Mgr Oktawian Nawrot

Institute of Philosophy and Sociology

University of Gdansk

Bielanska 5

80-851 Gdansk



Liberty as a Relation


What is liberty, that “magic” word, which could give reasons for envy to Protheus himself, and which is referred to so often that we seem to know every single one of its faces? Since August the 26th, 1789, the day when The Declarations of the Rights of Man was proclaimed, it has been being said more and more loudly and commonly that Men are born and remain free and equal in rights [5, art. 1] (It is not meaningful for the discourse that this document for a long time actually regulated only the legal situation of men, the clear evidence of which can be found in Robespierre’s order to guillotine Olympia de Gouges, the author of The Declaration of the Rights of Woman and Citizen, with its first paragraph saying: Every woman is born free and has the same rights as a man [4, p.32].). What does the above statement mean? What are we actually dealing with? Should we understand liberty as the freedom to do whatever comes to our minds, including “walking in the clouds”? Do we see liberty as the situation in which no compulsion occurs? Or maybe we should understand it as an inner state, which is dependent only on the individual and its view on the world, and which cannot be changed by even the strongest shackles? Should we then repeat after St. Ambrose: a wise man, even if he is a slave, is free, which means that a fool, even if he rules, is enslaved [1, p. s. 196], or after Helvétius: a free man is a man who is not handcuffed, nor imprisoned, nor lives as a slave in constant fear of punishment [2, p. 36]? What is liberty, then?


Article Four of the already mentioned Declaration of the Rights of Man says that: Liberty consists in the freedom to do everything which injures no one else [5]. The quoted words seem to put an end to all anarchist theories of liberty describing it as a lack of any compulsion. In the light of the above definition, liberty is some relation which at the same time puts the limits on itself. Using the expression which injures no one else forces us to look at liberty not as something inner, some feeling, state of mind something so intangible on one hand, or as the lack of any limits, and therefore de facto other subjects on the other hand, but rather as at objective reality, the state that we can submit to falsification. If we have the reference to another human being, and a particular reference, we can surely speak about a relation, and therefore a particular interpersonal reality. Having investigated this relation, which I will call a liberty relation, we will discover that it has some characteristic features.


Above all, it should be noted that every human being possesses some definite sphere of liberty, just as everyone has some definite height, weight, IQ etc. It is obvious then that at a definite moment, everyone has such a scope of liberty as he has, exactly as everyone has such a height or weight as he has – no more, no less. Therefore we can say that the liberty relation is a reflexive relation in class A. This conclusion is a natural consequence of assuming the rule of non-contradiction ~(p^~p), which in this case can be transcribed in the following way: it is not possible for anybody to be like something in some aspect and at the same not to be like it, or in other words: it is not possible for anybody to possess some feature (to some degree) and at the same time not to possess it [7, p. 379]. This statement itself is not a great discovery, together with some other qualities of the liberty relation, however, it will let me present some interesting implications of the latter. Therefore:


ΛxεA xWx

            Where: x stands for the individual

                        A – the society

                        W – the liberty relation


The Declaration of the Rights of Man claims next: the exercise of the natural rights of each man has no limits except those which assure to the other members of the society the enjoyment of the same rights [5, art. 4] , therefore stating that liberty has limits, and moreover, that it clearly defines the limits itself: the limit of the liberty of the individual is the liberty of another individual. As John Locke noticed: So that, however it may be mistaken the end of law is not to abolish or restrain, but to preserve and enlarge freedom: for in all the states of created beings capable of laws, where there is no law, there is no freedom: for liberty is, to be free from restraint and violence from others; which cannot be, where there is no law: but freedom is not, as we are told, a liberty for every man to do what he lists: (for who could be free, when every other man's humour might domineer over him?) [3, sec. 57]. Therefore to let everyone the widest possible sphere of liberty, it is necessary for every person in society A to have identical spheres of liberty. It is worth mentioning that Kant’s categorical imperative Act only on that maxim which you can will as a universal law or the biblical you shall love your neighbour as you love yourself. The idea was accurately reflected by the UN General Meeting who, when on December the 10th, 1948 declaring The Universal Declaration of Human Rights, in Article One of this document claimed that: All human beings are born free and equal in dignity and rights [6]. If we assume that it is necessary that everyone have (at least at the starting point) the same degree of liberty as the other members of a given society, then we can say that the liberty relation is not only reflexive, but also symmetric:


