All Things Indefinitely Extensible
Stewart Shapiro, Crispin Wright · 2006
Abstract The direct concern of our chapter is not with unrestricted quantification. Or at least: not unrestrictedly unrestricted quantification quantification over absolutely everything there is. Our direct concern is with whether it is admissible to quantify over sets without restriction whether it is coherent to speak of, and have bound variables ranging over, all pure sets, or all pure set-like totalities (see also Shapiro, 2003). (‘Well, but didn’;t you just do so?’;) Closely connected questions, also within our focus, are whether it makes sense and if so, what kind of sense to speak of all cardinal numbers, or all cardinalities, and all ordinal numbers, or all order-types of well-orderings.