PRACTICAL LOGIC (Currently under constructionthis webpage is NOT complete or accurate. Students should not rely on it.
Bryan Rennie
GENERAL NOTES ON THIS CLASS
THE SET TEXTS
TAR = The Art of Reasoning, by David Kelley (4th edition).
ISBN: 9780393930788
Etext: ISBN: 9780393521573
COURSE OBJECTIVES
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.
The overall objective 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 objective of this course.
So the course objectives 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?
COURSE REQUIREMENTS
Attendance
Since discussion is required to ensure that each point is fully understood and absorbed 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 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.
Readings
The assigned reading and schedule of classes is a guideline designed to cover the entire textbook in the span of the semester. Readings and assignments may be changed according to student performance.
Homework
There will be a certain amount of reading homework after most classes 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 must be studied beforehand as homework.
GRADING
Grading will be done on a points system up to a maximum of 400 total possible
points:

Quizzes (5 @ 40 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 point for that quiz. 200 points = c.50%.
 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. 100 points = c.25%
The written quizzes will take a form similar (but not identical) to these
sample quizzes. (WARNING: As of August 2017 these quizzes have not been adapted to the new Fall course.)
SAMPLE QUIZ QUESTIONS
The first FOUR quizzes are correct for Fall 2017.
(This quiz will be on TAR Chapters One through Three)

For each of the given pairs of concepts, first determine which is the genus, which the species; and then name two other species of the same genus. Eg. HUMAN, ANIMAL; BASEBALL, SPORT.

Arrange the given lists in terms of order of increasing abstractness. Eg. Telephone, iPhone, cellphone, communication device.

Fill in the blanks indicated by XXX in the given classification diagram(s).

For each proposed definition, identify the genus (if it has one) and the differentia. Eg. A bargain is an opportunity to buy something at an unusually low price.

Identify the rule violated by each of the given definitions. If the definition is too broad or too narrow, find a counterexample. Eg. An antidote is a substance that counteracts snakebite.

Arrange the following concepts in a classification diagram, showing the species–genus relationships. Then define each concept.
Eg. TABLE, BED, FURNITURE, DESK, CHAIR.

For each of the given pairs of sentences, determine whether or not the sentences express the same proposition.

In each of the given examples, identify the connective and the propositions it connects. Then determine whether those component propositions are asserted (a) or unasserted (u). Eg. The paintings were interspersed with the drawings. The painting were among the drawings.

