Phil 351

Reasoning and Logic

Time: Monday/Wednesday 3:30-4:45

Location: VKC 256

Instructor: Kenny Easwaran - easwaran AT usc DOT edu

Office: STO 227

Office Hours: My office hours are Monday/Wednesday 2:00-3:30. I can also be available at other times if you e-mail me for an appointment.


Learning objectives in philosophy.

Stanford Encyclopedia of Philosophy - a very useful free resource with discussions of many topics in philosophy. (In particular, you may find the entry on Classical Logic interesting, as well as entries on topics like Conditionals, Theories of Meaning, the Philosophy of Computer Science, and other topics.)


Language, Proof, and Logic, by Jon Barwise and John Etchemendy, including software. All readings for the class will come from this book, unless otherwise indicated.


Much of the homework for this class will be submitted electronically using the software from the book, so it is important that you are able to have access to it. If you don't have a computer of your own with a CD drive, it may be possible for me to arrange for the software to be installed in some public computer labs, but you will unfortunately still need to have the Registration ID from the CD that came with your own book. Note that for this reason it is important that you get a new copy of the book, including the software, rather than a used copy, since the publishers only allow one student to use each Registration ID number.

Most assignments will involve some use of the software for submission, and will also have some written elements. I generally prefer to receive written assignments by e-mail, so that I have electronic records of all homework assignments, but some of them may involve diagrams or proofs or other things that are hard to create electronically, so handwritten hard copies will also be accepted. For electronic submissions, I would prefer for text to just be in the body of the e-mail, but you can also include homework as an attached .pdf file. If necessary, it is possible for me to accept files in Microsoft Word format, but since files often display differently on computers running different versions of MS Word, I prefer not to deal with that ever if I don't have to.

There will be no exam for the class - it will be graded entirely on homework and class participation, though there will be three exercises due during final exam week, which you might think of as small take-home tests.

Each three-week period of homework is worth an equal amount, and the three final exercises together are worth half as much as each of those three-week periods.

Academic integrity:

All students are expected to understand and abide by these principles. SCampus, the Student Guidebook, contains the Student Conduct Code in Section 11.00, while the recommended sanctions are located in Appendix A (.pdf file). Students will be referred to the Office of Student Judicial Affairs and Community Standards for further review, should there be any suspicion of academic dishonesty. The Review process can be found in Section 14.00.

I am happy to allow students to work together on homework. However, I ask that you separately write up and submit your files. For written assignments, please give credit to anyone who you worked with.

Statement for students with disabilities:

Any student requesting academic accommodations based on a disability is required to register with Disability Services and Programs (DSP) each semester. A letter of verification for approved accommodations can be obtained from DSP. Please be sure the letter is delivered to me as early in the semester as possible. DSP is located in STU 301 and is open 8:30 a.m. to 5:00 p.m., Monday through Friday. The phone number for DSP is (213) 740-0776.


Jan. 10, 12

Reading: Chapter 1, sections 1-4


Exercise 1.2 due Tuesday, Jan. 11

Exercises 1.4, 1.8, 1.10 due by Wednesday, Jan.19

Jan. 19 (note MLK holiday)

Reading: Chapter 2, section 1


Exercise 2.1 due by Monday, Jan. 24

Jan. 24, 26

Reading: Chapter 2, sections 2-5


Exercises 2.8, 2.9, 2.10, 2.11, 2.14 due by Wednesday, Jan. 26

Exercises 2.15, 2.18, 2.22, 2.25, 2.26, 2.27 due by Monday, Jan. 31

Jan. 31, Feb. 2

Reading: Chapter 3, sections 1-7


Exercises 3.7, 3.10 due by Wednesday, Feb. 2

Exercises 3.14, 3.15, 3.18, 3.20, 3.24 due by Monday, Feb. 7

Feb. 7, 9

Reading: Chapter 4, sections 1-4


Exercises 4.2, 4.8, 4.19 due by Wednesday, Feb. 9

Exercises 4.20, 4.21, 4.27, 4.28 due by Monday, Feb. 14

Feb. 14, 16

Reading: Chapter 5, sections 1-4


Exercises 5.1, 5.3, 5.5, 5.10 due by Wednesday, Feb. 16

Exercises 5.19, 5.27 due by Wednesday, Feb. 23

Feb. 23 (note President's Day holiday)

