Special Topics In Logic

Logic underwent a revolution in the late 19th and early to middle 20th century. Starting with Peirce and Frege, mathematicians and philosophers developed logical systems that were much more powerful than the traditional logical systems inherited from thinkers such as Aristotle. It became clear that by using these new tools, it was possible to formalize large swaths of mathematics, and many mathematicians and philosophers started to think that it may even be possible to reduce mathematics to formal logic. However, in the wake of this optimism, a number of results were proven that demonstrated several fundamental limitations inherent in our best formal logical systems. This class introduces students to the major positive results - including the soundness and completeness theorems of first-order logic - and the major limitation results, in particular Godel's incompleteness theorems and Church's undecidability theorem. The philosophical implications of the results will be emphasized.