PRACTICAL LOGIC
Bryan Rennie
GENERAL NOTES ON THIS CLASS
THE SET TEXTS
Introduction to Logic, by Irving Copi, Carl Cohen, and Kenneth McMahon (14th edition) = ITL.
COURSE OUTCOMES
This course is an introduction to the basics of logic as an academic discipline. We will consider
what logic is. It is the study of the distinction between valid and invalid reasoning. Having
established our working attitude to logic we will investigate the basic terms, forms, types, and
style of argument and the uses of language in argument. To that end the basic vocabulary of logic
and argument must be learned.
Our most extensive analysis will be of deductive logic, that is to say, arguments which produce
logically necessary conclusions once their premises are accepted. The standard forms of such
arguments will be analyzed, and their accompanying fallacies noted. The symbol systems used to
express and analyze these forms will be practiced. However, inductive arguments, the conclusions of which follow
with a certain degree of probability rather than being logically necessary, will also be briefly considered.
The overall outcome of this is twofold: first, it will inform students of the precise and formal
nature of logical proof (and its relative rarity); second, exposure to and practice with arguments
and their identification as valid or invalid should greatly sharpen the students' natural skill at
validating arguments and constructing their own valid arguments. This last is in many ways the
final outcome of this course.
The course will include a detailed consideration of informal fallacies, those common, and often unidentified, errors which yield sometimes convincing,
but always invalid, arguments in ordinary language. Once again the difficulties of irrefutable argument and final proof will be encountered.
So the course outcomes can be stated to be:
 To learn what an argument is. What components does it contain, what assumptions does it make?
 To learn what makes a good argument. Why does a given conclusion follow from certain assumptions?
 To learn what makes a bad argument. Why are certain conclusions not entailed by certain propositions?
 To practice and become more adept at the use of argumentation
COURSE REQUIREMENTS
Attendance
Attendance is crucial. Missed classes will be penalized.
Learning good logic skills is like learning both language and manual
skillthey require practice, both physical and mental. To that end all students will be required to
answer questions, solve problems, and do exercises from the textbook in
class. Note that these exercises are not graded. All you need to do is to demonstrate to the
instructor and to the class that you have made an effort to complete them. It is your
responsibility to complete enough exercises to understand the points and to raise questions about points which you have not understood.
This is your opportunity to seek clarification on difficult passages. You are NOT automatically expected to
fully understand everything you read.
IF STUDENTS DO NOT MAKE AN EFFORT TO PERFORM THESE EXERCISES
POINTS WILL BE SUBTRACTED FROM THEIR TOTAL.
Homework
There will be a certain amount of reading homework after every class to ensure a constant
and ongoing effort to master each section before moving on to the next. This homework will not
be handed in and will not be graded as such. It is for your own good rather than for the grading
process. However, questions will be asked about the homework at the start of each class, and if it
is apparent that you have not done it POINTS WILL BE SUBTRACTED. Time will be allowed
in class to attempt the exercises but they should be studied beforehand as homework.
GRADING
Grading will be done on a points system up to a maximum of 400 total possible
points:
