Logic Matters 2008-03-26

Absolute Generality 22: Parsons on varieties of Russell's paradox

Parsons, however, doesn't think that the principal problems about quantifying over everything arise from a supposed commitment to metaphysical realism but are "logical difficulties ... [which] arise from considering how sentences or discourses containing quantifiers are interpreted. This apparently innocent talk of interpretation turns out to have considerable weight." Why?Here's how I think the dialectic goes in the compressed but elegant Section 3 of Parsons's paper (with some changes in notation):Quantifiers are standardly interpreted as ranging over some domain, predicates are interpreted by subsets of the domain etc. A domain is understood to be a set. In standard set theory, no set contains absolutely everything. (Going for a set + classes theory just shuffles the problem upstairs.) So quantifications aren't over absolutely everything.But in fact, Parsons says, it isn't specific issues about sets or classes that generate the difficulty here. ...

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