   It was clearly a part of Russell’s view that in conducting an analysis of a domain such as mathematics, and reducing its primitive conceptual apparatus and unproven premises to a minimum, one is not merely reducing the vocabulary of a certain theory, but also showing a way of reducing the metaphysical commitments of the theory. In first showing that numbers such as 1, 2, etc., could be defined in terms of classes of like cardinality, and then showing how apparent discourse about “classes” could be replaced by higher-order quantification, Russell made it possible to see how it is that there could be truths of arithmetic without presupposing that the numbers constitute a special category of abstract entity. Numbers are placed in the category of “logical fictions” or “logical constructions” along with all other classes.