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AXIOMATIC PROPERTY THEORY

1. Possession (property relations)

Property relations can be described in the form of graphical model. For this purpose we shall determine three initial notions, they are - "object", "owner" and "possession".

Object

Objects. The object is an or concrete material object (as that: the car, the building, money and other things), or set of the information (music, inventions, writing, etc.), but without connection with the concrete owner.

Possession (ownership). Possession joins the owner with objects. As a result of such joining objects become the property. We shall image possession of the concrete owner as a covering rectangular which unites in itself and the concrete owner (on the scheme he is named ) and a full set of all objects which belong to this owner (they are represented as points p, q and r). The surface of this rectangular can be understood as area of owner possession - all the objects which are being inside, are accessible to the owner for using (Fig. 1).

possession

Fig. 1 Owner A owns objects p, q and r

In a schematic form possession is represented quite compact, however in real life the contents of possession has no certain borders at all: the property can be in the different remote places, but the main thing - the area of possession is inaccessible for observations at all. Nevertheless such graphic representation of possession is rather convenient for the theoretical analysis: it enables to represent all owners: a usual citizen, a family, a public organization, a business firm or even the state - absolutely identical.

Possession also can be represented algebraically. In this case it is possible to write down the possession of objects p, q and r by owner A in the form - p, q, r.

2. Act of using

The property using are intentional (i.e. operated by the owner) changes of objects conditions. Concrete using acts can be diversified: and various changes of the form of object, and connection of different objects in something the whole, and change in space position.

Fig. 2 Act of using. Object p1 is converted to condition p2

Let us assume that baker (owner A) has put the dough into the oven (the initial condition of object is p1) and, having waited when bread will bake, takes out ready loaf (the final condition is p2). On the scheme the way how baker has influenced on object is shown by the arrow directed from the initial object condition to final (Fig. 2).baker

This using act can be designated by one symbol u, or it is possible to write down in the form as algebraic operation (it is represented as arrow)

u = ( p1p2 )

That means - as a result of the using act u the owner's A object p1 has been converted to the condition p2.

3. Voluntary interactions

Whichever using acts are made by owner with his property, it is changes only the conditions of objects, but not their belonging. Possession of objects can be changed only as result of interaction with exterior owners.

Voluntary interaction is concerted changes of possession of cooperating owners. Schematically voluntary interaction is represented by the arrows showing direction of possession change.

Voluntary interaction

Fig. 3 Voluntary interaction between A and B owners (property moving is represented by arrows)

booksFor example, the owner A comes into the shop and buys there for money (object $q) the book (object p) from the owner B (Fig. 3). On the scheme it is visible, as in the given interaction act the contents of property are changed at both owners: the object $q leaves from the property of the owner A, but his possession is replenished with object p; and at owner B, on the contrary: the property is replenished with object $q, but object p leaves his possession.

This action of objects exchange can be written down by algebraic operation - we shall designate its by vertical line (or, even more shortly, by symbol )

A,B = $q | pB

Moving process of objects from one owner to another is not stretch in time, it occurs instantly, without the intermediate stages. Objects during the moment of possession change may not change their spatial position. The property movements displayed on the scheme have only theoretical but not mechanical meaning.

4. Restricted possession

Unrestricted possession. Some of objects can be in unrestricted possession. Unrestrictedness means, that the owner can make with that object absolutely any actions, in particular: to move anywhere, to transmit to any exterior owner in any terms, to not use object, to spoil or even to destroy it completely.

Restricted possession. Unrestricted possession can be divided by the owner into areas - the restricted possession. It occurs when at interactions the owners transmit objects in some restrictive frames of possession (on time, in a using place, on interactions conditions with other owners, etc.). Thus, the possession of one object can be divided into independent possessions between several owners.

Restricted possession

Fig. 4 The moving act of object p to restricted possession α of owner A

For example, the owner S (suppose, the state) has transmitted object p (parcel of land) to owner A (farmer) in the restricted possession (rent). It means that both owners A and S possess the one object p. More particularly, A can sow cultures on p, irrigate crops, harvest, sell p to exterior owner, etc. We shall designate such restricted possession (area) of owner A over object p by symbol α (Fig. 4). Thus owner's A possession of the object p can be written down as αpA.

