No class: Russell on contextual definition and the elimination of sets

Philosophical Studies 139 (2):213 - 218 (2008)
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.
Keywords Russell  Classes  No-class theory  Propositional functions  Higher-order quantifiers  Intensional  Extensional  Principia mathematica  Soames  Dawn of analysis
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John P. Burgess (2005). Fixing Frege. Princeton University Press.

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