**Hassan Ajami**

Justice is usually defined in terms of freedom and/or equality. Yet peace is also an essential component of justice, leading us to formulate a unique conception of justice, which is justice as peace. This conception could be developed through the mathematization of justice.

**Freedom, Equality, and Peace**

Justice should be analyzed in terms of peace because without peace there will be neither freedom nor equality, and hence, justice could not be maintained without peace. People living in war zones are either killed or wounded, or illegally imprisoned or kidnapped, and their different kinds of freedom, such as the freedom of speech and movement, are violated due to the atrocities of war, which violate human rights. This is why justice as freedom could not be obtained in the time of war. And hence, maintaining peace is the first condition that should be satisfied to have justice as freedom.

Similarly, in wartime, people are not treated equally, given that war violates the human rights of some people through the killings and wounding, and through oppressing some and illegally imprisoning or kidnapping others. This shows that peace should be established and protected to have justice as equality.

In light of these considerations, peace should be considered to be the first principle of justice to maintain any sort of justice, such as justice as freedom or justice as equality. And this is why justice should be defined in terms of peace, and not only in terms of freedom and equality. Justice without peace is senseless, while justice without freedom and equality is incomplete.

**Mathematization of Peace**

According to the mathematization of philosophy, philosophical theories could be successfully presented in mathematical equations, and concepts could be mathematically analyzed. For example, we could mathematically analyze justice in the following way: justice = peace x freedom x equality. In this mathematical theory of justice, justice is analyzed in terms of peace, freedom, and equality, such that justice is a mathematical equation, according to which, justice is equal to peace multiplied by the freedom which is in turn multiplied by equality. This mathematical equation of justice implies that the best kind of justice or the maximum amount of justice is obtained if and only if we have the maximum amount or degree of peace, freedom, and equality for every individual.

**Different Kinds of Justice**

It follows from this mathematical equation that there are different kinds of justice. Since justice = peace x freedom x equality, it mathematically follows that peace is equal to justice, such that justice is divided by the multiplication of freedom and equality. And thus, justice could be maintained when peace is established, even if freedom and equality are minimum but not equal to zero (given that whatever is divided by zero is indefinite). This is the first kind of justice, according to which, justice exists due to the existence of peace.

Moreover, since justice = peace x freedom x equality, it also mathematically follows that freedom is equal to justice, such that justice is divided by the multiplication of peace and equality. Thus, justice could be achieved when freedom is maintained and maximized, even if peace and equality are minima yet not equal to zero (given that whatever is divided by zero is indefinite). This would be justice as freedom. And it is the second kind of justice, according to which, justice consists of freedom and the maximization of freedom, regardless of the maximization of peace and equality.

The third kind of justice follows from the same equation. Since justice = peace x freedom x equality, it mathematically follows that equality is equal to justice, such that justice is divided by the multiplication of peace and freedom. Therefore, justice is maintained when equality is established and maximized, even if peace and freedom are minimum but not equal to zero (given that whatever is divided by zero is indefinite). This is justice as equality. And it is the third kind of justice.

Equality, in this context, could be understood as equality before the law, equality of opportunity, and/or social and economic equality. Yet the best kind of justice is the fourth kind, according to which, justice is maintained if and only if peace, freedom, and equality are maximized at the same time, given that justice = peace x freedom x equality. All of this shows that the mathematical conception of justice accounts for the different kinds of justice, leading to its success and acceptance.

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