Elementary Logic (PHIL 1030-01: 32147)             

Dr. Edgar Boedeker             Mo,We,Fr: 2-2:50      Lang 211        Fall 2012        

 

Office hours: 2:00-2:45pm Tuesdays and Thursdays, and 3-3:30 Wednesdays in my office, 145 Baker Hall. I would also be happy to meet with you at another time, to be arranged in advance. If you would like to schedule such a meeting, just send me an e-mail at edgar.boedeker@uni.edu or give me a call at 273-7487.

 

Required Text: Patrick J. Hurley, A Concise Introduction to Logic, Ninth Edition (Wadsworth, 2005; ISBN: 9780534585051), available at University Book & Supply and numerous online venues.

 

Why Study Logic? A brilliant (but rather eccentric) Austrian named Ludwig Wittgenstein (1889-1951) wrote what is surely the greatest philosophical work on logic, the 50-page-long Tractatus Logico-Philosophicus. When he was 23 years old, hard at work on this book, he wrote to his friend and mentor, the logician Bertrand Russell: “Logic must turn out to be of a totally different kind than any other science.” Soon, he would discover that it is not a “science” at all – at least not in the way that biology, chemistry, and even higher mathematics are sciences. That is, logic does not try to make true and abstract statements about particular kinds of things, such as living things, molecules, or various kinds of numbers. (Statements, also known as propositions, beliefs, etc., are whatever is either true or false.)  But this does not mean at all that logic is merely “subjective”, so that I have my logic and you have yours. Rather, logic occupies an absolutely central place within statements, and especially within the relations among them. For example, biology tells us that all whales are mammals, and that no mammals are fish. From these two statements, we can logically draw the conclusion, or “infer,” that no whales are fish (and thus that quite a number of statements in Moby Dick are false).

            Logic occupies a similarly central place in ordinary, everyday speaking and thinking. For example, if someone tells you that they’ll either study tonight or go to a movie, and they don’t end up going to a movie tonight, then you can infer – at least if what they’ve said is true – that they’ll study tonight. Logic examines these and other kinds of inferential relations among statements. Indeed, logic (as an academic discipline) can be defined as the study of inferential relations among statements.

            Thus logic is absolutely central to genuine thinking (as opposed to merely experiencing sensations or images) and to genuine language (as opposed to the sort of thing that parrots or newborn infants do). For this reason, we already understand logic, and have as long as we have been able to genuinely speak and think. What, then, is the point of studying logic as an academic discipline?

            The answer is that the “natural” languages we speak, such as English or German, did not arise solely for the purely logical purpose of making inferences between some statements and others. Instead, they developed for a host of reasons, many having to do with convenience and brevity. For such reasons, our languages sometimes mislead us into inferring some statements that really don’t follow from others, even though they might seem to.

Essentially, the point of studying logic is to make us aware of these kinds of errors. This helps us in three ways. First, the study of logic can help us avoid errors in our own thinking, so that we can come to make only those inferences that really do follow from what we believe. Second, logic can help us be clearer when we present our thoughts, in speech or in writing, to others. Third, and perhaps most importantly, studying logic can help us to avoid being swayed by people who – whether they know it or not – try to persuade us to accept some conclusion that really doesn’t follow from what we know to be true. In this way, studying logic can help make us sharper, more critical readers, thinkers, and citizens.

 

Course Content: This course will introduce you to different formal and informal methods of analyzing, symbolizing, and evaluating arguments. Topics covered will include sentence logic, basic predicate logic, and informal fallacies.

 

Course Format: Class meetings will consist of lecture, questions, discussion, and quizzes. Also be aware that there will be a lot of homework for this class!

 

Grading: Your final grade will be determined as follows:

1. There will be about 12 quizzes, each worth about 5% of your total grade, for a total of exactly 60% of your final grade.

2. The assigned homework will be worth a total of 40% of your final grade. The homework due since the last quiz will be accepted only in class at the beginning of the class meeting on the day on which it is due. Homework will be graded with a “check” (full credit), “check-minus” (half credit) or a “check-plus” (credit-and-a-half), based on the perception of your good-faith effort in completing it.

