ABSTRACT
Mathematics studies the relation between number and multiplicity and as such it intersects with one of the main domains of philosophy: the study of one and many in the structure of the universe. Rilke’s metaphor about the bees and the invisible acquires a stunningly literal meaning in Socrates’ examination of the question in the Meno. While searching for a single de nition of virtue, he encounters a “swarm” (smēnos) of examples. Ba ed by this plurality, he observes:
I seem to be in luck. I wanted one virtue and I nd that you have a whole swarm of virtues to o er. But seriously, to carry on this metaphor of the swarm suppose I asked you what a bee is, what is its essential nature (peri ousias hoti pot’ estin), and you replied that bees were of many di erent kinds … what is that character in respect of which they don’t di er at all, but are all the same? (Men. 72a4-b2, trans. Guthrie)
With Socrates, the Neoplatonists also look for the single essence (ousia) of things that are many. Multiplicity, discrete or continuous, is the rst most apparent feature of physicality. If unexamined, it appears chaotic, random and in nite. But for Socrates and the Neoplatonists, behind the overwhelming diversity of physical magnitude and multitude, there is a permanent intelligible order. e concept of number is in the privileged position to be both “the honey the bees collect” when measuring the quanti able properties of multiplicity and “the bee” itself in modelling the paradigm of reality.
