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.”

Come Let Us Reason Flashcards by Caleb Nelson

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.

Inductive

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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).

No argument

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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.

Deductive

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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.”

No argument

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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.

Deductive

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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.

Inductive

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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.

No argument

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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.

Deductive

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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.

No argument

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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.

Inductive

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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.

Q S C P
1.[All] [Christians] [are] [saved].

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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.

Q S C P
2.[No] [Baptists] [are] [Presbyterians].

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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.

Q S C P
3. [Some] [people who attend church] [are not] [true believers].

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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.

S C P
4. [Salvation] [is] [a free gift]. (Q implied)

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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.

S C P
5. [Bertrand Russell] [is] [an atheist]. (Q implied)

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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.

Q S C P
6. [Some] [atheists] [are] [communists].

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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.

S P
7. [David Hume] [wrote an argument against believing in miracles]. (Q
& C implied)

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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.

Q S C P
8. [All] [communists] [are] [atheists].

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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.

S
9. [Christians who study their Bibles, pray, and obey
Christ], P
[will remain in fellowship with God]. (Q & C implied)

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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.

Q S P
10. [No] [nonbelievers] [will go to heaven]. (C implied)

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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.

S P
11. [God] [does not change]. (Q & C implied)

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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.

S C P
12. [I] [am not] [an atheist]. (Q implied)

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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.

Q S C P
13. [All] [people] [are] [descendants of Adam].

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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.

Q S C P
14. [Some] [descendants of Adam] [are] [believers in Christ].

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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 are not believers in Christ.

Q S C P
15. [Some] [people] [are not] [believers in Christ].

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Identify the following propositions as either universal or particular and as
affirmative or negative.

Some people are nonChristians.

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Identify the following propositions as either universal or particular and as
affirmative or negative.

No atheists are Christians.

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Identify the following propositions as either universal or particular and as
affirmative or negative.

Some Hindus are not pantheists.

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Identify the following propositions as either universal or particular and as
affirmative or negative.

Sharon is a member of First Baptist Church.

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Identify the following propositions as either universal or particular and as
affirmative or negative.

All believers are going to heaven.

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Identify the following propositions as either universal or particular and as
affirmative or negative.

Logic is not used by everybody.

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Identify the following propositions as either universal or particular and as
affirmative or negative.

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.

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Identify the following propositions as either universal or particular and as
affirmative or negative.

God cannot sin.

Do the same here. You should get a UN proposition.

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Identify the following propositions as either universal or particular and as
affirmative or negative.

Unhappy people are people who need the Lord.

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Identify the following propositions as either universal or particular and as
affirmative or negative.

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.

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Identify the following propositions as either universal or particular and as
affirmative or negative.

Some Christians are not obedient people.

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Identify the following propositions as either universal or particular and as
affirmative or negative.

Some Christians are non-obedient people.

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Identify the following propositions as either universal or particular and as
affirmative or negative.

No man has seen God.

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Identify the following propositions as either universal or particular and as
affirmative or negative.

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.

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Identify the following propositions as either universal or particular and as
affirmative or negative.

All nonbelievers are nonChristians.

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Identify the following propositions as either universal or particular and as
affirmative or negative.

Many unsaved people are good neighbors.

PA. Terms like many and most are just greater somes.

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Identify the following as either A, E, I, or O propositions.

No disciples are unkind.

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Identify the following as either A, E, I, or O propositions.

Paul was a champion of Christianity.

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Identify the following as either A, E, I, or O propositions.

Some church attenders are not paying attention.

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Identify the following as either A, E, I, or O propositions.

All Scripture is inspired. (2 Tim. 3:16)

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Identify the following as either A, E, I, or O propositions.

Some theologians are wrong.

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Identify the following as either A, E, I, or O propositions.

Each and every person needs to trust Christ for his salvation.

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Identify the following as either A, E, I, or O propositions.

