Logic grades
Course grades are posted on eGradebook and have been submitted to the registrar.
May 15, 2008
Logic - Final exam grades
Final exam grades are now posted on eGradebook. Course grades will be posted soon.
May 14, 2008
Attention: "Prove it Or Lose It" contestants
Dear logic students,
I'm afraid I didn't get a complete list of the contestants and winners of "Prove It or Lose It!" on Friday. Please remind me by email (mcgin017@d.umn.edu) if you competed (automatic B minimum for third participation increment), and also if you won (automatic A for third participation increment).
Thanks, and have a nice summer.
-"Zip"
May 13, 2008
Logic - Monday May 12
The final exam was given. Final grades will be submitted and posted to eGradebook within a week.
Have a great summer!
May 09, 2008
Logic - Friday May 9
We played "Prove It Or Lose It!" (with your host, Zip Martin). All contestants won Dum-Dums and participation credit.
While doing proofs we listened to some killer tunes, including: "You Gotta Fight for Your Right to Party", "Rock the Casbah," "Eye of the Tiger", "Never Gonna Give You Up", "Superstitious", and "We Built this City on Rock and Roll"!
Here is the cheesy video to the Survivor song:
And here is the awesome video of Stevie Wonder on Sesame Street:
May 07, 2008
Logic - Wed May 7
We discussed some important properties of relations and worked through a bunch more symbolizations in relational predicate logic with identity.
I'm pretty sure my symbolization of "In China some couples have more than two children" was the longest logical formula I have ever written in my life (about 25 feet, across two blackboards!).
Reminder: participation logs due Friday
On Friday: Prove it or Lose It! (with Zip Martin)
May 06, 2008
Logic - Tues May 6
We worked through lots of symbolization problems.
Reminder: participation logs due Friday
Click here to download the study guide for the final (PDF).
May 05, 2008
Logic - Monday May 5
We worked through some problems from the current homework and the quiz that was given on Friday. (I "downgraded" the quiz to an "in-class exercise".)
No new reading was assigned.
Reminder: participation logs due Friday.
In class I was temporarily stumped by two questions about possible ways of symbolizing "Every dog likes some cat". The best symbolization (using what I hope is obvious notation) is
(1) (x)(Dx => (Ey)(Cy . Lxy))
This is the symbolization I used in class. Joe B. asked if it could be symbolized as
(2) (x)(Ey)(Dx => (Cy . Lxy))
It turns out that (2) is logically equivalent to (1). It is an inferior translation, however. (Note that any given sentence has infinitely many logical equivalents.)
Proving that (1) and (2) are equivalent is quite difficult. (Try it if you don't believe me!)
Matt M. asked if the sentence could be symbolized as
(3) (x)(Ey)((Dx . Cy) => Lxy)
The answer is "no." Consider an interpretation with exactly one object in its domain -- something that is a dog and not a cat. This interpretation makes (3) true but (1) and (2) false.
May 04, 2008
Logic - Friday May 2
We talked about how to symbolize sentences involving definite descriptions and discussed some important properties of relations.
There was a quiz at the end of class.
May 01, 2008
Logic - Wed Apr 30
We worked on symbolizing sentences involving identity.
For Fri.: read pp. 291-294
April 30, 2008
Logic - Tues Apr 29
We introduced the rules for identity (=) and worked through some proofs and symbolizations.
HW #14 (last one!): Ex 10-12 (5, 7, 9), 13-1 (1,3,5), 13-2 (all odd)
For Wed.: pp. 289-290
April 28, 2008
Logic - Mon Apr 28
We worked through a couple more problems from the current homework, then worked through some zero-premise deductions in predicate logic.
For tomorrow: read pp. 283-288
April 25, 2008
Logic - Friday April 25
We worked through some problems from the current homework.
Quiz #8 was given at the end of class.
For Mon.: finish Chapter 12 (skip Section 6)
April 23, 2008
Logic - Wed April 23
We worked through some evens from 10-10.
For Fri.: read pp. 269-275
April 22, 2008
Logic - Tues April 22
We talked a little more about proof strategy. We then got into groups and worked on Exercise 10-9. Finally, we worked through a couple of proofs from 10-10.
HW #13: Ex 10-10 (all odds), 10-11 (#1 only) – only one more after this!
Hint on 10-10, #7: instantiate with u, v, and w (don't use x, y, or z).
For Wed.: no new reading!
Logic - omission in textbook
In Exercise 10-1, problem 13, the authors do not provide an individual constant for Shakespeare. (Thanks to Becky E. for bringing this to my attention.) You can use "s" (even though it's used for something else in an earlier problem).
April 21, 2008
Logic - Monday April 21
We worked through some problems from Exercise 10-3 and talked about proof strategy for relational predicate logic.
