Logic is only the beginning of wisdom.
— Spock, Star Trek VI
If you didn’t have prior experience in Modern Algebra, Philosophy 160A was one of the toughest courses in the Symbolic Systems Program at Stanford University. If you eat Modern Algebra for breakfast, stop reading this musing immediately! If count yourself among the common folk, however, continue reading and enjoy this short introduction to the wonderful world of logic.
Symbolic Systems Bonding
Why the heck did the folks running the Symbolic Systems Program include the Philosophy 160A program into their core curriculum? They certainly knew that the students would rarely, if ever, use the material in the class in their day-to-day lives (though I can think of a few who use their vast knowledge of “logik” as means to attract members of the opposite sex). I feel that they made this class mandatory because, through great suffering, 160A accomplishes the very important goal of creating a lasting bond between the Symbolic Systems students.
We started off as a group of people who didn’t know each other. Sure, I had taken Chem 32 with Marissa Mayer during our freshman year, but heck, that was two years ago! I knew Edwin from my CS109A class during our sophomore year, and I do remember distinctly how attentive he seemed when Maggie Johnson was teaching us about induction. When I saw Nelson for the first time, I thought to myself, “Gee, he looks a little old to be in this class. He must be smart!” At the end of the class, I knew Marissa a lot better, and, with regard to Edwin and Nelson, I realized how far off first impressions are (sorry guys)! Seriously though, because 160A encouraged students to form study groups to work together, it promoted class bonding more than any other class I attended at Stanford. We went through to hell and back, struggling through all-night problem set crunching sessions and hourly fits of logic-induced insanity. Like in the Teahouse, my 160A study group had its share of regulars: Marissa Mayer, Nelson Reilly, Edwin Ong, Matt Kodama, Julie Khavlasky, Chris Wiedmann, and Ken Lenga.
A Mathematical Introduction to Enderton
The book pictured on the right is the Bible of Logic, Herbert B. Enderton’s A Mathematical Introduction to Logic. Professor Enderton has the special gift of being able to ellicit diammetrically opposite emotions from people in 160A. His dry humor caused us to laugh uncontrollably in times of desperation, and his terse explanations made us scream in anger at the injustice of the class in the study rooms of Kimball Hall. Nevertheless, I can think of few books from my Stanford career that I would rather keep than this wonderful tome of logic.
In fact, Philosophy 160A has such a profound experience on its students that virtually all choose to retain their treasured copies of A Mathematical Introduction to Logic following the completion of the class. Some former students have been known to sleep with the book nestled safely under their pillows at night (which I did during Finals), while some prefer it in the classic position on top of the coffee table.
Oops, Enderton’s did it again! In early 2001, the long-awaited second edition of A Mathematical Introduction to Logic will be published. While I, as well as every logician around the world I imagine, am anxiously awaiting this book, I’m not so sure about about the book’s cover. In my opinion, the new cover lacks the seriousness, the defiant statement of “I am a hardcore book!” of the first edition’s.
I recently learned that Professor Enderton is a graduate of Stanford University! That explains the magical spell he has weaved upon the Philosophy 160A students on the Farm! In all fairness and seriousness, I would like to thank Professor Enderton for writing A Mathematical Introduction to Logic, since it is an excellent book and has helped bring together the Symbolic Systems Program in its role in Philosophy 160A. I’ve never met the man, but if he’s ever in the Bay Area, I’ll make it a point to round up the old gang for a round of drinks with Professor Enderton!
All-Nighters and the Longest Final Exam Ever
The problem sets to this class were most difficult, prompting us to pull all-nighters the night before the problem sets were due. I fondly remember the long nights at Synergy house or in the study rooms at Kimball Hall, working feverishly with Nelson, Edwin, Marissa, and the rest of the gang. We “relaxed” by doing handstands, by consoling each other, and by generally acting crazy all night. We were in this together, and doggone-it, we were going to get this problem set done together even if we all died doing so! Philosophy 160A pushed the limits of human hygiene to an all-time low in that class; man, did it get bad, but we loved each other nonetheless since we were all in the same boat.
I remember that my completed final exam, which was of the take-home variety, was over 80 pages in length and took me an incalculable number of hours to finish! I recall corralling a table at the Stanford CoHo all to myself, with my past problem sets, notes, and, of course, A Mathematical Introduction to Logic, spread all over. After my 12 hour fest at the CoHo, I went to the Physics Lounge on top of Varian to continue working with the rest of my 160A study group. I don’t know how we did it, but we completed the final on time. When we handed the inimitable Professor Kremer our completed final (which we even had binded!), we had done it, we had survived Philosophy 160A with (most of) our sanity intact!
At the end of my tour of duty in Philosophy 160A, I had the idea that I would take Philosophy 160B the following quarter. After a few weeks in the class, I realized I was stricken with an extreme case of Logic Fever and quickly dropped the class. I didn’t want to subject myself to another quarter of pain and suffering.
I heard that the powers that be in the Symbolic Systems Program have watered down the class somewhat in the years following my graduation. Still, I continue to hear the horror stories of the devilish problem sets, along with the positive stories of SSP students bonding together in a class and program that can only exist at Stanford.
The rest of this musing can be inferred using a simple reductive theorem. It is left as an exercise for the reader to complete.