Quizzes (7 @ 30 points) These quizzes are the most important element
of the course and are meant to ensure steady effort and ongoing understanding.
WARNING: Failure to score a passing grade on any quiz will result in the
loss of all points for that quiz. 210 points = c.52%.
 Computer Exercises. Although these exercises will not be graded for
performance 100 points will be given for simply completing them. Up to one
quarter of your total grade points can be lost by not doing the required exercises.
100 points = 25%
 Final examination This will review the whole course so the start is
not forgotten at the end. WARNING: Failure to pass the final is failure to
pass the course. 90 points = c.23%
The written quizzes will take a form similar (but not identical) to these
sample quizzes.
SCHEDULE OF CLASSES
The class will meet Monday, Wednesday, and Friday from 10:30 to 11:30 in Patterson Hall 105.
I will be available in my office in Patterson 336 from 9:30 to 10:30 everyday, and by arrangement.
Click the number to see the week.
Week 1.
Wednesday, 8/28
Introduction to the course, the textbook (don't forget the Glossary/Index!), and the class webpage.
ITL Chapter One: Basic Logical Concepts.
ITL 1.1  What Logic Is.
ITL 1.2  Propositions and Arguments.
Exercises in class from pages 911.
Homework: Read ITL Chapter One to page 24. Do exercises from pages 2024.
Friday, 8/30
ITL Chapter One: Basic Logical Concepts.
ITL 1.3  Recognizing Arguments.
ITL 1.4  Arguments and Explanations.
Exercises in class from pages 2024.
Homework: Read ITL Chapter One. Do exercises from page 32.
Week 2.
Monday, 9/2
ITL 1.5  Deductive and Inductive Arguments.
ITL 1.6  Validity and Truth.
Exercises in class from page 32.
Wednesday, 9/4
Summary of Chapter 1. Preparation for the quiz.
Friday, 9/6
QUIZ ON CHAPTER ONE (Sample)
Homework: Read Chapter Two. Do exercises from pages 3638 and 4348.
Week 3.
Monday, 9/9
Chapter Two  Analyzing Arguments.
ITL 2.1  Paraphrasing Arguments; 2.2  Diagramming Arguments.
Exercises in class from pages 3638 and 4348.
Homework: Read ITL 2.3 and 2.4. Do exercises from pages 5253 and 5961.
Wednesday, 9/11
ITL 2.3  Complex Argumentative Passages; 2.4  Problems in Reasoning.
Exercises in Class from pages 5253 and 5961.
Homework: Reread ITL Chapter Two. Prepare for Quiz #2.
Friday, 9/13
QUIZ ON CHAPTER TWO (Sample).
Homework: Read ITL 3.1, 3.2, and 3.3. Do exercises from pages 6671, 7375, and pages 7679.
Week 4.
Monday, 9/16
Chapter Three: Language and Definitions.
ITL 3.1  Language Functions; 3.2  Emotive and Neutral Language and Disputes; 3.3  Disputes and Ambiguity.
Exercises in class from pages 6671, 7375, and pages 7679.
Homework: Read ITL 3.4. Do exercises from page 86.
Wednesday 9/18
ITL 3.4  Definitions and their Uses
Exercises in class from page 86.
Homework: Read ITL 3.5 and 3.6. Do exercises from pages 8991.
Friday 9/20
ITL 3.5  The Structure of Definitions: Extension and Intension; 3.6  Definition by Genus and Difference.
Exercises in class from pages 8991.
Homework: Read ITL 4.1, 4.2, and 4.3. Do exercises from pages 121126.
Week 5.
Monday, 9/23
ITL 4.1  What is a Fallacy?; 4.2  Classification of Fallacies; 4.3 Fallacies of Relevance.
Exercises in class from pages 121126.
Homework: Read ITL 4.4, 4.5, and 4.6. Do exercises from pages 138140 and pages 148154.
Wednesday, 9/25
ITL 4.4  Fallacies of Defective Induction; 4.5  Fallacies of Presumption; 4.6  Fallacies of Ambiguity.
exercises in class from pages 138140 and pages 148154.
Homework: prepare for Quiz #3.
Friday, 9/27
QUIZ ON CHAPTERS THREE AND FOUR (Sample).
Homework: Reread ITL Chapters Three and Four.
Week 6.
Monday, 9/30
Review of QUIZ #3. Review of Chapter Three: Language and Definitions.
Exercises in class from pages 6671; 7375; 7679; 98.