Identify the relative clause in each sentence below, and determine whether it is restrictive or non restrictive. Eg. We are looking for a person who was last seen wearibg a Cleveland Indians baseball cap.
 For each of the following sentences, identify the propositions it asserts (a) and those it does not assert (u). Eg. He is convinced that two plus two equals four.
(This quiz will be on TAR Chapters Four and Five)
 For the following paragraphs, determine whether it contains an argument. If so, identify the premises and the conclusion.
Eg. In an experiment involving twins raised in different families, psychologists found that the children had significantly similar rates of depression. This indicates that depression is more strongly affected by one’s genetics than by one’s environment.
 For the following arguments, you will be given the structure of the diagram; fill in the numbers at the appropriate places.
Eg. (1) I shouldn’t go home this weekend not only because (2) I have too much studying to do, but also (3) because I can’t afford the trip.
 In the following arguments, identify the conclusion. Then determine whether the premises are dependent or in dependent.
Eg. To be a lawyer, you need to be good at keeping track of details, and Lenny is terrible at that, so he shouldn’t go into law.
 Diagram the following arguments.
Eg. I don’t think it would be a good idea to take the American Revolution course this term, because it conflicts with a course I need for my major, and my schedule would have more balance if I took a science course instead.
 Each pair of arguments that follow has the same conclusion. Determine which one has the greater logical strength. Remember that your assessment should depend not on whether you agree with the premises or the conclusion but on whether the relationship between the premises and the conclusion is strong. Eg.
a. Gelato is a better product than ice cream because it’s pop u lar with young, progressive people who are concerned about politics and the arts.
b. Gelato is a better product than ice cream because it has fewer calories, less fat, and a richer taste.
 Determine whether each of the following arguments is inductive or deductive. If it is deductive, is it valid or invalid?
Eg. No Greek philosopher taught in a university, but some Greek philosophers were great thinkers. Therefore, some great thinkers have not taught in a university.
 Identify the implicit premise(s) in each of the following arguments.
Eg. The traditional wax record, played on topoftheline equipment, can reproduce the spatial features of music such as the positions of the instruments in an orchestra. So in that respect it is superior to most compact disc recordings.
 Distill and diagram the following arguments—Eg. a scene from “The ‘Gloria Scott ’ ” by Arthur Conan Doyle:
“Come now, Mr. Holmes,” said he, laughing good humoredly. “I’m an excellent subject, if you can deduce anything from me.”
“I fear there is not very much,” I answered; “I might suggest that you have gone about in fear of some personal attack within the last twelvemonth.”
The laugh faded from his lips, and he stared at me in great surprise.
“Well, that’s true enough,” said he, . . . “though I have no idea how you
know it.”
“You have a very handsome stick,” I answered. “By the inscription I observed that you had not had it more than a year. But you have taken some pains to bore the head of it and pour melted lead into the hole so as to make it a formidable weapon. I argued that you would not take such precautions unless you had some danger to fear.”
 Identify which of the fallacies discussed in this section—subjectivism, appeal to majority, appeal to emotion, or appeal to force—is committed in the statement(s) below.
Eg. I think you will find that this merger is the best idea for our company, especially because disagreement may indicate that this company is not the right place for you.
 Identify which of the fallacies discussed in this section— appeal to authority or ad hominem— is committed in the each of statements below.
Eg. How can you say that animals have rights and should not be killed, when you eat meat?
 Identify which of the fallacies discussed in this section— false alternative, post hoc, hasty generalization, composition, division— is committed in the statements below.
Eg. It’s good to put water in your body, so it must be good to put water in your lungs.
 Each of the following arguments commits one or more of the fallacies of logical structure discussed in this section; identify them.
