My current work has been on the foundational programs in mathematics in the 1920's and 30's, specifically in the epistemological structure of Hilbert's Program and the contributions of Herbrand, Bernays, and Gentzen. I find that in many ways current research in the foundations of mathematics has departed from the spirit of its founders so that it no longer speaks to their philosophical motives. In my doctoral thesis I present techniques for the foundations of mathematics that answer directly to the epistemological setting of Hilbert's Program and describe how the technical results founded on these techniques differ from classical results.
I am also working on epistemological issues directly through an investigation of the variety of responses to "foundational crises" in science. I see the recognition of a foundational crisis as a type of skeptical concern and am interested in how a formal foundational program is supposed to resolve this skepticism.
Since the setting of most of my current work is in weak fragments of formal theories of arithmetic, I have developed interests also in the logical structure of these theories. This setting is particularly illuminating for exploring the logical relationships between classical metatheoretic phenomena. For example the relationship between self-referentiality and the unprovability of consistency can be sharpened considerably in weak arithmetics.
Curtis Franks' Curriculum vitæ
Selected BibliographyThe metamathematics of very weak arithmetics
David Hilbert's naturalism
Conference Procedings"The Giuoco Peano" 6th Midwest Philosophy of Mathematics Workshop
Recent CoursesLPS 29 "Critical Reasoning"
LPS 104 "Introduction to Logic"
Education:B.A. Philosophy, Mathematics, Rice University
Contact InformationOffice: 793 SST
Phone: (949)824-3812 (messages cannot be left)