Quiz #7 was given at the end of class.
For Tues.: read through p. 265
April 18, 2008
Logic - Friday April 18
I told a really good lawyer joke and analyzed if from a logical perspective.
Then I bored y'all to tears with the details of the proof rules for relational predicate logic.
For Mon.: read pp. 254-60.
April 17, 2008
A helpful note from one of my logic graders
Victor writes:
"I noticed that nearly everyone has been making the same
mistake in problem 9 of 9-3. Save one person, everyone instantiated
with either x or y via UI and then later instantiated again using the
same free variable they instantiated with while using UI. This
violates the second restriction on EI, as (...w...) cannot have
appeared free anywhere else in the proof. Maybe you want to note that
to the class as nearly everyone made the same mistake. I learned that
you nearly always want to use EI before UI."
He's right. In general it's a good idea to instantiate existentials before
universals. (I may not have emphasized this enough in class.)
April 16, 2008
Logic - Wed Apr 16
I handed back exam #2. We worked through some problems from the current homework and the exam.
For Fri.: read through p. 249
April 15, 2008
Logic - Tues Apr 15
Today we worked through some more difficult symbolizations in relational predicate logic.
We also introduced a new class mascot: "Predicate" the Logic Horse! (thanks to Kristine O.)
HW #12: Ex 9-5 (every third odd: 1, 7, 13, 19); Ex 10-1, 10-3, 10-7 (all odd)
For Wed.: read through p. 242
April 14, 2008
Logic - Mon April 14
We introduced relational predicate logic and worked through some symbolizations.
For Tues.: read through p. 234
April 10, 2008
Logic - Wed Apr 9
We reviewed the restrictions on the rules UI, UG, EI, and EG, and introduced the new rule QN. We also worked through a bunch of proofs from exercises 9-3 and 9-5.
For Fri.: read through p. 230
April 08, 2008
Logic - Tues Apr 8
We discussed and illustrated the restrictions on the EI and UG rules. We then worked through some problems from Exercise 9-1.
HW #11: Ex’s 9-1, 9-3 (all odd problems)
For Wed.: Finish Chapter 9
April 07, 2008
Logic - Monday Apr 7
The second midterm exam was given (and taken).
For tomorrow: read through p. 215.
April 05, 2008
Logic - Friday Apr 4
We reviewed for the upcoming exam. No new reading was assigned.
April 02, 2008
Logic - Wed Apr 2
We started discussing proofs in predicate logic.
On Friday we will review for the upcoming exam, so come prepared with questions and/or problems you want to work through.
For Fri: Read through p. 212
Participation logs due on Friday!
April 01, 2008
Logic - Tues Apr 1
We worked through some problems from exercise 8-1.
Quiz #6 was given at the end of class.
For tomorrow: Read through p. 209
HW #10: 7-5, 7-6, 7-7, 7-9 (every other odd: 1, 5, 9, etc.)
March 31, 2008
Logic - Mon March 31
I handed out a study guide for Exam #2 (which is a week from today), and talked about what will be on it. For some reason I agreed to let y'all have a full sheet of paper (8.5" x 11"), rather than just a 3" x 5" card, as a "cheat sheet".
We then worked through some problems from the current homework.
Reminder: Participation logs due this Friday April 4
For Tues.: read through p. 204
March 29, 2008
Logic - Friday March 28
We discussed the semantics of predicate logic.
Participation logs due Friday April 4
Exam #2 Monday April 7 (study guides handed out on Monday)
Reading for Mon.: read Chapter 8
March 26, 2008
Logic - Wed March 26
We talked some more about English symbolizing sentences in predicate logic and worked through some problems from Exercises 7-6, 7-7, 7-9, and 7-10.
For Friday: Finish Chapter 7
March 25, 2008
Logic - Tues March 25
We talked about the four basic sentence forms that make up the four corners of the "square of opposition", and went over some common mistakes that students make when symbolizing English sentences in predicate logic. Then we got into groups and worked through some symbolization problems (the odds in exercise 7-6). We will go over these tomorrow.
2nd participation log is due Friday, April 4.
2nd midterm will be on Monday, April 7. It will focus primarily on the material in Chapters 4-8.
HW #9: Ex’s 6-1, 7-1, 7-3, 7-4 (ALL odd problems)
Reading for Wed.: through p. 181.
March 24, 2008
Logic - Mon March 24
We started on predicate logic today, introducing some of the basic concepts such as predicates, individual constants, and quantifiers.
For tomorrow: read through p. 177
March 14, 2008
Logic - Friday March 14
We played "Truth Tree Showdown". Prizes were distributed and fun was had by all (or at least some).
No new reading was assigned.
