ABSTRACT
Does “7 > 5” express a binary relation between two objects? If we say yes, it at first becomes difficult to see how it could be an instance of a completely general logically valid form or be a logical truth, as logicism demands. In this chapter, I sketch the development of Russell’s logicism from a yes-answer to this question towards a no-answer, according to which statements about numbers and similar “objects” are not about objects at all, and how this development was prompted by his attempt to solve Cantorian and other paradoxes plaguing the fundamentals of his logic. Russell ends up with a position according to which so-called “abstract objects” should be understood not as objects but fragments of logical forms. Mathematical truths are instances of fully generally valid logical forms, after all, as logicism demands, despite misleading surface syntax that obscures this.
