All of us have been told that an argument that we have (or someone else has) made is logical, or illogical. What does it mean for an argument to be logical, or for a conclusion to be obvious? We all have intuitions for what is “an obvious consequence” as well as for what “is not obvious”. How do these intuitions come about, and why should my intuitions agree with yours? Even if they do, would they have agreed with those of Aristotle or Confucius or Avicenna, for instance? Why is it that mathematicians can (and do!) have good faith disagreements about the existence of infinity? In this course, we will investigate the cognitive and sociological processes of performing logical deductions for the purposes of creating knowledge and formulating sound proofs. Our goal is to become mindful of and attentive to the details and nuances of what is obvious and what is not, and to investigate how communities of thinkers have conceptualized the obvious throughout history and geography. By the end of this course, we will have gained experience investigating the processes of inference and deduction, and you will have learned: ● To explore varying conceptions of valid inference across intellectual traditions, cultures, and historical periods; ● To appreciate the intrinsic humanness of the intellectual endeavor that is the synthesis of knowledge and the conventional nature of what is obvious, and the fundamentally sociological function of proof and argument; ● To recognize the resulting ambiguities of our intellectualization and conceptualization of the world. During the seven weeks of the course, we will explore a large number of proofs of a particular relatively simple mathematical proposition through student-guided presentations, and we will discuss the underlying assumptions, argument structure, and power to compel. These investigations will be supplemented by readings in the history and philosophy of logic, spanning the ancient, medieval, and modern periods, and including Greek, Islamic, Indian, and Chinese perspectives on logic.