No class: Russell on contextual definition and the elimination of sets |
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| Authors: | Scott Soames |
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| Affiliation: | (1) School of Philosophy, University of Southern California, 3709 Trousdale Parkway, Los Angeles, CA 90089-0451, USA |
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| 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. |
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| Keywords: | Russell Classes No-class theory Propositional functions Higher-order quantifiers Intensional Extensional Principia mathematica Soames Dawn of analysis |
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