Logical Methodology and the Structure of Logic Syllabi

This paper starts from a dissatisfaction with the way logic is currently taught in philosophy departments. In such a context, we would want logic to be developed from first principles, in such a way that it can then be applied to any other domain of study. But standard “rigorous” logic courses make it depend on a substantial amount of set theory, which itself seems to require notions from logic—confusing students, if not striking them as circular. Instead, this paper proposes to start from a rejuvenated version of the Aristotelian notion of an argument schema, and to use this idea to develop a limited collection of concepts from logic that is sufficient for the introduction of the axioms of set theory. Once set theory is in place, mathematical logic can be taught as usual.