Come Let Us Reason Flashcards
(393 cards)
1
Q
Identify which of the following are arguments and, if they are, which are
deductive and which are inductive.
Our university campus study of one hundred students showed a
dramatic increase in grades after their becoming Christians; therefore
we conclude that conversion to Christianity helps your grade point
average.
A
Inductive
2
Q
Identify which of the following are arguments and, if they are, which are
deductive and which are inductive.
Jesus said, “I am the way, the truth, and the life. No man comes to
the Father but through me” (John. 14:6).
A
- No argument
3
Q
Identify which of the following are arguments and, if they are, which are
deductive and which are inductive.
According to the Bible, all sinners need to trust Christ, and you are a
sinner. So you need to trust Christ.
A
- Deductive
4
Q
Identify which of the following are arguments and, if they are, which are
deductive and which are inductive.
“There are no miracles, Jesus was not the Son of God, and there is
no God.”
A
- No argument
5
Q
Identify which of the following are arguments and, if they are, which are
deductive and which are inductive.
Robert is a Christian and Christians don’t know logic, so it’s
obvious that Robert doesn’t know logic.
A
- Deductive
6
Q
Identify which of the following are arguments and, if they are, which are
deductive and which are inductive.
I know Jesus rose from the dead because he appeared to the
disciples, the tomb is empty, and even some of his enemies like Paul
came to believe in him.
A
- Inductive
7
Q
Identify which of the following are arguments and, if they are, which are
deductive and which are inductive.
In last night’s campus meeting there were thirty-two Catholics,
twenty-four nonreligious, and sixteen of various Protestant
denominations.
A
- No argument
8
Q
Identify which of the following are arguments and, if they are, which are
deductive and which are inductive.
The Bible is historically accurate and anything that is historically
accurate is trustworthy. So the Bible is trustworthy.
A
- Deductive
9
Q
Identify which of the following are arguments and, if they are, which are
deductive and which are inductive.
Christianity is unique from all the other religions in the world. It is
unlike Buddhism, Hinduism and Islam.
A
- No argument
10
Q
Identify which of the following are arguments and, if they are, which are
deductive and which are inductive.
I know the Bible is trustworthy because of three things: it never
contradicts itself, it doesn’t contradict other historical writings, and the
manuscript evidence is greater than any other writing of ancient times.
A
- Inductive
11
Q
Identify the quantifier (Q), the subject term (S), the copula (C), and the
predicate term (P) in the following propositions. Put brackets around each of the
four terms.
- All Christians are saved.
A
Q S C P
1.[All] [Christians] [are] [saved].
12
Q
Identify the quantifier (Q), the subject term (S), the copula (C), and the
predicate term (P) in the following propositions. Put brackets around each of the
four terms.
- No Baptists are Presbyterians.
A
Q S C P
2.[No] [Baptists] [are] [Presbyterians].
13
Q
Identify the quantifier (Q), the subject term (S), the copula (C), and the
predicate term (P) in the following propositions. Put brackets around each of the
four terms.
- Some people who attend church are not true believers.
A
Q S C P
3. [Some] [people who attend church] [are not] [true believers].
14
Q
Identify the quantifier (Q), the subject term (S), the copula (C), and the
predicate term (P) in the following propositions. Put brackets around each of the
four terms.
- Salvation is a free gift.
A
S C P
4. [Salvation] [is] [a free gift]. (Q implied)
15
Q
Identify the quantifier (Q), the subject term (S), the copula (C), and the
predicate term (P) in the following propositions. Put brackets around each of the
four terms.
- Bertrand Russell is an atheist.
A
S C P
5. [Bertrand Russell] [is] [an atheist]. (Q implied)
16
Q
Identify the quantifier (Q), the subject term (S), the copula (C), and the
predicate term (P) in the following propositions. Put brackets around each of the
four terms.
- Some atheists are communists.
A
Q S C P
6. [Some] [atheists] [are] [communists].
17
Q
Identify the quantifier (Q), the subject term (S), the copula (C), and the
predicate term (P) in the following propositions. Put brackets around each of the
four terms.
- David Hume wrote an argument against believing in miracles.
A
S P
7. [David Hume] [wrote an argument against believing in miracles]. (Q
& C implied)
18
Q
Identify the quantifier (Q), the subject term (S), the copula (C), and the
predicate term (P) in the following propositions. Put brackets around each of the
four terms.
- All communists are atheists.
A
Q S C P
8. [All] [communists] [are] [atheists].
19
Q
Identify the quantifier (Q), the subject term (S), the copula (C), and the
predicate term (P) in the following propositions. Put brackets around each of the
four terms.
- Christians who study their Bibles, pray, and obey Christ, will remain in fellowship with God.
A
S
9. [Christians who study their Bibles, pray, and obey
Christ], P
[will remain in fellowship with God]. (Q & C implied)
20
Q
Identify the quantifier (Q), the subject term (S), the copula (C), and the
predicate term (P) in the following propositions. Put brackets around each of the
four terms.
- No nonbelievers will go to heaven.
A
Q S P
10. [No] [nonbelievers] [will go to heaven]. (C implied)
21
Q
Identify the quantifier (Q), the subject term (S), the copula (C), and the
predicate term (P) in the following propositions. Put brackets around each of the
four terms.
- God does not change.
A
S P
11. [God] [does not change]. (Q & C implied)
22
Q
Identify the quantifier (Q), the subject term (S), the copula (C), and the
predicate term (P) in the following propositions. Put brackets around each of the
four terms.
- I am not an atheist.
A
S C P
12. [I] [am not] [an atheist]. (Q implied)
23
Q
Identify the quantifier (Q), the subject term (S), the copula (C), and the
predicate term (P) in the following propositions. Put brackets around each of the
four terms.
- All people are descendants of Adam.
A
Q S C P
13. [All] [people] [are] [descendants of Adam].
24
Q
Identify the quantifier (Q), the subject term (S), the copula (C), and the
predicate term (P) in the following propositions. Put brackets around each of the
four terms.
- Some descendants of Adam are believers in Christ.
A
Q S C P
14. [Some] [descendants of Adam] [are] [believers in Christ].
25
Identify the quantifier (Q), the subject term (S), the copula (C), and the
predicate term (P) in the following propositions. Put brackets around each of the
four terms.
15. Some people are not believers in Christ.
Q S C P
15. [Some] [people] [are not] [believers in Christ].
26
Identify the following propositions as either universal or particular and as
affirmative or negative.
1. Some people are nonChristians.
PA
27
Identify the following propositions as either universal or particular and as
affirmative or negative.
2. No atheists are Christians.
UN
28
Identify the following propositions as either universal or particular and as
affirmative or negative.
3. Some Hindus are not pantheists.
PN
29
Identify the following propositions as either universal or particular and as
affirmative or negative.
4. Sharon is a member of First Baptist Church.
UA
30
Identify the following propositions as either universal or particular and as
affirmative or negative.
5. All believers are going to heaven.
UA
31
Identify the following propositions as either universal or particular and as
affirmative or negative.
6. Logic is not used by everybody.
UN
32
Identify the following propositions as either universal or particular and as
affirmative or negative.
7. Some angels fell with Satan.
This is the first time we have a proposition that has no copula, so we
must supply one. Change the sentence to “Some angels are beings that
are going to heaven.” Now it becomes a PA proposition.
33
Identify the following propositions as either universal or particular and as
affirmative or negative.
8. God cannot sin.
8. Do the same here. You should get a UN proposition.
34
Identify the following propositions as either universal or particular and as
affirmative or negative.
9. Unhappy people are people who need the Lord.
UA
35
Identify the following propositions as either universal or particular and as
affirmative or negative.
10. None is righteous.
Propositions that begin with “None” by itself are treated as if they
began with “No one” and are negative. This proposition is UN. However, if
a proposition begins with “None but,” then it is an exclusive proposition
like “Only.” See exercise 2.6, #8 for handling exclusive propositions.
36
Identify the following propositions as either universal or particular and as
affirmative or negative.
11. Some Christians are not obedient people.
PN
37
Identify the following propositions as either universal or particular and as
affirmative or negative.
12. Some Christians are non-obedient people.
PA
38
Identify the following propositions as either universal or particular and as
affirmative or negative.
13. No man has seen God.
UN
39
Identify the following propositions as either universal or particular and as
affirmative or negative.
14. All men are not saved.
This can be either UN or PN depending on how one sees it. Because
“All … are not …” really means “Not all are …,” or “Some … are not …,”
we will always interpret these as PN. It might help if you rewrite the
sentence each time you see it.
40
Identify the following propositions as either universal or particular and as
affirmative or negative.
15. All nonbelievers are nonChristians.
UA
41
Identify the following propositions as either universal or particular and as
affirmative or negative.
16. Many unsaved people are good neighbors.
PA. Terms like many and most are just greater somes.
42
Identify the following as either A, E, I, or O propositions.
1. No disciples are unkind.
E
43
Identify the following as either A, E, I, or O propositions.
2. Paul was a champion of Christianity.
A
44
Identify the following as either A, E, I, or O propositions.
3. Some church attenders are not paying attention.
O
45
Identify the following as either A, E, I, or O propositions.
4. All Scripture is inspired. (2 Tim. 3:16)
A
46
Identify the following as either A, E, I, or O propositions.
5. Some theologians are wrong.
I
47
Identify the following as either A, E, I, or O propositions.
6. Each and every person needs to trust Christ for his salvation.
A
48
Identify the following as either A, E, I, or O propositions.
7. Nobody seeks God. (Rom. 3:10)
E
49
Identify the following as either A, E, I, or O propositions.
8. God is immutable.
A
50
Identify the following as either A, E, I, or O propositions.
9. They are not among the believers.
9. E. “They” = “[all] the people in this group to which I refer.”
51
Identify the following as either A, E, I, or O propositions.
10. Those books are in the Bible.
A. “They” = “[all] the people in this group to which I refer.”
52
Identify the following as either A, E, I, or O propositions.
11. Not all preachers are Protestant.
O. This can be either UN or PN depending on how one sees it. Because
“All … are not …” really means “Not all are …,” or “Some … are not …,”
we will always interpret these as PN. It might help if you rewrite the
sentence each time you see it.
53
Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.
1. All enemies of Christ will be defeated.
1. A: Distributed (D), Undistributed (U)
54
Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.
2. No nonbelievers can understand the things of the Spirit.
2. E: D, D
55
Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.
3. The Apostle John is the disciple whom Jesus loved.
3. A: D, U
56
Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.
4. The Bible is the Word of God.
4. A: D, U
57
Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.
5. Some roads lead to destruction.
5. I: U, U
58
Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.
6. Some who are standing here will see the kingdom of God.
6. I: U, U
59
Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.
7. Most atheists are immoral.
7. I: U, U; “Most” is not all, but is only some.
60
Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.
8. All unhappy people are not nonbelievers.
8. O: U, D; Remember “All … are not …” rule (Because
“All … are not …” really means “Not all are …,” or “Some … are not …,”
we will always interpret these as PN. It might help if you rewrite the
sentence each time you see it.)
61
Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.
9. Judy is not being a good witness for Christ.
9. E: D, D
62
Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.
10. Some Christians are not nonsmokers.
10. O: U, D
63
Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.
11. These arguments are ineffective for Christianity.
11. A: D, U
64
Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.
12. Christ is impeccable.
12. A: D, U
65
Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.
13. Some who obey Christ are not unfulfilled.
13. O: U, D
66
Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.
14. No nonChristians will see heaven.
14. E: D, D
67
Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.
15. Immoral persons can’t be trusted.
Because this is missing the copula, it can be difficult to figure out. It can
actually be stated two different ways. The easiest is “Immoral persons are
persons who can’t be trusted.” It would then be A: D, U. However you can
also say “Immoral persons are not persons you can trust” which would be
E: D, D. Although either would be acceptable, in general, you should use
the one that changes the original the least.
