Introduction to Formal Logic I

 The goal of this class that fulfills the ARP (Analytical Reasoning) requirement is to learn a formal language (first order logic) and practice it in daily exercises. Some of them are similar in spirit to formal riddles and board games. Others are more like calculations. But this is also a philosophy class in which you learn that formal languages are special. For instance, it seems initially great that, in the formal language you learn, every true sentence can be effectively proven. But it also limits what features of natural languages can actually be expressed in this formal language. On the other hand, two-valued logic serves perfectly well as the basis for digital computers.

Learning Outcomes

After successful completion of this course, students will be able to:

• Apply, as appropriate, principles of analytical reasoning, using as a foundation the knowledge of mathematical, logical, and algorithmic principles.
• Recognize and use connections among mathematical, logical, and algorithmic methods across disciplines.
• Identify and describe problems using formal symbolic methods and assess the appropriateness of these methods for the available data.
• Effectively communicate the results of analytical reasoning and problem solving.
• Identify the logical structures of ordinary language statements and arguments.
• Use the symbolism of first-order logic to represent those logical structures.
• Explain and apply the logical properties of validity, satisfiability, consistency, logical truth, and logical equivalence.
• Apply deductive techniques for the evaluation of arguments couched in the symbolism of first-order logic.