PHIL 155H.001 – Honors: Truth and Proof: Introduction to Mathematical Logic

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Instructor: John T. Roberts. This course meets MWF 11:15 a.m. – 12:05 p.m. in CW 103.

Logic is the branch of philosophy that focuses on the question of what follows from what — in other words, which arguments and inferences are the valid ones?  Mathematical logic, a.k.a. symbolic logic, is a style of logic that originated in the late 1800s and was, at first, developed by philosophers and mathematicians who hoped to use it to place all of mathematics on a firm logical foundation.  That project didn’t work out — or at least, it didn’t work out in the ways these philosophers and mathematicians hoped it would.  But mathematical logic turned out to be a source of many important insights, and it has taken on a life of its own, giving birth to computer science and to the study of artifical intelligence, as well as becoming an important tool in modern linguistics.

In this course, we will start from the beginning in mathematical logic and master one important basic theory which is called by the fancy name “classical first-order relational predicate logic with identity.”  We will also examine some additional topics, such as some logical paradoxes, Peano arithmetic, and Godel’s incompleteness theorem.

This course has no prerequisites.