Homework: Reread ITL Chapter 4. Do exercises from pages 121126; 138140; 148154; 156159.
Wednesday, 10/2
Review of ITL Chapter 4 – Informal Fallacies.
Exercises in class from pages 121126; 138140; 148154; 156159.
Homework: prepare to retake Quiz #3.
Friday, 10/4
REPEAT QUIZ ON CHAPTERS THREE AND FOUR (Sample).
Homework: Read ITL 5.1, 5.2, and 5.3. Do exercises from page 170.
Week 7.
Monday, 10/7
ITL 5.1  The Theory of Deduction; 5.2  Classes and Categorical Propositions; 5.3  The Four Kinds of Categorical Propositions.
Exercises in class from page 170.
Homework: Read ITL 5.4. Do exercises from pages 175176.
Wednesday, 10/9
ITL 5.4  Quality, Quantity, and Distribution.
Exercises in class from pages 175176.
Homework: Read ITL 5.5. Do exercises from page 180.
Friday, 10/11
ITL 5.5  The Traditional Square of Opposition.
Exercises in class from page 180.
Homework: Read 5.6. Do exercises from pages 186188.
Week 8.
Monday, 10/14
ITL 5.6  Further Immediate Inferences.
Exercises in class from pages 186188.
Homework: Read ITL 5.7. Do exercises from pages 196197 and 202203.
Wednesday, 10/16
ITL 5.7  Existential Import and the Interpretation of Categorical Propositions; 5.8  Symbolism and Diagrams for Categorical Propositions.
Exercises in class from pages 196197 and 202203.
Homework: Prepare for Quiz #4.
Friday, 10/18
QUIZ #4 (Sample).
Homework: read ITL 6.1. Do exercises from pages 209210.
Week 9.
Monday 10/21
ITL 6.1  Standard Form Categorical Syllogisms.
Exercises in class from pages 209210.
Homework: Read ITL 6.2. Do exercises from pages 212213.
Wednesday 10/23
ITL 6.2  The Formal Nature of Syllogistic Argument.
Exercises in class from pages 212213.
Homework: Read ITL 6.3. Do exercises from pages 222224.
Friday 10/25
ITL 6.3  The Venn Diagram Technique for Testing Syllogisms.
Exercises in class from pages 222224.
Homework: Read ITL 6.4. Do exercises from pages 231234.
Learn the rules and fallacies for syllogisms.
MidTerm Break Monday October 28th.
Week 10.
Monday Classes meet Tuesday 10/29
6.4  Syllogistic Rules and Syllogistic Fallacies.
Exercises in class from 231234.
Homework: Read ITL 6.5 and Appendix. Do exercises from pages 238 and 242.
Wednesday, 10/30
ITL 6.5  Exposition and Deduction the 15 Valid Forms of Categorical Syllogism.
Exercises in class from page 238 and 242.
Homework: Prepare for Quiz #5.
Friday, 11/1
QUIZ #5 (Sample).
Homework: Read ITL 7.1 and 7.2. Do exercises from pages 248249.
Week 11.
Monday, 11/4
ITL Chapter Seven  Syllogisms in Ordinary Language: 7.1  Syllogistic Arguments; 7.2  Reducing the Number of Terms to Three.
Exercises in class from pages 248249.
Homework: Read ITL 7.3. Do exercises from pages 257258.
Wednesday, 11/6
ITL 7.3  Translating Categorical Propositions into Standard Form.
Exercises in class from page 257258.
Homework: Read ITL 7.4. Do exercises from pages 260263.
Friday, 11/8
ITL 7.4  Uniform Translation.
Exercises in class from pages 260263.
Homework: Read ITL 7.5 and 7.6. Do exercises from pages 266269 and 270272.
Week 12.
Monday 11/11
ITL 7.5  Enthymemes; 7.6  Sorites.
Exercises in class from pages 266269 and 270272.
Homework: Read ITL 7.7 and 7.8. Do exercises from 276278 and 282285.
Wednesday 11/13
ITL 7.7  Disjunctive and Hypothetical Syllogisms; 7.8  The Dilemma.
Exercises in class from pages 276278 and 282285.
Homework: Prepare for Quiz #6.
Friday 11/15
QUIZ #6 (Sample).
Homework: Read ITL 8.1 and 8.2. Do exercises from pages 297300.
Week 13.
Monday, 11/18
ITL 8.1  Modern Logic and its Symbolic Language; 8.2  The Symbols for Conjunction, Negation, and Disjunction.
Exercises in class from pages 297300.
Homework: Read ITL 8.3 and 8.4. Do exercises from pages 308310 and 312313.
Wednesday, 11/20
ITL 8.3  Conditional Statements and Material Implication; 8.4  Argument Forms and Refutation by Logical Analogy.