68
Identify the
type and distribution of the following propositions.
1. Nothing ventured, nothing gained.
1. A: D, U; just insert a copula.
69
Identify the
type and distribution of the following propositions.
2. God loves you.
2. A: D, U
70
Identify the
type and distribution of the following propositions.
3. Some person is not going to heaven.
E: D, D; “Some person” is singular (not “Some persons”) and for
our purposes, singulars are always treated as universals.
71
Identify the
type and distribution of the following propositions.
4. All atheists are not cruel.
4. O: U, D
72
Identify the
type and distribution of the following propositions.
5. Not to trust Christ is to disobey Scripture.
5. A: D, U; the ‘not’ here modifies the subject term, not the copula.
73
Identify the
type and distribution of the following propositions.
6. All who are not guilty are innocent.
A: D, U; the ‘not’ here modifies the subject term, not the copula.
74
Identify the
type and distribution of the following propositions.
7. Something is better than nothing.
7. A: D, U; “something” is singular.
75
Identify the
type and distribution of the following propositions.
8. None but believers will go to heaven.
This is what is called an exclusive sentence. Another way to put it
would be “Only believers will go to heaven.” Exclusive sentences
need to be changed into an A, E, I, or O proposition before we can
work with them. This is a two-step process: 1) change “only” or “none
but” to “all” and 2) switch the subject and the predicate terms. So our
original sentence becomes “All who go to heaven are believers,”
which is A: D, U.
76
Identify the
type and distribution of the following propositions.
9. Everyone except George became a Christian at last night’s meeting.
This is what is called an exceptive sentence. It also needs to be
changed into an A, E, I, or O proposition. However, we have a couple
of different options to choose from. This example could be translated,
“All who are not George became Christians at last night’s meeting,”
which would be A: D, U (the “are not” here is modifying the subject
term, not the copula). It could be translated, “George is not someone
who became a Christian at last night’s meeting,” which is E: D, D.
There is no preference for which you use, either will work.
77
Identify the
type and distribution of the following propositions.
10. Only Jesus can answer the world’s problems.
This is what is called an exclusive sentence. Exclusive sentences
need to be changed into an A, E, I, or O proposition before we can
work with them. This is a two-step process: 1) change “only” or “none
but” to “all” and 2) switch the subject and the predicate terms. So our
original sentence becomes “All the answers to the world’s problems are answers found
in Jesus”; A: D, U
78
Identify the major (M), minor (m), and middle (mid) terms and major (M)
and minor (m) premises in the following syllogisms.
All agnostics deny any knowledge of God.
Those who deny any knowledge of God do not make
sense.
Agnostics do not make sense.
m mid
1. All agnostics deny any knowledge of God. (m)
mid M
Those who deny any knowledge of God do not make sense. (M)
m M
Agnostics do not make sense.
79
Identify the major (M), minor (m), and middle (mid) terms and major (M)
and minor (m) premises in the following syllogisms.
Some people attend church.
All Christians attend church.
Some people are Christians.
m mid
2. Some people attend church. (m)
M mid
All Christians attend church. (M)
m M
Some people are Christians.
80
Identify the major (M), minor (m), and middle (mid) terms and major (M)
and minor (m) premises in the following syllogisms.
Everything that has a beginning must have had a cause.
The universe had a beginning.
The universe must have had a cause.
mid M
3. Everything that has a beginning must have had a cause. (M)
m mid
The universe had a beginning. (m)
m M
The universe must have had a cause.
81
Identify the major (M), minor (m), and middle (mid) terms and major (M)
and minor (m) premises in the following syllogisms.
Some atheists are not moral.
Renee is an atheist.
Renee is not moral.
mid M
4. Some atheists are not moral. (M)
m mid
Renee is an atheist. (m)
m M
Renee is not moral.
82
Identify the major (M), minor (m), and middle (mid) terms and major (M)
and minor (m) premises in the following syllogisms.
No books of the Bible are in error.
Some books of the Bible are books written by Paul.
All books written by Paul are not in error.
mid M
5. No books of the Bible are in error. (M)
mid m
Some books of the Bible are books written by Paul. (m)
m M
All books written by Paul are not in error.
83
Identify the major (M), minor (m), and middle (mid) terms and major (M)
and minor (m) premises in the following syllogisms.
All men are sinners.
I am a man.
I am a sinner.
mid M
6. All men are sinners. (M)
m mid
I am a man. (m)
m M
I am a sinner.
84
Identify the major (M), minor (m), and middle (mid) terms and major (M)
and minor (m) premises in the following syllogisms.
All S is M.
No M is P.
No S is P.
m mid
7. All S is M. (m)
mid M
No M is P. (M)
m M
No S is P.
85
Identify the major (M), minor (m), and middle (mid) terms and major (M)
and minor (m) premises in the following syllogisms.
The Bible is the Word of God.
The Word of God cannot err.
The Bible cannot err.
m mid
8. The Bible is the Word of God. (m)
mid M
The Word of God cannot err. (M)
m M
The Bible cannot err.
86
Identify the major (M), minor (m), and middle (mid) terms and major (M)
and minor (m) premises in the following syllogisms.
All who have faith in Jesus are saved.
Sharon does not have faith in Jesus.
Sharon is not saved.
mid M
9. All who have faith in Jesus are saved. (M)
m mid
Sharon does not have faith in Jesus. (m)
m M
Sharon is not saved.
87
Identify the major (M), minor (m), and middle (mid) terms and major (M)
and minor (m) premises in the following syllogisms.
Those who obey Christ are believers.
Some Christians do not obey Christ.
Some Christians are not believers.
mid M
10. Those who obey Christ are believers. (M)
m mid
Some Christians do not obey Christ. (m)
m M
Some Christians are not believers.
88
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
1. No Christians are unsaved.
Some people are unsaved.
Some people are not Christians.
Valid
89
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
2. Every a is b.
Every b is c.
Every c is a.
2. Invalid, illicit minor (Im)
90
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
3. Nothing is better than heaven.
Life on earth is better than nothing.
Life on earth is better than heaven.
3. Invalid, four terms (4T)
91
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
4. No a is b.
No b is c.
No c is a.
4. Invalid, exclusive premises (EP) (i.e., conclusion drawn from two
negative premises)
92
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
5. All men are substances.
All who are saved are substances.
All who are saved are men.
5. Invalid, undistributed middle (UM)
93
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
6. No P is Q.
Some S is P.
Some S is not Q.
Valid
94
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
7. Some believers are Americans.
Some church attenders are not Americans.
Some believers are church attenders.
7. Invalid, weaker premise (WP)
95
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
8. All Bible manuscripts have errors.
Some errors are certain.
No manuscripts are certain.
8. Invalid, two affirmative premises/negative conclusion (NC). (This
also commits the fourterm fallacy, since “have errors” means “are
manuscripts that have errors,” which is not identical to “errors” in the
second premise.)
96
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
9. All that exists is matter.
God is not matter.
God does not exist.
Valid
97
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
10. A moral absolute is necessary.
God is necessary.
God is the moral absolute.
10. Invalid, UM
98
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
11. Miracles do not exist.
Miracles prove the existence of God.
Proof of the existence of God does not exist.
11. Invalid, Im
99
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
12. Evil is not a substance.
All substances are created by God.
Evil is not created by God.
12. Invalid, Illicit Major IM
100
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
13. Jesus Christ is not a sinner.
Jesus Christ rose from the dead.
Jesus Christ is God.
13. Invalid, 4T
101
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
14. No unbelievers are heaven-bound.
Some who are heaven-bound are not church attenders.
Some unbelievers are not church attenders.
14. Invalid, EP
102
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
15. What can be perceived with our senses is true.
The existence of the soul is not perceived with our
senses.
The existence of the soul is not true.
15. Invalid, (IM)
103
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
1. All agnostics deny any knowledge of God.
Those who deny any knowledge of God do not make
sense.
Agnostics do not make sense.
1. Valid
104
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
2. Some people attend church.
All Christians attend church.
Some people are Christians.
2. Invalid, UM
105
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
3. Everything that has a beginning must have had a cause.
The universe had a beginning.
The universe must have had a cause.
3. Valid
106
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
4. Some atheists are not moral.
Renee is an atheist.
Renee is not moral.
4. Invalid, UM
107
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
5. No books of the Bible are in error.
Some books of the Bible are books written by Paul.
All books written by Paul are not in error.
5. Invalid, Im
108
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
6. All men are sinners.
I am a man.
I am a sinner.
6. Valid
109
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
7. All S is M.
No M is P.
No S is P.
7. Valid
110
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
8. The Bible is the Word of God.
The Word of God cannot err.
The Bible cannot err.
8. Valid
111
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
9. All who have faith in Jesus are saved.
Sharon does not have faith in Jesus.
Sharon is not saved.
9. Invalid, IM
112
Determine the validity or
invalidity of the following syllogisms. If any are invalid, name the rule being
broken.
Remember: The validity of an argument does not make it true
and truthfulness does not make an argument valid. Don’t be fooled!
10. Those who obey Christ are believers.
Some Christians do not obey Christ.
Some Christians are not believers.
10. Invalid, IM
113
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
1. All agnostics deny any knowledge of God.
Those who deny any knowledge of God do not make
sense.
Agnostics do not make sense.
1
114
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
2. Some people attend church.
All Christians attend church.
Some people are Christians.
2
115
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
3. Everything that has a beginning must have had a cause.
The universe had a beginning.
The universe must have had a cause.
1
116
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
4. Some atheists are not moral.
Renee is an atheist.
Renee is not moral.
1
117
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
5. No books of the Bible are in error.
Some books of the Bible are books written by Paul.
All books written by Paul are not in error.
3
118
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
6. All men are sinners.
I am a man.
I am a sinner.
1
119
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
7. All S is M.
No M is P.
No S is P.
1
120
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
8. The Bible is the Word of God.
The Word of God cannot err.
The Bible cannot err.
1
121
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
9. All who have faith in Jesus are saved.
Sharon does not have faith in Jesus.
Sharon is not saved.
1
122
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
10. Those who obey Christ are believers.
Some Christians do not obey Christ.
Some Christians are not believers.
1
123
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
1. No Christians are unsaved.
Some people are unsaved.
Some people are not Christians.
2
124
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
2. Every a is b.
Every b is c.
Every c is a.
4
125
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
3. Nothing is better than heaven.
Life on earth is better than nothing.
Life on earth is better than heaven.
No figure. A middle term must occur in both premises and not in the conclusion. Syllogisms that commit the four-term fallacy have no middle term. So since figure is determined by placement of the middle term, such syllogisms have no figure.
126
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
4. No a is b.
No b is c.
No c is a.
4
127
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
5. All men are substances.
All who are saved are substances.
All who are saved are men.
2
128
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
6. No P is Q.
Some S is P.
Some S is not Q.
1
129
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
7. Some believers are Americans.
Some church attenders are not Americans.
Some believers are church attenders.
2
130
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
8. All Bible manuscripts have errors.
Some errors are certain.
No manuscripts are certain.
1
131
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
9. All that exists is matter.
God is not matter.
God does not exist.
2
132
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
10. A moral absolute is necessary.
God is necessary.
God is the moral absolute.
2
133
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
11. Miracles do not exist.
Miracles prove the existence of God.
Proof of the existence of God does not exist.
3
134
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
12. Evil is not a substance.
All substances are created by God.
Evil is not created by God.
1
135
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
13. Jesus Christ is not a sinner.
Jesus Christ rose from the dead.
Jesus Christ is God.
No figure. A middle term must occur in both premises and not in the conclusion. Syllogisms that commit the four-term fallacy have no middle term. So since figure is determined by placement of the middle term, such syllogisms have no figure.
136
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
14. No unbelievers are heaven-bound.
Some who are heaven-bound are not church attenders.
Some unbelievers are not church attenders.
1
137
Identify the figure of the middle
term for each syllogism. Remember that the figure depends on placing the major
premise first.