Restricted possession

Fig. 5 Owners A and S own one object p in restrictions α and β


On the other hand, the former owner S also now can be restricted on possession of this object p. We shall designate this possession restriction of the owner S by symbol β (Fig. 5). Full possession of the given object p consists of two possessions areas:

p = α pA + β pS.

Let's note basic sense of the restricted possession - owners A and S own the same object p not together, but separately. Each of the restricted owners, being in the certain restricted frames, uses the object p only under the own wish without dependence from desires of other restricted owner.

5. Owners

Any owner has next abilities:

Self-feeling. Actions over the property can influence on the owner differently: "positively", "negatively", "more positively", "less positive", etc. We shall name such perception of actions over the property the self-feeling. The self-feeling is resided in each owner initially and cannot change by the owner directly by his desire. The owner can change his self-feeling only as result of actions over the property.

Routes of actions. The purpose. As a rule, using acts are rigidly linked by cause-and-effect relations. And the important feature of this interrelation is that not the initial act as inevitability leads to the subsequent act (as the material world develops), but quite contrary: to achieve a final condition of objects - the purpose, - it is necessary for owner to pass the certain chain of preliminary actions (in particular, using acts). Such time sequence of actions forms the route of actions. The route can be described as the chronologically ordered set of using acts R ={a1, a2, ...an}, where aiєU (set of using acts), an - the route purpose.

For example, to drink a cup of tea it is the purpose, - the owner should make the whole series of preliminary using acts: to boil water (u1), to make tea (u2), to pour tea and boiled water in a cup (u3), to put there sugar (u4), and only then to drink tea (u5). In the given example the route will be the chronologically connected sequence of using acts R(u1, u2, u3, u4, u5), where the last act - u5 - is the purpose of this route.

Intentions. Effect. Shall name all routes of the future development which are considered by the proprietor, - intentions. All owners are arranged so, that they aspire to realize those intentions which would provide the most high indications of their self-feeling for all time of they existence. In other words, for the owner the basic criterion in a choice of the route of future development is the integral of self-feeling taken over time - shall name such value the route effect.

6. Elementary and compound owners

The person-owner (intellect). In theoretical sense the person-owner is not appearance of the concrete person but only its mental faculties - ability to feel the objective world and to influence it. In a human civilization the human minds are elementary owners. Their self-feelings display a mental condition of concrete man: his positive, neutral or negative feelings.

Compound owners. By means of interactions the elementary owners can create compound owners who are consist of combination of two or more owners. Depending of a kind of combination of component owners, the compound owners can be one of two kinds - collectives or subdivisions:

7. Collective (co-ownership, share possession )

Collectives consist of two or more owners - co-owners, - which own property on shared base. Combination of co-owners in collective occurs by means of the coefficient named share. We shall designate a share by symbol λ - its values lay in an interval 0≤ λ ≤1, where 1 - sum of all shares.

C = ∑λi ci , where

C - collective;
ci - i-th co-owner;
λi - the share of i-th co-owner;

The more the concrete co-owner has λ value, the greater share in collective property he owns. Investigating λ values, it is possible to find out two boundary cases. When the co-owner share value decreases to zero (λ =0) its means that he is not the co-owner at all. If the share value rises up to unit (λ =1) - its means this co-owner is the single owner of all collective property.

Co-ownership

Fig. 6 Owners A and B co-own object p

Let's consider an example (Fig. 6). We shall admit, there is a stock-company C, where all shares belong to two shareholders (co-owners) - A and B. The shareholder A owns 70% of shares (λ=0,7), and the shareholder B owns 30% of shares (λ=0,3). Thus, the collective C - it is 0,7A + 0,3B.

8. Subdivisions (nested owners)

chief Owners can create inside of themselves new owners whom they will own. We shall name the owner who owns other owner the chief , and the owner who is in possession - subdivision. Schematically we shall represent subdivision as the owner inside of the chief property.