Λx,yεA (xWy → yWx)


According to the above: for every two subjects, who are members of society A, if x is in the liberty relation to y, then y is also in the liberty relation to x. Therefore when someone is born as a slave, or his rights are limited in comparison to others for whatever reason, in the light of the above comments we cannot speak of the liberty relation, but rather about the relation of subordination, since the liberty relation as a symmetric relation must be followed by equality in the sphere of liberty among individuals, this being its constitutive feature. With such an understanding of liberty, it is not necessary to speak of the natural equality among people, since the latter is included in the former. It is also worth mentioning that using a conjunction by the General Assembly of the United Nations means that a situation when somebody is born free and at the same time has limited rights in comparison to other members of the society is not possible. According to the above statement, the situation when somebody is born with the same rights as others but at the same time enslaved is not possible, either.


To go further this way of thinking, we must claim that if the liberty relation occurs between x and y and between y and z, then it must occur between x and z as well. If x is free in relation to y and if y is free in relation to z, then x is free also in relation to z. Therefore, the next feature of the liberty relation is its transitiveness. In this way, the liberty relation is extended on all the members of society A and “connects” with each other even the individuals that are completely different in all other aspects.


Λx,y,zεA (xWy ^ yWz → xWz)


If at this point we connect all the features of the liberty relation that we have enumerated, that is its reflexiveness, symmetricalness and transitiveness, we discover that this relation is actually an equivalence relation. What we get is a view of society in which all individuals have exactly the same scope of liberty. In other words, there appears a class of abstractions, a class of individuals who in this case remain in the equivalence relation towards each other, and therefore are identical as to the scope of liberty they possess. It is not irrelevant to note that the liberty relation generates something like the human family or the human community.


To sum up, we can state the following: if individual x is free in society A, then the liberty relation of which the individual is a subject is at the same time reflexive, symmetric and transitive in the class consisting of all the members of society A:


WL(x,A)→ Λx,y,zεA [xWx ^ (xWy → yWx) ^ (xWy ^ yWz → xWz)]

WL(x,A) – x is free in society A


All the above comments refer on the one hand to the relation between individuals, and on the other to the state which we would call initial, which is the situation when the liberty of no individual is limited (because of the individual’s state, for example incapacitation resulting from insanity, or his deeds, such as crime). A few questions and doubts appear at this point, out of which two seem to be most important. First of all, some might say that it is easy to imagine a society where all the above conditions are met but it would be difficult to say that all the people living in it can enjoy their freedom. Let us imagine for example a society where the liberty of the individual is limited to the freedom of thought. All the members of the society are still members of a liberty relation, but the sphere of liberty of all the individuals is so limited that de facto they are all enslaved.


At a first glance, the above charge seems to be easy to refute: it is enough to notice that in fact not everybody will be enslaved to the same extent because there will always exist someone who – in this case – will actually enjoy an unlimited scope of liberty and make a profit on the others’ enslavement. Therefore the symmetry will be broken and as we have already proved, this symmetry is a constitutive element of the liberty relation, and in this situation we can only speak of a relation of subordination. The case is much more complex, though, since the problem refers to the conditions that must be met by society A to let the people living in it enjoy real liberty.


Pointing out the symmetricalness of the liberty relation, we have said that the limit for the individual’s liberty can only be set by the liberty of some other individual. However, the existence of the State machine can at times spoil this order, as there are a number of obligations that a citizen has towards the state and therefore the sphere of his freedom becomes limited. If we consider the liberty relation between the individuals, the condition necessary for this relation to be retained seems to be the individual’s abstinence from activities which result in invading the liberty of another individual. At this level we mostly deal with negative obligations: don’t kill, don’t steal etc. In the case of the relation citizen - state or citizen - society there appear some positive obligations, demanding a particular action from the individual: paying taxes, military service etc. In such case it is necessary to define the spheres of life in which the individual can act unrestricted or with a certain freedom. Consequently, there can exist laws that would regulate the actions of the individuals and at the same time it would undoubtedly be possible to speak of liberty. Freedom is a liberty to dispose, and order as he lists, his person, actions, possessions, and his whole property, within the allowance of those laws under which he is, and therein not to be subject to the arbitrary will of another, but freely follow his own [3, sec. 57].