Fig 1 Fig 2 Fig 3 Fig 4
Major Prem M P P M M P P M
\ | | /
Minor Prem S M S M M S M S
15. What can be perceived with our senses is true.
The existence of the soul is not perceived with our
senses.
The existence of the soul is not true.
1
138
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
1. All agnostics deny any knowledge of God.
Those who deny any knowledge of God do not make
sense.
Agnostics do not make sense.
AAA. ("Not" modifies the terms, not the copulas, in the propositions.)
139
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
2. Some people attend church.
All Christians attend church.
Some people are Christians.
AII (Notice that mood lists major premise first, minor premise second, and conclusion last.
140
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
3. Everything that has a beginning must have had a cause.
The universe had a beginning.
The universe must have had a cause.
AAA
141
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
4. Some atheists are not moral.
Renee is an atheist.
Renee is not moral.
OAE
142
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
5. No books of the Bible are in error.
Some books of the Bible are books written by Paul.
All books written by Paul are not in error.
EII
143
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
6. All men are sinners.
I am a man.
I am a sinner.
AAA
144
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
7. All S is M.
No M is P.
No S is P.
AEE
145
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
8. The Bible is the Word of God.
The Word of God cannot err.
The Bible cannot err.
AAA
146
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
9. All who have faith in Jesus are saved.
Sharon does not have faith in Jesus.
Sharon is not saved.
AEE
147
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
10. Those who obey Christ are believers.
Some Christians do not obey Christ.
Some Christians are not believers.
AOO
148
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
1. No Christians are unsaved.
Some people are unsaved.
Some people are not Christians.
EIO
149
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
2. Every a is b.
Every b is c.
Every c is a.
AAA
150
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
3. Nothing is better than heaven.
Life on earth is better than nothing.
Life on earth is better than heaven.
EAA (Notice that "Nothing" in the major premise is really "no thing.")
151
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
4. No a is b.
No b is c.
No c is a.
EEE
152
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
5. All men are substances.
All who are saved are substances.
All who are saved are men.
AAA
153
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
6. No P is Q.
Some S is P.
Some S is not Q.
EIO
154
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
7. Some believers are Americans.
Some church attenders are not Americans.
Some believers are church attenders.
OII
155
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
8. All Bible manuscripts have errors.
Some errors are certain.
No manuscripts are certain.
IAE
156
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
9. All that exists is matter.
God is not matter.
God does not exist.
AEE
157
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
10. A moral absolute is necessary.
God is necessary.
God is the moral absolute.
AAA
158
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
11. Miracles do not exist.
Miracles prove the existence of God.
Proof of the existence of God does not exist.
EAE
159
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
12. Evil is not a substance.
All substances are created by God.
Evil is not created by God.
AEE
160
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
13. Jesus Christ is not a sinner.
Jesus Christ rose from the dead.
Jesus Christ is God.
EAA
161
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
14. No unbelievers are heaven-bound.
Some who are heaven-bound are not church attenders.
Some unbelievers are not church attenders.
EOO
162
Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.
15. What can be perceived with our senses is true.
The existence of the soul is not perceived with our
senses.
The existence of the soul is not true.
AEE
163
Obvert the following proposition:
1. All believers are saved.
1. No believers are nonsaved people.
164
Obvert the following proposition:
2. Some arguments for God are not valid.
2. Some arguments for God are nonvalid.
165
Obvert the following proposition:
3. Jesus Christ is God.
3. Jesus Christ is not non-God.
166
Obvert the following proposition:
4. No person is righteous.
4. All persons are unrighteous (or nonrighteous).
167
Obvert the following proposition:
5. Some atheists are immoral.
5. Some atheists are not moral (or non-immoral).
168
Obvert the following proposition:
6. Morality is universally recognized.
6. Morality is not non-universally recognized.
169
Obvert the following proposition:
7. All nonbelievers are unsaved.
7. No nonbelievers are saved (or non-unsaved).
170
Obvert the following proposition:
8. No book of the Bible is uninspired.
8. All books of the Bible are inspired (or non-uninspired).
171
Obvert the following proposition:
9. Some philosophers are not nonChristians.
9. Some philosophers are Christians (or non-non-Christians).
172
Obvert the following proposition:
10. God is a necessary being.
10. God is not a non-necessary being.
173
Convert the following proposition:
1. Some angels are fallen.
1. Some fallen beings are angels.
174
Convert the following proposition:
2. No theologians are infallible.
2. No infallible persons are theologians.
175
Convert the following proposition:
3. All the books in the Bible are inerrant.
3. Some inerrant things are books in the Bible.
176
Convert the following proposition:
4. Tom is not a believer.
4. None of all the believers is Tom.
177
Convert the following proposition:
5. Some deists are not British.
5. Not convertible.
178
Convert the following proposition:
6. Some people are unsaved.
6. Some unsaved beings are people.
179
Convert the following proposition:
7. Tom is a nonbeliever.
7. One of the nonbelievers is Tom.
180
Contrapose the following proposition:
1. All religions are unequal.
1. All equal movements are nonreligions.
181
Contrapose the following proposition:
2. Some nonbelievers are not unkind.
2. Some kind people are not believers.
182
Contrapose the following proposition:
3. No Christians are nonbelievers.
3. Some believers are not nonChristians.
183
Contrapose the following proposition:
4. Some beliefs are not unwarranted.
4. Some warranted ideas are not nonbeliefs.
184
Contrapose the following proposition:
5. The Bible is invaluable.
5. All non-invaluable books are nonBibles. Note: “valuable” is not the
negation of “invaluable.”
185
Contrapose the following proposition:
6. Some logical statements are almost impossible to understand.
6. Not contraposable.
186
Contrapose the following proposition:
7. All non-atheists are believers.
7. All nonbelievers are atheists.
187
Contrapose the following proposition:
8. No book of the Bible is incorrect.
8. Some correct writings are not books not of the Bible (or “nonbooks
of the Bible”).
188
Contrapose the following proposition:
9. Nonhumans are unintelligent.
9. Intelligent beings are human.
189
Contrapose the following proposition:
10. Some propositions are not contraposable.
10. Some contraposable statements are not nonpropositions.
190
Using the Square of Opposition, along with the relationships of
independence and equivalence, determine the truth value (i.e., true, false, or
undetermined) of the propositions that follow the original.
1. “All atheists are enemies of Christ.” is true:
a. No atheists are enemies of Christ.
b. Some atheists are enemies of Christ.
c. Some atheists are not enemies of Christ.
1. a. F
b. T
c. F
191
Using the Square of Opposition, along with the relationships of
independence and equivalence, determine the truth value (i.e., true, false, or
undetermined) of the propositions that follow the original.
2. “No people are seeking God.” is true:
a. Some people are seeking God.
b. All people are seeking God.
c. No seekers after God are people.
2. a. F
b. F
c. Equivalent, T
192
Using the Square of Opposition, along with the relationships of
independence and equivalence, determine the truth value (i.e., true, false, or
undetermined) of the propositions that follow the original.
3. “Some humans are nonbelievers.” is false:
a. No humans are nonbelievers.
b. All believers are people.
c. Some humans are not nonbelievers.
3. a. T
b. Independent, U
c. T
193
Using the Square of Opposition, along with the relationships of
independence and equivalence, determine the truth value (i.e., true, false, or
undetermined) of the propositions that follow the original.
4. “No books of the Bible are inerrant.” is false:
a. All books of the Bible are inerrant.
b. Some books of the Bible are not inerrant.
c. All books of the Bible are errant.
4. a. U
b. U
c. Equivalent, F
194
Using the Square of Opposition, along with the relationships of
independence and equivalence, determine the truth value (i.e., true, false, or
undetermined) of the propositions that follow the original.
5. “Some atheists are not immoral.” is true:
a. Some immoral persons are not atheists.
b. No atheists are immoral.
c. All atheists are not immoral.
5. a. U
b. U
c. Equivalent, T
195
Using the Square of Opposition, along with the relationships of
independence and equivalence, determine the truth value (i.e., true, false, or
undetermined) of the propositions that follow the original.
6. “All biblical manuscripts are erroneous.” is true:
a. No nonbiblical manuscripts are erroneous.
b. All non-erroneous things are biblical manuscripts.
c. No non-erroneous things are nonbiblical manuscripts.
6. a. Independent, U
b. Independent, U
c. Independent, U
196
Using the Square of Opposition, along with the relationships of
independence and equivalence, determine the truth value (i.e., true, false, or
undetermined) of the propositions that follow the original.
7. “Some P is not Q.” is false:
a. All P is Q.
b. No P is Q.
c. Some P is Q.
7. a. T
b. F
c. T
197
Using the Square of Opposition, along with the relationships of
independence and equivalence, determine the truth value (i.e., true, false, or
undetermined) of the propositions that follow the original.
8. “No religion is completely wrong.” is true:
a. Some religions are completely wrong.
b. No completely wrong things are religions.
c. All religions are completely wrong.
8. a. F
b. Equivalent, T
c. F
198
Using the Square of Opposition, along with the relationships of
independence and equivalence, determine the truth value (i.e., true, false, or
undetermined) of the propositions that follow the original.
9. “All created things are contingent.” is true:
a. No created things are contingent.
b. Some created things are contingent.
c. Some created things are not contingent.
9. a. F
b. T
c. F
199
Using the Square of Opposition, along with the relationships of
independence and equivalence, determine the truth value (i.e., true, false, or
undetermined) of the propositions that follow the original.
10. “All created things are contingent.” is false:
a. No created things are contingent.
b. Some created things are contingent.
c. Some created things are not contingent.
10. a. U
b. U
c. T
200
Determine the validity or invalidity of the following arguments. If any are invalid
explain why. You may have to change (obvert, convert, contrapose) some of the
premises before determining validity. These are tricky, so think hard.
1. Julie loves Jesus.
Paul loves Julie.
Paul loves Jesus.
1. Invalid, 4T. I call this the “lovers triangle fallacy” and it’s a good
one to remember. Although it appears to have only three terms, it
actually has four. Let’s put it in standard logical form:
Julie is a lover of Jesus.
Paul is a lover of Julie.
Paul is a lover of Jesus.
See the four terms: “Julie,” “lover of Jesus,” “Paul,” and “lover of
Julie.” Be careful of those missing copulas!
201
Determine the validity or invalidity of the following arguments. If any are invalid
explain why. You may have to change (obvert, convert, contrapose) some of the
premises before determining validity. These are tricky, so think hard.
2. All atheists are nonbelievers.
All believers are going to heaven.
No atheists are going to heaven.
2. Invalid. Obvert the first premise to “No atheists are believers.” The
resulting syllogism is Figure 1 and mood AEE (notice which premise
has the major term). That mood is never valid in that figure. This is the
fallacy of Illicit Major because the major premise does not tell us that
all who go to heaven are believers.
202
Determine the validity or invalidity of the following arguments. If any are invalid
explain why. You may have to change (obvert, convert, contrapose) some of the
premises before determining validity. These are tricky, so think hard.
3. Since some Christians are good debaters, it follows that
some Christians are not good debaters.
3. Invalid. Using the square of opposition, and given that the first
proposition (I) is true, then the second proposition (O) is
undetermined. Since the argument is claiming the second proposition
is true, based only on the first proposition, it is invalid. This particular
invalidity is called illicit subcontrary.
203
Determine the validity or invalidity of the following arguments. If any are invalid
explain why. You may have to change (obvert, convert, contrapose) some of the
premises before determining validity. These are tricky, so think hard.
4. All who are not guilty are innocent.
Some are not guilty.
Some are innocent.
4. Valid. “Not” is modifying the predicate term “guilty” in the minor
(second) premise and not the copula. It was established as part of the
middle term in the major premise.
204
Determine the validity or invalidity of the following arguments. If any are invalid
explain why. You may have to change (obvert, convert, contrapose) some of the
premises before determining validity. These are tricky, so think hard.
