Introduction to Mathematical Logic (PHIL 155, Section 001)

Logic studies what counts as good reason for what and why. Since reasoning appears in many academic disciplines and even in real life, logic has wide applications. The course focuses on a particular kinds of inferences and the good reasoning based on them, viz. valid inferences. Valid inferences hold in virtue of purely formal features of the relevant claims.

Instead of studying arguments states in the English language directly, we study formal languages in which what inferences are valid is precisely defined. We can then evaluate English arguments by translating them into this formal language. The advantage of a formal language (a language that has been made-up and that no one actually speaks) is that everything is well-defined in it and we do not have to deal with the ambiguities of actual English.

The goal of the class is to introduce students to the immense power of this approach in clarifying our everyday reasoning. The course covers propositional logic and first-order predicate logic (involving quantifiers). By the end of the course, each student should be able to take English arguments, translate them into formal languages, and assess their validity.

The Textbook we will use is:
Language, Proof and Logic. Jon Barwise and John Etchemendy. CSLI Publications: Stanford, California. 2007. ISBN 1-57586-374-X.

We will use the software that comes with the book for doing exercises. Do not buy a used copy of the book! Once the software that comes with the book is registered to one person, it cannot be reused by another person. Thus, you’ll need a new copy of the book and the software package it comes with.

Christian Loew’s webpage