he wish to behead a criminal, would not do it himself, but would give a command to his subordinate executioner.

System function. The result of the system’s performance is its function. To achieve the purpose the system should perform purposefully certain actions the result of which would be the system’s function. The purpose is the argument for the system (imperative), while the result of action of the system is its function. The system’s functions are determined by a set of executive elements, their relative positioning and control block. The notions of “system” and “function” are inseparable. Nonfunctional systems are non-existent. “Functional system” is a tautology, because all systems are functional. However, there may be systems which are non-operational at the moment (in a standby mode). Following certain external influence upon the system it will necessarily yield certain specific result of action (it will function). In the absence of the external influence the system produces no actions (does not function). When taking into account the purpose, the argument is not the external influence, but the purpose. One should distinguish internal functions of the system (sub-function) belonging to its elements (to subsystems, SFU) and the external functions belonging to the entire system as a whole. The system’s external function of emergent property is the result of its own action produced by the system. Internal functions of the system are the results of action of its elements.

Effectiveness of systems. Correspondence of the result of action to the goal set characterizes the effectiveness of systems. Effectiveness of systems is directly linked with their function. The system’s function in terms of effectiveness may be sufficient, it may by hyperfunction, decelerating and completely (absolutely) insufficient function. The system performs some actions and it leads to the production of the result of its action which should meet the purpose for which the given system is created. Effectiveness of systems is based on their specialization. “The boots should be sown by shoemaker”. Doing the opposite does not always result in real systems’ actions that meet the target/preset results (partial effectiveness or its absence). The result of action of the system (its function) should completely correspond qualitatively and quantitatively to the preset purpose. It may mismatch, be incidental or even antagonistic (counter-purposeful); at that, real systems may produce all these kinds of results of action simultaneously. Only in ideal systems the result may completely meet the preset purpose (complete effectiveness). But systems with 100% performance factor are unknown to us. Integral result (integral function) is the sum of separate collateral/incidental and useful results of action. It is this sum that determines the appurtenance of the given object to the notion of “system” with regard to the given purpose. If the sum is positive, then with respect to the preset purpose the given object is a system of one or other efficiency. If the sum is equal to zero, the object is not a system with respect to the given purpose (neutral object). If the sum is negative, the given object is an anti-system (the system with minus sign preventing from the achievement of the goal/purpose). It applies both to systems and their elements. The higher the performance factor, the more effective the system is. Discrepancy of the result of action of the given system with the due value depends on unconformity of quantitative and qualitative resources of the system, for example, owing to breakage (destruction) or improper and/or insufficient development of its executive elements (SFU) and/or control. Therefore, any object is an element of a system only in the event that its actions (function) meet the achievement of the preset goal/purpose. Otherwise it is not an element of the given system. Effectiveness of systems is completely determined by limitation of actions of the systems.

Limitation of system’s actions. Any system is characterized by qualitative and quantitative resources. The notion of resources includes the notion of functional reserve: what actions and how many of such actions the system may perform. Qualitative resources are determined by type of executive elements (SFU type), while quantitative resources by their quantity. And since real systems have certain and finite (limited) number of elements, it implies that real systems have limited qualitative and quantitative resources. “Qualitative resources” means “which actions” (or “what”) the given system is able to perform (to press, push, transfer, retain, supply, secrete, stand in somebody’s light, etc.). “Quantitative resources” means “how many units of measure” (liters, mm Hg, habitation units, etc.) of such actions the given system is able to perform.

Discrecity (“quantal capacity”) of the system’s functions. The system’s actions are always discrete (quantized) as any of its SFU work under the “all-or-none” law. There exists no smooth change of the system’s function, but there always exists phased (quantized) transition from one level of function to another, since executive elements actuate or deactivate regular SFU depending on the requirements of system. Transition of systems from one level of functions to another is always effected by way of a leap. We do not always observe this gradation/graduality because of the fact that the amplitude of the result of action of individual SFU can be very small, but still it is always there. The amplitude of these steps of transition from one level to another determines the maximum accuracy of the result of action of systems and is stipulated by the amplitude of the result of action of individual SFU (quantum of action). Probably, elementary particles are the most minimal SFU in our World and consequently indivisible into smaller parts subjected to laws of physics of our World.

Communicativeness of systems. Conjugate systems interact with each other. Such communication implicates the link/connection between the systems, i.e. their communicativeness. We discern open and closed systems. However, there are no completely isolated (closed) systems in our world which are not affected by some kind of external influence and which are nowise influencing any other systems. One may find at least two systems which are nowise interacting with each other (do not react) among themselves, but one can always find the third system (and probably the group of intermediate systems will be required) which will interact with (react to) the first two, i.e. be a link between them. If any system does not react at all to any influences exerted by any other systems and its own results of action are absolutely neutral with respect to other systems, and it is impossible to find the third system or a group of systems with which this system could interact (react to), it means that the given system does not exist in our World. Interaction between systems may be strong or weak, but it should be present, otherwise the systems do not exist for each other. Interaction is performed for the account of chains of actions: “... external influence → result of action...” By closing the end of such chain to its beginning we will get a closed (self-contained) system. The result of action after its “birth” does not depend on the system which has “gave birth” to it. Therefore, it may become external influence for the system itself. Then it will be a cyclically operating system, a generator with positive feedback. But the generator, too, requires for its performance the energy coming from the outside. Consequently, it is to some extent opened either. That is why the absolutely closed systems are non-existent. Each system has a certain number of internal and external links/connections (between the elements and between the systems, accordingly), through which the system may interact with other external systems. Closeness (openness) of a system is determined by the ratio of the number of internal and external links/connections. The larger the ratio, the greater the degree of closeness of a system is. Space objects of a “black holes” type are assumed to be referring to closed systems because even photons cannot break off from them. But they react with other space bodies through gravitation which means that they “are opened” through the gravitation channel through which they “evaporate” (disappear).