5. All religious persons are moral persons.
All immoral persons are scoundrels.
No religious persons are scoundrels.
5. Invalid, IM. Obvert the first premise.
205
Determine the validity or invalidity of the following arguments. If any are invalid
explain why. You may have to change (obvert, convert, contrapose) some of the
premises before determining validity. These are tricky, so think hard.
6. Not to obey the Bible is to disobey God.
Not to evangelize is not to obey the Bible.
Not to evangelize is to disobey God.
6. Valid. Use the square of opposition again.
206
Determine the validity or invalidity of the following arguments. If any are invalid
explain why. You may have to change (obvert, convert, contrapose) some of the
premises before determining validity. These are tricky, so think hard.
7. Since no religious person is completely in the dark, it is
false that some religious persons are completely in the
dark.
7. Valid.
207
Determine the validity or invalidity of the following arguments. If any are invalid
explain why. You may have to change (obvert, convert, contrapose) some of the
premises before determining validity. These are tricky, so think hard.
8. Only people are savable.
Some living things are savable.
All people are living things.
8. Invalid, Im. The first premise is an exclusive statement.
208
Determine the validity or invalidity of the following arguments. If any are invalid
explain why. You may have to change (obvert, convert, contrapose) some of the
premises before determining validity. These are tricky, so think hard.
9. No P are M.
All S are M.
Some S are not P.
9. Valid. This falls under the category of a weaker conclusion.
(Caution: in some texts this would be considered invalid due to the
“existential fallacy.” However, this doesn’t concern us in this text.)
209
Determine the validity or invalidity of the following arguments. If any are invalid
explain why. You may have to change (obvert, convert, contrapose) some of the
premises before determining validity. These are tricky, so think hard.
10. All explosives are flammable.
All inflammable things are unsafe.
All safe things are nonexplosives.
10. Valid. A really tricky one. First, remember that “flammable” and
“inflammable” mean the same thing and can be treated as the same word.
Second, you want to avoid changing the conclusion, so always hold it off to
last. If you contrapose both premises, you’ll see the light.
210
Put the following hypothetical arguments into symbolic logic. Determine
if they are using modus ponens or modus tollens and if they are either valid or
invalid. If any are invalid, explain which fallacy they are committing.
1. If God exists, then man has meaning in life.
Man has meaning in life.
God must exist.
G>M
M
^ G Invalid, Affirming the Consequence
211
Put the following hypothetical arguments into symbolic logic. Determine
if they are using modus ponens or modus tollens and if they are either valid or
invalid. If any are invalid, explain which fallacy they are committing.
2. If Christ did not rise from the dead, then we are lost in
our sins. (1 Cor. 15:17)
It is not the case that Christ did not rise from the dead. We are not lost
in our sins.
~C>L
~(~C)
^~L Invalid, Denying the Antecident
212
Put the following hypothetical arguments into symbolic logic. Determine
if they are using modus ponens or modus tollens and if they are either valid or
invalid. If any are invalid, explain which fallacy they are committing.
3. If the Bible is the word of God, then it is inerrant.
The Bible is the word of God.
It is inerrant.
B>I
B
^I Valid, Modus Ponens
213
Put the following hypothetical arguments into symbolic logic. Determine
if they are using modus ponens or modus tollens and if they are either valid or
invalid. If any are invalid, explain which fallacy they are committing.
4. Sally will go to church, if she becomes a Christian.
Sally went to church.
She became a Christian.
C>S
S
^C Invalid, Affirming the Consequent
214
Put the following hypothetical arguments into symbolic logic. Determine
if they are using modus ponens or modus tollens and if they are either valid or
invalid. If any are invalid, explain which fallacy they are committing.
5. If evolution is true, then the second law of thermodynamics
is wrong.
But the second law of thermodynamics is not wrong.
Evolution is not true.
E>~S
~(~S)
^~E Valid, Modus Tollens
215
Put the following hypothetical arguments into symbolic logic. Determine
if they are using modus ponens or modus tollens and if they are either valid or
invalid. If any are invalid, explain which fallacy they are committing.
6. Christ deceived the apostles concerning his resurrection,
if he did not rise in the same physical body he died in.
Christ cannot deceive the apostles concerning his resurrection.
Christ rose in the same body he died in.
~R>D
~D
^~(~R) Valid, Modus Tollens
216
Put the following hypothetical arguments into symbolic logic. Determine
if they are using modus ponens or modus tollens and if they are either valid or
invalid. If any are invalid, explain which fallacy they are committing.
7. If two propositions contradict, then they both can’t be
true.
These two propositions don’t contradict.
They both must be true.
C>~T
~C
^~(~T) Invalid, Denying the Antecendent
217
Put the following hypothetical arguments into symbolic logic. Determine
if they are using modus ponens or modus tollens and if they are either valid or
invalid. If any are invalid, explain which fallacy they are committing.
8. If the antecedent is affirmed in a hypothetical syllogism,
then it is valid.
The antecedent is affirmed in this hypothetical syllogism.
It is valid.
A>V
A
^V Valid, Modus Ponens
218
Put the following hypothetical arguments into symbolic logic. Determine
if they are using modus ponens or modus tollens and if they are either valid or
invalid. If any are invalid, explain which fallacy they are committing.
9. There must be a necessary being, if the universe has a
cause.
The universe has a cause.
There must be a necessary being.
C>N
C
^N Valid, Modus Ponens
219
Put the following hypothetical arguments into symbolic logic. Determine
if they are using modus ponens or modus tollens and if they are either valid or
invalid. If any are invalid, explain which fallacy they are committing.
10. If God exists, then miracles are possible.
Miracles are possible.
God must exist.
G>M
M
^G Invalid, Affirming the Consequent
220
Put the following disjunctive syllogisms into symbolic logic. Determine if
they are either valid or invalid. If any are invalid, explain the fallacy being
committed.
1. Either God exists or he doesn’t exist.
It is not the case that God doesn’t exist.
God exists.
Ev~E
~(~E)
^E Valid
221
Put the following disjunctive syllogisms into symbolic logic. Determine if
they are either valid or invalid. If any are invalid, explain the fallacy being
committed.
2. Either Jesus rose from the dead or he is not God.
Jesus rose from the dead.
He is God.
Rv~G
R
^G Invalid, Affirmed the Alternant
222
Put the following disjunctive syllogisms into symbolic logic. Determine if
they are either valid or invalid. If any are invalid, explain the fallacy being
committed.
3. Either God exists or evil exists.
Evil exists. God doesn’t exist.
GvE
E
^~G Invalid, Affirmed the Alternant
223
Put the following disjunctive syllogisms into symbolic logic. Determine if
they are either valid or invalid. If any are invalid, explain the fallacy being
committed.
4. Either the law of entropy is not true or the universe had
a beginning.
The law of entropy is not ‘not true.’
The universe had a beginning.
Uv~E
~(~E)
^U Valid
224
Put the following disjunctive syllogisms into symbolic logic. Determine if
they are either valid or invalid. If any are invalid, explain the fallacy being
committed.
5. Either Christ fulfilled the prophecies concerning the
Messiah or the Bible is untrustworthy.
Christ fulfilled prophecies concerning the Messiah.
The Bible is trustworthy.
FvU
F
^U Invalid, Affirmed the Alternant
225
Put the following dilemmas into symbolic logic. Determine if they are
constructive or destructive. Then determine if they are valid or invalid. If any are
invalid, explain the fallacy being committed.
1. If you trust Christ, then you will go to heaven, and if
you don’t trust Christ, then you will go to hell.
But, either you trust Christ or you don’t.
So either you go to heaven or you go to hell.
(T>H).(~T>L)
Tv~T
^HvL Valid, Constructive Dilemma
226
Put the following dilemmas into symbolic logic. Determine if they are
constructive or destructive. Then determine if they are valid or invalid. If any are
invalid, explain the fallacy being committed.
2. If atheism is true, then there is no possibility for meaning
in life, and if theism is true, then there is the potential
for a meaningful life.
There is either no meaning in life or there does exist the
potential for a meaningful life.
So either atheism is true or theism is true.
(A>~M).(T>M)
~MvM
^AvT Invalid, Affirming the Consequent
227
Put the following dilemmas into symbolic logic. Determine if they are
constructive or destructive. Then determine if they are valid or invalid. If any are
invalid, explain the fallacy being committed.
3. If the conclusion of a syllogism just states something already given in the premises, then it adds nothing to our knowledge and is useless, and if the conclusion states something not contained in the premises, then it is invalid.
So, either the conclusion just states something already
given in the premises, or it states something not contained in the premises.
Therefore all syllogisms are either useless or invalid.
(G>U).(N>I)
GvN
^UvI Valid, Constructive Dilemma
228
Put the following dilemmas into symbolic logic. Determine if they are
constructive or destructive. Then determine if they are valid or invalid. If any are
invalid, explain the fallacy being committed.
4. If the Bible can be trusted, then Jesus rose from the
dead, and if Jesus did not rise from the dead, then we
have no hope for salvation.
This means that either the Bible can be trusted or there
is no hope for salvation.
So either Christ rose from the dead or he didn’t.
(B>J).(~J>~H)
Bv~H
^Jv~J Invalid, Affirmed one consequent
229
Put the following dilemmas into symbolic logic. Determine if they are
constructive or destructive. Then determine if they are valid or invalid. If any are
invalid, explain the fallacy being committed.
5. If evil exists, then God cannot be omnipotent, and if evil
exists, then he cannot be omnibenevolent.
However, it is not true either that God is not omnipotent
or that he is not omnibenevolent.
So evil doesn’t exist.
(E>~P).(E>~B)
~(~Pv~B)
^~E Valid, Destructive Dilemma
230
Put the following dilemmas into symbolic logic. Determine if they are
constructive or destructive. Then determine if they are valid or invalid. If any are
invalid, explain the fallacy being committed.
6. If there is morality, then there must be a moral law
maker, and if there is a moral law maker, then there is a
God.
Either there is a moral law maker or there isn’t one.
Hence either there is morality or there is no God.
(M>L).(LvG)
Lv~L
^Mv~G Invalid, Denied one consequent
231
Put the following dilemmas into symbolic logic. Determine if they are
constructive or destructive. Then determine if they are valid or invalid. If any are
invalid, explain the fallacy being committed.
7. If God exists, then his existence is necessary, and if he
doesn’t exist, then his existence is impossible.
Either God exists or he doesn’t exist.
Therefore his existence is either necessary or impossible.
(G>N).(~G>I)
Gv~G
^NvI Valid, Constructive Dilemma
232
Put the following dilemmas into symbolic logic. Determine if they are
constructive or destructive. Then determine if they are valid or invalid. If any are
invalid, explain the fallacy being committed.
8. If Jesus is God, then he fulfilled prophecy, and if Jesus is
God, then he performed miracles.
It is not the case that Jesus either fulfilled prophecy or
performed miracles.
So, Jesus is not God.
(J>F).(J>M)
~(FvM)
^~J Valid, Destructive Dilemma
233
Put the following dilemmas into symbolic logic. Determine if they are
constructive or destructive. Then determine if they are valid or invalid. If any are
invalid, explain the fallacy being committed.
9. If atheists are not wise, then Christians are, and if the
Bible is the source of wisdom, then those who do not
read it will not be wise.
Either Christians are wise or those who don’t read the
Bible won’t be wise.
Hence, either atheists are wise or the Bible is the source of
wisdom.
(A>C).(B>T)
CvT
^AvB Invalid, Affirming the Consequent
234
Put the following dilemmas into symbolic logic. Determine if they are
constructive or destructive. Then determine if they are valid or invalid. If any are
invalid, explain the fallacy being committed.
10. If those who attend church regularly grow spiritually,
then it vindicates church attendance, and if those who
read their Bible regularly grow spiritually, then it vindicates
Bible reading.
