Justice is Like Pi

There are truths that do not arise from our understanding but precede it. These truths exist, whether we comprehend them or not. In mathematics, Pi is one such example: the ratio between the circumference and the diameter of a circle. Pi is not a product of our construction but a given constant—a property of the circle itself. Yet, although this value exists, it cannot be grasped rationally. It becomes visible only through approximation: through the successive refinement of geometric figures, iterative methods, and structured limit processes.

The idea of true justice behaves in a similar manner. Justice is not a product of political systems, moral theories, or social conventions. It is a fact—not in the sense of empirical observability but as a transcendent, universal form that surpasses all particular notions of justice. Yet, like Pi, this justice is not directly tangible. It is revealed not through a single insight but through continuous approximation: through discourse, revision, and the broadening of horizons.

The path to justice is open to different methods. Just as mathematics allows for relationships between area and circumference, area and diameter, or diameter and circumference—and all methods converge toward the same limit, Pi—so too can different political, cultural, or legal processes strive for justice. What matters is not the iterative rule but the form they approximate: the target form.

In mathematics, this target form is the circle—a perfect, closed shape that is not composed of segments but is whole in itself. In the philosophy of justice, this target form is the ideal of an order that gives each their due, without ever being fully realizable. Justice as a target form is universal—but not rigid. It remains open, sensitive to contradictions, and receptive to new perspectives.

In this sense, democracy is not the fulfillment of justice but its iterative space of possibility. Democracy allows for approximation, balancing, and correction. And by creating procedures where the relationship between social breadth, institutional circumference, and normative reach is constantly recalibrated, it approaches—like the polygon to the circle—that which has always been there: true justice.