Proof Theory: An Intensive MA/PhD Course
The PPP project together with IFIKK and CSMN are arranging an intensive M.A./Ph.d course in Proof Theory. The course will be taught by Jon Litland (IFIKK/PPP) and Ole Hjortland (LMU/MCMP). The course will take place August 26 - September 6, with daily meetings 12:15 to 14:00 in BL16 152.
Description of the course:
One can use formal systems to prove things; in Proof Theory one
studies the formal systems themselves. Proofs themselves become
objects for mathematical and philosophical study. Prominent
philosophers (Dummett, Prawitz, Tennant) have held that considerations
from proof-theory have important philosophical consequences. In
particular, they have argued that we have to give up classical logic
in favor of intuitionistic logic. Others (Rumfitt, Read) have tried to
counter these arguments by developing proof systems for classical
logic that are, allegedly, not susceptible to these arguments. More
generally, proof theory is important for inferentialism, the philosophical
program that tries to account for the meaning of the logical constants in
terms of the rules governing their use.
Knowledge of proof theory is essential for philosophers of logic and
mathematics and is important for philosophers of language and
linguistics. More generally: proof theory is an important part of the
philosopher's tool kit. We can often get a good handle on important
notions using proof-theory where we either don't have a semantic
account at all (e.g. metaphysical grounding), or the semantic accounts we
have are very unwieldy (e.g. relevance logic).
The goal of this course is to allow the students to master the
technical background necessary to grapple with these important
arguments. We'll consider natural deduction and sequent calculus for
intuitionistic and classical logic and prove normalization and
cut-elimination theorems and examine some of their important
The course is suitable for students having finished an introductory
course in logic. Graduate students not at the University of Oslo are most
welcome to attend the course.
More information will follow shortly.