3. You will have the opportunity to make up between 2 and 4 quizzes of your choice. I’ll announce the exact number of quizzes during the last week of the semester. These can be either quizzes that you missed or ones on which you’d like to improve your score. The make-up quizzes will be graded on a “no penalty” basis. That is, if your grade on the make-up quiz differs from that on the original quiz for the corresponding week, only the higher of the two grades will be counted. Naturally, the make-up quizzes will be different from the quiz given in class of the corresponding week, although they will cover roughly the same material. I plan to hold the make-up session on our last regular class meeting: Friday, December 7. But if it turns out that we get sufficiently behind schedule by the end of the semester, then the make-up session will be held in our regular classroom at our officially-scheduled final exam time, Monday, December 10, 3-4:50. I plan to let you know the date of the make-up session by Monday, December 3.

Each time that I notice you ‘texting’ on an electronic device, I will ask you to leave, and will reduce your final grade by 1/3 of a letter grade, e.g., from B to B-. I have instituted this policy because texting is very distracting to me, reduces my ability to teach effectively, and hence does a disservice to the students in the class.

 

Further note: Each semester, I teach well over 100 students. Although I give each as much individual time and attention as I possibly can during the semester, I will not be able to send you your individual grade for the course at the end of the semester. I submit the grades to the Registrar as soon as I can during the week of final exams, and ask you to kindly wait to see your grade until it has been reported electronically.

 

Website: The Department of Philosophy and World Religions has relatively few funds available for photocopying (or for anything else, for that matter!). The great majority of our course materials will therefore be placed on our website: http://www.uni.edu/boedeker. These materials include handouts to supplement the textbook. Please check the website frequently for updates.

 

MAILSERV: From time to time, I will send announcements pertaining to the class via e-mail. To facilitate our electronic communication, a MAILSERV distribution list has been created for this class using your UNI e-mail addresses. The list members include myself and the students who were registered for the class when the list was created. It is a private list (i.e., only the list members may post to it), but has open subscription. To send to the list, use PHIL-1030-01-SPRING@uni.edu.

If you registered late, or if you wish to be able to send and receive e-mails at an e-mail address other than your UNI one, then please add your e-mail address to this list by sending a message to

mailserv@uni.edu

where the body (not the subject heading) contains these two lines:

SUB PHIL-1030-01-SPRING

END

In a similar manner, if you drop this course, you may remove yourself from the list by sending a message to

mailserv@uni.edu

where the body (not the subject heading) contains these two lines:

UNSUB PHIL-1030-01-SPRING
END

 

It will be your responsibility to make sure you are subscribed to the MAILSERV right away, check your e-mail regularly, and read the announcements.

 

Cheating and plagiarism (from UNI’s academic ethics policy): “Students at UNI are required to observe the commonly accepted standards of academic honesty and integrity. Except in those instances in which group work is specifically authorized by the instructor of the class, no work which is not solely the student's is to be submitted to a professor... Cheating of any kind on examinations… is strictly prohibited… Students are cautioned that plagiarism is defined as the process of stealing or passing off as one’s own the ideas or words of another, or presenting as one's own an idea or product which is derived from an existing source.”

 

Disabilities: I will make every effort to accommodate disabilities. Please contact me if I can be of assistance in this area. All qualified students with disabilities are protected under the provisions of the Americans with Disabilities Act (ADA), 42 U.S.C.A., Section 12101. The ADA states that “no qualified individual with a disability shall, by reason of such disability, be excluded from participation in or be denied the benefits of the services, programs or activities of a public entity, or be subjected to discrimination by any such entity.” Students who desire or need instructional accommodations or assistance because of their disability should contact the Office of Disability Services located in 213 Student Services Center (273-2676 Voice, or 273-3011 TTY).

 

Tentative Course Schedule:

General note on the homework assignments: The answers to all exercises marked with a star are given at the back of the book. Unless I specifically ask you to in a particular homework assignment, I won’t require that you complete any of these exercises. Nevertheless, you’re welcome to do so if you feel that you could use some extra practice.