Nobody seeks God. (Rom. 3:10)

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Identify the following as either A, E, I, or O propositions.

God is immutable.

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Identify the following as either A, E, I, or O propositions.

They are not among the believers.

E. “They” = “[all] the people in this group to which I refer.”

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Identify the following as either A, E, I, or O propositions.

Those books are in the Bible.

A. “They” = “[all] the people in this group to which I refer.”

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Identify the following as either A, E, I, or O propositions.

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.

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Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.

All enemies of Christ will be defeated.

A: Distributed (D), Undistributed (U)

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Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.

No nonbelievers can understand the things of the Spirit.

E: D, D

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Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.

The Apostle John is the disciple whom Jesus loved.

A: D, U

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Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.

The Bible is the Word of God.

A: D, U

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Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.

Some roads lead to destruction.

I: U, U

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Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.

Some who are standing here will see the kingdom of God.

I: U, U

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Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.

Most atheists are immoral.

I: U, U; “Most” is not all, but is only some.

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Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.

All unhappy people are not nonbelievers.

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.)

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Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.

Judy is not being a good witness for Christ.

E: D, D

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Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.

Some Christians are not nonsmokers.

O: U, D

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Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.

These arguments are ineffective for Christianity.

A: D, U

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Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.

Christ is impeccable.

A: D, U

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Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.

Some who obey Christ are not unfulfilled.

O: U, D

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Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.

No nonChristians will see heaven.

E: D, D

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Determine the type of the following propositions (A, E, I, or O) and the
distribution of both the subject and predicate terms.

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.

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Identify the
type and distribution of the following propositions.

Nothing ventured, nothing gained.

A: D, U; just insert a copula.

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Identify the
type and distribution of the following propositions.

God loves you.

A: D, U

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Identify the
type and distribution of the following propositions.

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.

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Identify the
type and distribution of the following propositions.

All atheists are not cruel.

O: U, D

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Identify the
type and distribution of the following propositions.

Not to trust Christ is to disobey Scripture.

A: D, U; the ‘not’ here modifies the subject term, not the copula.

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Identify the
type and distribution of the following propositions.

All who are not guilty are innocent.

A: D, U; the ‘not’ here modifies the subject term, not the copula.

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Identify the
type and distribution of the following propositions.

Something is better than nothing.

A: D, U; “something” is singular.

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Identify the
type and distribution of the following propositions.

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.

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Identify the
type and distribution of the following propositions.

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.

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Identify the
type and distribution of the following propositions.

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

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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!

No Christians are unsaved.
Some people are unsaved.
Some people are not Christians.

Valid

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Every a is b.
Every b is c.
Every c is a.

Invalid, illicit minor (Im)

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Nothing is better than heaven.
Life on earth is better than nothing.
Life on earth is better than heaven.

Invalid, four terms (4T)

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No a is b.
No b is c.
No c is a.

Invalid, exclusive premises (EP) (i.e., conclusion drawn from two
negative premises)

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All men are substances.
All who are saved are substances.
All who are saved are men.

Invalid, undistributed middle (UM)

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No P is Q.
Some S is P.
Some S is not Q.

Valid

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Some believers are Americans.
Some church attenders are not Americans.
Some believers are church attenders.

Invalid, weaker premise (WP)

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All Bible manuscripts have errors.
Some errors are certain.
No manuscripts are certain.

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.)

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All that exists is matter.
God is not matter.
God does not exist.

Valid

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A moral absolute is necessary.
God is necessary.
God is the moral absolute.

Invalid, UM

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Miracles do not exist.
Miracles prove the existence of God.
Proof of the existence of God does not exist.

Invalid, Im

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Evil is not a substance.
All substances are created by God.
Evil is not created by God.

Invalid, Illicit Major IM

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Jesus Christ is not a sinner.
Jesus Christ rose from the dead.
Jesus Christ is God.

