Abstract

I offer an understanding of what it is for a term to be rigid which makes no serious metaphysical commitments to or about identity across possible worlds. What makes a term rigid is not that it 'refers to the same object(property) with respect to all worlds' - rather (roughly) it is that the criteria of application for the term with respect to other worlds, when combined with the criteria of identity associated with the term, ensure that whatever meets the criteria of identity also meets the criteria of application and vice versa - in the simplest case, the criteria of application just are the criteria of identity - but things can be more complex to allow for the necessary a posteriori. This makes rigidity a non-metaphysically loaded semantic matters, and allows us to see that the phenomenon of and involving rigidity - especially the necessary a posteriori - are of no metaphysical significance on their own.