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conviction of its comprehensibility, Cantor’s revolutionary treatment of infinity arises
predominantly from his novel philosophy of mathematics. Jourdain evaluates Cantor’s
contributions in the following way: “The philosophical revolution brought about by Cantor’s
work was even greater, perhaps, then the mathematical one. With few exceptions,
mathematicians joyfully accepted, built upon, scrutinized, and perfected the foundations of
Cantor’s undying theory; but very many philosophers combated it.” 146 Cantor saw consistency as
the only requirement for validity in mathematics and considered sets and functions to be the
proper objects of mathematics. Aquinas and Bonaventure followed the Aristotelian view of
mathematics in which quantity was the object of mathematics and the unit its fundamental
principle. Therefore, Cantor’s mathematics is intrinsically open to an actual infinity while the
mathematics of Aquinas and Bonaventure is fundamentally finite allowing only for a potential
infinity. Despite these profound differences and Cantor’s unprecedented openness to the
existence of an actual infinity, Cantor agrees with Aquinas and Bonaventure that mathematics
alone, even when fortified by the theory of the transfinite numbers, is insufficient to
demonstratively answer the question of the temporal beginning of the world.
146
Cantor, Contributions, vi.
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