**Elementary
Logic (PHIL-1030-01 [2827]) Dr. Edgar Boedeker**

**Fall
2013, Mon., Wed., Fri., 2:00-2:50 Lang
211**

**Office
hours:** Mondays, Wednesdays, and Fridays, 12:45-1:45 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*

**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; please see the end of the syllabus for more
on the make-up sessions. ** 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; **Please
see the very bottom of the syllabus for the date and time**. I
plan to let you know the date of the make-up session the Monday of the last day
of classes.

__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. In addition, it’s
important to break the habit of feeling the need to text during inappropriate
times.__

**Further note:** Each semester, I teach about 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 is supposed to be constantly
updated to include just those students who are registered for the class at a
given time. Unfortunately, the new policies by the Powers that Be in charge
of this allow only me, and not students, to send to the list.

**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:**

**26 Aug.: **Introduction.

**28 Aug.: **Read
section 1.1 and this handout. Do
exercises 1.1: I: 1-30 and II: 1-10. Please note
that on this assignment, as well as others throughout the semester, you should
feel free to use ellipses “[…]” to abbreviate longer sentences; do make it
clear exactly which sentence you’re indicating, however, by including its first
and last couple of words. Do not include
premise or conclusion indicator words (e.g., “since”, “therefore,” etc.) in
your premises or conclusions; such words only serve to *indicate *that what follows is a premise or conclusion, but are not *part *of these statements.

**30 Aug.: **Read
section 1.2, but only pp. 219-23 (on explanations and conditional statements);
also read this handout. Do
exercises 1.2: I: 1-35. Since
explanations and conditional statements are the only kinds of passages we’ve
dealt with that don’t contain arguments, change the second sentence of the
instructions (p. 23) to the following: “For those that are not, write, where
appropriate, either ‘Explanation’ (stating the *explanandum*, i.e., the statement
explained); ‘Conditional statement’; or ‘Other non-argumentative passage.’”

**4 Sept.: **Do exercises 1.2: II:
1-10 and VI: 1-10.

**II. Propositional Logic:**

**6 Sept.:** Read
section 6.1, this handout, and this handout. Do
exercises 6.1: I: 1-50.

**9 Sept.:** Do exercises 6.1: II:
1-20 and III: 1-10.

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

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

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

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

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

**23 Sept.:** Read
section 6.5. Change the instructions in 6.**4**: I and 6.

**25 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

**27 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

**30 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:**

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

**4 Oct.:** Do exercises 8.1:
31-60, including those exercises marked with a star.

**7 Oct.: **Read
section **4**.7 and this handout. Change
the instructions in

**9 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*)(*Sx*É*Px*) = ~($*x*)~(*Sx*É*Px*) = ~($*x*)~(~*Sx*Ú*Px*) = ~($*x*)(~~*Sx*×~*Px*) = ~($*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*)(*Sx*É*Px*) = ($*x*)~(*Sx*É*Px*) = ($*x*)~(~*Sx*Ú*Px*) = ($*x*)(~~*Sx*×~*Px*) = ($*x*)(*Sx*×~*Px*) = Some *S *are
not *P*;

3. Some *S *are *P *= ($*x*)(*Sx*×*Px*) = ~(*x*)~(*Sx*×*Px*) = ~(*x*)(~*Sx*Ú~*Px*) = ~(*x*)(*Sx*É~*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*)(~*Sx*Ú~*Px*) = (*x*)(*Sx*É~*Px*) = No *S *are *P*.

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

**11 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

**IV. Categorical Propositions**

**14 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.

**16 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.

**18 Oct.:
C**hange 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.

**21 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.

**23 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.

**25 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:**

**28 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.

**30 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.”

**1 Nov.:** 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.

**4 Nov.: **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.

**6 Nov: **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

**VI. Enthymemes**

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

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

**13 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

**VII. Informal logic:**

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

**15 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.

**18 Nov.: **Also read section 1.4. Do exercises 1.4: I: 1-15,
II: 1-15, III: 1-20, and V: 1-15.

**20 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).

**22 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).

**2 Dec.: **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).

**4 Dec.:** 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

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.

**6 Dec.:** 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

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.

**9 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 (Monday, December 9),
I hope to have sent out via e-mail indicating just how many quizzes you may make
up (on Friday, December 13) 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 9.

**11 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 11) 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 Wednesday night, and bring the printout with
you to class on Friday, December 13.

**13 Dec: **Make-up’s.

**Monday, Dec 16, 3:00-4:50, in our regular classroom****:
**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 13.