ABSTRACT. According to Feferman, categorical notions of arrows cannot be logically prior to set-theoretic accounts of objects. Dummett argues that the term “structuralism” ought to only be applied to structuralism at the abstract level. Lucas argues that we can see how we might have almost expected Gödel’s theorem to distinguish self-conscious beings from inanimate objects: the essence of the Gödelian formula is that it is self-referring. Benacerraf argues that numbers are not objects and that numerals are not singular terms: elementary arithmetic is concerned with systems that share the common structure, and not with any particular ontology.