Eg. Mary says she loves me. I don’t know whether to believe her or not, but I guess I do, because I don’t think she would lie to someone she loves about something that important.
(This quiz will be on TAR Chapters Six and Seven)
 For each of the following propositions, identify the subject and predicate terms, the quality, and the quantity. Then name the form (A, E, I, O).
Eg. Some movie stars are good actors.
 Put each of the following statements into standard form; identify the subject and predicate terms, the quality, and the quantity; and name the form (A, E, I, or O).
Eg. All human beings are rational.
 For each pair of propositions, given that the first one is true, determine whether the second is true, false, or undetermined, in accordance with the traditional square of opposition.
Eg. All S are P  Some S are P.
 For each pair of propositions, given that the first one is true, determine whether the second is true, false, or undetermined, in accordance with the modern square of opposition.
Eg. All S are P  Some S are P.
 Put each of the following statements into standard form as a categorical proposition. Th en construct a Venn diagram for the proposition. (Instead of labeling the circles S and P, you can use lett ers appropriate to the actual subject and predicate terms.)
Eg. Some cats are friendly.
 State the converse of each of the following propositions, and indicate whether the proposition and its converse are equivalent.
Eg. Some trees are leafshedding plants.
 State the obverse of each of the following propositions. Make sure that you use genuinely complementary terms.
Eg. None of the athletes is an injured person.
 For each proposition below, find the converse, obverse, or contrapositive as indicated in parentheses, and determine whether the resulting proposition is the equivalent of the original.
Egs. Some S are P. (contrapositive)
Some S are not P. (obverse)
 For each mood and figure, write out the syllogism it describes. Hint: Start with the figure, and lay out the positions of S, M, and P; then use the mood to fill in the quantifier and copula for each proposition.
Eg. AII 1
 Put each of the following syllogisms into standard form (remember to put the major premise first), and then identify the mood and figure.
Eg. Any ambitious person can learn logic, and anyone reading this book is ambitious. So anyone reading this book can learn logic.
 Relying on your sense of the logical relationships among terms, try to determine
whether the following syllogisms are valid or invalid.
Eg. All P are M
No S is M
No S is P
 Find the missing premise (or conclusion) in each of the following enthymemes, put the argument into standard form, and identify its mood and figure. Be sure to complete the syllogism so that it is valid, if that is possible.
Eg. Any food that generates stomach acid is bad for an ulcer patient, and fried foods generate stomach acid.
 Put the following propositions into standard form (if they are not already), then identify the subject and predicate terms, and mark each term with a D if it is distributed or a U if it is undistributed.
Eg. No one with any manners would clean his teeth at the dinner table.
 Use the rules to test the validity of the following syllogisms. (These are the same syllogisms you evaluated intuitively in Exercise 7.2.) If the syllogism is invalid, state the reason.
Eg. All M are P
No M is S
Some S is not P
 First put each of the following syllogisms into standard form, and identify its mood and figure. Then use the rules to determine whether it is valid or invalid. If it is invalid, state the rule that it violates.
Eg. It’s obvious that Tom has something to hide. He pled the Fifth Amendment in court last week; people with things to hide always plead the Fifth.
 For each of the following enthymemes, use what you have learned about the rules of validity to supply the missing premise or conclusion that will result in a valid syllogism.
Eg. Trees need water because they are plants.
 For each of the following syllogisms, diagram the premises and the conclusion to determine whether the syllogism is valid.
Eg. Some P are M
No M is S
Some S are not P
 For each of the enthymemes that follow, use what you have learned about Venn diagrams to find the missing element and to prove that the resulting syllogism is valid.
Eg. Since some M are S, some S are P
 Use Venn diagrams to determine whether each of the following syllogisms is valid (a) on the modern view of existential import and (b) on the traditional view.