March 12, 2008
Logic - Wed March 12
We worked through some more truth tree problems, and discussed how to use truth trees to check:
- whether an argument is valid
- whether a sentence is a tautology, contradiction, or contingent
- whether a set of sentences is consistent
Quiz #5 was given at the end of class.
Reading for Fri: finish Chapter 6
March 11, 2008
Logic - Tues March 11
We finished up Chapter 5 and started on Chapter 6 (truth trees).
HW #8:
Ex’s 5-3, 5-5, 5-6, 5-8 (every other odd – i.e. 1, 5, 9, 13 in each exercise)
Reading for Wed.: through p. 159
March 10, 2008
Logic - Mon March 10
We worked through some zero-premise deductions (proving theorems) and talked about adding valid argument forms.
For Tues: read through p. 157
March 08, 2008
Logic - eGradebook update
The glitches have been resolved, and everything should be correct and up to date in eGradebook now.
March 07, 2008
Logic - Friday March 7
We introduced the indirect proof rule, IP, and worked through a number of proofs that use it.
Reading for Mon: through p. 153
March 05, 2008
Logic - eGradebook glitches
We (the graders and I) have been experiencing a weird glitch with eGradebook. In particular, some of you have "F"s when you should have "A"s, "B"s, etc. We're looking into it, and the problem will be corrected soon. So don't panic!
Don't worry, your grades are safe. We back up everything. (Still, you should hold on to all graded work in case there's an error.)
Philosophy Colloquium (Extra Credit Opportunity!)
Students in my logic class can get (a small but not-insignificant amount of) extra credit for attending this colloquium and writing a brief (about one page, double spaced) report on what it was about. The report is due by Wed., March 12.
Philosophy Department Colloquium
Thursday, March 6, 4 p.m. ABAH 345
“Contradiction in Fiction (How to Imagine the Impossible without Inferring the Insane)"
A presentation by Casey McGinnis
Logic plays a role in determining what’s true in a work of fiction. For example, if X is true in a work of fiction, and X logically implies Y, then Y is also true in that work of fiction. Many works of fiction are inconsistent or contradictory — some even deliberately so. For example, the philosopher and logician Graham Priest has written a thought-provoking story (“Sylvan’s Box”) about a mysterious box that is somehow both empty and not empty (at the same time). Classical logic tells us that contradictions imply everything, so, from a classical point of view, everything must be true in an inconsistent work of fiction! Intuitively, this seems wrong.
For this and other reasons, some (such as Priest) have recommended that we give up classical logic in favor of a paraconsistent (inconsistency-tolerant) logic. I will argue that replacing classical logic with paraconsistent logic is neither necessary nor sufficient for solving the puzzle about inconsistent fiction. The alternative solution I propose appeals to what I call logical relativism — roughly, the view that judgments about what follows from what are correct or incorrect only relative to a set of background assumptions about what is considered a “live” possibility.
Logic - Wed March 5
After talking about "gumball logic" (you had to be there), we worked through some fairly simple proofs involving the very useful rule CP (conditional proof).
Reading for Friday: finish Chapter 5
March 04, 2008
Logic - Tues March 4
We worked through some proofs from the homework that was due today.
Quiz #4 was given at the end of class.
For Wed.: no new reading!
HW #7 (due next Tues.): Ex 4-14 (problems 1-4), Ex 5-1 (all odd problems)
March 03, 2008
Logic - Monday March 3
We finished up Chapter 4 and started on Chapter 5.
I noted that the problems in Exercise 4-13 are extremely hard. (Even I found some of them difficult.) Just give them your best shot!
Reading for Tues: through p. 143
February 29, 2008
Logic - Friday Feb 29
We worked through problem #7 in Exercise 4-11.
We then got into groups and discussed questions 1-4 and 7 in Exercise 4-14. On Monday I will review the answers.
Quiz #3 was given at the end of class.
February 27, 2008
Logic - Wed Feb 27
We basically finished up Chapter 4 today. At the end of class, we began working on Exercise 4-11, #7. Here's a big juicy hint: The proof can be completed in 3 steps (4 lines altogether), using Dist, Simp, and Comm (though not necessarily in that order).
Reading for Fri: through p. 138
February 26, 2008
Logic - Tues Feb 26
Today we discussed more proof strategies and worked through a bunch of proofs.
Homework #6:
Ex 4-6, 4-7, 4-8, 4-9, 4-10, 4-11, 4-12, 4-13 (every third odd: 1, 7, 13, 19 in each exercise)
Reading for Wed: through p. 133
February 25, 2008
Logic - Mon Feb 25
Exam #1 was given today. I've graded them already (took all afternoon). All in all, you did pretty well! There were a few As, tons of Bs, a few Cs, a few Ds, and not a single F. I graded by percentage of the highest score (which was 930/1000), and then made a few minor adjustments for natural breaks.
