Elementary Logic
(650:045:01)
Fall 2009 Dr. Edgar Boedeker Mon., Wed., Fri.: 11:00-11:50am Lang 20
Office
hours: Tuesdays and Wednesdays,
2:00-3:00pm, in my office, 145 Baker
Hall. I would also be happy to meet with you
at another time. To arrange 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 (ISBN: 9780534585051).
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 24 years old, hard at work on
this book, he wrote to himself: “Whatever logic will turn out to be, it will be
a very unique 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. 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 the statements 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. On Tuesday, December 15, from 10:00am to 11:50am in our regular classroom, you will have the opportunity to make
up between 2 and 4 quizzes of your choice.
I’ll announce the exact number of quizzes by our last class meeting, on
Friday, December 11. These can be either
quizzes that you missed or ones on which you did poorly. 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.
Further note: Each semester, I teach almost 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 650-045-01-FALL@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
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(not the subject heading) contains these two lines:
SUB 650-045-01-FALL
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In a similar
manner, if you drop this course, you may remove yourself from the list by
sending a message to
where the body
(not the subject heading) contains these two lines:
UNSUB
650-045-01-FALL
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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:
24 Aug.: Introduction.
26 Aug.: Read section 1.1 and this handout. Do exercises 1.1: I: 1-30 and II: 1-10.
28 Aug.: Read section 1.2 and this handout. Do exercises 1.2: I: 1-35.
31 Aug.: Do exercises 1.2: II: 1-10 and VI: 1-10.
2 Sept.: Read section 1.3 and this handout. Do exercises 1.3: I: 1-30 and III: 1-15.
4 Sept.: Read section 1.4. Do exercises 1.4: I: 1-15 and II: 1-15.
9 Sept.: Do exercises 1.4: III: 1-20 and V: 1-15.
II. Propositional Logic:
11 Sept.: Read section 6.1, this handout,
and this handout. Do exercises 6.1: I: 1-50.
14 Sept.: Do exercises 6.1: II: 1-20 and III: 1-10.
16 Sept.: Read section 6.2. Do exercises
6.2: I: 1-10.
18 Sept.: Do exercises 6.2: II: 1-15, III: 1-25,
and IV: 1-15.
21 Sept.: Read section 6.3, this handout,
and this handout. Do exercises 6.3: I: 1-15 and II: 1-15.
23 Sept.: Do exercises 6.3: III: 1-10, including the exercises marked with
a star.
25 Sept.: Read section 6.4 and this handout. Do exercises 6.4: I: 1-7 and II: 1-9.
28 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: 8-10.
(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.
30 Sept.: Change the instructions in 1.5: I 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.
2 Oct.: 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.
5 Oct.: 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:
7 Oct.: Read section 8.1, this handout, and this handout. Do exercises 8.1: 1-30, including those
exercises marked with a star.
9 Oct.: Do exercises 8.1: 31-60, including those exercises marked with a
star.
12 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.
14 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):
It’s not the
case that no S are P = “No S are
P” is false;
These logical equivalences will be useful as we
proceed to chapters 4 and 5.
16 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
19 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.
21 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.
23 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.
26 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.
28 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.
30 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:
2 Nov.: 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.
4 Nov.: 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.”
6 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.
9 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.
11 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 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
13 Nov.: Read section 5.6. Do exercises 5.6: I: 1-15.
16 Nov.: Do exercises 5.6: II: 1-15.
18 Nov.: Do exercises 5.6: III: 1-10.
20 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. Definitions and
informal logic:
For the assignments below,
please also do the exercises marked with stars.
30 Nov.: Read section 2.4 (“Definitional
Techniques”), but only pp. 98-9 (on
definitions by genus and difference).
Construct definitions by genus and
difference for the terms in exercises 2.4: II: 1, 2, 3, 4, 5, 7.
2 Dec.: Read section 3.1 (“Fallacies in General”). Do exercises 3.1: 1-10. Handout.
4 Dec.: Read, in 3.2 (“Fallacies of
Relevance”), sections 4 (“Argument Against the Person [Argumentum ad Hominem]” pp. 116-119), 6 (“Straw Man:” pp. 120-1),
and 8 (“Red Herring:” pp. 122-3).
