LA STRUTTURA FRATTALE DELLA SCIENZA DELLA LOGICA

Ivan Saracino

This paper proposes an interpretation of Hegel’s Science of Logic through the model of fractal geometry. The traditional geometric representation of the Hegelian system as a simple circle proves inadequate to capture the complexity of dialectical movement. Hegel himself recognized this limitation by introducing the formula “circle of circles”, suggesting a more complex geometric structure. This study demonstrates how fractal geometry provides a more accurate formal model for understanding the logical structure described by Hegel. The analysis addresses a preliminary methodological objection: applying mathematical models to a system that explicitly rejected the mathematization of thought. The proposed use is heuristic and retrospective — fractal geometry describes formal properties already operative in Hegel’s text — rather than foundational or constitutive. Hegel’s concept of Wirklichkeit, as the unity of logical and ontological structure, provides the ontological justification for this descriptive application. Three formal correspondences are then established. First, fractal self-similarity offers a geometric model for Hegel’s thesis that each logical moment essentially contains the totality of moments. Second, the recursive structure of fractals renders visible the “circle of circles” and the scalar articulation of dialectical movement. Third, the structural invariance of fractals with respect to the observation point formally illustrates the indifference of the beginning with regard to systematic totality. The limits of the analogy are explicitly recognized: fractal geometry is spatial, whereas the Logic is purely conceptual; fractal iteration is mechanical, whereas dialectical development is qualitative and teleological. The fractal model is therefore a heuristic instrument, not a literal ontological description.