PHIL 155.001 – Truth and Proof: Introduction to Mathematical Logic

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Instructor: Yifan Li. This course meets TR 8:00 – 9:15 a.m. via remote only instruction.

Logic can be seen as the study of arguments and inferences: it inquires into what follows from what, and why that is the case. Mathematical logic is the study of arguments and inference with the tool of modern mathematics, which gives the whole area of inquiry a high degree of clarity and intellectual rigor. This course is an introduction to the fundamentals of the latter.

At the end of this course, you are expected to have knowledge about the following topics: the symbolization of ordinary language, proof theory for classical first-order logic, model theory (theory of truth) for classical first-order logic, and how proof and truth are related. At various points of this course, depending on the progress, we will also touch upon topics concerning the extensions, applications, or limitations of the logic we study in this course.

Mathematical logic, similar to mathematics, is used in many areas of inquiries: philosophy, linguistic, computer science, etc. In addition, logic can also serve as a valuable tool in evaluating the reasonings you would encounter in day-to-day life. Therefore, the primary goal of this course is to build up a basic logical tool kit for students so that they can use it in various scenarios. However, it is also expected that in doing so you will learn to take on a logical perspective on things, where clarity of thoughts, rigor of arguments, and freedom from biases and preoccupations are the guiding principles.

The work for the course will consist mostly in homework and exams, and they will be more like the ones you would encounter in a math class than in a philosophy class. Your final grade would be determined mainly by your performance on the homework and exams.

There is no prerequisite for this course. Also, since the textbook and materials we will use are freely available online, this course does not require textbook purchase.