Invalid, 4T

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No unbelievers are heaven-bound.
Some who are heaven-bound are not church attenders.
Some unbelievers are not church attenders.

Invalid, EP

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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.

Invalid, (IM)

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All agnostics deny any knowledge of God.
Those who deny any knowledge of God do not make
sense.
Agnostics do not make sense.

Valid

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Some people attend church.
All Christians attend church.
Some people are Christians.

Invalid, UM

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Everything that has a beginning must have had a cause.
The universe had a beginning.
The universe must have had a cause.

Valid

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Some atheists are not moral.
Renee is an atheist.
Renee is not moral.

Invalid, UM

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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.

Invalid, Im

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All men are sinners.
I am a man.
I am a sinner.

Valid

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All S is M.
No M is P.
No S is P.

Valid

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The Bible is the Word of God.
The Word of God cannot err.
The Bible cannot err.

Valid

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All who have faith in Jesus are saved.
Sharon does not have faith in Jesus.
Sharon is not saved.

Invalid, IM

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Those who obey Christ are believers.
Some Christians do not obey Christ.
Some Christians are not believers.

Invalid, IM

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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

All agnostics deny any knowledge of God.
Those who deny any knowledge of God do not make
sense.
Agnostics do not make sense.

How well did you know this?

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Perfectly

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

Some people attend church.
All Christians attend church.
Some people are Christians.

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Perfectly

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

Everything that has a beginning must have had a cause.
The universe had a beginning.
The universe must have had a cause.

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Perfectly

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

Some atheists are not moral.
Renee is an atheist.
Renee is not moral.

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Perfectly

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

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.

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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

All men are sinners.
I am a man.
I am a sinner.

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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

All S is M.
No M is P.
No S is P.

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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

The Bible is the Word of God.
The Word of God cannot err.
The Bible cannot err.

How well did you know this?

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Perfectly

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

All who have faith in Jesus are saved.
Sharon does not have faith in Jesus.
Sharon is not saved.

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Perfectly

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

Those who obey Christ are believers.
Some Christians do not obey Christ.
Some Christians are not believers.

How well did you know this?

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Perfectly

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

No Christians are unsaved.
Some people are unsaved.
Some people are not Christians.

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Perfectly

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

Every a is b.
Every b is c.
Every c is a.

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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

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.

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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

No a is b.
No b is c.
No c is a.

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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

All men are substances.
All who are saved are substances.
All who are saved are men.

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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

No P is Q.
Some S is P.
Some S is not Q.

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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

Some believers are Americans.
Some church attenders are not Americans.
Some believers are church attenders.

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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

All Bible manuscripts have errors.
Some errors are certain.
No manuscripts are certain.

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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

All that exists is matter.
God is not matter.
God does not exist.

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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

A moral absolute is necessary.
God is necessary.
God is the moral absolute.

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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

Miracles do not exist.
Miracles prove the existence of God.
Proof of the existence of God does not exist.

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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

Evil is not a substance.
All substances are created by God.
Evil is not created by God.

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Perfectly

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

Jesus Christ is not a sinner.
Jesus Christ rose from the dead.
Jesus Christ is God.

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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

No unbelievers are heaven-bound.
Some who are heaven-bound are not church attenders.
Some unbelievers are not church attenders.

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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

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.

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Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

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.)

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Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

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.

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Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

Everything that has a beginning must have had a cause.
The universe had a beginning.
The universe must have had a cause.

AAA

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Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

Some atheists are not moral.
Renee is an atheist.
Renee is not moral.

OAE

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Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

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

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Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

All men are sinners.
I am a man.
I am a sinner.

AAA

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Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

All S is M.
No M is P.
No S is P.

AEE

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Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

The Bible is the Word of God.
The Word of God cannot err.
The Bible cannot err.

AAA

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Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

All who have faith in Jesus are saved.
Sharon does not have faith in Jesus.
Sharon is not saved.

