Halfway Up To the Mathematical Infinity I: On the Ontological & Epistemic Sustainability of Georg Cantor’s Transfinite Design

Georg Cantor was the genuine discoverer of the Mathematical In-finity, and whatever he claimed, suggested, or even surmised should be taken seriously – albeit not necessary at its face value. Because alongside his exquisite in beauty ordinal construction and his funda-mental powerset description of the continuum, Cantor has also left to us his obsessive presumption that the universe of sets should be subjected to laws similar to those governing the set of natural num-bers, including the universal principles of cardinal comparability and well-ordering – and implying an ordinal re-creation of the continuum. During the last hundred years, the mainstream set-theoretical research – all insights and adjustments due to Kurt Gödel’s revolutionary in-sights and discoveries notwithstanding – has compliantly centered its efforts on ad hoc axiomatizations of Cantor’s intuitive transfinite de-sign. We demonstrate here that the ontological and epistemic sus