# Syllabus

 Lectures: January 13 - May 2, 2003 Mo, We, Fr  10:30-11:20am DH 1209 Webpage: http://www.contrib.andrew.cmu.edu/~dschlimm/80-211spring03 Instructor: Dirk Schlimm Email: dschlimm@andrew.cmu.edu Office: Baker Hall A 60 B Phone: 268-5737 Office hour: By appointment TA: Tyler Gibson Email: tylerg@andrew.cmu.edu Office: Baker Hall 143 Phone: 268-8148 Office hour: Mo 2:30-3:30, Tu 12-1. Textbook: E. J. Lemmon, Beginning Logic, Hackett, 1978, (available in bookstore).

This course is an introduction to symbolic logic. The development 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 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 Gödel and Church).

Philosophical and historical discussions will provide the context for the formal work.

Goals.

• Be able to translate informal English statements into the languages of propositional and predicate logic.
• Be able to deduce theorems from given premises using the rules of predicate logic.
• Be able to define and give examples of basic mathematical concepts, like syntax, semantics, definition, axiom, valid argument, proof, mathematical induction.
• Be able to explain in what sense formal reasoning is objective and rigorous.

Assessment.
Class participation: Class participation is expected. This includes showing up regularly (if you have to miss a class, please tell the instructor), showing up prepared, making an effort to answer questions posed, contribute to class discussions. It is a well-known fact that active learning (e.g., participating in discussions) is much more effective than passive learning (e.g., reading). Thus, you get more out of the course if you are actively involved.

Homework: Usually a set of problems will be assigned once a week, and due the following week. The assignments will be posted on the class web-site. It is your responsibility to obtain the assignment if you miss class.
In order to obtain a better grade written assignments can be redone once and handed in again within one week after they were handed back. This allows you to go over your work again and gives you the opportunity to learn from previous errors.

You are free to collaborate on homework, but not to copy answers from friends. Assignments are due at the beginning of class on the date mentioned in the assignment, and have to be turned in on paper. You may type them up or turn them in in legible handwriting. If you use a word-processor, make sure to use the spell-checker.

Tests: Three tests will be held for each section of the course. The first two will cover propositional logic and predicate logic, respectively. The final test will be comprehensive.

Essay: A 3-5 page essay on an application of logic must be handed in a week before classes finish. The topic can be chosen by the student, but must be approved by the instructor. An outline must be presented to the instructor two weeks before classes finish.
The essay provides you the opportunity to study in more detail a particular subject of the course that interests you. Further information regarding the essay will be provided in class. Starting early with the essay gives you the advantage of having more time to work on it, discuss it with the instructor, and allows you to avoid being cluttered with work at the end of the semester.