Course Information

Time: MWF 1:30--2:20
Place: Porter Hall 226B
Instructor: Steve Awodey <awodey@andrew>
    Office: BH 152
    Office Hour: Wednesday 3--4, or by appointment
Teaching Assistant: Dan Handley <dhandley@andrew>
    Office:
    Office Hour:
Secretary: Baker Hall 135
Course URL: www.andrew.cmu.edu/course/80-211

Description

This course is an introduction to symbolic logic. The development in this century of a rigorous, formal calculus for logical reasoning is a signifcant scientifc breakthrough, the culmination of a line of research stretching back literally to Aristotle. With it, reasoning becomes amenable to treatment by formal methods and symbolic logic becomes the science of correct reasoning. This watershed in the development of logic has spurred its recent further development and opened the way for numerous applications. This course introduces students to these modern logical methods. We specify symbolic languages of propositional and quantifcational logic, in which large parts of ordinary English can be expressed. Logical calculi for these languages then permit the analysis of arguments, leading to the characterization of the important notion of logical validity. By way of application, we systematically explore informal reasoning in natural language and in elementary mathematics. Thus, students are also familiarized with the basic techniques of set theory and arithmetic, in addition to the methods of symbolic logic, with their many applications in mathematics, computer science, linguistics and cognitive science. Time permitting, the course will conclude with an examination of the concept of computability (using Turing machines) and its consequences regarding the limitations of formalized reasoning (the theorems of Goedel and Church).

Topics to be Treated

• Informal and formal reasoning
• Propositional calculus
• Quantification and predicate calculus
• Natural deduction
• Elementary theories of sets, relations, functions, and numbers
• Computability according to Church and Turing

Attendance in class is required.  In addition, the following written
homework and examinations are required and will be used to determine
grades, as indicated:

• Problem sets (50%): Due every Monday in class
• Midterm exam (20%): In class Wednesday, March 7
• Final exam (30%): During the final exam period

• E. J. Lemmon, Beginning Logic (Hackett: 1978)

Homework

Here are the weekly homework exercises.