GABRIELE LOLLI

The Incompleteness Theorems

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.

I. Panorama

II. Attese, speranze e timori

III. Anticipazioni

IV. La formula (e la dimostrazione)

V. Equivoci e incomprensioni

VI. Altre dimostrazioni

VII. Le reazioni dei mostri sacri

VIII. Altre reazioni

IX. L’interpretazione di Gödel

X. La mente e l’io

XI. Bellezza e magia