Digital Continent Digital Continent_Template amended | Page 65

remains inaccessible even to the entire transfinite structure. One can even argue that Cantor’s
theory improves our understanding of the absolute transcendence of God. 133
Cantor’s response to the impossibility of the existence of an actual infinite. Cantor is
“a mathematical realist of a Platonic sort.” 134 He holds that the transfinite numbers already exist
in the divine intellect; therefore, his constructions don’t create transfinite numbers but are a
method for their discovery. However, for Cantor it is not the obligation of mathematics to show
the actual existence of its objects either in the reality or in the mind. Mathematics consists in
developing methods of construction of new objects and then finding mathematical theorems that
explain their relationships. 135 Russell agrees that pure mathematics is indifferent even to the truth
of its axioms. Mathematicians take any consistent set of axioms that seems interesting and
deduces their consequences, leaving it to scientists to decide which mathematical theories best
approximate the actual world. 136 Therefore, Cantor, as a mathematician, argues only for the
validity of transfinite numbers based on the consistency of their properties: “there is no
133
Kai Hauser, "Cantor's Absolute in Metaphysics and Mathematics," International Philosophical Quarterly 53, no.
2 (2013): 171.
134
Rioux, "Cantor's Transfinite Numbers,” 103.
135
Jean W. Rioux, "What Counts as a Number?" International Philosophical Quarterly 53, no. 3 (2013): 229-230.
136
Russell, “Mathematics and the Metaphysician,” 107.
Page 55 of 62