The car is designed for transportation, a calculator for calculations, and a flashlight for lighting. The system of external gas exchange is designed to exchange metabolic gases between the surrounding atmosphere and blood. Pumping systems of blood circulation (right and left ventricles of the heart) - for pumping blood, urinary system - for normalization of water-salt metabolism, the system of stabilization of arterial pressure - to maintain blood pressure at a constant level, etc.
But the purpose of transportation is needed not to the car, but to someone or something external to it. The car needs only its ability to fulfill this goal. The purpose to pump blood with the heart's ventricle is not needed by the ventricle, but by other tissues of the body. The heart ventricle needs only the ability to fulfill this goal. The purpose is the need for something for something external, and this system only performs it, serving it external. Consequently, the purpose of the system is put from the outside, and the system only needs the ability to fulfill this goal. This external is another system or system, because the World is filled with only systems.
The arm prosthesis is designed for the same purpose as its own "native" arm. Another thing is that today the prosthesis is far from perfect. But if you make a full-fledged prosthetic arm that is as flexible, dexterous and strong as your hand, plus it would have tactile and other sensitivity, it would be completely irrelevant for a disabled person whether his hand is "native" or prosthetic. The main thing is that the prosthetic arm fully corresponds to the purpose for which the hand exists. And this purpose is not needed for the hand, but for the owner of this hand.
If there is a complete correspondence between what a given object has and what it can do, this object (or group of elements) is a system for accomplishing this purpose (intended for this purpose of this group of elements). If this correspondence is not present, then in relation to this goal, this group of elements is a random set of elements (not a system). Although this group of elements can be a system with respect to another goal, if this correspondence is observed in relation to another purpose. The purpose unites a group of elements in the system.
Therefore, the definition of the system can be represented in the following form: - "A system is a set of interacting elements that can fulfill one common, definite purpose."
"A system is a group of purposefully interacting elements."
Assigning a goal always excludes an independent choice of a purpose by the system. The target can be set to the system as a setpoint and as an installation. There is a difference in these concepts.
The setting is a rigid directive, it is necessary to execute only IT with the given accuracy and only SO and not otherwise. Ie, the system is not given the right to choose actions to achieve the goal, all its actions are strictly defined. The setting rigidly defines the algorithm of the system actions.
"Algorithm is an exact instruction to the performer to perform a certain sequence of actions to achieve the purpose in a finite number of steps".
Installation is a softer concept, only IT is given, but the right to choose actions for the achievements of IT is given to the system itself. Therefore, the purpose is set by setting the system, but the choice of action algorithms is provided to the system itself, or rather to its control unit (see below). The installation can be set to systems only with a sufficiently developed control unit, which can make the choice of the necessary actions.
No system has free will and can not set (set) its own purpose. The goal is dictated by the need for something by something or by someone that is outside this system. Consequently, the purpose for the system is always put by another system. In other words, the purpose is not produced by the system itself, but comes into it from the outside. But what actions need to be done for this (choice of an algorithm of actions) the system can choose itself, it has the freedom to choose actions.
Think at leisure why we have 5 fingers, not 4 or 6!