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Exercises for Studies 1-5 & Informal Fallacies

1.0 | 1.2 | 2.1 | 2.2 | 3.1 | 3.2 | 3.3 | 4.0 | 5.1 | 5.2 | 6.1 | 6.2

Exercise 1.1: The Four Forms

 Instructions:   Choose the letter for the correct answer for each of the following.

a A(ab) f undistributed
b I(ab) g quantity
c O(ab) h quality
d E(ab) i universal
e distributed j particular
1 The forms A and E are said to have _____ quantity.
2 The forms I and O are said to be _____ in quantity.
3 If the subject terms of forms are _____ , the forms are universal.
4 If the predicate terms of forms are _____ , the forms are affirmative in quality.
5 If the predicate terms of forms are _____ , the forms are negative in quality.
6 The forms A(ab) and I(ab) are similar in _____ , but dissimilar in _____ .
7 The form with both particular quantity and affirmative quality is _____ .
8 The form with both terms undistributed is _____ .
9 The form with a distributed subject term, and an undistributed predicate term is the _____ .
10 The form with both terms distributed is _____ .
11 The form A(ab) differs from form _____ in both the distribution of terms, quantity, and quality.
12 The formal qualities of the forms are defined in terms of whether or not the subjects and predicates of the forms are _____ or _____ .

 Exercise 1.2: Translating Propositions into Standard Form
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Instructions: Rewrite each of the following propositions as standard A, E, I, or O forms. Use the letters in parentheses for subject and predicate terms for each. The Answers in the back of this book do the same. (If you cannot put them in standard form, you do not know what they mean.)
1 No Christian is a secularist. (c,s)
2 Some children run to school. (c,s)
3 Only good students get A's. (s,g)
4 None but the brave deserve the fair. (f,b)
5 All except workers may enter. (w,e)
6 Only freshmen need use the back door. (b,f)
7 The poor always ye have with you. (w,p)
8 You always squirm out of an argument. (a,o)
9 Except the Lord build the house, they labor in vain who build it. (l,i)
10 Logic is the science of necessary inference. (l,s)
11 Whosoever committeth sin transresseth also the law. (l,s)
12 The fall brought mankind into an estate of sin and misery. (f,e)
13 Nothing worthwhile is easy. (w,e)
14 Whoso loveth instruction loveth knowledge. (i,k)
15 There is therefore now no condemnation to those who are in Christ Jesus. (j,c)
16 The sacraments of the New Testament are Baptism and the Lord's supper. (s,a)
17 In order to say something meaningful, one must use the law of contradiction. (m,l)
18 Some hold that God's sovereignty and man's responsibility are paradoxical. (s,p)
19 Most of the questions in this exercise are easy (q,e)
20 Fifty percent of eligible voters did not vote. (f,v)

Exercise 2.1: Definitions Four Forms

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Instructions: Fill in the blanks in each statement with the letter of the most correct answer.

a affirmative forms f proposition
b distributed term g undistributed term
c immediate inference h universal forms
d negative forms i valid
e particular forms j none
1 A(n) _____ is defined as the meaning of a declarative sentence
2 _____ is composed of two propositions with two terms.
3 Whenever the form of the conclusion is true every time the forms of the premises are, we say the inference is _____ .
4 The forms A and I are _____ .
5 The forms E and O are _____ .
6 A(n) _____ is one modified by the adjective all or no.
7 A(n) _____ is one modified by the adjective some.
8 _____ do not distribute their predicates.
9 _____ distribute their predicates.
10 _____ distribute their subjects.

