The mathematics in the Schopenhauer´s philosophy: Intuition versus demonstration by means of an experiment.

Intuição versus demonstração por meio de um experimento

Abstract

Schopenhauer puts in opposition two ways to acquire the mathematical knowledge: the intuition against the demonstration. The demonstration is the Euclidean geometrical demonstration or the synthetic method. The intuition (Intuition or Anschauung) refers to the immediate knowledge of the a priori notion of space, ie the pure and a priori intuition of space. For the German philosopher, these two types of knowledge occur through two distinct faculties: the Reason (Vernunft), the creator of the concepts used in the demonstration, and the Understanding (Verstand), related to intuitions. The concepts are transformed forms of the intuitions and therefore less reliable. Thus, Schopenhauer suggests that mathematics should be learned by the use of the intuition and not by the use of the Euclidean demonstrations. Our paper presents this conception of Schopenhauer through the Pythagoras´ theorem. We present the Schopenhauer’s proposal through an  mathematical experiment, whose conclusions will be drawn from the reader.

Keywords: Concept. Demonstration. Euclid. Geometry. Intuition. Schopenhauer.