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). |

**About the course.**

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.

**Grading.**

The grade in this course depends on your
continuous effort
during the semester. The final grade will be based on six components according
to the following weights:

Homework: | 45 % |

1. Test: | 10 % |

2. Test: | 10 % |

3. Test: | 20 % |

Essay: | 10 % |

Participation: | 5 % |

Grades for homeworks, tests, and essay will be on a scale between 0 and 10. The corresponding letter grades are: 10-9

© Dirk Schlimm, Last modified: 1/12/03