Logical Systems Philosophy 340, Mathematics 340, Computer Science 340

Tue 12:00-1:00, Wed 2:30-4:00, Fri 2:30-4:00	Peter Suber
Carpenter 322	Fall 2002-03

Syllabus

Reading

Assignments

The required reading for this courses consists of a few web hand-outs and the following books:

1. Douglas R. Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid, Basic Books, 20th anniversary edition, 1999.
2. Geoffrey Hunter, Metalogic: An Introduction to the Metatheory of Standard First Order Logic, University of California Press, 1971.

Hunter is the main text. Hofstadter is for spice, motivation, illustration, application, and cogitation. We will read all of each of these two books, but only give page-by-page attention to Hunter. Our pace through Hunter may seem slow if you only consider the number of pages per night, or it may seem fast if you consider the density of the material. I hope I've hit it about right; if so, we can take most Fridays off and discuss Hofstadter.

I've written a large number of hand-outs to supplement Hunter. I used to distribute them as a mountain of photocopies. Now they're on the web with links to them from the appropriate spots in the reading schedule below.

• Most of the hand-outs were designed to clarify difficult points or expand on topics covered too briefly in Hunter. Hence they are recommended but not required. If any are required, I will say so in class.
• Many of the pieces were written in response to student requests. I'm happy to write more. Let me know when you run across an especially difficult or fascinating topic on which I could write an additional hand-out.

Web access is required for this course.

I've created a course home-page containing a collection of hand-outs and course-related web links at http://www.earlham.edu/~peters/courses/logsys/lshome.htm.

Pages will be discussed in class on the days for which they are listed. Pages in brackets are recommended but not required.

Reading

Week 1, August 26-30
Tue	No class
Wed	First class; no reading due.
Fri	Hunter Day 1, pp. xi-xiii, 3-10 Recommended: Today's exercises, Terms and symbols of propositional logic, Map of some logical systems, Glossary of first-order logic
Week 2, September 2-6
Tue	Hunter Day 2, pp. 10-21 Recommended: Today's exercises, How to read proofs, Formal system assignment, The shadow problem, Sample formal system, System-machine isomorphism
Wed	Hunter Day 3, pp. 21-30 Recommended: Today's exercises, Map of some expressions, A crash course in the mathematics of infinite sets, Quirk problem, Non-standard logics
Fri	Hunter Day 4, pp. 30-41 Recommended: Today's exercises	Optional office-door quiz through Day 4
Week 3, September 9-13
Tue	Hunter, Day 5, pp. 45-54 Recommended: Today's exercises, Non-contradiction and excluded middle
Wed	Hunter Day 6, pp. 54-62 Recommended: Today's exercises, Turing machines I
Fri	Hofstadter, have finished Ch. II (to p. 60) Recommended: Hunter-Hofstadter map
Week 4, September 16-20
Tue	Hunter Day 7, pp. 62-71 Recommended: Today's exercises
Wed	Hunter Day 8, pp. 71-77 Recommended: Today's exercises
Fri	Hofstadter, have finished Ch. IV (to p. 102)
Week 5, September 23-27
Tue	Hunter Day 9, pp. 78-83 Recommended: Today's exercises
Wed	Hunter Day 10, pp. 84-91 Recommended: Today's exercises, Mathematical induction	Office-door exam through Day 10
Fri	Hofstadter, have finished Ch. VI (to p. 176)
Week 6, September 30 - October 4
Tue	Hunter Day 11, pp. 91-96 Recommended: Today's exercises
Wed	Hunter Day 12, pp. 96-105 Recommended: Today's exercises
Fri	Hofstadter, have finished Ch. VIII (to p. 230)
Week 7, October 7-11
Tue	Hunter Day 13, pp. 105-116 Recommended: Today's exercises
Wed	Hunter Day 14, pp. 116-20 Recommended: Today's exercises
Fri	Hofstadter, have finished Ch. X (to p. 309)
Week 8, October 14-18
Tue	Hunter Day 15, pp. 120-125, [125-134] Day 15 is the last day of TFPL. Recommended: Today's exercises, Mid-term review
Wed	Exam day, no reading due.	In-class exam through Day 15
Fri	No class. Mid-term break.
Week 9, October 21-25
Tue	Hunter Day 16, pp. 137-141 Recommended: Today's exercises, Terms and symbols of predicate logic
Wed	Hunter Day 17, pp. 141-152 Recommended: Today's exercises, Satisfaction, Three levels of truth
Fri	Hunter Day 18, pp. 152-166 You may skim metatheorems 40.12-40.21 iff you can explain the assertions in the metatheory and have read enough to trust the proofs, which depend on 40.12. Read 40.22 (pp. 160ff) and the unnumbered metatheorem at the bottom of p. 165 with care. Recommended: Today's exercises
Week 10, October 28 - November 1
Tue	Hunter Day 19, pp. 166-173 Recommended: Today's exercises
Wed	Hunter Day 20, pp. 173-180 Recommended: Today's exercises	Core of formal system due
Fri	Hofstadter, have finished Ch. XII (to p. 390)
Week 11, November 4-8
Tue	Hunter Day 21, pp. 180-194 Recommended: Today's exercises, Löwenheim-Skolem theorem
Wed	Hunter Day 22, pp. 195-201 Recommended: Today's exercises	Office-door exam through Day 21
Fri	Hofstadter, have finished Ch. XIV (to p. 460)
Week 12, November 11-15
Tue	Hunter Day 23, pp. 201-208 Recommended: Today's exercises
Wed	Hunter Day 24, pp. 208-215 Recommended: Today's exercises
Fri	Hofstadter, have finished Ch. XVI (to p. 548)
Week 13, November 18-22
Tue	Hunter Day 25, pp. 219-223 Recommended: Today's exercises
Wed	Hunter Day 26, pp. 224-230 Recommended: Today's exercises, Gödel's proof	Formal system due
Fri	Hofstadter, have finished Ch. XVIII (to p. 632)
Week 14, November 25-29
Tue	No class, Thanksgiving break.
Wed
Fri
Week 15, December 2-6
Tue	Hunter Day 27, pp. 230-236 Recommended: Today's exercises, Turing machines II
Wed	Hunter Day 28, pp. 236-249 You may skim pp. 239-249 iff you can still give an accurate, high-level summary of its contents; otherwise read it with care. Recommended: Today's exercises, Recursive function theory
Fri	Hunter Day 29, pp. 249-259 Recommended: Today's exercises Also recommended: Hofstadter, have finished Ch. XX (to p. 742)
Week 16, December 9-13
Tue	Hunter Day 30, pp. 259-61. Review day.	Evaluation form due before next class
Wed	Last class. Oral evaluation
Fri	No class