AEE

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Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

Those who obey Christ are believers.
Some Christians do not obey Christ.
Some Christians are not believers.

AOO

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Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

No Christians are unsaved.
Some people are unsaved.
Some people are not Christians.

EIO

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Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

Every a is b.
Every b is c.
Every c is a.

AAA

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Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

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.”)

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Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

No a is b.
No b is c.
No c is a.

EEE

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Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

All men are substances.
All who are saved are substances.
All who are saved are men.

AAA

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Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

No P is Q.
Some S is P.
Some S is not Q.

EIO

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Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

Some believers are Americans.
Some church attenders are not Americans.
Some believers are church attenders.

OII

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Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

All Bible manuscripts have errors.
Some errors are certain.
No manuscripts are certain.

IAE

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Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

All that exists is matter.
God is not matter.
God does not exist.

AEE

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Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

A moral absolute is necessary.
God is necessary.
God is the moral absolute.

AAA

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Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

Miracles do not exist.
Miracles prove the existence of God.
Proof of the existence of God does not exist.

EAE

Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

Evil is not a substance.
All substances are created by God.
Evil is not created by God.

AEE

Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

Jesus Christ is not a sinner.
Jesus Christ rose from the dead.
Jesus Christ is God.

EAA

Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

No unbelievers are heaven-bound.
Some who are heaven-bound are not church attenders.
Some unbelievers are not church attenders.

EOO

Name the mood for each
syllogism. Be sure to list the types of statements in the order of major premise,
minor premise, conclusion.

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

Obvert the following proposition:

All believers are saved.

No believers are nonsaved people.

Obvert the following proposition:

Some arguments for God are not valid.

Some arguments for God are nonvalid.

Obvert the following proposition:

Jesus Christ is God.

Jesus Christ is not non-God.

Obvert the following proposition:

No person is righteous.

All persons are unrighteous (or nonrighteous).

Obvert the following proposition:

Some atheists are immoral.

Some atheists are not moral (or non-immoral).

Obvert the following proposition:

Morality is universally recognized.

Morality is not non-universally recognized.

Obvert the following proposition:

All nonbelievers are unsaved.

No nonbelievers are saved (or non-unsaved).

Obvert the following proposition:

No book of the Bible is uninspired.

All books of the Bible are inspired (or non-uninspired).

Obvert the following proposition:

Some philosophers are not nonChristians.

Some philosophers are Christians (or non-non-Christians).

Obvert the following proposition:

God is a necessary being.

God is not a non-necessary being.

Convert the following proposition:

Some angels are fallen.

Some fallen beings are angels.

Convert the following proposition:

No theologians are infallible.

No infallible persons are theologians.

Convert the following proposition:

All the books in the Bible are inerrant.

Some inerrant things are books in the Bible.

Convert the following proposition:

Tom is not a believer.

None of all the believers is Tom.

Convert the following proposition:

Some deists are not British.

Not convertible.

Convert the following proposition:

Some people are unsaved.

Some unsaved beings are people.

Convert the following proposition:

Tom is a nonbeliever.

One of the nonbelievers is Tom.

Contrapose the following proposition:

All religions are unequal.

All equal movements are nonreligions.

Contrapose the following proposition:

Some nonbelievers are not unkind.

Some kind people are not believers.

Contrapose the following proposition:

No Christians are nonbelievers.

Some believers are not nonChristians.

Contrapose the following proposition:

Some beliefs are not unwarranted.

Some warranted ideas are not nonbeliefs.

Contrapose the following proposition:

The Bible is invaluable.

All non-invaluable books are nonBibles. Note: “valuable” is not the
negation of “invaluable.”

Contrapose the following proposition:

Some logical statements are almost impossible to understand.

Not contraposable.

Contrapose the following proposition:

All non-atheists are believers.

All nonbelievers are atheists.

Contrapose the following proposition:

No book of the Bible is incorrect.

Some correct writings are not books not of the Bible (or “nonbooks
of the Bible”).

