‘Let me give you a simple example of what I mean, and you will see the
rest for yourself.’ This is how Plato usually introduces mathematical
examples to illustrate important philosophical puzzles. The research
presented in this book offers a systematic analysis of these examples
and demonstrates their crucial psychagogical function. Providing a
toolkit of paradoxical objects that challenge the soul and summon
thought, mathematical examples do not convey demonstrative rigor or
exact calculations, but instead induce psychic states of aporia and
wonder. The gaze of Plato’s mathematicians is directed both downwards
and upwards: precisely for this reason mathematics have the power to
awaken the soul and to lead it towards the Forms.
“Take a little example, and you’ll know all I mean.” Thus Plato introduces mathematical examples aimed at illustrating particularly problematic philosophical issues. This study provides a systematic analysis of such examples and shows their crucial psychagogical function. Like a toolkit of paradoxical objects that confuse the soul and set thought in motion, the mathematics of the examples do not convey demonstrative rigor and exact calculations, but induce psychic states of aporia and wonder. Precisely by virtue of their bifurcated gaze, directed not only upwards but also downwards, mathematics has the power to awaken the soul and draw it towards Ideas.