Exercise 2.2: Relations between Propositions
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Instructions: Fill in the blanks in each statement with the letter of the correct answer.

a contraries f subcontraries
b contradictories g true
c false    h reflexive
d undetermined i symmetrical
e subalternation j transitive
1 A and E are opposed as _____ .
2 I and O are opposed as _____.
3 A and O are opposed as _____.
4 E and I are opposed as _____ .
5 _____ both universal in quantity, may both be false together.
6 _____ both particular in quantity, may both be true together.
  Assuming the same subject terms and the same predicate terms: (7-10)
7 If A is true, then E _____ I _____ O _____.
8 If E is false, then I _____ A_____ O _____ .
9 If I is true, then E _____ A _____ O _____ .
10 If O is false, then A _____ E _____ I _____ .
11 If one of the subcontraries is true, then a pair of diagonals will be _____ .
12 A relationship that holds between one of its objects and that object itself is _____ .
13 A _____ relationship is one which, if it holds between two of its objects, a and b, also holds between b and a.
14 A relationship is _____ , if, when it holds between two of its objects, a and b, and also holds between b and c, it holds as well between a and c.
15 Match the lists below with the correct answer from the list above.
1 ... equal ... ________
2 ... is less than ... ________
3 ... is the twin of... ________
4 ... is greater than ... ________
5 ... is the cousin of ... ________
6 ... is the ancestor of... ________
7 ... is subsequent to ... ________
8 ... implies ... ________

Exercise 3.1: Definition of Terms Standard Syllogism
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Instructions: Fill in the blanks in each statement with the letter of the correct answer.

a conversion per accidens g minor term
b first figure h fourth figure
c major premise i second figure
d major term j simple conversion
e middle term k standard syllogism
f minor premise l third figure 
1 A _____ is an inference with two premises and three terms, each appearing twice but never twice in the same proposition.
2 The _____ is the predicate of the conclusion of a standard syllogism.
3 The _____ is the subject of the conclusion of a standard syllogism.
4 The term that occurs in both premises, but not in the conclusion is the _____ .
5 The _____ is the one that contains the major term.
6 The _____ is the one that contains the minor term.
7 The lower case letter "s" in the names of valid syllogism means _____ of the preceding form.
8 The lower case "p" in some of the names of valid syllogisms means _____ .
9 The _____ is the subject term of the major premise and the predicate term of the minor premise of a standard syllogism.
10 The _____ is the predicate of both premises of a standard syllogism.
11 The _____ is the subject of both premises of a standard syllogism.
12 _____ is the predicate of the major premise and the subject term of the minor premise of a standard syllogism.

Exercise 3.2: Syllogisms  
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Instructions: Determine the validity of each by comparison with the frame names of valid syllogisms or by means of the Five Rules.

Use "V" for valid; "I" for invalid.

1 All thinking beings are existing beings. I am a thinking being; therefore, I am an existing being.
2 Some good Christians are communists because Some good Christians practice what they preach; and All communists practice what they preach."
3 Suppose someone argues: No logic students swallow propaganda. The premises are: (1) No logic students are stupid; and (2) All stupid people swallow propaganda.
4 All whom the Son makes free are free indeed, because all who know the truth are free indeed; and all whom the Son makes free know the truth.
5 Descriptive sciences have no place for evaluations. Psychology is a descriptive science, among others. Therefore, psychology has no place for evaluations.
6 All that God does is good. God clearly predestinates evil. Therefore, God does good in predestinating evil.
7 No person who knows the Truth is a slave of sin. All whom the Son makes free are persons who know the Truth. Therefore, no person whom the Son makes free is a slave of sin.
8 Does it make sense to argue that some poor scholars are theologians because all theologians are former seminary students, and some seminary students were poor scholars?
9 Our sense organs change either by reason of aging or by reason of disease leading to deception. These changes usually occur without our knowing it. Therefore, we are often or almost always deceived.
10 Every system of philosophy must have a starting point, an axiom or set of axioms, for otherwise it could not start. Starting points cannot be demonstrated. Therefore, every system of thought must be based on an indemonstrable axiom.

 Exercise 3.3: Definition of Terms - Deduction
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Instructions: Fill in the blanks in each statement with the letter of the correct answer.

a axioms            e strengthened form
b theorem f weakened form
c Rule I (Deduction) g Five Rules (Validity of Syllogisms)
d Rule II (Deduction) h necessary & sufficient
1 _____ are never deduced because they are the starting points of all deduction.
2 _____ states that if in any valid mood the premise and the conclusions be interchanged and contradicted, the result is a valid implication.
3 _____ states that if any valid implication, if its premise be strengthened or its conclusion weakened, a valid implication will result.
4 The premise of a valid implication is a _____ of its consequent and the conclusion is a _____ of its premise.
5 There are _____ by which any standard syllogism may be tested for validity.
6 One proves a _____ by applying rules to the axioms.
7 The five rules are _____ , if you can't do without them and there is at least one invalid syllogism to which the given rule alone applies.