I. Some Basic Logical Concepts:

20 Aug..: Introduction.

22 Aug.: Read section 1.1 and this handout. Do exercises 1.1: I: 1-30 and II: 1-10.

24 Aug.: Read section 1.2 and this handout. Do exercises 1.2: I: 1-35.

27 Aug..: Do exercises 1.2: II: 1-10 and VI: 1-10.

II. Propositional Logic:

29 Aug..: Read section 6.1, this handout, and this handout. Do exercises 6.1: I: 1-50.

31 Aug.: Do exercises 6.1: II: 1-20 and III: 1-10.

5 Sept.: Read section 6.2. Do exercises 6.2: I: 1-10.

7 Sept.: Read section 6.3, this handout, and this handout. Do exercises 6.3: I: 1-15 and II: 1-15.

10 Sept.: Do exercises 6.2: II: 1-15, III: 1-25, and IV: 1-15.

12 Sept.: Do exercises 6.3: III: 1-10, including the exercises marked with a star.

14 Sept..: Read section 6.4 and this handout. Do exercises 6.4: I: 1-7 and II: 1-9.

17 Sept.: Read section 6.5. Change the instructions in 6.4: I and 6.4: II to “Use indirect truth-tables to determine whether the following arguments are valid or invalid,” and do exercises 6.4: I: 8-10 and 6.4: II: 8-20. (You’ll see that using indirect truth-tables will save you a lot of “busy work” here.) Also do exercises 6.5: I: 1-15 and 6.5: II: 1-10.

19 Sept.: Change the instructions in 1.5: II to “Use indirect truth-tables to determine whether the following arguments are valid or invalid,” and do exercises 1.5: II: 1, 2, 3, 4, including those exercises marked with a star.

21 Sept.: Read section 6.6, the summary on pp. 336-7, and this handout. Do exercises 6.6: I: 1-20. Please note that the last sentence of the instructions for 6.6: I is misleading, since it’s not the case that all arguments without a named form (modus ponens, modus tollens, etc.) are invalid. That is, some arguments without a named form are valid.

24 Sept.: Do exercises 6.6: II: 1-20. Please note that the last sentence of the instructions for 6.6: II is misleading, for the same reason as was mentioned in the previous assignment. Also do exercises 6.6: III: 1-10 and IV: 1-10.

III. Predicate Logic:

26 Sept.: Read section 8.1, this handout, and this handout. Do exercises 8.1: 1-30, including those exercises marked with a star.

28 Sept.: Do exercises 8.1: 31-60, including those exercises marked with a star.

1 Oct.: Read section 4.7 and this handout. Change the instructions in 4.7: I to “Translate the following statements into predicate logic,” and do exercises 4.7: I: 1-30. Use the predicate letters given in this homework help.

3 Oct.: Do exercises 4.7: I: 31-60, using the same instructions as in the previous assignment and the predicate letters given in this homework help. Also read from p. 411 to the top of p. 412 (at the beginning of section 8.3), summarized in this handout, and note that the following sets of propositions are logically equivalent (by the Change of Quantifier Rule combined with the rules of inference discussed in 6.6):

1.      All S are P = (x)(SxÉPx) = ~($x)~(SxÉPx) = ~($x)~(~SxÚPx) = ~($x)(~~Sx×~Px) = ~($x)(Sx×~Px) = It’s not the case that some S are P = “Some S are not P” is false;

2.      “All S are P” is false = It’s not the case that all S are P = ~(x)(SxÉPx) = ($x)~(SxÉPx) = ($x)~(~SxÚPx) = ($x)(~~Sx×~Px) = ($x)(Sx×~Px) = Some S are not P;

3.      Some S are P = ($x)(Sx×Px) = ~(x)~(Sx×Px) = ~(x)(~SxÚ~Px) = ~(x)(SxÉ~Px) =

It’s not the case that no S are P = “No S are P” is false;

4. “Some S are P” is false = It’s not the case that some S are P = ~($x)(Sx×Px) = (x)~(Sx×Px) = (x)(~SxÚ~Px) = (x)(SxÉ~Px) = No S are P.

These logical equivalences will be useful as we proceed to chapters 4 and 5.

5 Oct.: Use predicate logic to do exercises 5.7: III: 1-10, including those exercises marked with a star. You’ll be using the inference-rules of pure hypothetical syllogism, transposition (which is close to contraposition), and double negation (look them up in the index at the back of the book), modified to apply to predicate logic. Note that in all of the exercises except 1 and 3 you’ll need to specify the “universe of discourse,” i.e., the set of things that all propositions in the argument are talking about. For example, the universe of discourse in exercise 2 is persons; the universe of discourse in exercise 4 is birds; the universe of discourse in exercise 5 is fruits, etc. Make sure to reduce the number of terms whenever possible; that is, if two predicates occurring in an argument have (close to) opposite meanings (e.g., “dances” and “declines to dance”), use a single predicate and its negation (e.g., “Dx” and “~Dx”) to express both. (In exercise 6, use either the predicate “x is a daughter” or “x is a son,” but not both.)

