Mathematics is often lauded as the surest of disciplines, where arguments are made on the most solid of foundations, and no further disputation can be had. Learning how to argue mathematically often means justifying sequences of deductions so that each claim is either an assumption or follows "obviously" from the claims which precede. What does it mean for something to be obvious? When I was a student, I found that what is obvious and what is not is a matter of a certain intuition whose origin is uncertain. The goal of a large part of scholarship is to understand and to clarify, and so we are compelled to investigate these intuitions. One quickly finds that what is obvious and what is not is a convention rather than an immutable truth.
I am excited to discuss questions of what constitutes "obvious consequence", and more formally what constitutes the rules of deduction. I hope to guide students in an exploration of how conceptualizations of deduction and justification have changed throughout time and across different intellectual traditions, and to encourage students to formulate their own justifications for rules of logical deduction.