Is Absolutely General Quantification Possible?

The possibility of absolutely general quantification is often taken to be obvious, since even those who deny it seem to presuppose its existence in order to express the claim that no quantification is unrestricted. Presumably, the argument goes, the quantification in the previous sentence is not restricted in any way. In this paper, I assess critically and reject various arguments for the possibility of absolutely general quantification and develop an alternative that acknowledges the restrictions in each kind of quantification. As an example, I examine second-order quantification and indicate the nature of the restrictions in this case, contrasting the resulting proposal with the conception advanced in Hellman's “Against ‘Absolutely Everything’!”. The result is a more nuanced account of the issue.

Otávio Bueno is Professor of Philosophy and Chair of the Philosophy Department at the University of Miami. His research is in philosophy of science, philosophy of mathematics, philosophical logic, metaphysics, epistemology, and philosophy of art. He has published over 200 papers in prominent journals, is the author and editor of several books, and the editor in chief of Synthese.