# Philosophy 1880: Course Description

#### What Is Advanced Deductive Logic?

Philosophy 1880 is an introduction to the so-called `limitative' theorems
concerning first-order logic. The most famous of these are the Gödel
incompleteness theorems, but we shall also study Church's theorem, on the
undecidability of first-order logic, and Tarski's theorem, on the
undefinability of truth.

We will begin with what is known as "recursion theory" and develop a
rigourous account of what it is for a function to be computable, or for a
predicate (or property) to be decidable. We will meet concrete examples of
uncomputable functions and then turn to the study of first-order logic itself
and of its relation to computability. We will give a rigorous proof of the
completeness of first-order logic, and see how this result can be understood
in terms of computability.

We will then turn our attention to theories of arithemtic. This will first
lead us to a proof of Church's theorem. Then we shall lay the groundwork for
a proof of the first of the incompleteness theorems and then discuss the proof
of the second incompleteness theorem, whose details we shall probably not have
time to study.