PHI 112: Language, Logic, and Mathematics
Illinois State University
Sec 01: MW 8:00am – 8:50am, Stevenson 350A
Sec 02: MW 9:00am – 9:50am, Stevenson 350A
This course provides an introduction to symbolic logic. After a brief introduction to arguments, premises, and conclusions, the course divides into two parts. In the first part, we study sentential logic, the logic of ‘not’, and’, ‘or’, and ‘if…then…’. We introduce an artificial language, SL, and learn how to represent information in this language. And we introduce truth tables and a system of natural deduction. These give us two different ways to explore the logical properties of sentences and arguments expressed in SL. In the second part, we study predicate logic, the logic of ‘all’, ‘only’, ‘some’, and ‘none’. We extend SL, introducing a new language, PL. We learn how to represent information in this new language. We extend our system of natural deduction, and extend the idea of a truth table to the more general idea of a semantic model. Again, we use these tools to explore the logical properties of sentences and arguments expressed in PL.
The course is “flipped”: out-of-class time is spent working through the text; in-class time is spent asking questions and solving problems; I will lecture only rarely.
The text is free, interactive, and online. It contains integrated how-to videos and video lectures, along with machine graded practice problems. You are expected to read the text, watch the videos, and attempt to complete the problems. This should generate questions and confusion, which we can then address in class.
The course is officially listed as “hybrid”. We meet for 50 minutes on Mondays and Wednesdays. We do not meet on Fridays. That gives you 50 extra minutes each week, giving you more time to work through the text and exercises.
There will be no exams. The material is divided into several units. Each unit contains several exercises, and ends with a short “mastery check”. To complete a unit, you must complete the exercises and pass the mastery check. Your course grade is based upon how many units you complete by the end of the term. There is a generous retake policy for mastery checks.
This means that the course is also self-paced. Units have “expiration dates”, which are based on the minimum pace you need to sustain in order to pass the course. But the successful student will want to keep well ahead of this pace, in order to earn a higher grade.