Philosophy 1501

Spring(?) '02

Prof. M.A. Rice

One can view this as a first course in "formal systems" which will provide one with some elementary concepts applicable to formal logic, formal linguistics, mathematics, and simple computer languages. We will deal primarily with two systems of formal symbolic logic, called a "propositional" and a "predicate" calculus, and learn to work proofs with both. Both of these calculi are part of a formal theory of deducibility whose purpose is to formalize our everyday reasoning process and certain aspects of natural language. As we learn our formal theory, we will develop an elementary formal language, learning some formal linguistics as we do. We will investigate some interesting properties and applications of our formal theory but primarily learn to work proofs with it.

Lemmon, Beginning Logic, Hackett.
Schumm, A Teaching Companion to Lemmon's Logic, Hackett.

At the end of each section of Lemmon, there will be problems and exercises. Your goal should be to do all the exercises. Even if you can't complete all of them you should at the least attempt all of them. We will work some problems in class, but certainly not all. I will be available for problem working sessions during my office hours. Occasionally problems will be assigned for homework to be turned in and graded. There will be 4 hourly exams spaced approximately 3 weeks apart.

1. Introduction & basic terminology; meaning vs. expressions; validity & soundness; counterexamples; the nature of logical proof.

2. The elementary symbols of the propositional calculus, rules of derivation, translating truth functional sentences into the propositional calculus.

3. Formal syntax and formal semantics of the propositional calculus; theoremhood, logical truth, derived vs. primitive rules; substitution instances & logical form.

4. Consistency and completeness of the propositional calculus.

5. Quantified statements in general; informal presentation of the elementary symbols of the predicate calculus; rules of derivation for quantifiers, translation of colloquial quantified statements into the predicate calculus.

6. Formal syntax and semantics for the predicate calculus. Consistency and completeness of the predicate calculus. The use of the identity sign, the logic of relations.

The schedule of readings, assignments, and topics to be covered will be announced in class.