The Journal of Philosophy

Volume 113, Issue 5/6, May/June 2016

Philosophy of Logic and Mathematics

Solomon Feferman
Pages 234-246

Parsons and I: Sympathies and Differences

In the first part of this article, Feferman outlines his ‘conceptual structuralism’ and emphasizes broad similarities between Parsons’s and his own structuralist perspective on mathematics. However, Feferman also notices differences and makes two critical claims about any structuralism that focuses on the “ur-structures” of natural and real numbers: (1) it does not account for the manifold use of other important structures in modern mathematics and, correspondingly, (2) it does not explain the ubiquity of “individual [natural or real] numbers” in that use. In the second part, Feferman presents a summary of his reasons for the skepticism he has towards contemporary metamathematical investigations of set theory. That skepticism led him to reject the Continuum Problem as a definite mathematical one. He contrasts that attitude sharply to Parsons’s “great sympathy for the current explorations of higher set theory.”