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Philosophy 0690: Problem Sets

If you wish, you can download the syllabus as a PDF. Please note, however, that all dates are approximate and the PDF version of the syllabus will not be kept up to date. You should check this website for updates as we proceed.

Some Reminders

It is a requirement of the class that all of the problem sets must be completed and submitted for marking. Failure to submit all of the problem sets will automatically lead to a grade of NC. Please note that the requirement is that the problem sets should be "completed", and by that I mean that one has given them a proper effort. Simply turning in a piece of paper with a few random jottings does not count as completing a problem set.

As with any mathematical subject-matter, it is impossible to learn this material without doing a lot of exercises. The book contains many more exercises than are assigned, and students are encouraged to do additional exercises to improve their understanding of the material. Students are also encouraged to work on the problems together—though, of course, submitted material should be a student's own work.

Grading

Problem set grades are not a major component of the overall grade for the course and should not be regarded as such. The 'grades' for problem sets are primarily intended to give students a sense for how well they have understood the material in that unit. To that end, problem sets are graded on a scale of 1-5, with the different scores having the following meanings:

• 5: Better than perfect
  To receive a 5, a problem set must not only get all the problems right (save possibly for a couple silly mistakes), but either do a number of the problems in a particularly elegant way, or else do some of the optional problems well.
• 4: More or less perfect
  To receive a 4, a problem set must get nearly all the problems right (save possibly for some silly mistakes). This should be thought of as meaning that the problem set demonstrates a understanding of the material that is better than adequate as a basis for what we shall do henceforth.
• 3: Satisfactory
  To receive a 3, a problem set must get most of the problems right, especially those that are "foundational", i.e., those that test understanding of the basic concepts covered in that part of the course. This should be thought of as meaning that the problem set demonstrates a understanding of the material that is adequate as a basis for what we shall do henceforth and hence that gives us no reason for concern.
• 2: Unsatisfactory
  A problem set that receives a 2 is one that reveals some misunderstanding of, or confusion about, the basic concepts covered in that section. Since the course is cumulative, it therefore gives us some concern about the student's ability to absorb the material in later parts of the course. Students who receive a 2 are encouraged to attend office hours to try to resolve whatever problems were apparent from the problem set.
• 1: Worrying
  A problem set will only receive a grade of 1 if it reveals a significant level of misunderstanding of, or confusion about, the basic concepts covered in that section. Since the course is cumulative, it therefore gives us serious concern about whether the student will be able to absorb the material in later parts of the course. Students who receive a 1 really must get in touch with one of the instructors as soon as possible, either by attending office hours or by making an appointment. Such students might also consider hiring a tutor.

To re-emphasize, then: A score of "3" on a problem set is meant to indicate that a student has successfully mastered that material and is prepared for what it is to follow in the course. While there is no easy 'map' from problem set scores to letter grades, someone who is routinely getting 3's on the problem sets can fully expect to get at least a B on exams covering that same material (and so to get at least a B for the course). Remember, too, that effort matters a lot to us, so if you are not doing so well, there are lots and lots of opportunities to get help.

The Problem Sets

Problem sets will be due one week after we complete the relevant material. Dates below are thus estimates. But the problem sets will never be due before those. You are advised, however, not to wait until we finish the material to begin the problem set. You will be much happier if you start working on the problems as we cover the relevant material. Among other things, this will reveal to you, right away, if there is something you do not really understand.

Please note that all the exercises are subject to revision until we get to that material.

1. First set of exercises for "Formal Background", covering sections 1-5: 15.1(i,ii), 15.2, 15.3, 15.5–15.8, and 15.10. Exercises 15.4 and 15.9 are optional.
   Due 28 May.
2. Second set of exercises for "Formal Background", covering sections 6-13: 15.11–15.17, and 15.19–15.20. Exercise 15.18 is optional.
   Due 11 June.
3. First set of exercises for Gödel's "On Formally Undecidable Propositions": These are exercises 2.1-2.6.
   Due 25 June.
4. Second set of exercises for Gödel's "On Formally Undecidable Propositions": These are exercises 2.7-2.12. Exercise 2.10(ii) is optional (and a bit challenging).
   Due 7 July.
5. Exercises for Tarski, Mostowski, and Robinson, Undecidable Theories: These are exercises 3.1-3.4, 3.6-3.7, and 3.9.
   Due 23 July.
6. Exercises for Boolos, The Logic of Provability, Ch. 2: These are exercises 4.1-4.8.
   Due 6 August.
7. Exercises on Feferman's "Arithmetization of Metamathematics in a General Setting": You should do all of these.
   We will not get to this material.

Doing Problem Sets Electronically

You are welcome to do your problem sets by hand or on a computer. But if you are going to do the latter, then I would strongly recommend that you not use a traditional 'word processor' to do so. They are simply not optimized for mathematics, and their output is awful. A much better option is LaTeX, and if you want to use LaTeX in an environment that feels a lot like a word processor, then you can use LyX, which can be downloaded for free from http://lyx.org/. (I am one of the lead developers of LyX, so you should feel free to ask me any questions you may have about it.) Especially if you have any intention of ever doing serious technical writing, you should start using LaTeX sooner rather than later. In the sciences, especially, it is the standard tool. Many scientific journals do not accept submissions in any other form.

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Richard Heck Department of Philosophy Brown University