Matemàtiques: una ciència incompleta

Abstract

[en] The present paper aims to show the consequences of Gödel’s incompleteness theorems on the foundations of mathematics and on the philosophy of mathematics. It has three sections. The first section shows the triggers of the stage known as ”the crisis in the foundations” as well as the two main philosophical currents that emerged in it: logicisim and formalism. In the second section, Gödel’s incompleteness theorems are presented as they were originally presented by adding comments that try to explain the different steps of the proof. This section also shows the subsequent advances that allowed enunciating them as we know nowadays. Finally, the third section tries to analyze the consequences that these two theorems had.