The Department of Philosophy congratulates Owain Griffin, who successfully defended his dissertation and will soon receive his Ph.D. in Philosophy from The Ohio State University.

Owain Griffin defended his dissertation, "On the Uniqueness and Determinacy of the Standard Model of Arithmetic." His advisor was Stewart Shapiro.

The dissertation concerns the intended interpretation of mathematical theories. Reasonably straightforward results in model theory show that the axioms of our mathematical theories fail to determine their own intended interpretation, often in quite radical ways. The worry, simply put, is that if the relevant axioms could not determine the subject matter of a theory, what possibly could? In the dissertation, Owain explores this problem.

He first shows how model-theoretic underdetermination can entail a skeptical conclusion about mathematics which presents a substantial challenge for philosophers. He then draws attention to the fact that existing discussion of this problem relies upon an unspoken assumption that the background logic is strictly classical, and demonstrate that an alternative theory cast in intuitionistic logic can provably avoid the problem. Finally, he proposes and defends a new, algebraic theory of mathematics, and argue that it is preferrable to existing philosophical theories of mathematics.

The department celebrates Owain's achievement and wishes him continued success in his future endeavors.