Contrapose the following proposition:

Nonhumans are unintelligent.

Intelligent beings are human.

Contrapose the following proposition:

Some propositions are not contraposable.

Some contraposable statements are not nonpropositions.

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.

“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.

a. F
b. T
c. F

“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.

a. F
b. F
c. Equivalent, T

“Some humans are nonbelievers.” is false:
a. No humans are nonbelievers.
b. All believers are people.
c. Some humans are not nonbelievers.

a. T
b. Independent, U
c. T

“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.

a. U
b. U
c. Equivalent, F

“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.

a. U
b. U
c. Equivalent, T

“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.

a. Independent, U
b. Independent, U
c. Independent, U

“Some P is not Q.” is false:
a. All P is Q.
b. No P is Q.
c. Some P is Q.

a. T
b. F
c. T

“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.

a. F
b. Equivalent, T
c. F

“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.

a. F
b. T
c. F

“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.

a. U
b. U
c. T

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.

Julie loves Jesus.
Paul loves Julie.
Paul loves Jesus.

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!

All atheists are nonbelievers.
All believers are going to heaven.
No atheists are going to heaven.

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.

Since some Christians are good debaters, it follows that
some Christians are not good debaters.

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.

All who are not guilty are innocent.
Some are not guilty.
Some are innocent.

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.

All religious persons are moral persons.
All immoral persons are scoundrels.
No religious persons are scoundrels.

Invalid, IM. Obvert the first premise.

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.

Valid. Use the square of opposition again.

Since no religious person is completely in the dark, it is
false that some religious persons are completely in the
dark.

Valid.

Only people are savable.
Some living things are savable.
All people are living things.

Invalid, Im. The first premise is an exclusive statement.

No P are M.
All S are M.
Some S are not P.

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.)

All explosives are flammable.
All inflammable things are unsafe.
All safe things are nonexplosives.

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.

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.

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

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

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

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

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

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

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

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

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

If God exists, then miracles are possible.
Miracles are possible.
God must exist.

G>M
M
^G Invalid, Affirming the Consequent

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.

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

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.

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

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.

Either God exists or evil exists.
Evil exists. God doesn’t exist.

GvE
E
^~G Invalid, Affirmed the Alternant

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.

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

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.

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

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.

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

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

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

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

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

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

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

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

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

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

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.

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.

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.

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.

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

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.

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.

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.

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.

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

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

I believe nature was created by intelligence, because nature is
complexly designed.

Supply the missing premise: “Everything complexly: designed is
created by intelligence.”

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.

Jesus Christ did miracles and only someone sent by God can do
miracles.

Supply the missing conclusion: Therefore, Jesus Christ was sent by
God.

If Christianity is not of God, it will die out. Christianity has not died
out.

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.”

Some believers will suffer loss at the judgment seat of Christ,
however all believers will be saved.

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.

I know that God exists because something must have started all of
this.

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.

To be a Christian you must believe in the bodily resurrection.
Bultmann does not believe in the bodily resurrection.

Supply the missing conclusion: Therefore, Bultmann is not a
Christian.

God loves all men and desires that every man be saved.

Invalid. There is no argument here.

Deism teaches that God does not intervene in the world. But, it is
true that Jesus Christ is God.

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.

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).

Determine if the following sorite is valid or invalid, and if invalid explain the fallacy being committed.

No P < Q
Q < S
S < T
No P < T

Invalid, Illicit Major

Determine if the following sorite is valid or invalid, and if invalid explain the fallacy being committed.

All Christians are Bible believers.
Some Bible believers are church attenders.
No church attenders are immoral.
No Christians are immoral.

Invalid, Undistributed Middle

Determine if the following sorite is valid or invalid, and if invalid explain the fallacy being committed.

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.

Valid.

Determine if the following sorite is valid or invalid, and if invalid explain the fallacy being committed.