IV. Categorical Propositions

8 Oct.: Read section 4.1. Do exercises 4.1: 1-8. Also read section 4.2, but only p. 186 through the second full paragraph on p. 187. Also read section 4.3, but only from the bottom of p. 192 (under “Venn Diagrams”) through the end of 4.3 (on p. 198). Please note that in this course the only interpretation of categorical logic that we’ll be using is the “modern,” or “Boolean,” interpretation – not the ancient and medieval “traditional,” or “Aristotelian,” one. Also do exercises 4.3: I: 1-8.

10 Oct.: Change the instructions in 4.3: II to “Use Venn diagrams to determine whether the following immediate inferences are valid or invalid from the Boolean standpoint,” and do exercises 4.3: II: 1-15. (Note that immediate inferences are discussed on p. 196.) Also change the instructions in 4.5: I to “Use Venn diagrams to determine whether the following immediate inferences are valid or invalid from the Boolean standpoint,” and do exercises 4.5: I: 1-8, including those exercises marked with a star.

12 Oct.: Change the instructions in 4.5: II: to “Use Venn diagrams to determine whether the following immediate inferences are valid or invalid from the Boolean standpoint,” and do exercises 4.5: II: 1-15, including those exercises marked with a star.

15 Oct.: In section 4.4, read just the second and third paragraphs on p. 202 (where “term complement” is defined), and commit the table on p. 207 (at the end of section 4.4) to memory. Then do exercises 4.4: I: 1-12 and II: 1-3. Our use of Venn diagrams makes a study of the fallacies in categorical logic unnecessary. Thus change the instructions in 4.4 III to “Use Venn diagrams to determine whether the following immediate inferences are valid or invalid from the Boolean standpoint,” and do exercises 4.4 IV: 1-20.

17 Oct.: Re-read section 4.7. Change the instructions for 4.7: I to “Express the following as Venn diagrams,” and do exercises 4.7: I: 1-30, including those exercises marked with a star. Use the same capital letters you used earlier (to express predicates) now to express terms, as given in this homework help.

19 Oct.: Change the instructions for 4.7: I to “Express the following as Venn diagrams,” and do exercises 4.7: I: 31-60, including those exercises marked with a star. Use the same capital letters you used earlier (to express predicates) now to express terms, as given in this homework help.

V. Categorical syllogisms:

22 Oct.: Read enough of pp. 237-238 in Section 5.1 to understand the concepts of syllogism, categorical syllogism, and the first three conditions of standard form (our use of Venn diagrams allows us to ignore the fourth condition). Also read section 5.2, but only from the beginning to the top of p. 251 (since we’ll be using just the Boolean – not the Aristotelian – interpretation of categorical propositions). Change the instructions in 5.1: I and 5.1: II to just “Use Venn diagrams to determine whether the following standard-form categorical syllogisms are valid or invalid from the Boolean standpoint,” and do exercises 5.1: I: 1-5 and II: 1-10; and 5.2: I: 1-20.

24 Oct.: Do exercises 5.2: II: 1-10. Note that the instructions are misleading, since there’s no such thing as “the” (one and only) conclusion that is validly implied by a pair of propositions. So if the two propositions taken together imply a conclusion that’s not logically equivalent to either of the premises, then write this down in standard form. (For example, don’t write down “No M are P” as a conclusion that follows from a premise of the form “No P are M,” even though this inference is of course valid.) If the premises don’t entail any such conclusion, then write “no conclusion.”

26 Oct.: Fortunately, the use of Venn diagrams renders the whole discussion in 5.3 unnecessary, so you don’t have to read it. Instead, change the instructions in 5.3: II to just “Use Venn diagrams to determine whether the following categorical syllogisms are valid or invalid from the Boolean standpoint,” and do exercises 5.3: II: 1-10.

29 Oct.: Read section 5.4. Ignore the phrase “or the rules for syllogisms” in the second sentence in the instructions for exercises 5.4, and do exercises 5.4: 1-10.

