The Problem of Foundations: An Adventurous Navigation from Sets to Entities. From Gödel to Thomas Aquinas

One of the more relevant – if not the most relevant – mathematical logicians of the 20th century, who was able to prove a theorem that, in the opinion of the ma- jority, states the failure of human knowledge even within mathematics (after Kant had definitively destroyed any epistemological and metaphysical realism, being followed by almost all the later thinkers), claims that «mathematics proper», and then science based on it, needs to be founded on something which is absolutely true, objective and evident! It seems that only ideological blindness may prevent perceiving such a situa- tion, and consequently engaging ourselves with a serious work about the problem of foundations. One may reasonably start from the foundational claims of contem- porary sciences and compare them with the results of the great syntheses of Greek and Mediaeval logic and metaphysics, which, historically allowed the development of modern sciences. The present book, would represent a small initial attempt in such direction. Translated from italian - Original title: Il problema dei fondamenti. Un’avventurosa navigazione dagli insiemi agli enti passando per Gödel e Tommaso d’Aquino, Cantagalli, Siena (I) 2009