 Exercise 4.0: Additional Argument Forms
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Instructions: Fill in the blanks in each statement with the letter of the correct answer.

a disjunctive syllogism f transitive syllogism
b affirming the consequent g modus ponens
c complete h modus tollens
d denying the antecedent i interdefinable
e dilemma j valid
1 _____ has an implication as a premise and the antecedent of the implication as a second premise from which one concludes the consequent of the first.
2 The form of argument in which the 1st premise is: x implies y, and the 2nd is: y is false; therefore: x is false, is known _____ .
3 The following argument form exemplifies the fallacy of _____ : x implies y, and y is true; therefore, x is true.
4 Argument Form: x implies y, and x is false; therefore, y is false, is the fallacy of _____ .
5 The _____ form consists of premises: x + y, and x is false, to conclude: y is true.
6 The argument form (x < y) (z < w) (x + z) < (y + w) is known as a(n) _____ .
7 If the first two premises of a dilemma are not _____ inferences, the dilemma fails.
8 The disjunction premise of a dilemma must be a _____ disjunction or the dilemma fails.
9 The formula: (xy)' = (x' + y') shows that conjunction and disjunction are _____
10 The implication (x < y) (y < z) < (x < z) is known as _____ .

Exercise 5.1: Truth Table - Functions
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Part A Instructions: Match the truth table values in the columns, a through g, with the correct forms, 1 through 7.

    a b c d e f g
x y              
T T T T F F T F F
T F F F T T T F F
F T T F T F T F T
F F T F T F F T T
1 conjunction     _________
2 disjunction      _________
3 implication _________
4 contradiction of conjunction _________
5 contradiction of disjunction _________
6 contradiction of implication _________
7 contradiction of x _________

 Part B Instructions: Match the truth table values in the columns, a through g, with the correct forms, 1 through 10.

    a b c d e f g
p q              
T T T F F T T T F
T F T F T F F T F
F T T F T T F F F
F F T F T T F F T
___ 1. (p + q)'            ___ 6. (pq')'
___ 2. (pp')'    ___ 7. (p' + q')
___ 3. (p + p')' ___ 8. (p' + q')'
___ 4. (pq)' ____9. (p < p')'
___ 5. (p' + q) ___ 10. (p' + p')'

Exercise 5.2: Truth Table Analysis
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Instructions: Do a truth table analysis of the following propositions.

Hawk Newton is good in either science or theology, but not both. Moreover, either he is good at logic or bad at theology. If he is not good in science, he is bad at theology. If he is bad at theology, he is good at logic.

What do these four premises imply, if anything? Is Hawk good in anything? In or at what?

1 Hawk is good in either science or theology, but not both. (s + t)(st)'
2 Hawk is good at logic or bad at theology.  (l + t' )
3 If he is not good in science, he is bad at theology. (s' < t' )
4 If he is bad at theology, he is good at logic.           (t' < l)
        1st 2nd 3rd 4th
  s l t (s + t) (st)' (l + t')   (s' < t' ) (t' < l)
1 T T T          
2 T T F          
3 T F T          
4 T F F          
5 F T T          
6 F T F          
7 F F T          
8 F F F          
  i ii iii iv v vi vii viii

 Exercise 6.1: Informal Fallacies, Definitions 
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Instructions: Choose the correct answer for each from this list.

