Philosophy | Systems of Modal Logic
P550 | 3411 | Moss
This course will introduce modal logic. It will emphasize systems of
modal logic that find application in areas of philosophy and
computer science. I have a special fondness for epistemic logic, but
the course will also cover temporal logic, deontic logic, and logics
for reasoning about space. I will try not to aim for the hardest or
prettiest mathematical results but instead to the ones that have
something to say about interesting application areas. What I want
to do most is to present the semantics of modal systems and then
discuss whether they "got things right". In order to do that, we
have to "dig in" and to some mathematics. But I am going to be a lot
less concerned with favored theoretical topics like completeness
theorems and decidability, though I will do that a little.
The course will probably be different from earlier installments of
P550, if only because I am doing it without reference to anyone
else's course. The course is jointly listed as Math X384; that
should not concern people who want graduate credit in Philosophy. I
mention this because the class will be open to undergraduates as
The background for the course is a good knowledge of propositional
logic, perhaps a bit of first-order logic, and basic ability with
mathematical proofs. P505 would be sufficient; for that matter, a
good undergraduate course in logic would be fine. P506 and and
graduate courses in logic in math are definitely not needed. I am
not aiming the class at the graduate students in logic; I will
suggest that they not take the course. The intended audience for the
course is Philosophy students at all levels who want to learn modal
logic, and also students with some math background who want a taste
of logic as an applied field.
The textbook for the course will be Sally Popkorn's book _First
Steps in Modal Logic_. For the application areas, I'll write my own
notes or use other sources.
The course will have regular homework assignments and exams.
Students wanting the graduate credit will have to write a short
paper based on individual reading. I hope that Philosophy students
will want to read about the controversies surrounding the notion
of 'possible worlds', or about Godel's version of the ontological
argument for the existence of God, or some other interesting topic.
(On the other hand, they *could* dig deeper into the mathematics if
they want to.) Other than that, I would say that the course would
be about as much work as a good undergraduate math class.