Diego Arana Segura

This course will introduce you to the fundamentals of modern formal deductive logic and its powerful applications to everyday reasoning. Our main object of study will be the argument, which represents a chain of reasoning and consists of premises (or starting assumptions) followed by a conclusion. We will learn to determine when such arguments are valid—i.e., when their conclusions necessarily follow from their premises. To do so, we will translate arguments into an artificial or formal language specifically designed to check for validity: truth-functional logic (TFL). We’ll thoroughly cover the syntax and semantics of TFL, translating complex natural language arguments into these formal languages, and learning to construct proofs and check for validity within them. By the end of the course, you will have a solid understanding of the notion of validity and be knowledgeable in several methods for determining whether an argument is valid.

In this course, you will learn how to reason effectively and make informed decisions using formal methods. We will cover the fundamentals of logic, probability, and decision theory, and apply these tools to real-world problems. The course is split into two halves. The first half is concerned with reasoning and formal logic. In this part of the course, we will explore the foundations of logical reasoning, drawing from mathematics to understand how to critically evaluate arguments and form valid conclusions. Topics will range from the basics of propositional logic to the rules of natural deduction and the methods of symbolic logic. You will learn how to convert complex statements into logical form and use logic to determine the validity of an argument. The second half of the course is concerned with decision-making. To make informed decisions, we must consider the possible outcomes, how likely they are, and how good they are compared to one another. In the framework of Decision Theory this is the same as knowing the probability and utility of each possible outcome, and we will see how to make decisions based on these.