On the Heine - Borel Property in the Theory of Abstract Sets

implication in general) to the rule of syllogism—is wholly fallacious; the real source of the difference lies in the change of sense of the middle term; that to confound in a middle term the sensus compositi and the sensus divisi is a source of danger has been a commonplace of logic since the time of the scholastics. That an inept symbolism is made use of in mathematics, which has for a fundamental interest the point and the "variable" (i. e., individuals, or singulars) would be of no consequence, but Russell and Peano treat this "addition" as constituting an important improvement over the logic which preceded them—that of Peirce and his school—instead of which it is simply erroneous.