Cantor ’ s response to the impossibility of comprehending an infinite . In the answer to this objection , Bonaventure hints at the manner in which a finite power can grasp an actual infinity . Some infinite series can be comprehended by the means of a single principle : since all solar revolutions are of the same kind , then to know one of them is to know them all even if there are infinitely many . Cantor ’ s definition of cardinal numbers suggests that his approach to the knowledge of an infinity is similar . “ The infinite collection of possible things can be taken as posited by a single thought operation , and if an infinite collection can exist , it can come into being all at once by a single creative act .” 127 This means that in comprehending the infinity of the transfinite number ω , one must grasp the wholeness of the set of natural numbers immediately and not try to come to know it by the mediation of its elements . 128 Related to this are the two stages of abstraction explained by Husserl :
The first stage in the constitution of a set consists in the collecting of distinct objects whereby a plurality is reconstituted as a Many , but not yet apprehended as a One . It is only at the second stage that we become conscious of the set as a new object . This is achieved by means of a reflection on the preceding act of collecting .” 129
127
Small , " Cantor and the Scholastics ," 425 .
128
Drozdek , " Number and Infinity ,” 38 .
129
Kai Hauser , " Is Choice Self-Evident ?" American Philosophical Quarterly 42 , no . 4 ( 2005 ): 244 . Page 53 of 62