The subdivision simultaneously is both - the owner and the object of possession. The possession of the subdivision consists in definition to it the purposes which it will realize in practice - we shall name such possession control. The subdivision owns the property not completely, but restrictedly, we shall name such restricted possession - execution.

subdivision

Fig. 7 Chief A and his subdivision B

Example. The person (owner A) has created the manufacturing firm (subdivision B). Now A is the chief of subdivision B - that is A controls , and obey to A. Let p - the property of subdivision B: machine tools, materials, finished goods - the subdivision B owns them restricted - only executes the purposes that are set by the chief A. Simultaneously the same objects p belong to A as to the chief, but already completely, without any restrictions.. We shall notice, the objects of the property related by the owner A to a personal property: as the house, the car, the TV, etc. - (we shall designate r), do not belong to subdivision B (Fig. 7).


The subdivision is formed every time when one owner (chief), sets the purposes for implementation to some exterior owner - the executor. Subdivisions can be very steady in time though executors can vary. For example, when executive director leaves his post, his place is occupied with other person, and the enterprise as the subdivision, remains constant.

Chief A and executor E create subdivision D

Fig. 8 Chief A and executor E create subdivision D.
d - post of executor.


Let, the owner A creates subdivision D and allocates there property p (Fig. 8). For this purpose A cooperates with exterior owner E (executor) that E will obey to him (execute his purposes). Let d - a post, as a set of characteristic actions executed by subdivision D. Thus E, occupying post d, becomes executer of subdivision D.

The subdivision is a result of obey of executor to his chief. Shall designate operation of obey by symbol "." (point). Thus, subdivision D can be described by the formula:

D = A.E

Subdivisions

Fig. 9 Subdivisions can create other subdivisions inside of themselves

Subdivisions, being owners, also can create inside of themselves other subdivisions in relation to which they will be chiefs (Fig. 9). Thus, between owners there can be a whole hierarchy of possessions in the form of the subordinations relations.

Administrative machine

Fig. 10 Administrative machine

If to examine only that subdivisions, which united in steady subordination hierarchy they create the administrative machine. We shall display connections between subdivisions as the arrows, continuing from chiefs to subdivisions (Fig. 10). The administrative machine always looks like the graph, beginning from the most senior chief and finishing in subdivisions of the lowest level.

9. Axioms

AxiomsWe formalize graphic model of property relations by following group of axioms

 

1° - Possession determines for the owner the actions area over objects.

2° - The owner can give possession over object to exterior owners only in the his possession area of this object.

3° - The self-feeling of owner is function of this actions (using, interactions).

4° - The owner determines the set of intentions.

5° - The owner realizes only those intentions which by his estimation provide to him the greatest effect.

All axioms is entered without proofs - they are true always.

10. Compulsion

Interaction which for one of the parties is not voluntary, we shall name force (or compulsion). The owner who the given interaction does not consider voluntary, we shall name victim, and another - forcer.
Compulsion

Fig. 11 Forcer X, appropriating another's object p, renders compulsion on victim A


For example, the thief (owner X) imperceptibly pulls out the purse (object p) from the citizen (owner A) (Fig. 11). As for A such influence does not concern to voluntary, A will be a victim of influence, and X - forcer. Schematically the fact of force influence we shall represent by empty circle on border of victim's possession. In other words, this circle shows break, infringement of borders integrity of possession.

Threats. We shall name intention to make force influence the threat. The owner analyzes the information on every possible exterior threats, making an amendments to the own intentions. Amendments at threats are leaded to one: effects values of those intentions, which are exposed to threats, are reduced. That is, if threat has concerned intentions which earlier was seemed as the best, after introduction of amendments on threat, this intentions become less attractive and even may be unacceptable for realization at all.

11. Justice and morality

Justice. Justice means identity of owners and determines symmetry of the organization of all society. We shall distinguish two kinds of justice:

Initial appropriation. We shall examine a task. There is a material world. In it owners appear. How these owners receive objects of a material world to the property initially? In particular, on what basis some set of owners M can confirm that the territory p located between the river q and mountains r, is their property? Feature of this task is that still nobody owns material objects, and consequently (according to 2), nobody can transfer it to the appeared owners.

Let's set initial appropriation of the property by two axioms without any proofs:

6° (principle of freedom) - The person's body belongs to this person.

7° (principle of equal co-ownership) - All living people own natural objects in an equal measure.

Let's name this axioms group the initial appropriation axioms. As we see, initial appropriation axioms correspond to criterion of equality: they determine model of a human society symmetric concerning all living in current time people.

