[FOM] Is Linnebo?s system MS inconsistent?

[laureano luna]

 Dear FOMers,Prof. Menzel and Prof. Linnebo (to whom I amhighly indebted) discovered the problem in my tentative proof of inconsistencyof system MS: step 3 in my proof sketch was wrong. Putting aside technicalities,ultimately, my mistake originated from the assumption that axiom schema P-Compquantified over absolutely all sets at all stages of the hierarchy, not overthe sets at the ‘actual’ stage. My assumption was inspired by thisconsideration of Prof. Linnebo in a previous paper (Linnebo 2010, “Pluralitiesand sets”, p 16: http://oysteinlinnebo.org/p&s.pdf):“A relatedquestion is which sets are actual with respect to the modality invoked above.One answer is that precisely those sets are actual that have been formed at ourcurrent stage of the process of forming sets. But this is uninformative. Forwhat is our current stage of this process? The most plausible response to thisfollow-up question is, I think, that set theorists do not generally regard themselvesas located at some particular stage of the process of forming sets but rathertake an external view on the entire process. It would therefore be wrong toassign to ourselves any particular stage of the process”.I assumedwe were committed to constant domain semantics. The mistake, however, wasentirely mine.
Laureano Luna.
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