However, neither church attendance nor Bible reading
has been vindicated.
So, neither attending church nor reading the Bible helps
spiritual growth.
(C>A).(R>B)
~(AvB)
^~(CvR) Valid, Destructive Dilemma
235
For those dilemmas that are valid, suggest a
refutation for them by either going between the horns, taking the dilemma by the
horns, or countering the dilemma.
1. If you trust Christ, then you will go to heaven, and if
you don’t trust Christ, then you will go to hell.
But, either you trust Christ or you don’t.
So either you go to heaven or you go to hell.
1. If one accepts the Bible as true, this dilemma cannot be overcome. If
one does not accept the Bible, then you might be challenged to take the
dilemma by the horns and challenge the first premise or counter with a
another dilemma, like purgatory for example. You can’t go through the
horns on this one.
236
For those dilemmas that are valid, suggest a
refutation for them by either going between the horns, taking the dilemma by the
horns, or countering the dilemma.
2. If atheism is true, then there is no possibility for meaning
in life, and if theism is true, then there is the potential
for a meaningful life.
There is either no meaning in life or there does exist the
potential for a meaningful life.
So either atheism is true or theism is true.
Invalid
237
For those dilemmas that are valid, suggest a
refutation for them by either going between the horns, taking the dilemma by the
horns, or countering the dilemma.
3. If the conclusion of a syllogism just states something
already given in the premises, then it adds nothing to
our knowledge and is useless, and if the conclusion
states something not contained in the premises, then it
is invalid.
So, either the conclusion just states something already
given in the premises, or it states something not contained
in the premises.
Therefore all syllogisms are either useless or invalid.
3. You also cannot go through the horns here because there is no third
alternative. However we can grasp the horns and challenge the first
premise. The usefulness of a syllogism is determined by the inference
between the premises drawn in the conclusion. A valid conclusion will
indeed have information from both premises, but it will not have
merely that.
238
For those dilemmas that are valid, suggest a
refutation for them by either going between the horns, taking the dilemma by the
horns, or countering the dilemma.
4. If the Bible can be trusted, then Jesus rose from the
dead, and if Jesus did not rise from the dead, then we
have no hope for salvation.
This means that either the Bible can be trusted or there
is no hope for salvation.
So either Christ rose from the dead or he didn’t.
Invalid
239
For those dilemmas that are valid, suggest a
refutation for them by either going between the horns, taking the dilemma by the
horns, or countering the dilemma.
5. If evil exists, then God cannot be omnipotent, and if evil
exists, then he cannot be omnibenevolent.
However, it is not true either that God is not omnipotent
or that he is not omnibenevolent.
So evil doesn’t exist.
5. The major premise can be denied because it is possible that an omnibenevolent and omnipotent God can use evil in order to achieve a
higher good, or he may create free creatures who can freely choose to
do evil.
240
For those dilemmas that are valid, suggest a
refutation for them by either going between the horns, taking the dilemma by the
horns, or countering the dilemma.
6. If there is morality, then there must be a moral law
maker, and if there is a moral law maker, then there is a
God.
Either there is a moral law maker or there isn’t one.
Hence either there is morality or there is no God.
Invalid
241
For those dilemmas that are valid, suggest a
refutation for them by either going between the horns, taking the dilemma by the
horns, or countering the dilemma.
7. If God exists, then his existence is necessary, and if he
doesn’t exist, then his existence is impossible.
Either God exists or he doesn’t exist.
Therefore his existence is either necessary or impossible.
7. It’s obvious that we’ve exhausted the logical possibilities of the
second premise, so we cannot go through the horns. The only way you
could challenge the first premise is to deny that God is necessary, and
propose that he is merely possible (it would be pretty tough to show
his existence is impossible). Some today do just that; their theory is
called process theology. However that both denies the Bible as literally
true and brings in a lot of other logical problems. Except for that
possibility, this dilemma is not overcomable.
242
For those dilemmas that are valid, suggest a
refutation for them by either going between the horns, taking the dilemma by the
horns, or countering the dilemma.
8. If Jesus is God, then he fulfilled prophecy, and if Jesus is
God, then he performed miracles.
It is not the case that Jesus either fulfilled prophecy or
performed miracles.
So, Jesus is not God.
8. We can take this one right by the horns and affirm that it is not
necessary to Christ’s deity that he either fulfill prophecy or do
miracles. He would be just as divine if a prophecy were never given of
him or if he never performed a miracle. Although once prophecies
were given he had to fulfill them, they are only signs to us of his deity,
not necessary conditions of it.
243
For those dilemmas that are valid, suggest a
refutation for them by either going between the horns, taking the dilemma by the
horns, or countering the dilemma.
9. If atheists are not wise, then Christians are, and if the
Bible is the source of wisdom, then those who do not
read it will not be wise.
Either Christians are wise or those who don’t read the
Bible won’t be wise.
Hence, either atheists are wise or the Bible is the source of
wisdom.
Invalid
244
For those dilemmas that are valid, suggest a
refutation for them by either going between the horns, taking the dilemma by the
horns, or countering the dilemma.
10. If those who attend church regularly grow spiritually,
then it vindicates church attendance, and if those who
read their Bible regularly grow spiritually, then it vindicates
Bible reading.
However, neither church attendance nor Bible reading
has been vindicated.
So, neither attending church nor reading the Bible helps
spiritual growth.
10. The major premise here is too vague to warrant any conclusion. What is
meant by terms like “regularly,” “grow spiritually,” and “vindicates”? Until
we can get a tighter grip on the meaning of these terms and the verifiability
of them, no conclusion follows validly.
245
In the following enthymeme, determine whether the missing statement is a premise or conclusion. Then supply the missing proposition, attempting to create a valid syllogism, if possible. If it is not possible, explain why the syllogism is invalid.
10. I believe nature was created by intelligence, because nature is
complexly designed.
Supply the missing premise: “Everything complexly designed is created by intelligence.”
246
In the following enthymeme, determine whether the missing statement is a premise or conclusion. Then supply the missing proposition, attempting to create a valid syllogism, if possible. If it is not possible, explain why the syllogism is invalid.
Pro-lifers should break the law and block the doors of abortion
clinics, because they are saving lives.
Supply the missing premise: Breaking the law and blocking the
doors of abortion clinics saves lives.
247
In the following enthymeme, determine whether the missing statement is a premise or conclusion. Then supply the missing proposition, attempting to create a valid syllogism, if possible. If it is not possible, explain why the syllogism is invalid.
Jesus Christ did miracles and only someone sent by God can do
miracles.
2. Supply the missing conclusion: Therefore, Jesus Christ was sent by
God.
248
In the following enthymeme, determine whether the missing statement is a premise or conclusion. Then supply the missing proposition, attempting to create a valid syllogism, if possible. If it is not possible, explain why the syllogism is invalid.
If Christianity is not of God, it will die out. Christianity has not died
out.
3. Invalid. The missing conclusion (Therefore Christianity is of God)
does not follow because the resulting syllogism commits the fourterm
fallacy. “Will die out” is future tense and so does not mean the same
thing as “has (not) died out.”
249
In the following enthymeme, determine whether the missing statement is a premise or conclusion. Then supply the missing proposition, attempting to create a valid syllogism, if possible. If it is not possible, explain why the syllogism is invalid.
4. Some believers will suffer loss at the judgment seat of Christ,
however all believers will be saved.
4. Invalid. If you use the first statement as a premise and the second as
the conclusion, you will end up with illicit process. If you switch the
two, you end up with an undistributed middle. If you try to make them
both premises, with believers as the middle term, then you are back to
illicit process.
250
In the following enthymeme, determine whether the missing statement is a premise or conclusion. Then supply the missing proposition, attempting to create a valid syllogism, if possible. If it is not possible, explain why the syllogism is invalid.
5. I know that God exists because something must have started all of
this.
5. This can be reworded without changing the meaning, and then add
the missing premise: Whatever started all this must exist, God started
all this, therefore God must exist. In doing enthymemes, some
rewording is allowed (and even necessary) as long as there is no
significant change in meaning.
251
In the following enthymeme, determine whether the missing statement is a premise or conclusion. Then supply the missing proposition, attempting to create a valid syllogism, if possible. If it is not possible, explain why the syllogism is invalid.
6. To be a Christian you must believe in the bodily resurrection.
Bultmann does not believe in the bodily resurrection.
6. Supply the missing conclusion: Therefore, Bultmann is not a
Christian.
252
In the following enthymeme, determine whether the missing statement is a premise or conclusion. Then supply the missing proposition, attempting to create a valid syllogism, if possible. If it is not possible, explain why the syllogism is invalid.
7. God loves all men and desires that every man be saved.
7. Invalid. There is no argument here.
253
In the following enthymeme, determine whether the missing statement is a premise or conclusion. Then supply the missing proposition, attempting to create a valid syllogism, if possible. If it is not possible, explain why the syllogism is invalid.
Deism teaches that God does not intervene in the world. But, it is
true that Jesus Christ is God.
8. This is kind of tricky and can best be placed in a hypothetical
syllogism: If, as deism teaches, God does not intervene in the world,
then Jesus Christ is not God. However, Jesus Christ is God. (i.e. it is
not true that Jesus Christ is not God.) Therefore, God does intervene
(does not not intervene) in the world (and deism is false). Since we
have denied the consequent, this is a valid syllogism.
254
In the following enthymeme, determine whether the missing statement is a premise or conclusion. Then supply the missing proposition, attempting to create a valid syllogism, if possible. If it is not possible, explain why the syllogism is invalid.
9. Some believers grow spiritually because of their church attendance,
and all Christians go to church.
Invalid. You will end up with either illicit major or undistributed
middle (or both).
255
Determine if the following sorite is valid or invalid, and if invalid explain the fallacy being committed.
1. No P < Q
Q < S
S < T
No P < T
Invalid, Illicit Major
256
Determine if the following sorite is valid or invalid, and if invalid explain the fallacy being committed.
2. All Christians are Bible believers.
Some Bible believers are church attenders.
No church attenders are immoral.
No Christians are immoral.
2. Invalid, Undistributed Middle
257
Determine if the following sorite is valid or invalid, and if invalid explain the fallacy being committed.
3. Some people do not believe in God.
All who do not believe in God sleep in on Sunday morning.
All who sleep in on Sunday morning miss church.
Some people miss church.
3. Valid.
258
Determine if the following sorite is valid or invalid, and if invalid explain the fallacy being committed.
4. Some K < L
No L < non-M
Some non-M non-N
Non-N < O
Some K < O
4. Invalid. A key help to remember is whenever you have two negative
premises or two particular premises in a sorites, it will be invalid. This
one has both!
259
Determine if the following sorite is valid or invalid, and if invalid explain the fallacy being committed.
5. Miracles are possible.
Natural events are not miracles.
The birth of babies is a natural event.
The birth of a baby is not a miracle.
5. Valid. The first premise is superfluous, but the conclusion follows
validly from the remaining premises (Figure 1, Mood EAE). An
argument that validly proves its conclusion from some of its premises
is not made invalid by the presence of superfluous premises (which of
course must not contradict the relevant premises).
260
Determine if the following sorite is valid or invalid, and if invalid explain the fallacy being committed.
6. Some philosophers are Christians.
All Christians are going to heaven.
All who are going to heaven are happy.
Some philosophers are happy.
Valid
261
Determine if the following sorite is valid or invalid, and if invalid explain the fallacy being committed.
7. Wayne needs proof of God’s existence.
Proof of God’s existence can be reasoned through natural arguments.
Reasons given through natural argument are not guarantees that
someone will believe.
Wayne is not a person who is guaranteed to believe.
Valid
262
Determine if the following sorite is valid or invalid, and if invalid explain the fallacy being committed.