Eg. No P is M
All S are M
Some S are not P
 Using any of the methods discussed in this chapter, determine whether the following argument forms are valid.
Eg. All P are M
Some S are not M
Some S are P
(TAR Chapters Eight and Nine)
 Put each of the following disjunctive syllogisms into standard form, identify the disjuncts and any implicit elements, and determine whether the syllogism is valid.
Eg. Either I’m hearing things or someone is out in the hall singing “Jingle Bells.”
I know I’m not hearing things. So there’s someone out there singing.
 Identify the antecedent and consequent in each of the following statements, then put the statement into standard form (if it is not in standard form already).
Eg. A married couple filing a joint return may deduct certain child care expenses if they itemize their deductions.
 Put each of the following hypothetical syllogisms into standard form, identify any implicit premise or conclusion, identify what type of hypothetical syllogism it is, and determine whether the syllogism is valid.
Eg. If he had even mentioned her name, I would have hit him. But he didn’t, so I didn’t.
 Put each of the following syllogisms into standard form, and determine whether each is valid. Be sure to identify any implicit premises.
Eg. Only computers with at least 1 gigabyte of internal memory can run Microsoft Windows 7, and my computer doesn’t have that much memory. So I can’t run Windows.
 Analyze each extended argument that follows. Identify the structure of the argument, formulate each step as a syllogism, adding assumed premises or conclusions where necessary, and determine whether the argument is valid.
Eg. The killer left fingerprints all over the place, so he couldn’t have been a pro. A pro would not have been so sloppy.
 Analyze each extended argument that follows. Identify the structure of the argument, formulate each step as a syllogism, adding implicit premises as needed, and determine whether the argument is valid.
Eg. If the direction of the flow of time, from past to present to future, depends on the expansion of the universe, then time will reverse its direction if the expansion stops and the universe begins contracting—as current evidence from astrophysics suggests it will.
 Construct a modus ponens syllogism to support this conclusion:
the economy will go into a recession next year.
 Put the following statement(s) into standard form as a categorical, hypothetical, or disjunctive proposition.
Eg. “If the Moral Law was one of our instincts, we ought to be able to point to some one impulse inside us which was always what we call good . . . But [we] cannot . . . The Moral Law is not any one instinct.” [C.S. Lewis, Mere Christianity]
 Put each of the following arguments into standard form as a categorical, hypothetical, or disjunctive syllogism, supplying any missing premise or conclusion. Then determine whether it is valid.
Eg. “As it is impossible for the whole race of mankind to be united in one great society, they must necessarily divide into many.” [William Blackstone, Commentaries on the Laws of England]
 For each of the following statements, identify the component propositions and the connective. Then put the statement in symbolic form, using the letters indicated in parentheses.
Eg. Jerry will either win the race or take second place.
 For each of the following statements, identify the component propositions and the connective. Then put the statement in symbolic form, using the letters indicated in parentheses.
Eg. I’m ready if you are.
 Identify the components and the connective in each of the following statements. Then put the statement into symbolic form. For this exercise, it will be up to you to pick appropriate letters to stand for the components.
Eg. Winning isn’t the important thing.
 Identify the main connective in each of the following statements.
Eg. (H • R) ≡ T
 Put each of the following statements into symbolic notation, using appropriate letters to abbreviate atomic components.
Eg. You may have a dog only if you get straight A’s this year.
 For each statement below, classify the statement by identifying the main connective and construct a truth table.
Eg. A ∨ (B ∨ A)
 Identify whether each of the statements below is a tautology, a selfcontradiction, or contingency by creating a truth table for the statement.
Eg. (A • B) ∨ A
 Determine whether the statements in each of the following sets are equivalent, contradictory, consistent, or inconsistent by creating truth tables for the statements.
