Phil 420/PHIL 522: Metalogic/Topics in Logic — course description (Winter 2016)

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.

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

[Last updated on April 14th, 2015.]