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Georg Cantor was the genuine discoverer of the Mathematical Infinity, andwhatever he claimed, suggested, or even surmised should be taken seriously --albeit not necessary at its face value. Because alongside his exquisite inbeauty ordinal construction and his fundamental powerset description of thecontinuum, Cantor has also left to us his obsessive presumption that theuniverse of sets should be subjected to laws similar to those governing the setof natural numbers, including the universal principles of cardinalcomparability and well-ordering -- and implying an ordinal re-creation of thecontinuum. During the last hundred years, the mainstream set-theoreticalresearch -- all insights and adjustments due to Kurt G\"odel's revolutionaryinsights and discoveries notwithstanding -- has compliantly centered itsefforts on \emph{ad hoc} axiomatizations of Cantor's intuitive transfinitedesign. We demonstrate here that the ontological and epistemic\emph{sustainability} of this design has been irremediably compromised by theunderlying it peremptory, Reductionist mindset of the XIXth century's ideologyof science.

Halfway Up To the Mathematical Infinity: On the Ontological and Epistemic Sustainability of Georg Cantor's Transfinite Design