The finitude or infinitude of the universe divided the ancient philosophers while fueling a debate intertwined with the subtleties of the very concept of infinity and the plausibility of its realization in the physical world. As the first steps in the formal domain of mathematical infinity were taken in the 19th century, the question of the cosmic size remained open and expecting better empirical evidence. At the end of the 20th century, the observational data of cosmology seemed to opt for an infinite volume, although the delicate metaphysical problems that such an option implies have rarely been highlighted.