O problema da divisibilidade infinita do espaço: um exame da Geometria segundo Hume

Abstract

The conception of space presented by Hume establishes his foundations over the disposition of the indivisibles sensible points, from which we became aware of the copy principle. For a better understanding, this principle shall be properly presented, demonstrating how, from it and from the distinction of reason, the mind get access to the simple ideas, through an imagination’s attention exercise. It is at this first moment that the bedrock for Hume to respond the questions pointed about your concept of space and infinity are settled down. Next, we’ll take a brief journey through ancient and modern Philosophy, so we can bring to the debate some of the conceptions of space and infinity built in periods prior to Hume’s. The space, according to him, is built up of indivisible sensible points and this definition brings us several issues to the proper functioning of the Euclidian geometry. Similarly, we’ll try to show that his own concept is judged as unsatisfactorily constructed, as pointed up by some commentators that consider Hume as a bad mathematician or as overlooking by adopting a concept of space that, according to those commentators’ allegations, it’s not supported by the copy principle. By saving the validity of his concepts, Hume casts doubts on the validity of the Euclidean geometry, since the indivisible points of which the space is compounded invalidate some of the main theorems of that geometry, just as the bisection and the Pythagorean theorem. Hume solves this dilemma bringing up this whole new comparison criteria, from which it is possible to test the equality or the inequality of geometric objects. Moreover, we’ll try to show that this method proposed by Hume allow us to correct, every time that it becomes necessary, our judges concerning the equality or the inequality between geometric objects compared.