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An argument is valid when its conclusion follows from, or is entailed by, its premises. In this course we will investigate an especially important and basic class of valid arguments, those whose validity depends only on the way in which words like 'and', 'or', 'not', 'if', 'some' and 'all' occur in the premises and conclusion. This investigation will also serve as an introduction to the use of formal methods to clarify our own reasoning and that of others.
Course Code: PHIL 0500, Group C, 00934
Instructor: Cian Dorr, 1001H Cathedral of Learning, office hours: *** or by appointment, email: csd6 at pitt.edu.
Lecture Times: 11 - 11.50, Tuesdays and Thursdays, 232 CL.
You must be enrolled in one of the recitation sections for the course, which will be led by Hamutal Dotan and Kris Duda.
John Barwise and John Etchemendy, Language, Proof and Logic. Stanford: CSLI Publications.
This textbook includes a package of software that we will be making extensive use of in the course. Because of the software licensing system, the textbook must be bought new. The software can be installed on your own computer (Mac or Windows), or run directly from the CD on the University's computers. There may be problems running the software on computers running the Windows XP operating system: if you encounter such problems, switch to a Mac or to a PC running a different version of Windows, of which there are many in the university's computer facilities.
There will be weekly problem sets. These will be handed out on Thursday and due in lecture the following Tuesday. Many of the problem sets will have a computerised element: they will involve constructing worlds, sets of sentences, proofs and truth-tables in Tarski's World, Fitch and Boole, and submitting them using Submit. To use Submit, you will need to enter your TA's email address: had24 at pitt.edu (Hamutal Dotan) or krisduda at hotmail.com (Kris Duda).
You can also use Submit to check your work before handing it in.
You must do all the problem sets. Provided you do all of them, your grade for the problem sets will be determined by averaging the top n - 3 of your grades, where n is the total number of problem sets that end up being distributed. However, if you just skip problem sets, the resulting F grades will count towards the final average.
If you hand in a problem set late without a valid medical excuse or equivalent, your grade will be diminished by one full grade, plus a third of a grade for every day the problem set is late after the first. So if you hand in a problem set on Friday which was due on Tuesday, and your grade for that problem set would have been A, it will instead be a C+.
There will be a final exam for the course, date TBA.
Your grade for the course will be whichever is lower of your final exam grade and your average grade on the problem sets. This is meant to remove any incentive there might be to cheat on the problem sets, and to ensure that you have an incentive to really learn the material. The final exam will be quite easy.
Assignments distributed on Thursday of one week are due in class on Tuesday of the following week.
| Week | Notes | Assignment for following week |
| 6-8 Jan | Lecture 1 (pdf) (html) Lecture 2 (pdf) (html) | Read introduction, sections 1.1-1.4, 2.1 Do exercises 1.2 (15%), 1.3 (25%), 1.5 (25%), 2.2 (35%). |
| 13-15 Jan | Lecture 4 (pdf) (html) | Finish chapter 2 Do exercises 1.9 (30%), 1.11 (25%), 2.6 (15%), 2.8-2.13 (30%). |
| 20-22 Jan | Lecture 5 (pdf) (html) Lecture 6 (pdf) (html) | Read 3.1-3.8; optionally, 4.1-4.4 Do exercises 2.22, 2.24 - 2.27, 3.6, 3.9, 3.13 - 3.15 (10% each). |
| 27-29 Jan | Read 4.1; optionally, 4.2-4.4 Do exercises 3.21 (48%), 4.2 (24%), 4.4-4.7 (7% each) NB: Only 3.21 is due next Tuesday (3 Feb); the other two exercises will be due on the 10th, along with next week's homework. | |
| 3-5 Feb | Lecture 8 (pdf) (html) Lecture 9 (pdf) (html) | Read 4.1-4.4; optionally, chapter 5 Do exercises 3.23 (30%), 4.13, 4.16, 4.17, (10% each), 4.22, 4.23 (15% each). |
| 10-12 Feb | Lecture 10 (pdf) (html) Lecture 11 (pdf) (html) | Read chapter 5; optionally, chapter 6 Do two truth-tables by hand (10% each) (see notes for Lecture 11) Do exercises 4.24 (20%); 5.8, 5.15, 5.17, 5.18 (15% each) |
| 17-19 Feb | Lectures 12 and 13 (no notes - see chapter 6) | Read chapter 6 Do exercises 6.3, 6.5, 6.6, 6.11, 6.12, 6.13, 6.15, 6.16, 6.19, 6.20 (10% each). |
| 24-26 Feb | Lectures 14 and 15 (no notes) Some example proofs from class: 1 2 | Read chapter 7 Do exercises 6.22, 6.23, 6.26, 6.27, 6.31, 6.32, 6.35-6.37, and 6.40 (10% each) (For 6.40, don't use Taut Con unless you're prepared to settle for half credit, but do heed the advice to base your proof on the proof of excluded middle given in 6.33) |
| 2-4 Mar | Lecture 16 (pdf) (html) Lecture 17 (pdf) (html) | Read: chapters 7 and 8; optionally, chapter 9. Do: exercises 7.6 - 7.8 (10% each); 7.11 (10%); 7.12 and 7.13 (20%); 8.3, 8.5, 8.6, 8.9 (10% each). |
| 16-18 Mar | Lecture 19 (pdf) (html) | Read: chapter 9; optionally, chapters 10 and 11. Do: exercises 8.31, 8.33, 8.34 and 8.37 (donÕt forget to look back at the informal proofs you gave in last weekÕs homework); 8.26 - 8.28 (you may use Taut Con to justify an instance of Excluded Middle); 9.1, 9.2, 9.6. (10% per exercise.) |
| 23-25 Mar | Lecture 20 (pdf) (html) | Read: chapter 10; optionally, chapters 11-12 Do: exercises 8.46, 8.47, 8.48, 8.52 (10% each) (note that you can use Taut Con freely to justify obvious steps in these proofs); 9.9 (8%), 9.10 (12%), 9.16 (15%), 9.17 (15%), 9.18 (10%). |
| 30 Mar-1 Apr | Lecture 22 (pdf) (html) | Read: through chapter 13 Do: 13.2, 13.3, 13.4, 13.7, 13.11, 13.12, 13.13, 13.16; (8% each); 12.2, 12.3 (10% each); write informal proofs based on your formal proofs of 13.2, 13.7, 13.13 and 13.16 (4% each). |
| 6-8 Apr | Lecture 23 (pdf) (html); some example proofs; some example translations. | Do: 11.9, 11.11, 11.12, 11.16, 11.17, 11.21 (10% each); 13.23-13.27, 13.44, 13.49, 13.52 (5% each). |
| 13-15 Apr | Sample Final Exam Solutions |
Last modified April 14, 2004