Philosophy students: introduction course in logic.
Others: some mathematical maturity.
All: the willingness and ability to follow an elementary mathematical argument.
In 1930 Kurt Gödel demonstrated that any attempt at a complete axiomatization of mathematics is doomed to fail. For any interesting candidate system he showed how to construct a sentence G such that (1) it cannot be derived from the system, but (2), when viewed from outside the system, G is seen to be true. Gödel’s reasoning is lengthy, but elementary. In the course the demonstration will be given with full details. Gödel’s work has given rise to a great mythology and reached public awareness with the blockbuster Gödel, Escher, Bach: An Eternal Golden Braid . The course will pay attention to attempts to use the Gödel Theorem to disprove mechanism: if man is a machine, it seems that we could be out-Gödeled and have unprovabale Gödel sentences but on the other hand we could prove it.
The course will also provide an introduction to the Philosophy of Mathematics, in particular to the traditional positions Logicism, Formalism and Intuitionism, and their contemporary successor postions.
Course objectives will be posted on Blackboard by the start of the course.
Mode of instruction
- Lectures and seminars
Written examination on the Gödel material
Take home examination in the Philosophy of Mathematics
A brief essay on a topic in the Philosophy of Mathematics on relevant literature chosen in consultation with the teacher/examiner
Blackboard will be used for posting of messages, texts, and assigments.
The instructor will develop his own proof of Gödel’s Theorem.
A number of presentations are available on the internet and will be indicated at the proper time.
The literature for the Philsophy of Mathematics will be chosen as the course progresses.
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