Do
exercises 3.2: I: 2, 3, 6, 8, 10, 11, 13, 16, 17, 18, 19, 21, 23, 24;
3.3:
III: 3, 4, 10, 13, 14, 20, 22, 23, 24;
3.4:
III: 1, 14, 17, 25, 31, 32; and
3.5:
I: 5, 6, 14, 18, 23, 24, 32, 39, 44, 51, 53, 56.
In each of these exercises, treat the argument as an enthymeme, and
state the missing assumption in the argument. Note that the argument is weak if this
missing assumption is false (and, in general, strong if this missing assumption
is true). Use the handout given in the
previous assignment for help in identifying the missing premise.
7 Dec.: Read section all of 3.3
(“Fallacies of Weak Induction”). This
includes the following informal fallacies: Appeal to Unqualified Authority,
Appeal to Ignorance, Hasty Generalization, False Cause, Slippery Slope, and Weak
Analogy.
Do
exercises 3.3: I: 1-15;
3.3:
III: 1, 6, 7, 11, 12, 15, 17, 19, 25, 27, 28, 29, 30;
3.4:
III: 3, 6, 8, 9, 11, 13, 16, 22, 33, 36, 37, 38, 45, 46, 48; and
3.5: I: 7, 10, 12, 13, 15,
18, 19, 22, 25, 29, 33, 36, 40, 41, 42, 43, 47, 48, 49, 52, 55, 57, 58, 60. In each of these
exercises, treat the argument as an
enthymeme, and state the missing assumption in the argument. Note that the argument is weak if this
missing assumption is false (and, in general, strong if this missing assumption
is true). Use the handout given in the
previous assignment for help in identifying the missing premise.
9 Dec.: Read sections 15-19 in
3.4. This includes the following
informal fallacies: Begging the Question (Petitio Principii; pp. 145-7), Complex Question
(pp. 148-9), False Dichotomy (pp. 149-50), Suppressed Evidence (pp. 150-1), and
Equivocation (pp. 152-3). Also read
section 3.5.
Do
exercises 3.4: I: 1, 3, 5, 7, 8, 9, 10, 16, 17, 18, 20, 22, 24, 25;
3.4:
III: 4, 7, 15, 20, 23, 27, 30, 35, 39, 40, 42, 43, 44, 50; and
3.5:
I: 1, 3, 5, 9, 11, 16, 17, 20, 23, 26, 28, 30, 37, 38, 39, 41, 42, 45, 46, 54, 59.
If any of these arguments commits a fallacy (and
most, but not all, of them do), explain why
it does. That is, state what question
(i.e., a premise that’s no less controversial than some premise) is “begged,”
what part of a complex question that’s assumed in the question is false, what
disjunction is assumed and why it might be false, what evidence is suppressed,
or which words are interpreted equivocally so as to render the argument weak or
invalid.
It
may help to note the following:
1. All Fallacies of Weak
Induction (discussed in section 3.3), as well as Argument Against the Person
and Suppressed Evidence, apply only to inductive
arguments.
2. All of the other fallacies
discussed in chapter 6 (i.e., Straw Man, Red Herring, Begging the Question,
Complex Question, False Dichotomy, and Equivocation) can apply to either inductive or deductive arguments.
3.
All formal fallacies (including Affirming the Consequent and Denying
the Antecedent) discussed on pp. 326-7 in section 6.6), Equivocation, and
Suppressed Evidence involve arguments with faulty presuppositions, as opposed to merely false assumptions in an enthymeme.
Both presuppositions and assumptions must be true for a deductive
argument to be valid or an inductive argument to be strong. An argument is presented as completely as possible
when all of its assumptions are stated as premises. A presupposition, however, would be pointless
to state as a premise, since doing so would lead to an infinite regress.
11 Dec.: review and/or catch-up day (no homework due). I plan
to begin this class meeting by announcing
how many make-up’s you may take on 15 December. I also plan to hand out a list with your grades on the quizzes,
as well as a sheet indicating roughly
what material the various quizzes covered; this should help you decide
which make-up’s you’ll take, and what to study in order to do well on them. I then plan to go over any of the homework
problems you had questions about from the previous assignment. 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!
Tuesday,
December 15, 10:00-11:50am: Make-up’s (held in our regular
classroom). The list with your grades on the quizzes will again be
distributed at the beginning of this period. In our last class meeting, I plan to announce
the exact number of make-up’s that you may take.