Reading for tomorrow: Finish Chapter 4.
Looks like an error, but it's not!
In Exercise 4-4, #1, it seems like the conclusion should be R, not Q. (Even I thought that this was a typo at first.) However, there is a sentence that can be placed in line 2 that will make the proof work. (Hint: a conditional can be part of a larger conditional!)
To download a list of real errors in the textbook, click here.
February 24, 2008
translating "unless"
Here are the answers to the exercise I posted here on Friday.
"I have enough money to last me the rest of my life, unless I buy something."
--Jackie Mason
M = "I have enough money to last me the rest of my life"
B = "I buy something"
~B => M
~M => B
M v B
(Note: I'm using '=>' for the horseshoe.)
If you set up a truth table for these three sentences (in the standard format, listing B first), the column under the main connective of each should read:
T
T
T
F
This shows that the three translations are logically equivalent.
February 22, 2008
Logic - Friday Feb 22
We reviewed for the exam on Monday.
Participation log #1 was turned in.
For Mon.: Study! (no new reading)
translating "unless"
Here's a little (unofficial) exercise that will help prepare you for the exam:
"I have enough money to last me the rest of my life, unless I buy something."
--Jackie Mason
Exercise: Give three logically equivalent translations of the above statement, using the following abbreviations:
M = "I have enough money to last me the rest of my life"
B = "I buy something"
Your translations should contain no more than two logical connectives.
Use truth tables to prove that your translations are logically equivalent.
(I will post the answers sometime over the weekend.)
February 20, 2008
A Nice Oxymoron
"Midlife Suicide Rises, Puzzling Researchers"
--headline, New York Times, Feb. 19
Logic - Question from a student
Question:
> I was just wondering one thing about
> the homework. Is it ok to write out a proof rather than rewriting
> just the answers like in the back of the book?
Answer: Yes, you should definitely write out the whole proof.
Logic - Wed Feb 20
We introduced a bunch of new rules and worked through a bunch of proofs.
Friday is a review day. We will work through a number of problems similar to what will be on the exam.
For Fri.: Read through p. 116, study for exam
February 19, 2008
Logic - Tues Feb 19
We talked about proof strategies and worked through some proofs.
Homework #5:
Exercises 3-10, 3-11, 4-1, 4-2, 4-3, 4-4, 4-5 (every other odd problem: 1, 5, 9, etc. in each exercise)
Note that the graders only grade selected problems in your homework--typically about half of the problems you are assigned. Of course, you don't know ahead of time which ones they will be grading.
For Wed.: Read through p. 111
February 18, 2008
Logic - Mon Feb 18
We continued discussing proofs and worked through some problems.
Homework #3 was handed back.
I handed out a study guide for the first exam, which will be a week from today.
For Tues: read through p. 103
February 15, 2008
Logic - Friday Feb 15
We started by talking about how the truth tables (especially for implication) can be justified. We then moved on to start talking about proofs.
Quiz #2 was handed back.
For Monday: read through p. 98.
February 13, 2008
Logic - Wed Feb 13
Since you guys bombed the quiz yesterday, we reviewed some problems similar to what was on the quiz. We also worked through a few problems from the current homework.
I announced that the first exam will be on Monday, Feb. 25. I will hand out a review sheet on Monday, Feb. 18, and we will have a review session (in class) on the Friday before the exam. For the exam, you will be allowed a 3" x 5" index card with any information you want on it (both sides). I will enforce the 3 x 5 inch restriction by arbitrarily ripping your card if it is too big!
For Friday: read through p. 93.
Tautological* quote of the day:
"Things are more like they are now than they have ever been."
--Gerald Ford
*This is a tautology in the colloquial sense, not in the logical sense.
February 12, 2008
Logic - Tues Feb 12
We talked about why an argument is automatically valid whenever either its premise set is inconsistent or its conclusion is a tautology. We also discussed the short truth table test for invalidity.
Quiz #2 was given at the end of class.
Reading for tomorrow: finish chapter 3
Homework #4 (due next Tues):
Exercises 3-1, 3-2, 3-3, 3-6, 3-7, 3-8, 3-9 (every other odd –i.e., do problems 1, 5, 9, etc. in each problem set)
February 11, 2008
Logic - Monday Feb 11
Today we covered the notion of logical equivalence, the truth table tests for validity and consistency, and the definition of an argument's "counterexample set".
Important to remember:
1. An argument is valid if and only if its counterexample set is inconsistent.
2. An argument is invalid if and only if its counterexample set is consistent.
(These two statements are equivalent.)
For tomorrow: read through p. 82.