Some K < L
No L < non-M
Some non-M non-N
Non-N < O
Some K < O

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!

Determine if the following sorite is valid or invalid, and if invalid explain the fallacy being committed.

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.

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).

Determine if the following sorite is valid or invalid, and if invalid explain the fallacy being committed.

Some philosophers are Christians.
All Christians are going to heaven.
All who are going to heaven are happy.
Some philosophers are happy.

Valid

Determine if the following sorite is valid or invalid, and if invalid explain the fallacy being committed.

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

Determine if the following sorite is valid or invalid, and if invalid explain the fallacy being committed.

A < B
B < C
C < D
No D < E
No B < E

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).

Determine if the following sorite is valid or invalid, and if invalid explain the fallacy being committed.

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.

Invalid, Illicit Process

Determine if the following sorite is valid or invalid, and if invalid explain the fallacy being committed.

Some X < Y
Y < Z
Every Z needs L.
All who need L are P. However, No P < M
Some X is not M.

Valid.

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.

Either we should believe in God or we should become nihilists.
We shouldn’t become nihilists.
We should believe in God.

Destructive Dilemma, Valid.

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.

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.

Hypothetical, Invalid, Denies One Alternant

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.

S < P
Q < P ^ S < Q

Categorical, Invalid, UM.

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.

(B> A) . (C> D)
~(A ν D)
~(B ν C)

Disjunctive, Valid.

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.

No child abusers are just.
Some atheists are just.

Categorical, Invalid, UM.

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.

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.

Constructive Dilemma, Valid.

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.

No A < B.
B < C
C < D
Some D < E
^ No A < E.

Sorites, Invalid, IM.

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.

J Q
Q
^ J

Hypothetical, Invalid, AC.

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.

God loves all men.
All men are sinners.
Therefore, God loves sinners.

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.)

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.

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.

Conjunctive, Valid.

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.

Man is completely free.
God is not a man.
Hence, God is not completely free.

Categorical, Invalid, IM.

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.

(N > L ) . (~N > S)
L ν S ^ N ν ~N

Dilemma, Invalid, AC.

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.

No contingent being is necessary.
God is necessary.
So, God is not a contingent being.

Categorical, Valid.

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.

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.

Sorites, Valid.

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.

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.

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.

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.

S < M
Some M < P
^ Some S < P

Categorical, Invalid, UM.

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.

If Jesus were God, then he would appear whenever I asked.
However, Jesus doesn’t appear whenever I ask.
Hence, Jesus is not God.

Hypothetical, Valid.

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.

George believes that Paul is truthful.
Paul believes in Jesus Christ.
Therefore George believes in Jesus Christ.

Categorical, 4T.

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.

If deism is true, then the Bible cannot be true.
Deism is false.
So, the Bible can be true.

Hypothetical, Invalid, DA.

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.

Z < G
Some L < Z
^ L < G.

Categorical, Invalid, Im.

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.

B ν O
~O
^ B

Disjunctive, Valid.

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.

If intelligence only comes from intelligence, then evolution can’t
be true.
Evolution can’t be true.
Hence, intelligence only comes from intelligence.

Hypothetical, Invalid, AC.

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.

(J K) . (F R)
J ν F
^ K ν R

Constructive Dilemma, Valid.

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.

All humanists are interested in human rights.
No Christian is a humanist.
Therefore, no Christian is interested in human rights.

Categorical, Invalid, Illicit Major (IM).

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.

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.

Dilemma, Invalid, AC.

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.

No B < T
Some T < V
^ Some < B

Categorical, Valid.

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.

(U ν I) . (E ν O)
(E ν O) ^ (U ν O) . (E ν O)

Conjunctive, Valid.

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.

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.

Sorites, Valid.

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.

(C ν D) > H
~(C ν D)
~H

Hypothetical, Invalid, DA.

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.

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.

Disjunctive, Invalid, Affirmed one Alternant (AA).