Abstract

The theory of beauty has always rested on the representation of the infinite, understood in its finite expression and perceptible through the senses. The relationship of beauty to truth, of art to science, is inevitably modified with the new way of treating the infinite in the modern conception of the world. Non-classical science works with the notions of “infinitely large” and “infinitely small,” modifying their meanings in terms of experimental observations. We put these words in quotation marks because the Whole may be considered as finite or infinite according to the angle from which it is viewed: the “infinitely small” only becomes so in determined circumstances, for example, when we consider the extended and discrete elements of space and time in a macroscopic approximation, as infinitely small elements of perpetual motion. Modern science studies these two poles of being—the Whole and its parts—in their interaction, admitting the dependence of macroscopic and even cosmic processes with regard to the processes being created in infinitely small spheres (or, according to another interpretation, finite but extremely small). However, as characteristic of our time as these concepts are—most often hypothetical—they nonetheless express a very old historical tradition that contemporary retrospection, turned toward classical science and the past of science in general, allows us to discern very clearly. All the culture of the past was dominated by the principle of the authority of the Whole over its parts. In peripatetic cosmology and physics, individual processes depended on the cosmic harmony of the center and frontiers of the universe, on the spheres and places toward which bodies tend. This authority of the general law, of universal harmony, of the system hinging on individual processes, is confirmed in Aristotle's Physics, but not only there: we find it in almost all the thinkers of antiquity. On the plane of general logic, it received expression in the Hegelian concept of the true infinite, a concept constituting to a high degree the philosophical equivalent of classical science. In Hegel's time, this last was already drawing away somewhat from the idea of an absolute and strict subordination of elementary processes to integrating systems and general laws, laws being realized through the probability of microprocesses, thus statistical laws, and whose exact application ignored individual acts, for example, the mechanism of molecules in thermodynamics. The statistical theory of heat has rendered continual a discrete microcosm—for the movement of individual molecules it substituted the average speed of the molecules—and continual laws became supreme points determining macroscopic processes. These laws had a differential nature. In other words, they prescribed the defined relationships between the infinitely small increases in size. Also, the schema of the classic law consisted in defining infinitely small processes by an infinitely large integral legality because of the number of processes. The infinitely true of Hegel is the actual infinite being realized in each of its finite elements; it is the subjection of the finite element to the infinite.