Exercises in class from pages 308310 and 312313.
Homework: Read ITL 8.5, 8.6, and 8.7. Do exercises from pages 322323.
Friday, 11/22
Online Class: Prof Rennie will be attending the American Academy of Religion Conference in Baltimore.
ITL 8.5  The Precise meaning of "valid" and "invalid"; 8.6  Testing Argument Validity using Truth Tables; 8.7  Some Common Argument Forms.
Exercises from pages 322323.
Homework: Read ITL 8.8. Do exercises from pages 328329.
Prepare for Quiz #7.
Week 14.
Monday, 11/25
QUIZ #7 (Sample)
Thanksgiving Break: Wednesday 27th through Sunday 1st.
Week 15.
Monday, 12/2
ITL 8.8  Statement Forms and Material Equivalence.
Exercises in class from page 328329.
Homework: Read ITL 8.9 and 8.10. Be prepared to discuss in class.
Wednesday, 12/4
ITL 8.9  Logical Equivalence, including De Morgan's Theorems; 8.10  The Three "Laws of Thought."
Homework: Revise everything.
Friday, 12/6
The Last Class. Student Assessments of the Course. Preparation for Final Examination.
Week 16.
Monday, 12/9
Final examination period Dec. 9^{th} & 10^{th}; Dec. 12^{th} & 13^{th}.
Reading Day, Wednesday, Dec. 11^{th}. Term ends Friday 13^{th}.
SAMPLE QUIZ QUESTIONS
(ITL Chapter One)
 What is "Logic"?
 Explain the difference between deduction and induction.
 Define "argument."
 What is "inference?"
 In the following argument mark the premises with "p," and the conclusion with a "c."
See ITL pages 911 for examples.
 Is the preceding passage an argument or an explanation?
See ITL pages 2024 for examples.
 Indicate which of the following sentences (13) are correctly described by the following terms (ac).
1) If I understood all this I'd be a genius. 2) What am I, a genius? 3) I'm a genius
a) rhetorical question, b) hypothetical statement, c) proposition
 Sort the following terms into conclusion indicators and premise indicators:
therefore . ., for the reason that . ., as a result . ., which implies that . ., . .
may be deduced from, inasmuch as . ., hence, accordingly, proves that . .,
for . ., so . ., I conclude that . ., because . ., since . ., follows from . . .
 What is "validity" in Logic?
 Construct a deductive argument of the form given below.
See ITL page 32 for examples.
(ITL Chapter Two)
 Paraphrase the following passages:
See ITL pages 3638 for examples.
 Diagram the following passages:
See Itl pages 4348 for examples.
 Diagram the following complex argumentative passage:
See ITL pages 5253 for examples.
 From the following passages construct a valid argument that both answers the question and proves that answer to be correct:
See ITL pages 5961 for examples.
(ITL Chapters Three and Four)
 Which of the various functions of language are exemplified by the following passage(s)? (Examples from ITL pages 6671.)
 Identify the kinds of agreement or disagreement exhibited by the following pairs. (Examples from pages ITL 7375.)
 Is the following dispute genuine or merely verbal? (Examples from ITL pages 7679.)
 Name the five ways in which definitions may be used. (ITL 3.4)
 Arrange the following group of terms in order of increasing/decreasing intension. (Examples from ITL page 89.)
 Define the following terms by genus and difference. (Examples from ITL page 98.)
Name and explain the following fallacies. These have been selected to be clear examples of certain single fallacies.
Select ONE explanation only for each example.
 You should avoid four letter words. “Work” is a four letter word. So you should avoid work.
 A public lecture was delivered on smoking as a cause of cancer in the Orr Auditorium.
Several students have undertaken never to smoke in that building again.
 Every player of the Washington Redskins is a better player than his opposite number in the Green Bay Packers. So the Redskins are the better team.

