Paradoxes of the Infinite and Ontological Dilemmas Between Ancient Philosophy and Modern Mathematical Solutions

The concept of infinity had, in ancient times, an indistinguishable development between mathematics and philosophy. We could also say that his real birth and development was in Magna Graecia, the ancient South of Italy, and it is surprising that we find, in that time, a notable convergence not only of the mathematical and philosophical point of view, but also of what resembles the first "computational approach" to "infinitely" or very large numbers by Archimedes. On the other hand, since the birth of philosophy in ancient Greece, the concept of infinite has been closely linked with that of contradiction and, more precisely, with the intellectual effort to overcome contradictions present in an account of Totality as fully grounded. The present work illustrates the ontological and epistemological nature of the paradoxes of the infinite, focusing on the theoretical framework of Aristotle, Kant and Hegel, and connecting the epistemological issues about the infinite to concepts such as the continuum in mathematics.