8. A < B
B < C
C < D
No D < E
No B < E
5. Valid. The first premise is superfluous, but the conclusion follows
validly from the remaining premises (Figure 1, Mood EAE). An
argument that validly proves its conclusion from some of its premises
is not made invalid by the presence of superfluous premises (which of
course must not contradict the relevant premises).
263
Determine if the following sorite is valid or invalid, and if invalid explain the fallacy being committed.
9. Some Christians reject theistic proofs.
Those who reject theistic proofs are sometimes called fideists.
Not all those who are called fideists are really fideists.
Some Christians are not really fideists.
9. Invalid, Illicit Process
264
Determine if the following sorite is valid or invalid, and if invalid explain the fallacy being committed.
10. Some X < Y
Y < Z
Every Z needs L.
All who need L are P. However, No P < M
Some X is not M.
10. Valid.
265
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
1. Either we should believe in God or we should become nihilists.
We shouldn’t become nihilists.
We should believe in God.
1. Destructive Dilemma, Valid.
265
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
5. If the resurrection is not true, then we are lost in our sins.
It is not the case that the resurrection is not true.
We are not lost in our sins.
5. Hypothetical, Invalid, Denies One Alternant
265
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
4. S < P
Q < P ^ S < Q
4. Categorical, Invalid, UM.
265
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
3. (B> A) . (C> D)
~(A ν D)
~(B ν C)
3. Disjunctive, Valid.
265
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
2. No child abusers are just.
Some atheists are just.
2. Categorical, Invalid, UM.
265
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
7. If the cosmological argument is true, then a personal God exists, and
if the universe is eternal, then the universe is God.
Either the cosmological argument is true or the universe is eternal.
Therefore, either a personal God exists or the universe is God.
7. Constructive Dilemma, Valid.
265
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
6. No A < B.
B < C
C < D
Some D < E
^ No A < E.
6. Sorites, Invalid, IM.
266
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
9. J Q
Q
^ J
Hypothetical, Invalid, AC.
266
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
8. God loves all men.
All men are sinners.
Therefore, God loves sinners.
8. Categorical, Valid. This argument best translates to:
All men are people loved by God.
All men are sinners.
Some sinners are people loved by God.
(Notice that “sinners” in the conclusion is undistributed.)
267
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
10. It is true that Jesus both deliberately tried to fulfill prophecy and is just
a man.
Jesus is not just a man.
So, it is not true that Jesus both deliberately tried to fulfill prophecy and is
just a man.
10. Conjunctive, Valid.
268
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
11. Man is completely free.
God is not a man.
Hence, God is not completely free.
11. Categorical, Invalid, IM.
269
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
12. (N > L ) . (~N > S)
L ν S ^ N ν ~N
12. Dilemma, Invalid, AC.
270
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
13. No contingent being is necessary.
God is necessary.
So, God is not a contingent being.
13. Categorical, Valid.
271
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
14. Archaeology supports the Bible.
That which supports the Bible is a good apologetic tool.
All good apologetic tools should be vigorously studied.
Anything that should be vigorously studied will be hard work.
Hard work is no fun.
Hence, archaeology is no fun.
14. Sorites, Valid.
272
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
15. Either every effect has a cause or some effects are uncaused.
Every effect has a cause.
So, it is not the case that some effects are uncaused.
15. This looks like a disjunctive syllogism that is invalid because it affirms
one alternant. In reality, the first premise is superfluous, and the conclusion
follows validly from the one remaining premise because of the law of
noncontradiction, since having a cause and being uncaused are
contradictory.
273
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
16. S < M
Some M < P
^ Some S < P
16. Categorical, Invalid, UM.
274
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
17. If Jesus were God, then he would appear whenever I asked.
However, Jesus doesn’t appear whenever I ask.
Hence, Jesus is not God.
17. Hypothetical, Valid.
275
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
18. George believes that Paul is truthful.
Paul believes in Jesus Christ.
Therefore George believes in Jesus Christ.
18. Categorical, 4T.
276
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
19. If deism is true, then the Bible cannot be true.
Deism is false.
So, the Bible can be true.
19. Hypothetical, Invalid, DA.
277
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
20. Z < G
Some L < Z
^ L < G.
20. Categorical, Invalid, Im.
278
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
21. B ν O
~O
^ B
21. Disjunctive, Valid.
279
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
22. If intelligence only comes from intelligence, then evolution can’t
be true.
Evolution can’t be true.
Hence, intelligence only comes from intelligence.
22. Hypothetical, Invalid, AC.
280
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
23. (J K) . (F R)
J ν F
^ K ν R
23. Constructive Dilemma, Valid.
281
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
24. All humanists are interested in human rights.
No Christian is a humanist.
Therefore, no Christian is interested in human rights.
24. Categorical, Invalid, Illicit Major (IM).
282
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
25. If you are a student of logic, then you can determine if syllogisms
are valid or invalid, and if you are a student of the Bible, then you can
explain a passage of Scripture to someone.
Either you can determine if syllogisms are valid or invalid, or you can
explain a passage of Scripture to someone.
So, either you are a student of logic or a student of the Bible.
25. Dilemma, Invalid, AC.
283
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
26. No B < T
Some T < V
^ Some < B
26. Categorical, Valid.
284
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
27. (U ν I) . (E ν O)
(E ν O) ^ (U ν O) . (E ν O)
27. Conjunctive, Valid.
285
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
28. In your faith you should supply moral excellence,
and in your knowledge, self-control;
and in your self-control, perseverance;
and in your perseverance, godliness;
and in your godliness, brotherly kindness;
and in your brotherly kindness, Christian love. (2 Pet. 1:5–7)
So, your faith should supply Christian love.
28. Sorites, Valid.
286
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
29. (C ν D) > H
~(C ν D)
~H
29. Hypothetical, Invalid, DA.
287
First identify the type of syllogism. Then determine if
any of the fallacies mentioned in this chapter are being committed and, if so,
which ones.
30. Either these exercises are over or you have to do some more.
These exercises are over.
Therefore, you do not have to do any more.
30. Disjunctive, Invalid, Affirmed one Alternant (AA).
288
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-1. Either God exists or evil exists, you can’t have both.
1. Faulty Dilemma.
289
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-2. There is no scientific proof for creation, therefore evolution must be
true.
2. Appeal to Ignorance.
290
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-3. All Christians are hypocrites, just look at Jim Bakker.
3. Hasty Generalization.
291
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-4. Where did God come from?
4. Category Mistake.
292
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-5. Most scholars reject the natural arguments for God’s existence.
5. Ad Populum.
293
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-6. I am firm in my belief that if you weren’t so pig-headedly stubborn,
you would see the truth of Christianity.
6. Special Pleading.
294
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-7. Your worldview suffers from axiomatic complications that render it
truth-functionally incoherent.
7. Prestige Jargon.
295
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-8. What’s wrong with TM? It reduces stress, helps concentration, and
is very relaxing.
8. Irrelevant Conclusion.
296
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-9. You are defending the existence of God because you already believe
in him, not because you are searching for truth. meaningful religious
life.
9. Genetic Fallacy.
297
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-10. Natural arguments for God’s existence are something that they did
during the Middle Ages when they had nothing better to do. Today what’s
important is living a meaningful religious life.
10. Appeal to Age.
298
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-11. If a person gives up belief in the inerrancy of the Bible, it won’t be long
before he stops believing in God.
11. Slippery Slope.
299
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-12. Some say that our belief in Christ’s second coming is just
sensationalism. Well, I think the Bible is a pretty sensational book.
12. Equivocation.
300
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-13. I know philosophers are intelligent people because if they weren’t
intelligent, they wouldn’t be philosophers.
13. Begging the Question.
301
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-14. The Declaration of Independence guarantees me the right to life, liberty,
and the pursuit of happiness. Having this baby would deny me those rights,
therefore I am justified in having an abortion.
14. Dicto Simpliciter.
302
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-15. My biology professor says there is no God, and he’s a scientist, so he
would know.
15. Appeal to Authority.
303
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-16. We should not feel bothered if we offend people with the gospel. After
all, in order to make an omelette you have to break a few eggs.
16. Faulty Analogy.
304
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-17. Have you stopped cheating on exams?
17. Complex Question.
305
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-18. You can’t trust anything he says. He’s an atheist and has no basis for
morality.
18. Ad Hominem (Abusive).
306
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-19. You Christians believe you are the only ones who have the truth.
19. Straw Man.
307
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-20. Salvation can’t be a free gift. As the old saying goes, “You get what you
pay for.”
20. Cliche Thinking.
308
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-21. Atheistic philosophers have made some good points, so atheism is a
legitimate world view.
21. Fallacy of Composition.
309
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-22. You’d better believe that Christianity is true or else you’ll go to hell!
22. Appeal to Force.
310
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-23. Nobody believes that Adam-and-Eve story anymore.
23. Consus Gentium.
311
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-24. We Christians must choose. We either break the law and block the doors
of abortion clinics, or we take the guilt of the death of these unborn babies
on ourselves.
24. Faulty Dilemma.
312
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-25. All philosophers have some truth and some good arguments, and none
of them are completely right. I guess you have to be a skeptic and not take
any view.
25. Argument of the Beard.
313
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-26. I know that every action we perform is predetermined because no one
has proved we have free will.
26. Appeal to Ignorance.
314
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-27. TV can’t be harmful to children, because it occupies their attention and
keeps them off the streets.
27. Irrelevant Conclusion.
315
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-28. I believe that everyone will go to heaven because God understands that
we aren’t perfect, but we try hard to be good.
28. Appeal to Pity.
316
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-29. Aristotle said in his Nichomachean Ethics that the ‘good’ is whatever a
good man approves of, and you can tell a good man because he always
approves of the good.
29. Begging the Question.
317
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-30. Where was the man when he jumped off the bridge?
30. Category Mistake (jumping is a process not a place).
318
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-31. If you study theology you will become so rationalistic that you will lose
your first love for God. Your heart for God will become pure head
knowledge.
31. Slippery Slope.
319
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-32. Kant disproved the ontological argument, therefore none of these
rational arguments are accepted anymore.
32. Hasty Generalization.
320
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-33. Most Americans are pro-choice.
33. Ad Populum.
321
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-34. The terms we used to discuss concepts like ‘soul’ and ‘mind’ are archaic
and outdated. Neurophysiology is on the verge of finding new physicalistic
ways of describing how our mind relates to our bodies. In the future we will
be able to do away with the ‘soul’.
34. Appeal to Future.
322
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-35. Our pastor told us that evolution couldn’t possibly be true.
35. Appeal to Authority.
323
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-36. I will not commit that act because it is unjust. I know it is unjust
because my conscience tells me so, and my conscience tells me so because
the act is wrong.
36. Begging the Question.
324
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-37. Leibniz contends that this world is the best of all possible worlds that
God could have made. What a ridiculous assertion! Everything in this world
is not as good as it could be.
37. Red Herring.
325
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-38. It is wrong to go to war because the Bible says, “Thou shalt not kill.”
38. Dicto Simpliciter.
326
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-39. Do you believe the Bible is true when it teaches that women are inferior
to men?
39. Complex Question.
327
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-40. All of the manuscripts of the Bible have variations, so this one can’t be
trusted.
40. Fallacy of Division.
328
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-41. Telling Christians that salvation is free and that they just need to believe
is like signing a contract to buy a house and never making any of the house
payments.
41. Faulty Analogy.
329
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-42. Advertisement: Just Received! A new stock of shirts for men with 15 to
19 necks.
42. Amphiboly.
330
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-43. We should question the Newtonian worldview because he believed that
God created the universe and that surely affected his view of things.
43. Ad Hominem (Circumstantial), Genetic.
331
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-44. If the church hadn’t had such a grip on the people during the Middle
Ages, Christianity would have died out before the Renaissance.
44. Hypothesis Contrary to Fact.
332
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-45. Most atheists reach a point in their lives where they reject God because
of a personal crisis, so their arguments can’t be taken seriously.