Assignments

Title	Due date	Weight	Description
Quiz on the infinite	September 6	??	Optional, at the consensus of the class. Through Day 4. Details.
First exam	September 26	15%	Through Day 10. Office-door exam. Details.
Second exam	October 16	20%	Through Day 15 (cumulative TFPL). In-class exam. Details.
Core of formal system	October 30	5%	A preview of your full formal system due Week 14. Details.
Third exam	November 6	15%	Through Day 21. Office-door exam. Details.
Formal system	November 20	15%	A real formal system of your own invention. Details.
Participation	n/a	10%	Attendance, preparation, leading discussion on Hofstadter. Details.
Evaluation form	December 9	0%	Due any time before the last day of class.
Final exam	December 16, 4:15 - 6:15	20%	Will cover all of Hunter. Details.
You must submit all assigned work to pass the course.

Exams

Two of the four exams will be "office-door exams". This means that I will put the blank exams in the rack outside my office door by 9:00 AM on the exam day. You come by anytime during the day, take a copy, go to a private place, take the exam, and return it by 4:00 PM the same day. The advantage is that exams do not take up class time. I put (most of) them on Wednesdays so you will have a little more flexibility in when you can take them. Please follow these guidelines:

• You are on your honor to work alone, and (if the exam instructions say so) to keep your books and notes closed. In this respect, office-door exams are no different from ordinary exams at Earlham, which are not proctored.
• I will design each ordinary exam to take 60 minutes and the final exam to take 120. But don't stop until you finish. If you don't finish in the allotted time, then draw a line across your page, label it ("60 minutes" or "time's up"), and keep writing. I'll decide later how much to count from below the line. This will help me design quizzes and exams that test your knowledge of the material rather than your speed.
• If you turn in your exam after I have left for the day, then push it under my door. (If you turn your exam after 4:00 PM, it is an NP.)
• Turn in the exam questions along with your answers, for security. I will return the question sheet as a study guide when I return your graded answers.

Missed quizzes and exams cannot be made up unless you have a medical or other substantial excuse for your absence.

None of the exams will cover my hand-outs. However, the exams will cover Hunter and my hand-outs are designed to help you with Hunter.

Please put your campus mailbox number on all your exams and submitted work. If you give me a self-addressed, stamped envelope for your final exam, then I'll mail your graded exam to you during the break.

If you want more feedback than the assigned work provides, do the exercises in my hand-out. Many of them are answered so that you can check your own progress.

If you want a quiz on Hunter's first section (on the infinite), I can give you one. You might want this to get feedback on your understanding or for some extra points in your final grade. I'll go with the consensus of the class on this. If you decide to have the quiz, it will cover the material up to Day 4. If you decide not to have the quiz, I may hand out the questions as a study guide.

