ABSTRACT
CERTAINLY most of the paradoxical statements encountered in the mathematical domain—though not, as Kästner ( 1 ) would have it, all of them—are propositions which either immediately contain the idea of the infinite, or at least in some way or other depend upon that idea for their attempted proof. Still less is it open to dispute that this category of mathematical paradoxes includes precisely those which merit our closest scrutiny, inasmuch as a satisfactory refutation of their apparent contradictions is requisite for the solution of very important problems in such other sciences as physics and metaphysics.
