通往数学无限的半路--康托超限设计的本体论和认识论的可持续性
Halfway Up To the Mathematical Infinity: On the Ontological and Epistemic Sustainability of Georg Cantor's Transfinite Design
摘要：
康托尔是真正的发现者数学的无限，无论他声称，建议，甚至猜测应该认真对待-虽然没有必要在其表面价值。因为除了他精致的美序结构和他对连续统的基本幂集描述之外，康托还留给我们一个强迫性的假设，即集合的宇宙应该服从与控制自然数的集合类似的定律，包括基数可比性和良序的普遍原则-并暗示连续统的有序再创造。在过去的一百年里，主流的集合论研究--尽管由于库尔特·哥德尔的革命性见解和发现而进行了所有的见解和调整--已经顺从地将其努力集中在康托直观超限设计的\emph{ad hoc}公理化上。我们在这里证明，这种设计的本体论和认识论的\emph{sustainability}已经被19世纪科学意识形态的潜在的专横的、还原主义的心态不可补救地损害了。
英文摘要：
Georg Cantor was the genuine discoverer of the Mathematical Infinity, 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 fundamental 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 numbers, 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 insights and discoveries notwithstanding -- has compliantly centered its efforts on \emph{ad hoc} axiomatizations of Cantor's intuitive transfinite design. We demonstrate here that the ontological and epistemic \emph{sustainability} of this design has been irremediably compromised by the underlying it peremptory, Reductionist mindset of the XIXth century's ideology of science.
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