of the number ω but not the existence of the ωth past day . 123 Whether the ωth day exists is not a question for mathematics but a question about the nature of time . 124
Cantor discussed another aspect of the notion of traversing an infinite in his correspondence with a Catholic theologian Constantine Gutberlet . In their letters , Cantor and Gutberlet consider a motion of a rigid wire which is infinite in one direction and possesses an infinitely distant end . The question Gutberlet asks is whether the pulling of the finite end away from its infinite end will cause the infinite end to move . Cantor responds that if such a wire existed then moving of the finite end would move all the finite points of the wire , but the infinite end would remain unmoved . Gutberlet objects that this would contradict the assumption of rigidity . The only possible solution is that an infinite force is needed to move an infinite rigid wire . 125 It seems that such infinite force would cause the finite end to take its place in the opposite infinity while pulling the infinite end into the finite , but would not make the wire finite . Therefore , the ends of the wire can traverse infinity in an instant . However , if by traversing a multitude , we mean exhausting it by taking away one equal part after another , then “ the infinite cannot be traversed by the finite , nor by the infinite .” 126
123
Small , " Cantor and the Scholastics ," 414 .
124
Ibid , 417 .
125
Ibid , 426 .
126
Adam Drozdek , " Number and Infinity : Thomas and Cantor ," International Philosophical Quarterly 39 , no . 1 ( 1999 ): 38 ,
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