At Belmont University, our Global Honors Program curriculum includes a Mathematical Inquiry Seminar as the only required mathematics course for students in this program. Since its inception, this course has included a unit on logic, argumentation, and critical thinking. We share recent course activities that attempt to bridge the gap between mathematical approaches to logic and real-world argument analysis. These include discussing authentic debates hosted by the nonpartisan, nonprofit organization Open to Debate and arguments created with the assistance of generative AI tools.