Halloween: Read section 5.5. Ignore the phrase “or the rules for syllogisms” in the first sentence in the instructions for exercises 5.5, and do 5.5: 1-15. Also, change the instructions in 1.5: I and 1.5: II to “Use Venn diagrams to show why the following standard-form categorical syllogisms are invalid from the Boolean standpoint,” and do 1.5: I: 1-10 (including those exercises marked with a star), and 1.5: II: 5, 6, 8 (these three exercises are a little tricky).

VI. Enthymemes

2 Nov.: Read section 5.6. Do exercises 5.6: I: 1-15.

5 Nov.: Do exercises 5.6: II: 1-15 and 5.6: III: 1-10.

7 Nov.: Change the instructions in 2.1 to “Treat the following arguments as enthymemes. Determine whether the missing statement is a premise or a conclusion. Then supply the missing statement, attempting whenever possible to convert the enthymeme into a valid argument. The missing statement need not be expressed as a standard-form categorical proposition.” Do exercises 2.1 II: 1-10, including those exercises marked with a star.

VII. Informal logic:

Please note: for all of the assignments for the rest of the semester, please also do the exercises marked with stars.

9 Nov.: Read section 1.3 and this handout (again, especially the parts on inductive logic). Do exercises 1.3: I: 1-30 and III: 1-15.

12 Nov.: Read section 1.4. Do exercises 1.4: I: 1-15, II: 1-15, III: 1-20, and V: 1-15.

14 Nov.: Read 3.1 (“Fallacies in General”), and do exercises 3.1: 1-10. If an argument commits a formal fallacy that has a name, give its name (see 6.6: pp. 323, 326-327, and 329-330).

16 Nov.: Read, in 3.2, section 4 (“Argument Against the Person [Argumentum ad Hominem]”: pp. 116-119, including the Tu quoque variety); and, in 3.3 (“Fallacies of Weak Induction”) sections 9 (“Appeal to Unqualified Authority”: pp. 128-129) and 10 (“Appeal to Ignorance”: pp. 130-131).

Do the following exercises:

3.2: I: 2, 6, 10, 11, 16, 17, 18, 23, 24;

3.3: I: 3, 7, 9, 10, 11, 14;

3.3: III: 3, 4, 6, 12, 14, 17, 20, 22, 23, 27, 29;

3.4: III: 1, 9, 16, 17, 32, 36, 45; and

3.5: I: 6, 10, 14, 18, 24, 32, 40, 43, 44, 49, 51, 52, 53, 56.

In these exercises, whenever possible treat the argument as an enthymeme, and state the missing but assumed premise that would render the argument valid. Note that, in general, the argument is weak if this missing assumption is false (and, in general, strong if this missing assumption is true).

26 Nov.: Read the rest of 3.3 (“Fallacies of Weak Induction”), i.e., sections 11-14 (pp. 131-138); this covers the fallacies of Hasty Generalization; False Cause, Slippery Slope; and Weak Analogy.

Do the following exercises:

3.3: I: 1, 2, 4, 5, 6, 9, 12, 13, 15;

3.3: III: 1, 7, 11, 15, 19, 27, 28, 30;

3.4: III: 8, 11, 13, 22, 33, 37, 38, 46, 48; and

3.5: I: 7, 9, 12, 13, 15, 18, 19, 20, 22, 25, 27, 29, 33, 36, 40, 41, 42, 43, 47, 48, 49, 52, 55, 57, 58, 60.

In these exercises, whenever possible treat the argument as an enthymeme, and state the missing but assumed premise that would render the argument valid. Note that, in general, the argument is weak if this missing assumption is false (and, in general, strong if this missing assumption is true).

28 Nov.: Read, in 3.4, section 18 (“Suppressed Evidence:” pp. 150-151). Note that, in general, arguments that commit the fallacy of Suppressed Evidence are inductive, weak, and hence uncogent.

Do the following exercises:

3.4: I: 9, 16;

3.4: III: 30; and

3.5: I: 1, 13, 28, 30, 54, 59.

In these exercises, state what ‘evidence’ is not mentioned as a premise, but that, if true, would render the argument weak.

30 Nov.: Read, in 3.2, section 6 (“Straw Man”: 120-121); and, in 3.4, sections 16 (“Complex Question”: pp. 148-149) and 17 (“False Dichotomy”: pp. 149-150). Also read the relevant sections of this handout, which we’ll be referring to for the rest of the course. Many of these arguments can be construed as valid, where those that commit fallacies are valid but unsound; i.e., the fallacies assume a false premise, whether explicitly or implicitly. Also read 3.5 (pp. 167-172) to solidify the basic idea of an informal fallacy, but don’t worry about the fact that most of the fallacies mentioned there will be covered in future reading assignments.