It is necessary then to define the spheres of life in which the individual will be allowed to direct his own person in a possibly unrestricted way. Again, we must note that the spheres cannot be chosen at random, because according to the above rules we would be able to create a totalitarian society, but only those that are crucial from the point of view of the individual’s interest. This is the place where it becomes clear why we started our discourse by referring to The Declaration of the Rights of Man. What we undoubtedly see as crucial spheres of life are the spheres that actually reflect the human rights: as Karl Vasak said, the rights of liberty (personal and political rights), the rights of equality (economic, social and cultural rights) and the rights of brotherhood (solidarity rights). There is no point in listing these rights here, it is only important for us to realise that we are speaking of particular spheres in the life of the individual and his rights, not some illusionary ideas.


In the light of the above comments the statement illustrating the liberty of individual x in society A must be completed:


WL(x,A) → Λx,y,zεA [xWx ^ (xWy → yWx) ^ (xWy ^ yWz → xWz) ^ Vi S(x,i) ^ Vni S(x,ni)]

Where: S – the freedom of action,

i – „crucial spheres of life” (the spheres in which the liberty must be guaranteed by law),

                ni – the spheres of life of the individual beyond the interest of the state,

            S(x,i) – individual x has the freedom to act in i,

            S(x,ni) – individual x has the freedom to act in ni.


To conclude, we should ask whether the existence of the classes of people whose liberty has been limited by law (the already mentioned incapacitated insane people or the criminals to whom legal means have been applied) will not disrupt the presented scheme or will not cause the necessity to complete it. It seems that it will not. The very notion of incapacitation, a person deprived of capacity suggests that in reference to those people we cannot speak of the liberty relation (we would say: as much freedom as responsibility). It seems interesting that the individuals being members of the second mentioned class have disrupted the liberty relation themselves, and therefore the disruption of the symmetry, which is necessary for freedom to exist, was caused by their own actions.


Pole tekstowe: p	q	p←q
1	1	1
1	0	1
0	1	0
0	0	0

One might wonder whether the above words are not a too simple solution to the problem. We might rightly ask: what about children? We know that even in liberal societies their liberty is considerably limited in comparison to that of adults. To take into consideration the categories of people with limited rights, ant therefore liberty, we must complete our statement. To do this, we must introduce the matrix of the unnamed extensional functor. What we have is a functor with the use of which we will always build a true compound sentence, if only the first clause is true. In other words, to make the compound sentence true, only the first argument must be true. I will ascribe to the functor the symbol “←” and I suggest to transcribe it as the expression “at the same time, it may happen that”. Why this matrix? Because the use of the functor means that the first of its arguments must be true in every case, if the compound sentence built with it is to be true. In this case it only means that the first part of the formula, which is the one that we have already presented, must always describe a particular society, if we want to call the individuals living in it free. The second argument does not have to appear at all. Naturally, in reality there always exist incapacitated people or people with restricted rights (together with sentenced criminals). However, we can easily imagine a society in which no such categories of people exist, and the individuals living in it we can still call free. Of course the introduced functor connects in a way stronger than material equivalence:


WL(x,A)↔ Λx,y,zεA [xWx ^ (xWy → yWx) ^ (xWy ^ yWz → xWz) ^ Vi S(x,i) ^

^ Vni S(x,ni)] ← VoεA ~S(o, i v ni)


where: S – the freedom to act,

o – the individuals with limited scope of liberty,

            ~S(o, i v ni) – individual o does not have the freedom to act in i or in ni.






1.      Berlin I., Cztery eseje o wolności, Warszawa 1994.

2.      Helvétius C.A., O umyśle, t. 1, Warszawa 1959.

3.      Locke J., Two Treatises of Government, Book II,

4.      Powinności Człowieka, Kronika Międzynarodowego Forum Jubileuszowego „Prawa i Powinności Człowieka”, Święto Człowieka, Posłanie Normana Daviesa, Gdańsk 2001.

5.      The Avalon Project : Declaration of the Rights of Man – 1789,

6.      The Universal Declaration of Human Rights,

7.      Witwicki W., Psychologia, t. I, Warszawa 1962.