The local chapter of Phi Sigma Tau has a collective I.Q. of 190, so Dr. Rennie, who is a member, must have an I. Q. of 190.

All plants produce chlorophyll, so the GM plant in Detroit produces chlorophyll.

“I think I like hot dogs more than you.”
“Well, if that’s the way you feel, I never want to see you again.”

A recent poll shows that 75% of the people have changed their voting allegiance. You should change yours, too.

I deserve a B+ on this course. If I don’t get a B+ I won’t be able to graduate next Fall.

You shouldn't take Dan’s arguments about farming subsidies seriously
since he manages one of the largest farms in the area..

Yesterday I had a wonderful stroke of luck just after I had seen a black cat. So black cats are lucky.

It is only when it is believed that I could have acted otherwise that I am held to be morally responsible for what I have done. For a man is not thought to be morally responsible for what it was not in his power to avoid.

There is no such thing as a leaderless group. For, though the style of leadership will differ with each group, a leader will always emerge in a task oriented group or the task will never get done.

Do you realize that the majority of painful animal experimentation has no relationship whatever to human survival or the elimination of disease?

Scientists hope that fish treated with new growth hormones will grow bigger,
faster than normal fish. Other scientists are developing fish that could be
introduced into cold Northern waters where they cannot now survive. The
intention is to boost fish production for food. The economic benefits may be
obvious, but not the risks. Does this make the risks reasonable? No, they
are not.
(ITL Chapter Five)

Name the form of the given propositions. Give both the name (eg. universal affirmative) and letter (eg. "A") identification.

Identify the subject and predicate terms in the following propositions. Are they distributed or undistributed. (egs.)
 Some television presenters are not responsible citizens.
 No poets are aggressive.
(More egs. ITL pages 17576.)

Draw the traditional/Aristotelian square of oppositions.
 What immediate inferences can be made from the following propositions? (Assuming these propositions to be true.) (egs.)
 All successful business executives are intelligent people.
 No college professors are entertaining lecturers.
(More egs. ITL page 180.)

Define the following immediate inferences (egs.):
 conversion
 obversion
 contraposition

Given a certain proposition determine whether following propositions are its
converse/obverse/contrapositive/subalternate. If the first given proposition
is true, are the following propositions true? That is to say, are these valid
immediate inferences?

Given a sequence of immediate inferences which are valid by Aristotelian logic, identify where an existential fallacy occurs.
 Express the following propositions as equations (eg. SP = 0, etc.) and as Venn diagrams for propositions.
(ITL Chapter Six)
Use a Venn diagram to test the validity of the arguments in #1. Write out the argument using S, P, and M, both in standard form (No S is P etc.) and in logical notation (SP = 0 etc.)
Fill in the blanks in the Six Rules and Fallacies for categorical syllogisms.
Name the fallacies committed or the rules broken by syllogisms of the following forms.
Name the fallacies committed or the rules broken by the following syllogisms.
 Some carbon compounds are not precious stones.
 Some carbon compounds are diamonds.
 Therefore some diamonds are not precious stones.
 All people who are most hungry are people who eat most.
 All people who eat least are people who are hungry.
 Therefore all people who eat least are people who eat most.
Answer the following questions with reference to the six rules. Explain how you reach your conclusion.
 In what figure or figures, if any, can a valid standardform
categorical syllogism have two particular premises?
 In what figure or figures, if any, can a valid standardform categorical syllogism have a particular premise and a universal conclusion?
 What are the possible valid forms of a standard form syllogism with an A/E/I/O conclusion?
(ITL Chapter Seven)
 Rewrite the following in standard form, indicating its mood and figure. Is it valid or invalid? What makes it invalid?
 All those who are neither members nor guest of members are excluded;
therefore, no nonconformists are either members or guest of members,
because all who are included are conformists.
 Translate the following propositions into standardform categorical propositions.
 Only powerhungry people become politicians.
 If he isn't rich he isn't successful.
 There are also positive reasons to vote.
 Translate the following syllogistic argument into standard form and then
 Name the mood and figure of the standard form translation.
 Test its validity using the six syllogistic rules.
 If it is invalid name the fallacy committed.
Everyone who smokes marijuana goes on to try heroin.
Everyone who tries heroin becomes addicted to it.
So everyone who smokes marijuana becomes addicted to it.
 Translate the following syllogistic argument into standard form and then
 Name its mood and figure.
 Test its validity using a Venn diagram.
 If it is invalid name the fallacy committed.
There are plants growing here, and since vegetation requires water, water must be present.
 Translate the following propositions into standard form with the help of appropriate parameters.
 Politicians always criticize other politicians when they want to conceal their own shortcomings.
 The use of violence is sometimes beneficial.
 People in subordinate positions do not complain unless provoked.
 Explain briefly what (a) Enthymemes and (b) Sorites are.
 Are the following arguments (I, II, and III)
(a) disjunctive, pure hypothetical, or mixed hypothetical?
(b) Are they valid or invalid?
(c) If they are invalid what fallacy do they commit? Identify modus ponens or modus tollens forms where applicable.
I. If the oneeyed prisoner does not know the color of the hat on his
own head, then the blind prisoner cannot have on a red hat. The oneeyed
prisoner does not know the color of the hat on his own head. Therefore the
blind prisoner cannot have on a red hat.
II. If this syllogism commits the fallacy of affirming the consequent then
it is invalid. It does not affirm the consequent, therefore it is valid.
III. The stranger is either a knave or a fool. The stranger is a knave,
therefore he is no fool.
 Discuss the various arguments that might be used to refute the following:
 If the conclusion of a deductive argument goes beyond the premises,
then the argument is invalid, while if the conclusion of a deductive argument
does not go beyond the premises, then the argument brings nothing new to
light. The conclusion of a deductive argument must either go beyond the
premises or not go beyond them. Therefore either deductive arguments are
invalid or they bring nothing new to light.
 If Socrates died, he died either when he was living or when he was
dead. But he did not die while he was living; for assuredly he was living,
and as living he had not died. Nor when he had died, for then he would be
dead twice. Therefore Socrates did not die.
(ITL Chapter Eight)
(questions could have multiple examples)

