Abstract

The article rebutts Michael Kremer’s contention that Russell’s contextual definition of set-theoretic language in Principia Mathematica constituted the ontological achievement of eliminating commitment to classes. Although Russell’s higher-order quantifiers, used in the definition, need not range over classes, none of the plausible substitutes provide a solid basis for eliminating them. This point is used to defend the presentation, in The Dawn of Analysis, of Russell’s logicist reduction, using a first-order version of naive set theory.