University
of Alberta

Faculty
of Arts

Department of Philosophy

PHIL 420/PHIL 522: Metalogic/Topics in Logic
— Winter term (2015/16)

Classical propositional and quantificational logics have a long history spanning more than a century. The elements of classical logic are studied in courses such as PHIL 120 and PHIL 220. (The latter is a prerequisite for PHIL 420, which can be waived in certain cases.)

This course takes a more rigorous approach to first-order logic.
*Proof systems* — including axiomatic calculi — are
introduced for propositional as well as for quantified classical logic.
*Semantical interpretations* are defined formally, which give rise to
precise notions of *truth* and *validity*, as well as of semantic
*consequence*. Of course, once we have separated the
proof-theoretical and the model-theoretical sides of first-order logic, we
have to scrutinize their relationship. This course focuses on
metalogic: we will prove *metatheorems*, such as the core theorems
stating the *soundness* and the *completeness* of the axiomatic
formulations, as well as, other principal results, for example, the
*compactness* theorem and the downward and upward
*Löwenheim–Skolem* theorems.

Classical first-order logic is an important and widely applied logic. However, it is not the only logic that is used in philosophy, mathematics, computer science and other disciplines. In order to better understand first-order logic itself, we briefly look at one or two more logics that are obtained via straightforward modifications of some of the assumptions of classical first-order logic.

**Time:**
M, W, F 15:00 pm – 15:50 pm

**Texts:**
Mendelson, E., *Introduction to Mathematical Logic*,
5th (or 6th) ed., Chapman and Hall/CRC Press, Boca Raton, 2010
(forthcoming in 2015). (required)

Some further text will be provided in class.

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

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

[Last updated on April 14th, 2015.]