Gödel's Incompleteness Theorems
Logic & Computation
Week Two - 9.00-10.30 - Level: F
The two incompleteness theorems given by Kurt Göodel in 1931 make part of the general mathematical culture. They are, however, not limited to mathematics but rather of interdisciplinary nature as they are fundmental for any scientific area which uses formal methods (of sufficient strength). But their impact within and outside of mathematical logic is often subject to misunderstandings.
The aim of this course is to give a concise introduction to the theorems, their proofs and their relevance. The technical part - which requires only basic knowledge of first-order logic - follows, in a simplified presentation, an article of Smorynski in the Handbook of Mathematical Logic. The philosophical discussion - which does not require any previous knowledge - starts from the fundamental distinction of syntax and semantics (in the logical sense) and finishes with questions concerning the limits of computability.
The classes will be split in 45 minutes technical presentation and 45 minutes philosophical discussion each.