He published a paradigm changing article entitled "What Numbers Could Not Be".

He developed an argument against the ontology of set-theoretic Platonism.

Shapiro and Resnik hold that all mathematical theories, even non-algebraic ones, describe ___.

It consists of places that stand in structural relations to each other

It instantiate the structure that is described by a non-algebraic theory are isomorphic with each other, and thus, for the purposes of the theory, equally good

In Shapiro’s view, they are not ontologically dependent on the existence of systems that instantiate them

It appears that it describes the notion of a structure in a somewhat circular manner

Denies that any concrete physical system is the unique intended interpretation of analysis

sometimes described as “structuralism without structures