# Valid and Invalid Forms of Logic

A valid argument can have a false or inconclusive conclusion but only if one or more of the premises is false.

1. If the grass is green then the sky is blue. (fallacy, if the grass is green, the sky is not necessarily blue.)
2. The sky is blue (form is invalid but the premise is true)
Therefore, the grass is green. (invalid form- affirming the consequent, but the conclusion is true.)

1. If molecules-to-man evolution actually took place, then the Bible has errors.
2. We know that evolution actually took place.
Therefore, the Bible has errors. (valid form, but false premise and conclusion)

An argument can have false premises and a true conclusion.

1. Grass is blue.
2. Sky is green.
Therefore, I exist. (valid form)

Some common types of logical arguments are listed below.

## Disjunctions or disjunctive arguments or disjunctive syllogisms

Using OR
valid form using OR:

1. Jesus says either you’re with Him or you’re against Him.
2. You’re not with Him.
So, you must be against Him. (valid form)

1. A or B
2. Not A
Therefore, B (valid form)

1. A or B or C or D
2. Not A
Therefore, B or C or D (valid form)

1. A or B or C or D
2. Not A
3. Not B
4. Not C
Therefore, D (valid form)

Either Christ speaks to His people (His sheep here His Voice.) or He does not.
Christ speaks to His people.
Therefore it can’t be the case that Jesus is like the mute idols, incapable of articulate speech. (valid form)
This is valid because both could not be true. One and only one of the two could be true.

1. A or B
2. A
Therefore, not B (valid form)

### Invalid form using OR:

1. Christ either speaks through Scripture or through some other means.
2. Christ speaks through Scripure.
Therefore, Christ doesn’t speak through any other means. (invalid form)

This is what is known as an inclusive or–both choices can be true. For this reason the logical argument is invalid.

1. A or B
2. A
Therefore, not B (invalid form)

## modus ponens:

### valid modus ponens:

1. If any person follows Christ then Christ is leading that person.
Therefore, Christ is leading them. (valid form)

1. If A then B
2. A
Therefore, B (valid form)

1. If any person won’t follow Christ then Christ is not their Lord.
2. Many people won’t follow Christ.
Therefore, Christ is not their Lord. (valid form)

1. If (not A) then (not B)
2. not-A
Therefore, not-B (valid form)

### Invalid modus ponens–affirming the consequent:

1. If evolution actually happened then we would see similarities in DNA of living things.
2. We see similarities in DNA of living things.
Therefore, evolution actually happened (invalid form- affirming the consequent)

1. If the Universe were billions of years old, then we would expect light from stars billions of light years away to have reached the earth.
2. Light from stars billions of light years away to has reached the earth.
Therefore, the Universe is billions of years old. (invalid form- affirming the consequent)

1. If the big bang had actually taken place, then we would find cosmic microwave background.
2. We find cosmic microwave background.
Therefore, the big bang actually took place. (invalid form- affirming the consequent)

1. If A then B
2. B
Therefore, A (invalid form- affirming the consequent)

### Valid modus tollens:

1. If evolution had actually taken place then we would find millions of intermediate forms rather than distinct kinds of living things in the fossil record.
2. We don’t, however, find millions of intermediate forms in the fossil record, but we find distinct kinds of living things.
Therefore, evolution didn’t actually take place. (valid form)

1. If the church were mature in Christ, then there would be total unity.
2. There is not total unity.
Therefore, the church is not mature in Christ. (valid form)

1. If A then B
2. Not B
Therefore, not A (valid form)

1. If millions of intermediate fossils are not found, then evolution did not actually take place.
Therefore, evolution did not actually take place. (valid form)

1. If not A then not B
2. Not A
Therefore, not B. (valid form)

### Invalid modus tollens–denying the antecedent:

1. If there ever were a catastrophic worldwide flood then we would expect to find remains of Noah’s ark.
2. No ark has been confirmed as found.
Therefore, there never was a catastrophic worldwide flood. (invalid form– denying the antecedent)

1. If we had found dinosaur fossils and human fossils next to each other, then we would know that they lived together at the same time.
2. We have not, however, found dinosaur and human fossils together.
Therefore, we know that they didn’t live together. (invalid form–denying the antecedent)

1. If God raised the dead right in front of me right now, then I would know that He exists.
2. However, God is not raising the dead in front of me right now.
Therefore, God doesn’t exist. (invalid form–denying the antecedent)

1. If God would speak to me in an audible voice right now, then I would know that He exists.
2. However, God is not speaking to me in an audible voice right now.
Therefore, God doesn’t exist. (invalid form–denying the antecedent)

1. If A then B
2. Not A
Therefore, not B (invalid form–denying the antecedent)

1. If there is not supernatural realm then I will not see supernatural things happening all around me.
2. I do not see supernatural things happening all around me.
Therefore, there is not supernatural realm. (invalid form–denying the antecedent)

1. If not A then not B
2. Not B
Therefore, not A. (invalid form–denying the antecedent)

## Hypothetical Syllogism

1.ï¿½ If we acknowledge God when He speaks to us then faith comes by hearing.
2.ï¿½ If faith comes by hearing then faith gives us access into God’s grace.
Therefore, if we acknowledge God when He speaks to us then faith gives us access into God’s grace. (valid form)

1.ï¿½ If A then B
2.ï¿½ If B then C
Therefore, if A then C (valid form)

Valid and Invalid forms using All and Some

1. All Christians are human beings.
2. All human beings are people who have committed sins and need to be forgiven.
Therefore, all Christians are people who have committed sins and need to be forgiven. (valid form)

1. All A are B
2. All C are A
Therefore, All C are B (valid form)

1. All Christ followers are led by Christ.
2. All who submit to Christ are Christ followers.
Therefore, All who submit to Christ are led by Christ. (valid form)

1. All A are B
2. C is an A
Therefore, C is a B (valid form)

1. All Christians are human beings.
2. All people in this church are human beings.
Therefore, all people in this church are Christians. (invalid form-backwards argument with all)

1. All Christians are human beings.
2. All human beings are people who have committed sins and need to be forgiven.
Therefore, all people who have committed sins and need to be forgiven are Christians. (invalid form-backwards argument with all)

1. Some Christians are hypocrites.
2. You are a Christian.
Therefore, you are a hypocrit. (invalid form)

1. Some A are B
2. C is an A.
Therefore, C is B (invalid form)

1. Some things found in textbooks are true.
2. Some truth is unknown.
Therefore, some things found in textbooks are unknown. (invalid form)

1. Some A are B
2. Some B are C
Therefore, some A are C (invalid form)