Philosophy
470: Intermediate logic
Course Web Page
http://courses.washington.edu/phil470/
COURSE DESCRIPTION: This course develops techniques for studying logical systems. We will introduce elementary concepts from set theory and the theory of relations in order to study consistency, compactness and completeness for first order logic. Time permitting, there will be a brief introduction to non-standard models of arithmetic and to Gödel's theorems.
Disclaimer: Philosophy 470 is a course in metalogic. It builds on the material in Philosophy 120 but it is very different in character. In 470 we will prove results informally about logical systems and the formal proofs they contain, whereas in 120 you constructed formal proofs in a particular system. Doing well in Phil 120 is no guarantee that what you will be asked to do in Phil 470 will come at all easily, or naturally.
PREREQUISITES: Philosophy 120, or the equivalent (i.e., a standard course in first order predicate logic).
TEACHING METHOD: Lecture-discussion.
EVALUATION: The grade for this course will be based on a midterm and final exam, plus some extra assignments.
TEXT: NONE There are three sets of notes on the webpage (PDF files on sets, sentential logic and predicate logic). They cover in detail many of the topics we will treat, and also set some problems. (They are by Penelope Maddy at UC Irvine, and are password protected.)
There is also a library reserve list to consult.
P. Halmos, Naive set theory (Princeton: Van
Nostrand, 1965)
Good introduction to non-axiomatic set theory.
QA248 .H26, Odegaard
G. Hunter, Metalogic (Berkeley: U. of
CA Press,1973)
A tedious but useful text.
BC128 .H85 1971a, Odegaard
E. Mendelson, Introduction to mathematical
logic, 2nd
Edition (Princeton: Van Nostrand, 1979)
More advanced text on the
metatheory that we will study.
QA9 .M4, Math & Suzzallo
R. Stoll, Set theory and logic (San
Francisco: W.H.
Freeman, 1963)
Not too sophisticated treatment of many topics we
will study.
QA248 .S7985, Math & Suzzallo
J. L. Zalabardo, Introduction to the theory
of logic
(Boulder, Co: Westview, 2000)
Covers much of what we will study in a mostly
readable way.
BC108 .Z35 2000, Suzzallo
DISCUSSIONS: There are no
discussion sections for
this course.
HOMEWORK:
Check the webpage. I will also assign homework problems as I go along.
The homework is for your own
practice and education. I will reserve class time, usually on Tuesday,
for questions relating to the homework.
TOPICS, WEEKS 1 AND 2:
Sets, Boolean Operations, Ordered Pairs (etc.), Relations, Equivalence
Relations,
Functions, Cardinality, The Natural Numbers, Other Number Systems,
Mathematical
Induction, Formal Systems.