a accent i amphiboly
b ad baculum j circular reasoning
c ad hominem (abusive) k complex question
d ad ignorantiam l composition
e ad misericordiam m division
f ad populum n equivocation
g ad verecundiam o post hoc
h accident p none of the above
1 When one appeals to force or threat of force to cause acceptance of a conclusion.
2 When instead of trying to disprove the truth of what is asserted, one attacks the person's situation, beliefs, or prejudices
3 Whenever it is argued that a proposition is true (false) simply on the basis it has not been proved false (true).
4 The attempt to win popular assent to a conclusion by arousing the feelings and enthusiasms of the multitude.
5 An appeal to the feeling of respect people have for the famous to win assent to a conclusion.
6 When a general rule is applied to a particular case whose accidental circumstances render the rule inapplicable.
7 When one considers only exceptional cases and generalizes to a rule that fits them alone.
8 When one assumes as a premise for an argument the very conclusion one intends to prove.
9 For a plurality of questions, a single answer is demanded to a complex question as if it were a simple one.
10 When we confuse the different meanings a single word or phrase may have.
11 When a statement's meaning is unclear because of the loose way in which its words are combined.
12 When words or phrases of a statement are emphasized or stressed producing different meanings from the original.
13 When one reasons fallaciously from the properties of the parts of a whole to the properties of whole itself.
14 Assuming without proof that a prior event explains or is the cause of a subsequent event.
15 When one argues fallaciously that what is true of a whole must be true of each of its parts.
16 When one argues that another must choose one of two options without having proven that the options are mutually exclusive and one or the other must be selected.
17 When it is clear that a conclusion is not necessitated by the premises and the fallacy does not fit the more familiar informal fallacy categories.
18 When one reasons that because two or more things are alike in some respect(s), they will therefore be found alike in some other respect(s).
19 When pity is appealed to for the sake of getting a conclusion accepted.
20 When an implausible, easily attacked, theory is substituted for one that is more plausible and less easily attacked.

Exercise 6.2: Informal Fallacies
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Instructions: Choose the most correct answer for each question.

a ad baculum h division
b ad hominem i equivocation
c ad ignorantiam j false dilemma
d ad misericordiam k hasty generalization
e amphibology  l circular reasoning
f complex question m post hoc
g composition n none of these
 1 Psychiatrist: 75% of the women in this city are neurotic; I know this because 75% of the women who come to see me are neurotic.
2 Reporter: The farmer blew out his brains after taking affectionate farewell of his family with a shotgun.
3 Coach asked: By what score will your team lose?
4 Wife: If my mother were here, I bet your wouldn't dare treat me like this.
5 Student: This argument is fallacious. I know it is fallacious because its not valid. It is not valid because it contains a fallacy.
6 Counselor: If you fail to take the tests, we'll have to drop you.Student: My father is in the hospital desperately ill; if you drop me, he may die.
7 Dealer: Since the Dynamobile is the best automobile made in America, the battery in this car must be the best battery in America.
8 Administrator: We must either deny freedom of speech to all critics of the policy or give the students a free hand in destroying the university.
9 Job Counselor: Just fall in love with your job, and success will be yours.
10 Politician: If anything is good for a crucial industry such as the steel industry, then it will be good for the country as a whole.
11 Student: Since we cannot disprove telepathy, we must conclude there is something to it.
12 Concert Goer: I certainly cannot see how you can enjoy this piece of music. It was a favorite of Hitler's!
13 Philosopher: The end of a thing is its perfection; death is the end of life, isn't it? Therefore, death is the perfection of life.
14 Friend: You are either part of the problem or part of the solution. Which is it?
15 Developer: A bad neighborhood is like a rotten apple in a basket of good apples. It must be removed before the rot spreads.
16 Student: Inasmuch as water extinguishes fire, and oxygen is a component of water, we may be sure that oxygen will also put out fire.
17 Speaker: Since we have so far been unable to discover any limit to the universe, we must conclude that space is infinite.
18 Textbook: Anthropology is the science of man embracing woman.
19 Parent to Child: Your mother said: "We should not speak ill of OUR friends!" (Not identical to the original.)
20 Student: That fraternity does some pretty silly things. Tom is a member of that fraternity; therefore, Tom, naturally, does some pretty silly things.
21 Politician: Don't let this educator mislead you. His reading program is not a success. There are still literally thousands of people in this county who are unable to read
22 Commuter: Oriental drivers are a danger on the highways. I saw two this morning and they almost caused accidents with other drivers.
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