Eg. ~(A • B) (~A ∨ ~B)
 Put each of the following statements into symbolic form, replacing English words and punctuation with connectives and parentheses.
Eg. p and either q or r
 Find (or create) statements in English that have the following logical forms.
Eg. (p ∨ q) • (r ∨ s)
 Translate the following legal statement into symbolic notation.
Eg. Employees must work their scheduled work day before and after the holiday if he or she is to be paid for the holiday, unless he or she is absent with prior permission from a supervisor.
(TAR Chapter 10.110.4.)
Egs.
1. Construct a truth table for the following statement form:
[(p ⊃ q) • p] ⊃ q
and state whether it is a tautology, self contradiction, contingency, equivalency, or contradiction.
2. Construct a truth table for the following argument. State whether it is valid or invalid and indicate which rows on your table show its validity or invalidity and explain why.
~Z
C ⊃ G
Z (A ⊃ C)
∴ ~G ⊃ ~A
3. Test the following argument for validity using the short form of the truth table. (If you are uncertain of your answer, create a full truth table for the arguement).
A • B
C ∨ B
∴ ~C
4. Each of the following arguments is na instance of one of the following four inference forms: Modus Ponens, Modus Tollens, Hypothetical Syllogism, or Disjunctive Syllogism. Identify the form:
C ∨ D
~C
∴ D
A ⊃ (B ≡ C)
~(B ≡ C)
∴ A
5. Each of the following arguments is an instance of one of the basic inference forms, Simplification, Conjunction, Addition, Constructive Dilemma, or Destructive Dilemma. Identify the form in each case.
A • B
∴ B
(A ⊃ B) • (B ⊃ C)
A ∨ B
∴ (A ∨ B) • [(A ⊃ B) • (B ⊃ C)]
6. Construct a proof for each of the following arguments using only the inference rules from TAR 10.3 (Simplification, Conjunction, Addition, Constructive Dilemma, or Destructive Dilemma).
(A ⊃ B) • (C ⊃ D)
~B ∨ ~D
∴ ~A ∨ ~C
7. For each of the following proofs state the justification for each step
1. A ⊃ B
2. ~A ⊃ C
3. ~B ∴ C
4. ~A
5. C
1. (M • O) ⊃ (L ∨ K)
2. O • (L ∨ B)
3. M • ~H ∴ (L ∨ K)
4. M
5. O
6. M • O
7. (L ∨ K)
8. Show that each of the following arguments is valid by contructing a proof.
A
A ⊃ ~B
B ∨ C
∴ C
9. For each of the following statements, find a statement that is equivlent by the specified rule. Since equivalence rules apply to component parts of a statement as well as to the statement as a whole, there may be more than one right answer.
B (by tautology)
A ∨ D (by commutation)
C ∨ (F ∨ G) (by Association)
~E • ~N (by DeMorgan's Theorem)
Week:
1  2  3  4  5  6  7  8  9  10  11  12  13  14  15 
Click the number to see the week.
Week 1.
Monday, 8/28
Introduction to the course, the textbook,
"Online Exercises,"
and the class webpage.
Homework: Read TAR Chapter One  Classification.
Wednesday 8/30
Questions on the Homework: Classification.
Homework: Read TAR Chapter Two  Definition.
Friday 9/1
Questions on the Homework: Definition.
Homework: Read TAR Chapter 3.1  Propositions and Word Meaning.
Do computer exercises from 1.1 to 2.3.
Week 2.
Monday, 9/4
Questions on the Homework: Propositions and Word Meaning.
Homework: Read TAR Chapter 3.2  Propositions and Grammar.
Wednesday, 9/6
Questions on the Homework: Propositions and Grammar.
Homework: Revise TAR Chapters 13. Prepare for Quiz #1. (Sample).
Friday, 9/8
QUIZ #1 (TAR Chapters 1 through 3).
Homework: Read TAR 4.1  Elements of Reasoning.
More Computer exercises on TAR chapter 3 to chapter 4.1.
Week 3.
Monday, 9/11
Questions on the Homework: Elements of Reasoning.
Homework: Read TAR 4.2  Diagramming Arguments.
Wednesday, 9/13
Questions on the Homework: Diagramming Arguments.
Homework: Read TAR 4.3 and 4.4  Evaluating Arguments and Induction and Deduction.
Friday, 9/15
Questions on the Homework: Evaluating Arguments and Induction and Deduction.
Homework: Read TAR 4.5 and 4.6  Implicit Premises and Distilling Arguments.
Computer exercises 4.2 to 4.6.
Week 4.
Monday, 9/18
Questions on the Homework: Implicit Premises and Distilling Arguments.
Homework: Read TAR 5.1 and 5.2  Subjectivist Fallacies and Fallacies Involving Credibility.
Wednesday, 9/20
Questions on the Homework: Subjectivist Fallacies and Fallacies Involving Credibility.
Homework: Read TAR 5.3  Fallacies of Context.
Friday, 9/22
Questions on the Homework: Fallacies of Context.
Homework: Read TAR 5.4  Fallacies of Logical Structure.
Computer exercises TAR 5.3 and 5.4.
Week 5.
Monday, 9/25
Questions on the Homework: Fallacies of Logical Structure.