45. Genetic Fallacy.
333
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-46. Most people believe in God, and they can’t all be wrong.
46. Consensus Gentium.
334
Determine which fallacy is being committed in the following exercises. There may be more than one fallacy present for each example.
-47. I don’t think we should ask people about their private religious beliefs
because we might offend them and it’s better to be safe than sorry.
47. Cliche Thinking.
335
In the following exercises, identify the Major term, the Minor term, and the Middle term, or identify the form if other than categorical, for example, Modus Tollens, Modus Ponens, etc., and put the arguments in syllogistic form. Finally, tell whether the arguments are formally valid or invalid, and if they are invalid, what fallacy(ies) they commit.
-Everyone present today is employed at the university. Every
member of the organization is present today. So, every member is
employed at the university.
Major term: Employee of the university
Minor term: Member of the organization
Middle term: One who is present today
Everyone present today is an employee of the university.
Every member of the organization is present today.
Thus, every member of the organization is an employee of the
university.
336
In the following exercises, identify the Major term, the Minor term, and the Middle term, or identify the form if other than categorical, for example, Modus Tollens, Modus Ponens, etc., and put the arguments in syllogistic form. Finally, tell whether the arguments are formally valid or invalid, and if they are invalid, what fallacy(ies) they commit.
-Bill must be a U.S. citizen because only U.S. citizens are allowed to
vote, and Bill has his voter registration card.
Major term: U.S. Citizen
Minor term: Bill
Middle term: Voter
All voters are U.S. citizens (only U.S. citizens are allowed to
vote).
Bill is a voter (Bill has his voter registration card).
Therefore, Bill is a U.S. citizen.
337
In the following exercises, identify the Major term, the Minor term, and the Middle term, or identify the form if other than categorical, for example, Modus Tollens, Modus Ponens, etc., and put the arguments in syllogistic form. Finally, tell whether the arguments are formally valid or invalid, and if they are invalid, what fallacy(ies) they commit.
-Only the “A” students are able to achieve success, for only those
who have above-average intelligence are able to succeed, and “A”
students have above-average intelligence.
Major term: “A” students
Minor term: Successful people
Middle term: People with above-average intelligence
All “A” students are people with above-average intelligence.
All successful people are people with above-average intelligence.
Therefore, all successful people are “A” students.
Invalid, UM
338
In the following exercises, identify the Major term, the Minor term, and the Middle term, or identify the form if other than categorical, for example, Modus Tollens, Modus Ponens, etc., and put the arguments in syllogistic form. Finally, tell whether the arguments are formally valid or invalid, and if they are invalid, what fallacy(ies) they commit.
-It is a matter of common knowledge that only those newspapers that
print sensational things like murders and illicit love affairs ever attain a
wide readership. And decent newspapers do not become involved in
this kind of sensationalism. Thus, decent newspapers cannot hope to
attain a wide readership.
Major term: Wide readership
Minor term: Decent newspapers
Middle term: Sensationalism
All newspapers with wide readership are newspapers that print
sensational items.
No decent newspapers are newspapers that print sensational
items.
Therefore, no decent newspapers are newspapers with wide
readership.
339
In the following exercises, identify the Major term, the Minor term, and the Middle term, or identify the form if other than categorical, for example, Modus Tollens, Modus Ponens, etc., and put the arguments in syllogistic form. Finally, tell whether the arguments are formally valid or invalid, and if they are invalid, what fallacy(ies) they commit.
-If the God of the Bible were really all-powerful and all-good he
would defeat sin. But there is still a lot of sin going on in this world
that isn’t yet defeated. But just because sin hasn’t been defeated yet
doesn’t mean it will never be defeated. Consequently, because we
know that the God of the Bible is all powerful and that he is all-good,
we can be assured that one day he will defeat sin.
Modus Ponens
If the God of the Bible is all-powerful and all-good He will defeat
sin.
The God of the Bible is all-powerful and all-good.
Therefore, God will ultimately defeat sin.
340
In the following exercises, identify the Major term, the Minor term, and the Middle term, or identify the form if other than categorical, for example, Modus Tollens, Modus Ponens, etc., and put the arguments in syllogistic form. Finally, tell whether the arguments are formally valid or invalid, and if they are invalid, what fallacy(ies) they commit.
-It is not possible for a thing to be the efficient cause of itself; for so
it would be prior to itself, which is impossible. (Thomas Aquinas,
Summa Theologica I, Question 2, Article 3)
Modus Tollens
If a thing could be the efficient cause of itself it would have to
have been prior to itself.
But nothing can be prior to itself.
Therefore, a thing cannot be the efficient cause of itself.
341
In the following exercises, identify the Major term, the Minor term, and the Middle term, or identify the form if other than categorical, for example, Modus Tollens, Modus Ponens, etc., and put the arguments in syllogistic form. Finally, tell whether the arguments are formally valid or invalid, and if they are invalid, what fallacy(ies) they commit.
-It was either Bill who made the final touchdown by receiving a pass,
or it was John who scored the final points by leaping over the center
for the touchdown. It couldn’t have been John because he was taken
out of the game just before the final score was made. It must have been
Bill who scored the last touchdown.
Disjunctive Syllogism
Either Bill scored the last touchdown or John scored the last
touchdown.
John did not score the last touchdown.
Therefore, Bill scored the last touchdown.
342
In the following exercises, identify the Major term, the Minor term, and the Middle term, or identify the form if other than categorical, for example, Modus Tollens, Modus Ponens, etc., and put the arguments in syllogistic form. Finally, tell whether the arguments are formally valid or invalid, and if they are invalid, what fallacy(ies) they commit.
-Every news reporter is involved in a certain amount of interpretation
of what he reports, since no reporter is able to report every detail of an
important event, and the selection of what is important enough to
report in the available time involves the act of interpreting the events
to identify what is important in the eyes of the reporter.
Major term: Interpreter
Minor term: News reporter
Middle term: Interpretative selection
Every news reporter is someone involved in interpretative
selection of events to report.
Everyone involved in interpretative selection is an interpreter.
Therefore, every news reporter is an interpreter.
343
Determine the average in the sense of mean, median, and mode for the
following.
-1, 3, 7, 11, 23, 47, 52, 64, 70
Mean: 30.9
Mode: None
Median: 23
344
Determine the average in the sense of mean, median, and mode for the
following.
-2, 4, 6, 6, 6, 10, 45, 78, 90
Mean: 27.4
Mode: 6
Median: 6
345
Using the four basic questions discussed under the heading “Figuring
Empirical Probability”, determine if the following inductive arguments are strong or weak. If weak, explain why.
-1. John, Bob, and I think the logic test was unfair.
1. Weak, not enough persons involved.
346
Using the four basic questions discussed under the heading “Figuring
Empirical Probability”, determine if the following inductive arguments are strong or weak. If weak, explain why.
-2. We took a survey of the entire church and 90% of the membership is
against a new building program at this time.
2. Strong.
347
Using the four basic questions discussed under the heading “Figuring
Empirical Probability”, determine if the following inductive arguments are strong or weak. If weak, explain why.
-3. A brief look at several biblical verses will show you that I am right
about this point.
3. Weak, not carefully examined.
348
Using the four basic questions discussed under the heading “Figuring
Empirical Probability”, determine if the following inductive arguments are strong or weak. If weak, explain why.
-4. We polled all the students at our Christian college and by the
numbers we asked, it is safe to say that the majority of Americans are
pro-life.
4. Weak, not representative of the country.
349
Using the four basic questions discussed under the heading “Figuring
Empirical Probability”, determine if the following inductive arguments are strong or weak. If weak, explain why.
-5. Several groups hold that the Holocaust never really happened,
instead we’re just being deceived.
5. Weak, contradicts known information.
350
Using the four basic questions discussed under the heading “Figuring
Empirical Probability”, determine if the following inductive arguments are strong or weak. If weak, explain why.
-6. Abundant historical evidence, both Christian and nonChristian,
points to the fact that Jesus lived and died in the first century A.D. and
that his followers reported his appearances shortly after his death.
6. Strong.
351
Using the four basic questions discussed under the heading “Figuring
Empirical Probability”, determine if the following inductive arguments are strong or weak. If weak, explain why.
-7. I spent all day looking at the evidence and I still don’t believe that
God exists.
7. Weak, not enough time and care.
352
Using the four basic questions discussed under the heading “Figuring
Empirical Probability”, determine if the following inductive arguments are strong or weak. If weak, explain why.
-8. I spoke with every person of the eighteen except two, and none of
them agrees with your version of the story.
8. Strong.
353
Give the type of certainty for the following. Assume that all statements are true.
-1. All girls are female.
1. Logical certainty.
354
Give the type of certainty for the following. Assume that all statements are true.
-2. I am a thinking being.
2. Existentially undeniable.
355
Give the type of certainty for the following. Assume that all statements are true.
-3. Abraham Lincoln was the sixteenth president of the United States.
3. Inductive certainty.
356
Give the type of certainty for the following. Assume that all statements are true.
-4. Stealing is wrong.
4. Moral certainty.
357
Give the type of certainty for the following. Assume that all statements are true.
-5. I attend First Church in Dayton.
5. Virtual certainty.
358
Give the type of certainty for the following. Assume that all statements are true.
-6. Jesus Christ rose from the dead.
6. Inductive certainty.
359
Give the type of certainty for the following. Assume that all statements are true.
-7. People should be treated as ends and not as means to ends.
7. Moral certainty.
360
Give the type of certainty for the following. Assume that all statements are true.
-8. My eyes are blue and my hair is brown.
8. Virtual certainty.
361
Give the type of certainty for the following. Assume that all statements are true.
-9. Triangles have three sides.
9. Logical certainty.
362
Give the type of certainty for the following. Assume that all statements are true.
-10. Logic applies to reality.
10. Existentially undeniable.
363
Using what we learned in this chapter, determine the probability of the following.
-1. A book shelf has thirty books and you want a particular one.
Selecting randomly, what is the probability of your getting the right
one?
1. 1 out of 30
364
Using what we learned in this chapter, determine the probability of the following.
-2. What is the probability in rolling four dice that they will all come up
the same number?
2. 1/6 x 1/6 x 1/6 x 1/6 = 1 out of 1296
365
Using what we learned in this chapter, determine the probability of the following.
-3. What is the probability of drawing four kings in a row from a
standard deck of fifty-two playing cards?
3. 4/52 x 3/51 x 2/50 x 1/49 = 24 out of 6,497,400 or 1 out of 270,725
366
Using what we learned in this chapter, determine the probability of the following.
-4. In a bowl that has three red ping-pong balls, four green ping-pong
balls, and five yellow ping-pong balls, what is the probability of
drawing a red ball on a single draw?
4. 3/12 = 1 out of 4
367
Using what we learned in this chapter, determine the probability of the following.
-5. Returning to our bookshelf above, this time you want six particular
books. Determine the probability of randomly selecting only those six
books from the thirty books on the shelf.
5. 6/30 x 5/29 x 4/28 x 3/27 x 2/26 x 1/25 = 720 out of 427,518,000 or
1 out of 593,775
368
Using what we learned in this chapter, determine the probability of the following.
-6. If you flip a coin one hundred times, and fifty-five times it has come
up heads and forty-five times tails, what are the chances that on the
next time it will come up heads?
6. 1 out of 2; this is a common mistake called the Gamblers Fallacy.
The probability factor doesn’t add up for independent events.
369
Using what we learned in this chapter, determine the probability of the following.
-7. There are sixty-six books in the Bible, 1189 chapters, and 31,102
verses. What is the probability of randomly selecting a particular verse
like John 3:16?
7. 1 out of 31,102; the numbers of books and chapters has nothing to
do with the answer, only the number of verses.
370
Using what we learned in this chapter, determine the probability of the following.
-8. Returning to our bowl of ping-pong balls above; what are the
chances of drawing two red ones in a row, not replacing the first ball
selected.
