According to Wikipedia, the title is the original formulation of the motto of the French revolution, which later became the motto of France. I believe understanding it actually helps us to overcome some common disagreements about tango!
This motto does not contain just some random three terms. The relationship of the terms to each other is as important as the terms themselves.
Liberté was probably used in the sense that political right uses it now, meaning that one has the right to the fruits of their own work — low taxation. And égalité was probably used in the sense of equality of outcome (rather than equality of rights as we understand it now) — high taxation. If we understand liberty and equality this way, they are actually opposing each other. Why would one use opposing terms in one motto?
There is another peculiarity about the terms:
The third term, Fraternité, was the most problematic to insert in the triad, as it belonged to another sphere, that of moral obligations rather than rights, links rather than statutes, harmony rather than contract, and community rather than individuality.
But if we consider the historical context, we can see that these features of the motto are not so strange after all. The triad follows structurally the model of thesis – antithesis – synthesis which was very much in vogue at that time. Synthesis is something “higher” that brings the two opposing “forces” together, creating harmony.
Liberty and equality were chosen as the first two terms exactly because they oppose each other. Their order is also significant: one cannot talk about taxation before there are some gains to be taxed. And as the third term, fraternity was chosen because only through community based on relationships, the inherent conflict between liberty and equality of outcome can be overcome, and harmony reached.
This original formulation also tells us what happens if we do not follow the motto: we will turn away from life, which is harmony, and create disharmony, death.
Perhaps it is also useful to remind ourselves that the triad contains all three terms, not only the last term. The struggle between the two first ones creates the potency of the last term. The last one would not exist by itself.
In Richness of Tango I described some discussions regarding tango in the internet. Behind each one of the discussions one can find an argument about equality of the roles in tango, the second term in the motto. This is natural reaction and “progress” in relation to the first term.
But, to help overcome these disagreements about the roles in tango and perhaps learn to understand the issues more deeply, one can apply some structural analysis to these discussions. What are the two missing terms, the first one, and the third one? What is the consequence if “harmony” is not reached?