In 1930 Kurt Gödel’s incompleteness theorems changed the course of philosophy of science. The proof that, within a theory fulfilling certain minimum conditions, one can devise a proposition that can be neither proved nor disproved within the theory itself is a cornerstone of scientific thought. The announcement of the two theorems at the Königsberg conference in 1930, dedicated to epistemology and the exact sciences, annihilated Leibniz’s vision of using a “calculemus” approach to address any controversy. Gödel’s theorems also ushered in a new logic comprising antinomies and paradoxes.

Gabriele Lolli formerly taught Mathematical Logic at the University of Turin and Philosophy of Mathematics at the Scuola Normale Superiore in Pisa.