  Benacerraf opens by defending what is now known as a structuralist view of the natural numbers, according to which the natural numbers have no properties other than those they have in virtue of being positions in an ω-sequence. For instance, there is nothing more to being the number 3 than having certain intrastructurally defined relational properties, such as succeeding 2, being half of 6, and being prime. No matter how hard we study arithmetic and set theory, we will never know whether 3 is identical with the fourth von Neumann ordinal, or with the corresponding Zermelo ordinal, or perhaps, as Frege suggested, with the class of all three-membered classes (in some system that allows such classes to exist).