Focus and Purpose

In Week 2, we cover Chapters 3 and 4 in our text, focusing on a hugely important part of logical practice: arguments and proofs.

Tasks and Resources

You'll complete the following 6 tasks this week:

Watch: Arguments & Validity (estimated time: 15 minutes). Professor Selçuk Özyurt of York University defines and explains these 2 key concepts.
Read: Chapter 3, Good Arguments (estimated time: 190 minutes). This chapter uses the framework of a fascinating historical case of medical reasoning, that of Doctor Ignaz Semmelweis, to both understand what a logical argument is, and what standards we apply to evaluate arguments. We'll understand why it's important not to confuse validity with truth; and we'll see our first applications of our friend the truth table as a tool to check, or evaluate, the validity of an argument. The final sections of this chapter will focus on some types of arguments that are closely related to logical arguments, but are not the same: scientific reasoning and reasoning from probability.
Submit Problems: Chapter 3 (estimated time: 40 minutes).
Watch: Proof Techniques (estimated time: 10 minutes). Professor Selçuk Özyurt of York University demonstrates proofs, direct proof, inference rules, modus ponens, modus tollens, and double negation.
Read: Chapter 4, Proofs (estimated time: 75 minutes). This chapter immediately turns around and shows us a serious limitation of the semantic method of evaluating arguments we learned in Chapter 3...! But never fear: we see how to develop a syntactic proof method, developing inference rules which allow us to get past that early limitation. We'll identify, and define, 3 different inference rules: modus ponens, modus tollens, and double negation. A major new practice this chapter: learning the terminology, shape, and symbols for writing and solving a direct proof.
Submit Problems: Chapter 4 (estimated time: 45 minutes).

- Optional (but Recommended!): use the Discussion Forum as your study group. You may find it very helpful to work through some of the problem sets together (especially later in the course).
- Optional (but Recommended!): I'm available for one-on-one consultations on Teams, by appointment: sign up through my Bookings link!

Recommended Schedule

Notice how long Chapter 3 is! As much as possible, schedule at least 4-5 uninterrupted 45-minute blocks throughout the week, to focus on the chapter readings. These readings are somewhat dense, and I recommend reading at least 2 times for strong comprehension. As you look at the problem sets, notice any that seem challenging, and post about them in the Discussion Forum by Tuesday: this will give your classmates time to respond! Last, please make sure that you've submitted the Chapter 3 problem set before you begin reading Chapter 4 (ideally, no later than Thursday): it definitely helps to keep each chapter's concepts separate.

Focus and Purpose

Tasks and Resources

Recommended Schedule

Onward!