Revise TAR Chapters 4 and 5. Prepare for Quiz #2 (Sample).
Wednesday, 9/27
QUIZ #2 (TAR chapters 4 and 5).
Homework: Read TAR 6.1  Standard Form Categorical Propositions.
Friday, 9/29
Questions on the Homework: Standard Form Categorical Propositions.
Homework: Read TAR 6.2  The Square of Opposition.
Computer exercises TAR 6.1 to 6.2.
Week 6.
Monday, 10/2
Questions on the Homework: The Square of Opposition.
Homework: Read TAR 6.3  Existential Import.
Wednesday, 10/4
Questions on the Homework: Existential Import.
Homework: Read TAR 6.4  Venn Diagrams for Propositions.
Friday, 10/6
Questions on the Homework: Venn Diagrams for Propositions.
Homework: Read TAR 6.5  Immediate Inferences.
Computer exercises TAR 6.3 to 6.5.
Week 7.
Monday, 10/9
Questions on the Homework: Immediate Inferences.
Homework: Read TAR 7.1 and 7.2  The Structure of a Syllogism and Validity.
Wednesday, 10/11
Questions on the Homework: The Structure of a Syllogism and Validity.
Read TAR 7.3 and 7.4  Enthymemes and Rules of Validity.
Friday, 10/13
Questions on the Homework: Enthymemes and Rules of Validity.
Read TAR 7.5  Venn Diagrams for Arguments.
Computer exercises TAR 7.1 to 7.5.
Week 8.
Monday, 10/16
Questions on the Homework: Venn Diagrams for Arguments.
Homework: Revise TAR Chapters 6 and 7  Categorical Propositions and Syllogisms.
Wednesday, 10/18
Revision of Categorical Propositions and Syllogisms. Preparation for Quiz #3 (Sample).
Friday, 10/20
QUIZ #3 (TAR chapters 6 and 7).
Midterm Break: Saturday 10/21 to Tuesday 10/24.
Homework: Read TAR 8.1 and 8.2  Disjunctive and Hypothetical Syllogisms.
Computer exercises TAR 8.1 to 8.2.
Week 9.
Wednesday 10/25
Questions on the Homework: Disjunctive and Hypothetical Syllogisms.
Homework: Read TAR 8.3  Distilling Deductive Arguments.
Friday 10/27
Questions on the Homework: Distilling Deductive Arguments.
Homework: Read TAR 8.4  Extended Arguments.
Computer exercises TAR 8.3 to 8.4.
Week 10.
Monday, 10/30
Questions on the Homework: Extended Arguments.
Homework: Read TAR 9.1  Connectives.
Wednesday, 11/1
Questions on the Homework: Connectives.
Homework: Read TAR 9.2  Statement Forms.
Friday, 11/3
Questions on the Homework: Statement Forms.
Homework: Read TAR 9.3  Computing Truth Values.
Computer exercises TAR 9.1 to 9.3.
Week 11.
Monday, 11/6
Questions on the Homework: Computing Truth Values.
Homework: Read TAR 9.4  Formal Properties and Relationships.
Wednesday, 11/8
Questions on the Homework: Formal Properties and Relationships.
Homework: Revise TAR Chapters 8 and 9, prepare for Quiz #4 (Sample, TAR chapters 8 and 9).
Computer exercises TAR 9.2 to 9.4.
Friday, 11/10
QUIZ #4 (TAR chapters 8 and 9).
Homework: Read TAR 10.1  Truth Tables.
Computer exercises TAR 10.1.
Week 12.
Monday 11/13
Questions on the Homework: Truth Tables.
Homework: Read TAR 10.2  Test of Validity and Short Form.
Wednesday 11/15
Questions on the Homework: Test of Validity and Short Form.
Homework: Read TAR 10.3  Proof.
Friday 11/17
Questions on the Homework: Proof.
Homework: Read TAR 10.4  Equivalence.
Computer exercises TAR 10.2 to 10.3.
Week 13.
Monday, 11/20
Questions on the Homework: Equivalence.
Computer exercises TAR 10.4.
Thanksgiving Break, Wednesday 11/22 to Sunday 11/26.
Revise TAR Chapter 10 (10.110.4), prepare for Quiz #5 (Sample).
Week 14.
Monday 11/27
Homework: Preparation for Quiz #5 (Sample).
Wednesday, 11/29
QUIZ #5 (TAR ch. 10.110.4).
Friday, 12/1
Revision of Quizzes 1 and 2: TAR chs. 15Language, Reasoning, Classification, Definition, and Fallacies.
Week 15.
Monday 12/4
Revision of Quizzes 3 and 4: TAR chs. 69Categorical Propositions and Syllogisms.
Wednesday, 12/6
Revision of Quiz 5: TAR ch. 10Propositional LogicArguments, and Explanation of Final Exam.
Friday, 12/8
Last Day of classes.
Loose ends: revision of areas of difficulty in preparation for the Final Exam.
The final examination will take place on Tuesday December 12^{th} from 8:00 a.m. to 10:30 a.m. in PH 208.
Term ends Friday,
Decemebr 16^{th}.
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) AND if the conclusion is negative one premise must be negative (affirmative premises, negative conclusion).
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.
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 
conditional 
consequence implication 
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 iff R 
biconditional 
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 ⋅ E 
H ∧ E 
conjunction 

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