University
of Alberta

Faculty
of Arts

Department of Philosophy

PHIL 120: Symbolic Logic 1 — Winter
term (2013/14)

*Logic* comprises formal theories that are suitable as models of
*correct reasoning* in various fields. This course is an introduction
to *classical first-order logic* (**FOL**), which is one of the
easiest logics to learn.

**FOL** has been investigated for well over 100 years, and there is an
immense amount of accumulated knowledge about this logic. (In the course,
we will only sample some of the basics though.) **FOL** is *widely
applied* in disciplines such as mathematics, informatics, computer science,
philosophy and artificial intelligence. A reliable understanding of this
logic is often essential in learning further logics such as modal,
substructural, relevance, dynamic, quantum and higher-order logics.
Experimental evidence shows that studying formal logic improves the learner's
everyday or informal *reasoning skills* too.

The course will use a textbook written by the famous and highly accomplished
logician Raymond M. Smullyan. We will start the course with solving
puzzles, in which the concept of truth and apt reasoning are the requisites
to obtain a solution. These simple puzzles are formulated in English and they
introduce some of the core notions of classical logic. The puzzles can be
solved without using a formal language or calculus — just like one might
proceed to solve an everyday reasoning problem — but it is easier to
solve them once they are formalized. The first formal system that we will
look at is *sentential logic* (**SL**). You will learn the syntax and
the semantics of **SL**. Paramount concepts in this part of the course
include truth-functional connectives, well-formed formulas, truth values,
truth functions and truth tables (among others). **SL**, however, has a
rather limited expressive power, which is considerably extended in **FOL**
by the addition of the *quantifiers* “for all” and
“there exists.” The introduction of the quantifiers elicits a new
way of thinking about the syntax of a logic, because quantifiers are concrete
examples of the abstract concept of operators.

*Formalizing* reasoning — especially formalizing more complicated
inferences — is the initial step toward deciding their
“goodness.” The next step is to establish that the conclusions
can (or cannot) be proved from the premises (whenever such a determination is
possible). *Analytic tableaux* are one of the ways to go about the
latter. In this course, you can learn this approach in a *unified*
framework, which was originally developed by the author of the textbook.

**Time:**
M, W, F 12:00 am – 12:50 am

**Textbook:** Smullyan, R. M., *Logical
Labyrinths*, A K Peters, Ltd., Wellesley, MA,
2009. (required)

For **further information**, please contact the instructor at
.

The (official) **course outline** is available in the e-classroom during
the course.

[Last updated on March 13th, 2013.]