Alice van’t Hoff (University of Vienna) – Against higher-order unrestrictedness

Generality absolutists argue that it is possible to quantify absolutely unrestrictedly over everything that there is. A challenge to their view arises if we take seriously the possibility of genuinely higher-order quantification. An influential proposal, first put forward by Timothy Williamson, however, suggests that to conclude on this basis against generality absolutism would be premature. Williamson's claim is that higher-order quantification in our object language is only a threat to generality absolutism if we, misleadingly, adopt a first-order metalanguage. I argue, though, that this approach is subject to a counter-example: intuitively, quantification in many-sorted languages need not be absolutely general. Yet both higher-order and many-sorted systems may involve multiple distinct quantifiers and there are, I claim, no differences of the kind relevant to a quantifier's unrestrictedness that distinguish these two versions of quantifier pluralism. This suggests, contra Williamson and others, that higher-order quantification is a threat to generality absolutism, at least insofar as we take quantification of this kind ontologically seriously.


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Michele Contente, Ludovica Conti and Caterina Sisti