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.