SENSIBLE THINGS, ESSENCES, MATHEMATICAL OBJECTS, AND OTHER AMBIGUITIES1

The least that we can say is that mathematical objects are mysterious objects. Some argue that they are the product of the mind. Others contend that they are pre-existing transcendental entities. And many do not understand how one can get to know something about them if we suppose that they are beyond human experience. Historically speaking, conceptualizations of mathematical objects rest on two major long-standing and opposing categories of Western thought, namely the realm of sensual things, on the one hand, and the realm of essences, concepts and the like, on the other hand. In this paper, I discuss, against the background of Greek philosophy, the way in which Kant attempted to resolve the distinction between essences and the sensible. In the last part of the article, I sketch a view of mathematical objects within a cultural theory of signification where mathematical objects are seen as fixed patterns of activity embedded in the always changing realm of reflective, semiotic- and artefact-mediated social practice