Mathematical model of explanation of the world’s structure in Plato’s Timaeus

Abstract

Plato?s cosmological dialogue The Timaeus initiates, among other things, the question of the status of mathematical entities: do they exist completely independently of the physical world whose structure they supposedly explain, are they present in a certain sense within the physical world, or are they, perhaps, exclusively psychological in nature. The author of the paper critically examines Johansen?s interpretation according to which the inherent structure of the human psyche, in the case of Plato?s Timaeus, is already mathematically ideal. Although Johansen?s interpretation is pervasive and well-grounded, the relationship between mathematical and sensory entities is considered mainly in the context of astronomy, disregarding Plato?s theory of micro-structures (the so-called geometric atomism). Thus, the author confronts Johansen?s interpretation with the opinions of other influential researchers of ancient philosophy, such as Cornford, Vlastos, Popper, Lloyd, Brisson, as well as the philosophers of the ancient era, Proclus, Aristotle, and others, in an effort to develop an interpretation that is as close as possible to the whole of Plato?s text. It seems that, when it comes to Plato?s Timaeus, one cannot discuss about the psychological origin of the mathematical model of explanation of natural phenomena without realizing that, in a quite complicated way, such mathematical model possesses a physical aspect as well. Plato himself, at the end of The Timaeus, claims that psychological disorders are caused by disruptions of the mathematically ideal proportions of bodily parts of the human organism (86b), which is only one of his claims that points to the psychophysical nature of mathematical entities.