Logic Matters 2008-03-22

Absolute Generality 20: Linnebo on sets, properties, etc.

And having said that I would write about Linnebo's paper next, I find myself rather regretting that promise, and this will be a non-comment!Linnebo begins by announcing that the "strongest argument against the coherence of unrestricted generalization" is Williamson's variant Russell paradox about interpretations; and he then takes the most promising line of reply on the market to involve adopting a kind of hierarchical type theory. Then Linnebo locates what he thinks to be a problem with the usual kind of "type-theoretic defences". So he changes tack, and offers a different, more revisionary response to Williamson's argument, which depends on rethinking the very idea of an interpretation (so that now predicates get not extensions but rather properties as their semantic values). He then needs a whole framework for talking about properties as well as sets (which has, he says, some ...

read more   

more posts from Logic Matters