Spring Semester 2013
Textbooks: There are two required books. Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter; and Logics, by John Nolt. In addition to the books, there will be some webpages and class handouts that you should consider to be required reading.
The two books are available at the CSUS Hornet Bookstore, but here is a website that compares book prices at many online bookstores: http://www.bookase.com. You can get the book used at Amazon.com for $150: http://www.amazon.com/Logics-John-Nolt/dp/0534506402. The book comes with a CD that we won't be using. We will be reading approximately half of the book Gödel, Escher, Bach; two copies of it are on reserve in the CSUS Main Library. If you understand a little about music theory, then this book will deeply enrich your understanding; but if you don't know about music theory, then you will be relieved to know that you won't be tested on any music knowledge, just knowledge of logic. The same goes for art and ancient Japanese poetry.
Your grade will be determined by four homework
assignments (each 14%), a midterm exam (20%), and a comprehensive final
exam (24%). Homework questions will be
handed out a week in advance of the due date. Class attendance is
optional, but you are responsible for material covered in class that
isn't in the book.
For homeworks, you are responsible for any announced changes to questions that are made after the homework is handed out but before it is due, even if you didn't attend class the day the change was made.
Course Description: Our course presupposes you have had a first course in deductive logic, such as Phil. 60, or have learned this material on your own. The first month will contain a review of Phil. 60, but also will enrich that material. Our goal is to appreciate what can be done with deductive symbolic logic and what can't be done. That is, we will explore the scope and limits of deductive logic rather than its depth in one particular area.
Deductive logic explores deductively valid reasoning, the most secure kind of reasoning. A mathematical proof is deductively valid reasoning. Inductive reasoning, by contrast, is about less secure reasoning from the circumstantial evidence of the lawyer, the documentary evidence of the historian, the statistical evidence of the economist, and the experimental evidence of the scientist.
For a helpful metaphor, you might think of our symbolic deductive logic as a machine for detecting the presence of the most secure reasoning. In our course, we will not only use the machine but also study what it can and cannot do, and whether it can be revised to do other things. For example, does it have the power to show that "Obama's father is working in his office" logically implies "Someone's father is working"? Can we use the machine to demonstrate that no use of the machine will lead to a contradiction?
Our course will survey the deep results yielded by the developments in symbolic deductive logic. These results concern the surprising extent to which human knowledge can not be freed of contradictions, to what extent our knowledge can be expressed without loss of content inside of a formal language, and what our civilization has learned from the field of symbolic deductive logic about the limits to what people can know and about the limits of what computers can do, the major results here being the Unsolvability of the Halting Problem, the Church-Turing Undecidability Theorem, Tarki's Undefinability Theorem for Truth, and Gödel's Incompleteness Theorems.
We will begin our course with a review of Phil. 60 while providing a rigorous development of both propositional logic (also called statement logic and sentential logic and propositional calculus and statement calculus and the theory of truth functions) and elementary predicate logic (also called first-order logic, relational logic, quantificational logic and predicate calculus). Then we will learn about their applications, extensions, meta-theory, and non-classical variants. Regarding non-classical variants, this comment in 1970 by the American logician W.V.O. Quine is helpful:
Logic is in principle no less open to revision than quantum mechancis or the theory of relativity.
My role in our course will be to cut through the jargon and help you understand as quickly as possible.
A good analogy for our course is that learning symbolic logic is much like learning a computer language. The big difference is that in symbolic logic the focus is on using the formal language to assess argument correctness rather than on getting a computing machine to follow its intended program. To continue with the analogy, in our course we will not be focusing on doing actual programming so much as learning the capabilities of the computer.
Speaking about the second textbook Gödel, Escher Bach, the M.I.T. senior student Justin Curry, who gives the online lectures about it, says, "I advise everyone seriously interested to buy the book, grab on and get ready for a mind-expanding voyage into higher dimensions of recursive thinking."
Relevance of logic to other subjects: If you are curious about the relevance of deductive logic to other subjects such as philosophy, mathematics, and computer science, then click on the ticket below:
Student outcome goals: The hope is that by the end of the
semester you will have achieved the following goals:
Laptops, cell phones: Photographing during class is not allowed without permission of the instructor. Audio recording is OK. During class, turn off your cellphone. Your computers may be used only for note taking, and not for browsing the web, reading emails, or other activities unrelated to the class. If you use a computer during class, then please sit in the back of the room or in a side row so that your monitor's screen won't distract other students.
Plagiarism and Academic Honesty: A
student tutorial on how not to plagiarize is available online from
our library. The University's policy on academic honesty is at http://www.csus.edu/umanual/AcademicHonestyPolicyandProcedures.hty
Food: Except for water, please do not eat or drink during class. You are welcome to leave class (and return) any time you wish.
Late assignments, and make-up assignments: I
realize that during your college career you occasionally may be unable
to complete an assignment on time. If this happens in our course,
contact me as soon as you are able. If you promptly provide me with a good
reason for missing a test or homework assignment (illness, accident, ...), then I'll use your grade on the final
exam as your missing grade. There will be no make-up tests nor make-up
homework. I do accept late homework with a grade
penalty of one-third of a letter grade per 24-hour period beginning at
the class time the assignment is due. Here are some examples of how this works.
If you turn in the assignment a few hours after it is due, then your A becomes an A-.
Instead, if you turn in the same assignment 30 hours late, then your A
becomes a B+. Weekends count, so scan your late, but finished work on the weekend and email it as an attachment. No late work will be accepted
after the answer sheet has been handed out (normally this will be at the
next class meeting), nor after the answers are discussed in class, even
if you weren't in class that day.
Professor: My office is in
Mendocino Hall 3022, and my weekly office hours are TuTh 9:30-10:30 and 12:00-12:30. Feel free to stop by at any of those times, or to call. If
those hours are inconvenient for you, then I can arrange an appointment
for an alternative time. You may send me e-mail at email@example.com or call my office at 278-7384 or the Philosophy
Department Office at 278-6424.
The fastest way to contact me is by email. My personal web page is at http://www.csus.edu/indiv/d/dowdenb/index.htm
Study tips: As you read an assignment, it is helpful first to skim the assignment to get some sense of what’s ahead. Look at how it is organized and how the author signifies main ideas (section titles, bold face, italics, full capitals, and so forth). Make your own notes as you read. Stop every twenty minutes to look back over what you’ve read and try to summarize the key ideas for yourself. This periodic pausing and reviewing will help you maintain your concentration, process the information more deeply, and retain it longer. Notice connections between one section and another. You’ll be given sample questions now and then to help guide your studying for future assignments, but the homework and test questions in our course will usually require you to apply your knowledge to new questions not specifically discussed in class nor in the book. This ability to use your knowledge in new situations requires study activities different from memorizing. You goal is to improve your skills, rather than to memorize information. Think of the textbook more as a math book than a novel, so re-reading is important.
Contact me at firstname.lastname@example.org if you'd like more information about our course.
Updated: May 4, 2013