There are still over twenty pages of Lavine’s paper remaining. Since, to be frank, Lavine doesn’t write with a light touch or Lewisian clarity, these are unnecessarily hard going. But having got this far, I suppose we might as well press on to the bitter end. And, as I’ve just indicated in the previous post in the series, I do have a bit of a vested interest in making better sense of his talk of schematic generalizations.
There are four Sections, 9 — 11, ahead of us. First, in Sec. 8, Lavine argues that even with schematic generalizations as he understands them in play, we still can’t get a good version of McGee’s argument that the quantifier rules suffice to determine that we are ultimately quantifying over a unique domain of absolutely everything, and so McGee’s attempt to respond to the Skolemite argument fails. I think I do agree that the rules even if interpreted schematically don’t fix a unique domain: but I’m still finding Lavine’s talk about schematic generalizations pretty murky, so I’m not sure whether that is right. Not that I particularly want to join Lavine in defending the Skolemite argument: but I am happy to agree that McGee’s way with the argument isn’t the way to go. So let’s not delay now over this.
In Sec. 9, Lavine discusses Williamson’s arguments in his 2003 paper ‘Everything’ and claims that everything Williamson wants to do with absolutely unrestricted quantification can be done with schematic generalizations. Is that right? Well, patience! For I guess I really ought now to pause here to (re)read Williamson’s paper, which I’ve been meaning to do anyway, and then return to Lavine’s discussion in the hope that, in setting his position up against Williamson, more light will be thrown on the notion of schematic general in play. But Williamson’s paper is itself another fifty page monster … So I think — just a little wearily — that maybe this is the point at which to take that needed holiday break from absolute generality and Absolute Generality.
Back to it, with renewed vigour let’s hope, in 2008!