infinite-divisibility

from James Dodd’s introduction to Jan Patočka’s “An Introduction to Husserl’s Phenomenology”

To thematize awareness, to make it into an “object” of reflection or inquiry–this is something that goes beyond mere being in the presence of things, developing something that is only hinted at in our awareness of things. It is a thematization of the sense, always at work in our understanding of individual things, that every entity that we encounter in the world is always encountered within a context, whether of our activity or of relations to other things. Things are never meaningful in themselves, only with others; they point to a context that is always more a horizon than an object. … This thematization of the horizon of the world in Greek though accounts for its mathematical character, in two basic senses. … A second sense is the Greek sensitivity to the mystery of things. Certain mathematical phenomena … inspire wonder. The infinite divisibility of the line, the incommensurability of the sides to the hypotenuse–all this at once highlights the presence of horizon of the whole in entities and, in one fell swoop, opens up an access to the mystery of things, the mystery that all this is. It is as if, as Patočka puts it, an infinity were suddenly discovered at the very core of the familiar objects of our everyday surroundings; as if we suddenly became acutely aware of the strangeness of our world, a strangeness that had nevertheless always been there, had always played a part, however subtle, in our experience.