Phil 220: Symbolic Logic 2 — course description (Fall 2015)

PHIL 220:   Symbolic Logic 2  —   Fall term (2015/16)

First-order logic (FOL) has been thoroughly investigated in the last 130 or so years, and it is a very well understood logic.  FOL gains its importance from its wide applicability and from its place in the landscape of logical calculi and formal languages.

Some elements of classical logic are studied in the course Phil 120, which is a prerequisite for this course.  (The prerequisite can be waived upon request in certain cases.)  This course is a more detailed and more formal study of some of the same topics that were touched upon in Phil 120, together with new and more complex questions and methods from FOL.  For example, we start to look at some first-order theories, which are concrete applications of FOL.

The course intends to develop and advance your understanding of certain components of FOL along with their interactions.  Among these components are the truth-functional connectives, the quantifiers, the identity predicate, as well as proof systems and models.  The course will enhance your ability to formalize some subtle and crafty natural language sentences.  Toward the end of the term, you will have a chance to learn about resolution, which is a quite practical proof system for FOL, and to take a glimpse at induction and set theory.

We will use a textbook that was written by world-class logicians who aimed at providing an excellent text and superior tools for learning logic.  The textbook is accompanied by a software package that contains Boole, Fitch and Tarski's world — three programs that are named after famous logicians.

• Boole makes easier and speedier the construction of truth tables.
• Fitch is an implementation of the so-called “Fitch-style natural deduction system.”  Using this program you can prove theorems of first-order logic in a rigorous way.
• Tarski's world allows you to construct a small model consisting of blocks, in which you can evaluate sentences.  You can vary the model and the sentences, and you can play games with Tarski's world to clarify and visualize the truth condition of a sentence in a concrete model.

These programs provide a lot of opportunity for experimentation, exploration and learning.  (No programming or computer science experience in needed for this course.)

Time:   M, W, F  12:00 pm – 12:50 pm
Text:   Barker-Plummer, D., J. Barwise and J. Etchemendy, Language, Proof and Logic, 2nd ed., CSLI Publications, Stanford, CA, 2011.   (required)