Controllability of systems. Any system contains elements (systems) of control which supervise the correspondence between the result of action of the system and the goal set. These control elements form the control block. Management of system is carried out through commands given to its control block, whereas the control over its executive elements is exercised through sending commands to their control blocks. Any reflex is the manifestation of the work of the control block. And as far as control block is the integral accessory of any systems, any systems have their own reflexes. Executive elements should fulfill the goal exactly to the extent preset by the command, neither more nor less than that (neither minimum nor maximum, but optimum) based on a principle “it is necessary and sufficient”. Control elements watch the fulfillment of the purpose and if the result exceeds the preset one, the control block would force the executive elements to reduce the system’s function, whereas if it is lower than the preset result it will force to increase the system’s function. The purpose is dictated by conditions external with respect to the system. The command is entered into the system through the special entry channel. All consequences represent continuation of axioms, are stipulated by purposefulness of systems, constructed under laws of hierarchy and limited by the conservation law. The list of consequences could be continued, but those listed above are quite sufficient for the evaluation of any system. Such evaluation applies to both the properties of the system and its interaction with other systems. Evaluation of the first consequence can be expressed in percentage, i.e. what is the percentage of fulfillment (failure of fulfillment) of the goal/purpose. The goal may be any due value. Other consequences may also be characterized either qualitatively or quantitatively, which actually represents the system evaluation, i.e. its diagnostics, systemic analysis. The system is characterized by: the purpose/goal (determines designation of the system); hierarchy (determines interrelations between all the elements of the system without an exception); executive elements (SFU performing actions); control block (watches the correctness of performance of actions for the achievement of the goal). Any object, not only material, is also a system, provided it satisfies the above listed axioms and their consequences. Groups of mathematical equations, logic elements, social structures, relations between people, intellectual/spiritual values, may also represent systems in which same principles of functioning of systems work under the same logical laws. All of them have a purpose, their own SFU and control blocks which watch the implementation of the goal/purpose. If the object has a purpose it is a system. And for the achievement of this purpose it should have corresponding executive elements and control block with corresponding analyzers, DPC and NF (which follows from the conservation law and the law of cause-and-effect limitations). Systemic analysis examines the systems and their elements in a coordinated fashion. The result of such analysis is the evaluation of correspondence of results of actions of the systems with their purposes and revealing the causes of the discrepancy for the account of determination of cause-and-effect relations between the elements of systems. The major advantage of systemic analysis is that only such an analysis allows establishing the causes of insufficiency of systems. The purpose/goal determines both the elementary structure of systems and interaction of its elements which is operated by the control block. The interaction of executive elements (SFU) only is not conducive to yielding stable result of action meeting the purpose preset for the system. Addition to a system of the control block adjusted to the preset purpose enables producing stable (constantly repeated) result of action of the system meeting the preset goal. The norm is such condition of a system which allows it to function and develop normally in the medium of existence which is natural for the given type of systems and to yield reactions of such qualitative and quantitative properties which allow the system to protect its SFU from destruction. The notion of “norm” is relative with respect to average state of the system in the given conditions. In case if conditions alter, the system’s condition should change, too. Reaction is the action of the system aimed at producing the result of action necessary for its survival in response to external influence, i.e. the system’s function. Reaction is always specific. Reaction may be: normal (normal reactivity), insufficient (hypo-reactivity), excessive (hyper-reactivity), distorted (unexpected reaction occurs instead of the expected one). Normal reactivity (normal reaction) means that functional reserves of systems correspond to the force of external influence and the operating possibilities of control block allow to adjust (control) SFU so that the result of action precisely corresponds to the force of external influence. Hypo-reactivity of the system (pathological reaction) arises in cases when functional reserves of the given system of living organism are insufficient for the given force of external influence. Hypo-reactivity is always a pathological reaction. Hyper-reactivity of the system (normal or pathological reaction) is the one where the result of action of the system exceeds the target. Distorted reaction is a reaction of the system which mismatches its purpose. Pathology is the lack of correspondence of the systems’ resources to usual norms. Pathology includes other two important notions: pathological condition (defect) and pathological process (including vicious circle). Restoration is active influence on the system with a view to: liquidate or reduce excessive external influences destroying the Systemic Functional Units; liquidate or reduce destructive effects of vicious circle if it has arisen; strengthen the function of the affected (defective) subsystem, provided it does not lead to the activation of vicious circle; strengthen the function of systems conjugated with the defective one, provided it does not lead to strengthening the destructive effect of the vicious circle associated with the affected system or the development of vicious circles in other conjugated systems (does not lead to strengthening of the “domino principle”); replace the destroyed SFU with the operational ones. Any owner of the car knows that if something is broken in his/her car (as a result of excessive external influence) and the defect turns up, the transportation possibilities of its car sharply recede. If failing immediately repairing the car, the breakages would accrue catastrophically (vicious circle) because the domino principle will be activated. And to “cure” the car it is necessary to protect it from excessive external influences and to liquidate the defects.