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Halfway Up To the Mathematical Infinity: On the Ontological and Epistemic Sustainability of Georg Cantor's Transfinite Design | | Edward G. Belaga
; | | Date: |
17 Dec 2008 | | Abstract: | 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 G"odel’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. | | Source: | arXiv, 0812.3207 | | Services: | Forum | Review | PDF | Favorites | |
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