   Throughout these analyses, Russell put into practice a slogan he stated as follows: “Wherever possible, logical constructions are to be substituted for inferred entities” (RSDP, 115; cf. LA, 326). Rival philosophies that postulate an ego or mind as an entity distinct from its mental states involve inferring the existence of an entity that cannot directly be found in experience. Something similar can be said about philosophies that take matter to be an entity distinct from sensible appearances, lying behind them and inferred from them. Combining Russell’s suggestions that talk of “minds” or “physical objects” is to be analyzed in terms of classes of sensible particulars with his general view that classes are “logical fictions”, results in the view that minds and physical objects too are “logical fictions”, or not parts of the basic building blocks of reality. Instead, all truths about such purported entities turn out instead to be analyzable as truths about sensible particulars and their relations to one another. This is in keeping with the general metaphysical outlook of logical atomism. We also have here a fairly severe application of Occam’s razor. The slogan was applied within his analyses in mathematics as well. Noting that sometimes a series of rational numbers converges towards a limit which is not itself specifiable as a rational, some philosophers of mathematics thought that one should postulate an irrational number as a limit. Russell claimed that rather than postulating entities in such a case, an irrational number should simply be defined as a class of rational numbers without a rational upper bound. Russell preferred to reconstruct talk of irrationals this way rather than infer or postulate the existence of a new species of mathematical entity not already known to exist, complaining that the method of “postulating” what we want has “the advantages of theft over honest toil” (IMP, 71).