8. 3/12 x 2/11 = 6/132 or 1 out of 22
371
Using what we learned in this chapter, determine the probability of the following.
-9. Here is a telephone number: 555-4879. How many possible numbers
are there in a single exchange (an exchange is the first three numbers)?
How many possible exchanges can you have (remember exchanges do
not use 0)? How many telephone numbers are possible without
considering area codes? There are one hundred thirty area codes in the
United States and Canada. How many possible phone numbers are
there in these two countries?
9. Possible numbers in an exchange: 10,000 Total possible number of
exchanges: 729 Total possible numbers w/o area code: 7,290,000 Total
possible numbers in US and Canada: 947,700,000
372
Using what we learned in this chapter, determine the probability of the following.
-10. One more trip to the bookshelf. Again you want six particular books,
but this time you want them in a particular order. Determine the probability
of getting all six in the right order.
10. 1/30 x 1/29 x 1/28 x 1/27 x 1/26 x 1/25 = 1/427,518,000
373
In each of the following cases, answer these questions:
a. What is (are) the datum (data) to be explained?
b. What hypothesis is proposed?
c. What experimental method or methods were used in each case?
1. In September of 1846, two astronomers, J. C. Adams and U. J. J. Leverrier,
discovered the planet Neptune. By studying the orbit of the planet Uranus, each
man observed that the planet’s orbit could not be accounted for by the
gravitational pull of the sun and the planets orbiting within Uranus’ own orbital
path. Each man proposed the existence of another planet outside of the orbit of
Uranus. Leverrier estimated the most probable position of this planet and began
to search the heavens for evidence of its existence. Upon examining the star
charts taken several nights in a row, it was noticed that one star changed its
position from night to night. This star was the planet for which they had been
searching.
1. a. The datum to be explained was the unusual orbital path of
Uranus, which could not be accounted for by known heavenly bodies.
b. The hypothesis was the existence of another planet outside the orbit
of Uranus. c. One method employed in the investigation was the
method of residues, the process of eliminating all those stars that did
not exhibit the characteristics of a planet, and arriving at the
identification of the one that did.
374
In each of the following cases, answer these questions:
a. What is (are) the datum (data) to be explained?
b. What hypothesis is proposed?
c. What experimental method or methods were used in each case?
2. By accident in 1879, Louis Pasteur discovered that the virus that had
proven to be the cause of chicken cholera had decreased in virulence (the
capacity of the virus to overcome bodily defenses) after having been left in a
culture for a long period of time. Pasteur believed that there was a relationship
between the time when new cultures of the virus were prepared and the length of
time the cultures were allowed to stand isolated before they began to decrease in
virulence. To demonstrate this relationship, Pasteur defined “the relative
virulence of two strains as proportional to the relative numbers of deaths they
produce in the same species when the creatures are infected in the same manner
and under the same conditions.”3 It turned out that there was indeed a relation
between time and the decrease of virulence.
2. a. The datum to be explained is the discovery that after a certain
period of time a virulent virus left in a culture was found to have
lessened in virulence. b. The hypothesis was that there was a
relationship between the amount of time the culture was allowed to
stand and the relative virulence of the virus. c. Pasteur employed the
method of concomitant variation. The relative virulence of the virus
varied proportionately with the amount of time the culture was allowed
to stand.
375
In each of the following cases, answer these questions:
a. What is (are) the datum (data) to be explained?
b. What hypothesis is proposed?
c. What experimental method or methods were used in each case?
3. One of the most often parroted objections to a capitalistic system is that it is
the cause of imperialism. In this argument, imperialism is defined as the effort to
extend the territory of one country by overtaking, through either violence or nonviolence,
the territory of another country. However, it can be demonstrated from
history that many noncapitalistic countries were imperialistic in this same sense.
Therefore, capitalism cannot be the cause of imperialism.
3. a. The datum to be explained is the historical record of imperialism
practiced by capitalistic nations. b. The hypothesis is that capitalism is
the cause of imperialism. c. The hypothesis is invalidated by the use of
the method of agreement. In this case, history demonstrates that the
effect, imperialism, is often present without the assumed cause,
capitalism.
376
In each of the following cases, answer these questions:
a. What is (are) the datum (data) to be explained?
b. What hypothesis is proposed?
c. What experimental method or methods were used in each case?
4. Nearly everyone has seen sleeping pets whimper, twitch their whiskers, and
seemingly pump their legs in pursuit of dream rabbits. But are they really
dreaming? Since animals can’t wake up the next morning and describe their
dreams, the question seemed unanswerable. But recently, Dr. Charles Vaughan of
the University of Pittsburgh devised an ingenious experiment so animals could
tell us, at last, that they were indeed dreaming. Rhesus monkeys were placed in
booths in front of a screen and taught to press on a bar every time they saw an
image on the screen. Then the monkeys were wired to an electroencephalograph
machine and placed back in their special booths. Eventually they fell asleep.
Soon the EEG was recording the special tracings produced by the dreaming
brains of the monkeys. But most important, the sleeping monkeys were eagerly
pressing the bars. Clearly they were seeing images on the screens of their minds
—they were dreaming. Or so Dr. Vaughan believes.
4. a. The data to be explained are the outward signs that seem to
indicate that animals are indeed dreaming and the data derived from
the EEG. b. The hypothesis is that animals, at least the Rhesus
monkey, actually dream. c. The hypothesis is tested by
experimentation and employs the method of agreement. However, the
findings are not conclusive because the experimentation has not
excluded other possible causes. The conclusion involves some causal
fallacies that will be discussed in the next chapter.
377
For each of the paragraphs, discover which, if any, causal fallacy is operative.
1. My neighbor has had a disastrous year with his farm, yet I have had the best
year ever. I have told him time and again to read his horoscope every day. I think
he is having these problems because he doesn’t follow the stars. I didn’t miss a
single day of reading my horoscope this entire year, and look at how good my
harvest is!
1. Post hoc fallacy. The reading or not reading of one’s horoscope has
not been demonstrated to be the cause of the success or failure of
crops. The arguer is assuming a causal relationship simply on the basis
of temporal relationship.
378
For each of the paragraphs, discover which, if any, causal fallacy is operative.
2. Ever since the Supreme Court decided to grant the accused more personal
rights, the crime rate in this country has grown steadily. This clearly
demonstrates that the increase of crime is the fault of the Supreme Court.
2. Post hoc fallacy. The actions of the Supreme Court may well have
been a factor in the rise of the crime rate, but this arguer is concluding
a causal relation merely on the basis of temporal relation. Further
study must be done and other factors must be considered before any
degree of causal relation can be established.
379
For each of the paragraphs, discover which, if any, causal fallacy is operative.
3. I never had problems with the air conditioner in my rental property until
this most recent tenant. I’m sure he has caused these problems.
3. Post hoc fallacy. The landlord is concluding that his tenant is the
cause of problems simply because the problems did not start until this
particular tenant moved in, i.e., a temporal relation. The landlord must
take into consideration many other factors, such as the age of the unit,
the severity of recent weather, etc., before he can accuse the tenant of
being the cause of these problems.
380
For each of the paragraphs, discover which, if any, causal fallacy is operative.
4. Shortly after the capture of the American ship Pueblo by the North
Koreans, Richard Nixon made the following claim in a presidential campaign
speech: “When a third-rate military power can capture a U.S. military ship on
the high seas, it’s time for a change in Washington.”
4. Emphasis on irrelevant factors. The implication is that the crisis was
the fault of the current administration, and, if Mr. Nixon were to be
elected, this kind of thing would not happen. Mr. Nixon
overemphasized a single factor that may not have played a part in the
cause of the incident at all.
381
For each of the paragraphs, discover which, if any, causal fallacy is operative.
5. Flying is a waste of time and money. I can’t understand why anyone would
want to fly rather than drive one’s own car. There are frequent news reports
about plane disasters, the airlines are constantly sending passengers’ luggage to
the wrong destination, and flights are never on time.
5. Neglect of negative evidence. The arguer has neglected to consider
many other factors relevant to the desirability of flying over other
means of transportation, such as the increased speed of travel enabling
the traveler to reach his destination sooner, the relative infrequency of
plane accidents per mile traveled as compared to car accidents, etc.
382
For each of the paragraphs, discover which, if any, causal fallacy is operative.
6. For the past several years the deficit of the federal government has grown.
With the election of conservative Republicans, the deficit has not been reduced.
In fact, it reached an all time high during the most recent administration. It is
clear that the Republicans are causing the rising deficit by their policies.
6. Fallacy of neglecting differences. The arguer has not considered the
fact that a similarity in effect does not necessitate an identity of cause.
Perhaps the continued rise of the national debt results from the
momentum of the economic and political machinery that was set in
motion in past years, and the present administration can only hope to
slow down the growth. Maybe the policies of a Democratic Congress
contribute to the deficit. Perhaps the debt would have been much
higher than it is without the efforts of the Republican administrations.
At the very least, it has not been demonstrated that the policies of the
recent administrations are the cause of continued growth. The arguer
has committed the fallacy of neglecting differences.
383
For each of the paragraphs, discover which, if any, causal fallacy is operative.
7. In the Gospel of John, the apostle begins with a declaration of the identity
of Jesus Christ as the Logos. In ancient Greek philosophy, the Logos was a
prominent idea used to express the orderly nature of the cosmos. It is obvious
that John developed his understanding of Jesus as the Logos of God from ancient
Greek philosophy.
7. Fallacy of neglecting differences. The arguer has not considered the
fact that similarity of effect does not necessarily indicate identity of
cause. It is quite possible that John developed his doctrine of the
Logos from the teaching of the Old Testament rather than from Greek
philosophy. At least, such an identity of cause cannot merely be
asserted. Rather, it must be demonstrated historically, theologically,
philosophically, etc.
384
For each of the paragraphs, discover which, if any, causal fallacy is operative.
8. In our town, a local businessman has developed a program in the public
schools to train young men and women to develop marketable business skills.
Since the institution of this program, many of those who took this elective
eventually became successful business executives. The plan is obviously
developing the skills that are needed.
8. Fallacy of reversing the cause and effect. It is quite possible that this
program is the cause of the success of these graduates. However, it is
equally possible that those who went on to be successful business
executives initially chose the program because they already possessed
the necessary skills, and it was the latent skills of these individuals that
caused their success. The question is, which is the cause and which is
the effect? Is the program the cause of the skills of these former
students, or were the latent skills of these individuals the cause of the
apparent success of the program?
385
For each of the paragraphs, discover which, if any, causal fallacy is operative.
9. Pornography has increased in our country, and the lowering of the moral
standard has followed. It is obvious that increased access to pornographic
material has lowered the standard of morality in our country.
9. Fallacy of reciprocal causality. This is the fallacy of reciprocal
causality. Perhaps causality in this case is not one-directional. Perhaps
the two factors feed each other, and as morality drops, pornography is
more accessible due to a lessening of the social stigma. Perhaps the
growth in the pornography industry has contributed to the relaxing of
moral standards. In this case, it may be incorrect to assume a onedirectional
causal relationship.
386
For each of the paragraphs, discover which, if any, causal fallacy is operative.
10. Down through the centuries men have killed and destroyed in the name of
God. Indeed, it has been said that more injustice has been committed in the name
of God than for any other reason. Atheism is a more human belief, because
history demonstrates that a belief in God is the cause of much inhumanity to
man.
10. Fallacy of confusing cause and condition. Although a personal
conviction, like belief in God or belief that there is no God, may be a
condition in which much inhumanity occurs, it is not the cause of this
evil. Individual acts of inhumanity and evil may be caused by political
aspiration, greed, hatred, etc., all of which may be operative in the
mind of someone who demonstrates deeply held convictions about
God and who wrongly attacks and hurts others in the defense of or the
propagation of his convictions. The cause is not the conviction itself.
The cause is the individual who endeavors to defend or propagate his
convictions in an evil manner.