Do the following exercises:

3.2: I: 8, 19;

3.3: III 10;

3.4: I: 1, 5, 11, 17, 18, 22;

3.4: III: 15, 20, 25, 44, 50; and

3.5: I: 3, 11, 17, 20, 37, 45.

If any of these arguments commits a fallacy (and most, but not all, of them do), explain why it does. That is, state (6) how the argument mischaracterizes what someone else has said; (17) what the two statements of a complex question are, and why one of these statements might be false; or (17) what disjunction is assumed and why it might be false, i.e., why there might be more than just the two alternatives mentioned in the disjunction.

3 Dec.: Read, in 3.2, section 8 (“Red Herring”: pp. 122-123); and, in 3.4, sections 15 (“Begging the Question” [Petitio Principii]: pp. 145-147), 19 (“Equivocation”: pp. 152-153), and 20 (“Amphiboly”, pp. 153-154). Unlike the exercises in the previous assignment, the arguments in this assignment that commit fallacies generally don’t do so because they assume some false premise. Arguments that commit the fallacies of Red Herring or Begging the Question may well be sound (or cogent), but are fallacious because they still fail to meet the pragmatic goal of arguments: giving someone a good reason to believe something that the person doesn’t already believe. A Red Herring is an argument that isn’t on the same topic as one’s opponent’s argument; and an argument ‘begs the question’ if it assuming a premise – whether explicit or implicit – that’s at least as controversial as the conclusion. Equivocations and amphibolies are arguments that are really invalid (or weak), but might appear valid (or strong) because of a wrong interpretation of the meaning of at least one statement in the argument. Equivocations are based on interpreting two (or more) occurrences of the same word as having the same meaning, whereas in fact they have different meanings; amphibolies are based in misinterpreting the meaning of a statement that’s ambiguous because of its grammar.

Do the following exercises:

3.2: I: 3, 13, 21;

3.3: III: 13, 24;

3.4: I: 3, 4, 7, 8, 10, 15, 20, 23, 24, 25;

3.4: III: 2, 4, 7, 14, 23, 26, 27, 31, 34, 35, 39, 40, 42; and

3.5: I: 1, 3, 5, 9, 13, 16, 20, 23, 26, 28, 28, 30, 31, 32, 38, 39, 41, 42, 46, 51, 52, 53, 54, 56, 59.

If any of these arguments commits a fallacy (and most, but not all, of them do), explain why it does. That is, state (8) why the argument given isn’t relevant to the opponent’s argument; (15) what premise – whether explicit or implicit – that’s no less controversial than the conclusion is “begged”, or assumed; (19) which word is interpreted equivocally (i.e., with different meanings in different occurrences) so as to render the argument weak or invalid; or (20) which statement in an amphiboly is misinterpreted and what the statement really means.

Please note: By this day (December 3), I hope to send out via e-mail indicating just how many quizzes you may make up (on Friday, December 7) as well as a list indicating roughly what material the various quizzes covered. Attached to this e-mail should be a Microsoft Excel spreadsheet showing your grades on the quizzes. This should help you decide which make-up’s you’ll take, and what to study in order to do well on them. Thus please check your e-mail on the night of Monday, December 3.

 

5 Dec.: (No homework due): My plan for this class is as follows. First, I’ll open the floor to any questions you might have on informal logic. Second, we’ll have our final quiz – on informal logic. The rest of class will be devoted to answering your questions on anything we’ve covered during this course – especially any lingering questions that you have about material to be covered in the make-up’s. Thus please come to class with questions!

Please note: We hope to have graded your quizzes from today (Wednesday, December 5) by this evening, and to send out via e-mail an updated gradesheet, with your scores on this quiz added. This should help you finalize your decision as to which quizzes you’ll want to make up. Thus please check your e-mail on the night of 7 Dec., and bring the printout with you to class on Friday, December 7.

7 Dec.: Make-up’s.

Monday, December 10, 3-4:50: This time will be reserved for make-up’s (held in our regular classroom), but we’ll meet only if we don’t have enough time during the semester to hold the scheduled make-up session on Friday, December 7.