Volume 56, Issue 2, June 2016
Damián Bravo Zamora
On the Soberer Conclusions that May Be Drawn from Kantian and Cantorian Antinomies
This paper explores the connection between Kant’s first antinomy and the set-theoretical paradox of the largest cardinal. The lesson to be drawn is that we should refrain from reifying (i.e., treating as an individual object or thing) the collections that generate the antinomies: the collection of all spatio-temporal objects (the world) in the case of Kant’s first antinomy, the collection of all objects whatsoever (the universe) in the case of the Cantorian paradox. This conclusion is not only one that we are entitled to draw but also one that does not generate new philosophical problems of its own. In this respect it is more attractive than other contemporary reactions to the paradoxes of set theory.