Morality. The morality in our intuitive overview is indissolubly connected with concepts of "good" and "evil". Speaking about morality, it is imply existence of its antithesis - immorality. As a rule, at many people the intuitive images, associating with concepts "moral" and "immoral", coincide, but in theoretical reasoning any subjective representations are necessary to expel. Strict logical proofs cannot base on intuition - they can be based only on axioms and logical laws. We shall define morality as a certain characteristic of owners actions at next axiom:

8° (principle of morality) - the owner actions, which is not lead to increase of a compulsions level in a society - are moral.

As opposed to concept of. morality we shall enter concept of immorality as its logic denying. That is, we shall put, that immoral actions is all which cause increase a compulsions level in a society. Having formalized concepts "morality" and "immorality", it is possible to take from these statements some consequences:

  1. as criterion of morality and immorality mutually exclusive, there can not be such actions, which would be both moral and immoral simultaneously;
  2. the criterion of morality is not local (where only direct participants of the given interaction take part), but global (where force influences on all owners of all society are considered);
  3. the moral estimation has unique absolute value, and does not depend upon any subjective owners view about morals;

Example. Punishment for criminals is compulsion. But as this compulsion leads to reduction of the general compulsions level in all society (the criminality decreases) such state actions are moral.

Morality and justice - absolutely different concepts. If the morality is connected with a compulsions level in a society, justice is not connected with compulsion at all, and concerns only equality of owners among themselves. Thus, there are quite possible such owners actions which can be moral and at the same time unjust, or on the contrary, - just, but immoral. For example, if the state exempts a part of owners from taxes (those who works in economic zones), such state actions are though moral (as the level of compulsions is decrease), but unjust (as owners are considered unequal).

The correct task decision must correspond to two criteria at once - both morals and justice. If the task does not have decision which would satisfy to both criteria simultaneously, the correct decision will be what correspond to criterion of morals as it guarantees a smaller compulsions level in a society.

12. Nature

The nature as the owner. All material objects are subject to influences from the physical forces of nature. To keep integrity of society model, we shall enter the special owner - the Nature, representing cause-and-effect changes of all objects of a material world. For this purpose we shall put, that:

13. The owner People and natural resources

People According to a principle of equal co-ownership natural resources: the land, the interior of the Earth, a water surface and air space - belong to all living people in an equal share. We shall define the compound owner People which initially owns all natural resources. People consists of equal co-owners - citizens - all living people. For control all national property, citizens can elect the executor, we shall name him President.

The owner People engages in all economic affairs connected with sale of natural resources. Basically People as well as any other owner can engage in absolutely any commercial activity.

14. The moral state

The state is the strongest owner in a society.
For construction of the society with a minimum level of compulsions it is necessary to determine for the owner-state the moral purpose to minimize the compulsions level in society.

C o n s e q u e n c e 1. As the purpose of the moral state do not depend from any exterior owners (including citizens) then, citizens are not co-owners of a state ownership, and consequently, citizens cannot participate in control of state affairs by voting.

In the moral state legal laws should be proved by carrying out of deductive reasonings proceeding from initial statements (axioms) - only such approach can guarantee both - morals of legal laws and consistency of all laws among themselves. Necessity to conduct strict deductive proofs demands from legislators high intellectual ability, so in the moral state legislators should pass selection on skill to conduct deductive reasoning (mathematical faculties).

Now we shall start filling the moral state by the necessary property. Force of the moral state consists in the maintenance of forces subdivisions, such as Army, Police. These subdivisions should have in the property all necessary that the moral state would be the strongest.

15. State and People

We have already determined two owners - State and People. They exist absolutely isolated from each other: People engages in the national commerce (mainly, rent of the land and a circulation of national money), and State engages only in suppression of the compulsions level in a society. However we still had unresolved last problem, - whence State to take property?

Complexity of the decision of this problem consists that State cannot offer anything in exchange - neither services, nor the goods (by definition it should engages only the morals subjects). How to be?

The decision will be the following: the owner State appropriates a necessary part of means from owner People. Certainly, such assignment is compulsion, however, this compulsion will be simultaneously and moral as these means will be spent for suppression of compulsions, that will not lead to increase of the general level of compulsions in all society, and just, as this means are taken from all citizens in an equal measure.

 

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