Reading: Chapter 6, sections 1-6


Exercises 6.2, 6.4, 6.9 due by Monday, Feb. 28

Feb. 28, Mar. 2

Reading: Still just Chapter 6


Exercises 6.10, 6.12, 6.19 due by Wednesday, Mar. 2

Exercises 6.22, 6.28, 6.31, 6.32 due by Monday, Mar. 7

Mar. 7, 9

Reading: Chapter 7, sections 1-3


Exercises 7.2, 7.3, 7.5, 7.6 due by Wednesday, Mar. 9

Exercises 7.12, 7.14, 7.18, 7.22 due by Monday, Mar. 14

Mar. 14, 16


Mar. 21, 23

Reading: Chapter 8, sections 1, 2, 4


Exercises 8.18, 8.19, 8.20, 8.21, 8.22, 8.23 due by Wednesday, Mar. 23

Exercises 8.24, 8.26, 8.28 (you can use Taut Con to introduce (P v ~P)), 8.44, 8.45 due by Monday, Mar. 28

Mar. 28, 30

Reading: Chapter 9, sections 1-6


Exercises 9.1, 9.2 due by Wednesday, Mar. 30

Exercises 9.9, 9.10, 9.12, 9.16 due by Monday, April 4

Apr. 4, 6

Reading: Chapter 10, sections 1-3


Exercises 10.1, 10.2, 10.4 due by Wednesday, April 6

Exercises 10.10, 10.11, 10.13, 10.14, 10.15 due by Monday, April 11

Apr. 11, 13

Reading: Chapter 11, sections 1-5


Exercises 11.2, 11.4, 11.11, 11.17, 11.39 due by Monday, April 18

Apr. 18, 20

Reading: Chapter 12, sections 1-4


Exercises 12.1, 12.4, 12.6, 12.8, 12.23 due by Monday, April 25

Apr. 25, 27

Reading: Chapter 13, sections 1-3


Exercises 13.2, 13.3, 13.7 due by Wednesday, April 27

Exercises 13.11, 13.12, 13.13, 13.17, 13.18 due by Monday, May 2

May 4

Final homework assignment, due 11:59 pm, Sunday, May 8

Final Exercise 1 - fill in the truth table and say whether or not the argument is tautologically valid. That is, say whether

U ^ (S v C)

(U <-> C) ^ (L <-> A)

together entail

(C -> (L -> (A -> ~S))) v ~S

Final Exercise 2 - create a world where all the sentences are true.

I've given some hints for how to think about the sentences when creating the world - it probably makes sense to make the first set work out, then the next set, and so on.

Final Exercise 3 - create a proof to show the argument is valid.

Some comments about the argument:

Before you go about trying to create the proof, you should think about why the argument is valid. To do this, note what each statement says.

1. For every chicken, there was an egg that came before it.

2. For every egg, there was a chicken that came before it.

3. If x came before y and y came before z, then x came before z.

4. Nothing came before itself.

5. There has been at least one chicken.

Conclusion. There have been at least two chickens.

An interesting observation, which is irrelevant to actually constructing the proof: the reasoning that makes this argument work could be extended to show that there have been at least three chickens, at least four chickens, and so on - thus, the premises actually entail that there have been infinitely many chickens! (And also infinitely many eggs.) Thus, since there have only been finitely many chickens in the history of the world, at least one of the premises must be false. Premises 3, 4, and 5 are all obviously true (in fact, 3 and 4 basically state part of the meaning of "came before"). Thus, there must either have been a chicken that didn't come from an egg, or an egg that didn't come from a chicken (or both?). (Of course, this argument, and this proof, don't give us any help in solving the ancient problem.)