Geodesic
Cantor e le antinomie
Matematica, cultura e società, Série 1, Tome 3 (2018) no. 3, pp. 193-209

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Cantor was aware, from the beginning of his work on infinite numbers in the early eighties of the 19thcentury, that not all conceivable collections could be assumed as existent sets; the totality of ordinal numbers was for him a symbol of the Absolute; in mathematics it led to antinomies; he tried to exclude such collections by carefully but ambiguously shaping the definition of “set”. In the end, he was tempted however to use them, in correspondence with Hilbert and Dedekind, to prove the great open questions of the theory, such as the trichotomy for cardinals and the well-ordering theorem, which were due to be solved later by Zermelo. 
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Lolli, Gabriele. Cantor e le antinomie. Matematica, cultura e società, Série 1, Tome 3 (2018) no. 3, pp. 193-209. http://geodesic.mathdoc.fr/item/RUMI_2018_1_3_3_a2/