Formal system assignment

This assignment is fully described in a separate hand-out.

The core of the formal system is due about three weeks before the system itself. The core may omit theorems, metatheorems, and proofs, but should include at least preliminary versions of the following:

• the formal language (both alphabet and grammar)
• the deductive apparatus (both axioms and rules of inference)
• the intended interpretation.

The system and its core are the only work for the course apart from exams and reading. I will accept rewrites of the formal system only if (1) the first edition comes in on time and (2) the first edition is a polished, finished paper, not a mere draft.

See my generic hand-out for details on lateness and rewrites. Here's the gist:  I apply a penalty to late work that arrives during the semester. I don't accept late work or rewrites after the last day of class.

Format

I will assume that you have read and understood the day's reading. In my lectures I will sometimes focus on the most difficult points from the reading, sometimes the most important, and sometimes fine points most likely to be overlooked. Sometimes I will omit detail in order to give the big picture; sometimes I will ignore all but one sub-topic in order to delve more deeply into detail. There are two important consequences for you.

• First, the lectures cannot convey everything that is important in the reading. Exams may legitimately cover everything in the assigned reading, even topics that never came up in lecture. But I promise you that exams will only cover what is most important in the reading. I won't try to trip you up on trivial details.
• Second, on some days you may have questions on parts of the text I did not cover in lecture. When this happens, please be sure to ask your questions. I am always willing to slow down, back up, or make mid-course corrections.

On most Fridays, a team of two or three of you will give a 15 minute presentation of material they found especially interesting or important from the reading in Hofstadter. In the remainder of the hour the team will lead a discussion on that material or on other interesting issues from Hofstadter. Any topics that arise from Hofstadter's book are fair game for a Friday discussion; they need not have any apparent connection to the logic in Hunter. Sign-up for a Friday slot as soon as you know your schedule. Slots will be allocated first-come, first-served.

I want each of you to lead a Hofstadter discussion at least twice. Depending on the enrollment, you may have to lead more than that.

For more information and some tips, see my hand-out on giving presentations and leading discussion.

Finding help

If you need help, please don't hesitate to talk to me in my office. I can go over material again and give you one-on-one assistance. Here are some other possibilities:

• Ask your questions in class. If you have questions, chances are that others do too. I'd like a chance to answer them for everyone, and to get the feedback on where questions are arising.
• Send your question by email to the electronic discussion list for this course, logsys or logsys@earlham.edu. Give everyone a chance at it.
• If you have a question that doesn't seem relevant to class, try it on me in my office or send it to me by email.
• Read my hand-outs. I wrote them to be helpful.
• Use my glossary. Consider printing a copy to keep with your book.
• Do my exercises. Some are answered in a separate hand-out (linked to the questions) to give you instant feedback. If you want to talk about the answers to the unanswered questions, raise them in class or drop by my office sometime.
• If the material you're having trouble with is also discussed by Hofstadter, read his account. It's always easier than Hunter. For an index of the major topics in Hunter that are also covered in Hofstadter, see my Hunter-Hofstadter map.
• As the web expands, more and more of our material is covered somewhere on the web. Check my list of course-related links for possible leads. Sometimes another perspective helps. (The web is so large now that I can't hope to link to all relevant and worthy sites. So also check Google.)
• If you have not had Symbolic Logic, then don't let my references to it intimidate you. Those are to help the students who have had the course. However, you might want to look at one or two of my Symbolic Logic hand-outs for review.
• Conversely, if you have no programming background, then don't let my references to programming terms and concepts intimidate you. Those are to help the students who do have a programming background.

A word on the hand-outs

Geoffrey Hunter and I planned to co-author a revised and expanded second edition of Metalogic. Most of the new material would consist of my hand-outs. In 1994 we had a contract with Macmillan and moved into the final stages of revision. Then Geoffrey had a serious setback in his health, requiring us to cancel the contract in 1995. Since the hand-outs work best when they presuppose Hunter's text, I did not try to revise them for separate publication. I'm happy to put them on the web where they can be used freely by anyone.

Disabilities

Any student with a documented disability who wishes to arrange reasonable accommodation should talk to me and the Director of the Center for Academic Enrichment (Runyan basement, phone x.1341) as soon as possible and at least within the first two weeks of the semester.

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This course is listed as Philosophy 43, Mathematics 43, and Computer Science 43. It satisfies requirements for the Computer Science major and minor. For that purpose, it shouldn't matter whether you signed up for it as a Philosophy course, a Mathematics course, or a CS course. If it does seems to matter to anyone, then please let me know.

This course does not satisfy any distribution requirement. It is simply for the glory of knowing.

Return to the course home-page.