Introduction to Logic
Time: Tuesday/Thursday, 11:10 am-12:25 pm
Location: YMCA 115
Instructor: Kenny Easwaran
Office: YMCA Building 314, 979-847-6128
Office Hours: Tuesday/Thursday 1-2 pm, or by appointment.
Course Description: This class covers the basic ideas of formal reasoning, both in logic and probability. Students will learn the meaning and importance of the concepts of valid and sound arguments, some methods for figuring out which arguments have each property, and ways of understanding arguments that hinge on probability when validity and soundness don't apply. Furthermore, students will develop skills to apply these methods to arguments phrased in ordinary language.
Grading Policies: 1/3 of the grade will be based on homework assignments. 1/3 of the grade will be from the midterm. 1/3 of the grade will be from the final. These assignments will be difficult, so it is very possible that an apparently low numerical score like 65/100 might turn out to be a B. I'll keep students updated about the connection as things go.
Working in Groups: I encourage people to work together on the homework assignments. If you work together with someone else on a homework assignment, you will get 2 bonus points, provided you meet the following conditions:
1. There are no more than 4 members in the group.
2. Everyone spends at least an hour working individually before the group meets. (If someone shows up to the meeting without already having worked on the assignment, that's unacceptable.)
3. The group works together for at least an hour.
4. Everyone completes the assignment on their own (copying someone else's final work counts as plagiarism).
To get the bonus points, list the names of the people you worked with in your group. I will take that as your pledge that you met these four conditions. The 2 bonus points per assignment is not likely to make much difference to your grade, but I've found that working together in groups does help many people immensely in learning. Explaining your thoughts to others, and hearing their explanations, often gives you totally new insights.
Readings: There is no required text to purchase for this class. Most of the material will be from freely available chapters of online textbooks by Graeme Forbes and Gary Hardegree. Some further readings and resources will be made available through the website or e-mail later in the semester.
Disability Statement: The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact Disability Services, currently located in the Disability Services building at the Student Services at White Creek complex on west campus or call 979-845-1637. For additional information, visit http://disability.tamu.edu.
Basic logical concepts (propositions, arguments, validity, soundness)
Chapter 1 of Forbes
Chapter 1 of Hardegree
Jan. 19, 21
Jan. 26 (no class Jan. 28 - I will be in Arizona)
Symbolism in propositional logic (aka sentential/Boolean logic)
Chapter 2 of Forbes
Chapter 4 of Hardegree
Feb. 2, 4
Homework 1 due in class on Feb. 4
Feb. 9, 11
Feb. 16, 18
Homework 2 due in class on Feb. 18
Semantics for propositional logic (truth tables)
Chapter 3 of Forbes
Feb. 25 (no class Feb. 23 - I will be in Pittsburgh)
Mar. 1 (no class Mar. 3 - I will be in Chicago)
Mar. 8, 10
Homework 3 due in class on Mar. 10
Mar. 15, 17 - Spring Break
Mar. 22, 24 - review and midterm
Mar. 24 - midterm
Consider the following arguments. Translate them into the language of sentential logic, indicating which sentences are premises and which is the conclusion. Use the truth table method to figure out whether they are formally valid.
I'll be happier not studying for the test. After all, if I will pass the test, I'll be happier if I hadn't studied, and if I won't pass the test, I'll also be happier if I hadn't studied.
If humans only reached the Americas 11,000 years ago, then they were the cause of the extinction of the woolly mammoth and other large mammals. But if the Monte Verde site is real, then humans reached the Americas much earlier than 11,000 years ago. So if the Monte Verde site is real, then humans were not the cause of the mass extinctions.
If artificial intelligence is possible, then thinking doesn't require a soul. But if thinking does require a soul, then humans have souls. So if artificial intelligence is possible, then humans don't have souls.
If I'm too hungry or too full I won't get any work done. If I don't eat the leftovers in my fridge, I'll be too hungry, and if I do then I'll be too full. So I won't get any work done tonight.
Probability and inductive logic
Chapter 2 of Brian Skyrms, Choice and Chance
further optional reading: Branden Fitelson, "Inductive Logic"; Alan Hàjek, "Interpretations of Probability"
Introduction to Bayes' Theorem - helpful for the homework assignment
Mar. 29, 31
Apr. 5, 7
Apr. 12, 14
Homework 4 due in class on Apr. 14
Quantifiers and predicate logic
Chapter 6 of Hardegree
Chapters 7 and 8 may be useful references: the whole book is here
Apr. 19, 21
Apr. 26, 28
Homework 5 due in class on Apr. 28
May 3 (no class, redefined day?)
May 5, 3:00-5:00 pm - Final Exam