Logic Matters 2008-03-30

Absolute Generality 25: Indefinitely extensible concepts, "big" and "small"

The Shapiro/Wright paper is a high point in the Absolute Generality collection. For a start,First, they focus on Dummettian considerations. I've already argued here that considerations against the possibility of absolutely general quantification based on Skolemite worries, or on worries about "metaphysical realism", don't seem particularly compelling. It seems to me that the key interesting issues hereabouts do indeed arise from considerations about indefinite extensibility (pressed by Dummett, but having their roots, as Shapiro and Wright remind us, in remarks of Cantor's and Russell's).It is also the case that, unlike some of the others in the collection, this paper is written with fairly relentless clarity and explicitness (and though it isn't free of technicalia, the details are kept on a tight rein).Shapiro and Wright take up a hint in Russell, and (in Sec. 2) consider the following -- at least ...

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