Using the truth tables definitions of conjunction, disjunction, and negation
determine which of the given statements are true. (egs. ITL page 297)

Symbolize the following statements using letters for simple statements and the symbols for conjunction, disjunction, and negation. (egs. ITL page 299)

If A and B are true statements and X and Y are false statements which of
the following are true? (egs. ITL page 308)

If A and B are true statements and X and Y are false statements and the
values of P and Q are unknown, which of the given statements can be
determined to be true or false?

Match the given specific forms with the given arguments. (ITL page 312)

Use truth Tables to identify which of the given statement forms are tautologous,
selfcontradictory, or contingent. (egs. ITL 322)

Which of the given biconditionals are tautologies? (egs. ITL page 331)
The Six Rules of StandardForm Categorical Syllogisms
(and corresponding fallacies)
 A valid standardform categorical syllogism must contain exactly three terms, each of which is used consistently in the same sense throughout the argument. (if notfallacy of four terms, quaternio terminorum)

In a valid standardform categorical syllogism, the middle term must be distributed in at least one premise. (if notfallacy of the undistributed middle)

In a valid standardform categorical syllogism, if either term is distributed in the conclusion, then it must be distributed in the premises. (if notillicit major or illicit minor depending on where the undistributed term occurs)

No standardform categorical syllogism having two negative premises is valid. (if it doesfallacy of exclusive premises)
Note that this rule renders all standardform categorical syllogisms of EO*, EE*, OE*, AND OO* moods INVALID, regardless of their figure.

If either premise of a valid standardform categorical syllogism is negative, the conclusion must be negative. (drawing an affirmative conclusion from a negative premise is a fallacy)
Note that this rule renders all standardform categorical syllogisms which have a positive conclusion (**A or **I) and any negative premises (E or O) INVALID regardless of their figure.

No valid standardform categorical syllogism having a particular conclusion can have two universal premises. (If it does it commits the existential fallacy.)
Note that this rule renders all standardform categorical syllogisms with particular conclusions (**I or **O) and two universal premises (AA, EE, AE, EA) INVALID regardless of their figure.
Symbols used in Basic Logic.
See The Wikipedia Site
Symbol used in class 
Alternative form of Symbol 
Name of symbol in class 
Alternative Name(s) of symbol 
Corresponding Verbal expressions 
S ⊃ R 
S ⇒ R 
material implication 
consequence 
S implies R.
R is a consequence of S.
S has R as a consequence.
If S then R.
R given S.
S only if R.
S is a sufficient condition for R.
R is a necessary condition for S. 
S ≡ R 
S ⇔ R 
equivalence 

S is equivalent to R.
R is equivalent to S.
S if and only if R.
R if and only if S. 
S ∨ R 

disjunction 

S or R.
Either S or R.
S unless R.
Note that all these can be reversed. 
~S 

negation 

not S It is not the case that S 
H and E 
H • E 
conjunction 

H and E
the conjunction of H and E
both H and E
H but E 
brennie@westminster.edu