Here is a running schedule of the problems that are assigned for as our problem sets throughout the term. Remember that the problem set exercises are not the upper limit of the problems you should do: The more exercises from the book you try, the better off you will be.

Unless otherwise noted, problem sets are always due by the beginning of class on the due date. Each PS is worth 30 points. Each individual problem is worth 6 points unless otherwise indicated.

If an assignment has a written-out portion, you may either (a) bring it to class on the day it’s due, (b) slip it under Mark’s office door before it’s due, or (c) send it in an e-mail it to Mark before it is due. Whenever you submit a written portion of a problem set via email, please make sure to write “Written Portion: PS #” in the subject line, letting us know that your e-mail contains a written portion to be graded and telling us which problem set number it is for.

Hints and Solutions for some of these exercises are available under the “For Students” section of the LPL web site, where indicated below.


Problem Set 9

Due: at the beginning of class on Friday, December 8.

There are four exercises from the textbook and one handout:


Problem Set 8

Revised Due Date: Monday, December 4 by the end of class

Proofs and/or Counterexamples! Start early, and use the strategy points laid out in Handout 14 if you get stuck.


Problem Set 7

Due: Monday, November 27

Start early! Even though it involves translations rather than proofs, this might be the hardest problem set of the semester. Students in previous years have been especially emphatic about the difficulty of Exercises 11.20 and 11.40.

Check your work with the Grade Grinder regularly, after every few sentences you attempt, rather than waiting until the end. Don’t make the mistake of thinking that just because your sentences are true in the specified world they must be correct.

For some of your answers to 11.20 or 11.40, the Grade Grinder might report that it “timed out” while checking your answer, and that you should confer with your instructor. This doesn’t mean that your answer is definitely wrong. But it also doesn’t mean that it is right. It only means that your answer was more complicated than the translation had to be and that the grade grinder couldn’t tell whether it was correct in the amount of time allotted to grading that problem. If your answer times out but is nevertheless correct, you don’t lose any points just because we have to check it by hand. However, experience teaches that the vast majority of timed out translations are incorrect. If you get one of these messages, you should confer with Mark or the tutor to figure out how you might begin to fix it.

Hints are available at the LPL website for parts of 11.17, 11.20, and 11.40.

Here is one more hint of my own for Exercise 11.20, Sentence 12. Notice that one of the things that is smaller than something that is larger than b will be b itself. The Grade Grinder expects you to understand that fact and assume it as you do your translation. Otherwise, your translation will “time out.”


Problem Set 6

Due: Friday, Nov. 3 if you want a guarantee that it will be returned by Friday, Nov. 10. Otherwise, due on Monday, Nov. 6.

Hints are available at the LPL website for Exercises 10.1 and 10.9.

Pay careful attention to the instructions for each of the problems, as well as the little symbol under the exercise number. Some will require you to write something out to hand in, others might call for a mixture of writing and Grade Grinder submission.

When part 1 of Exercise 10.9 asks you to translate/paraphrase the sentences into “clear, colloquial” English, please make sure to write smooth, plain English (“Every cube is small,” or “Everything in back of b is a tetrahedron”) that your relatives could understand over Thanksgiving dinner. Robo-, pseudo-English that uses variables (like, “For any object x, if x is a cube, then x is small”) isn’t acceptable as a finished product. You may use the robo- pseudo-English as a mid-way point—a scratch work to help you get from the FOL to the English—but don’t stop there. No translation that contains a variable like “x” in it is clear, colloquial English; hence, no such translation will earn any points. Including FOL names (a, b, etc.) in your translations is perfectly okay, and indeed necessary for getting a correct English translation of sentences about Tarski’s World objects.

See instructions above about the different ways you can submit a written assignment. (Make sure that if you send it in an e-mail that you write “Written Portion: PS 6” as the subject line of the message.)


Problem Set 5

Due: Friday, 10/27

Remember that checking your translations against worlds is helpful, but it does not guarantee that your translations are correct. Make sure to use the “just me” option in the grade grinder early and often to check your translations as you work.

You don’t have to wait until you’re done with all of the translations before you check your work in the grade grinder. If you want to check, say, the first four sentences you’ve written, you can do that; the grade grinder will report that your blank sentences are incorrect, but who cares? “Just me” submissions don’t count for a grade.

Hints are available at the LPL website for some of these problems.


Problem Set 4

Due: on Wednesday, Oct. 18

The problems from Chapter 8 involve proofs, so start working early!


Problem Set 3

Due: Wednesday, October 4 (Note the change of date!)

Make sure to read the instructions for each problem; some of them will ask you first to determine whether the argument is valid or invalid and then complete the exercise accordingly. (It is never fun to spend several hours trying to construct a proof of an argument only to find out that it is invalid and no proof is available.)

Start early! Proofs are hard, and you’re more likely to get stuck and need help with these problems than with the earlier problem sets.

My advice from the syllabus is especially apt when it comes to proofs: Treat the problem set as the bare minimum group of problems, and go on to do as many other exercises from the book as you can stand.

When you receive your official “Instructor Too” report for PS 3, the Grade Grinder will say some things that might worry you, but which are not really a problem:

Problem Set 2

Due: Monday, September 25, by the beginning of class

For Exercise 4.8, use worksheet from Handout 6, which has the Euler diagram already drawn on it.


Problem Set 1

Due: Friday, September 15

Note that this is a very late due date for this problem set; it is due in the third week of the semester. You can and should start working on this problem set earlier than this date would suggest.

Note: Problem 3.10 asks you to submit both files when you’re done. It’s asking for the world file that you modified and renamed as “World 3.10.wld”, and it also wants you to submit the sentence file. The Grade Grinder will complain if you do not submit the sentences, but I don’t care whether you do so or not, and you will not lose points for not submitting them. I am confident you can type.

If you get stuck on 3.21, you can find some help in the “Hints” file for Chapter 3 from the LPL web site. Also, note that Exercise 3.22, which is not assigned, can help you check your answers to Exercise 3.21.