Mathematica nos ducunt adpenitus absoluta-Philosophy of Mathematics of Nicolas of Cusa

Abstract

The author analyses the place of mathematics and its importance in the thought of Nicholas of Cusa. He understands mathematics as a mirror, where the infinite as the infinite is reflected in the finite. Mathematics is predominantly the science of the visible, and that enables a step-by-step transfer from »the vision of the eye« to »the vision of the mind«. Furthermore, the mathematical entities are the most certain of all the objects of the visible world, and this makes them the most suitable starting point for investigating the uncertain and the unknown. This mathematical certainty is based, according to Cusanus, on the ontological status of the mathematical entities. They are neither suprasensible entities (Plato), nor the principles of the real world (Pythagoreans), they are not abstracted from the material world (Aristotle) - they are entia rationis, beings in the reason, e. g. they exist only in the mind. The human reason can understand with certainty and precision only that which it has itself produced - everything else is only an approximation. Mathematics contains also an immanent tendency towards the infinite as the infinite. It enables us to think the coincidence of the opposites, which is the necessary precondition for the »touch« with the infinite as the infinite. The transfer from the finite mathematical entities to the infinite as the infinite takes place through the infinitization of the finite geometrical figures and, in a further step, in abstraction from such figures. To put it into a nutshell: mathematics does not lead directly to the infinite as the infinite, but has an immanent tendency towards it.