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# 4.7: Validity

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## Validity

### Validity

Understanding the concept of validity is crucial for evaluating arguments critically. Validity refers to the logical relationship between the premises and the conclusion of an argument. An argument is valid if, assuming the premises are true, the conclusion must also be true. Here's a breakdown of how validity works, with examples and tests for determining it.

1. Valid Argument:

• Example:
1. Violet is a dog.
2. Therefore, Violet is a mammal.
• Here, if the premise (Violet is a dog) is true, the conclusion (Violet is a mammal) must also be true, because all dogs are mammals.

2. Validity Independent of Actual Truth:

• Example:
1. Everyone born in France can speak French.
2. Barack Obama was born in France.
3. Therefore, Barack Obama can speak French.
• Despite the premises being false, the argument is valid because if the premises were true, the conclusion would necessarily follow.

3. Invalid Argument:

• Example:
1. George was President of the United States.
2. Therefore, George was elected President of the United States.
• This argument is invalid because it’s possible for the premise to be true while the conclusion is false. Gerald Ford was President without being elected, providing a counterexample.

4. Informal Test of Validity:

To determine validity, ask whether you can imagine a world where the premises are true and the conclusion is false. If you can, the argument is invalid.

• Example:
1. Joan jumped out of an airplane without a parachute.
2. Therefore, Joan fell to her death.
• This is invalid because it's possible Joan jumped from a plane on the ground, making the premise true but the conclusion false.
• Revised Example:
1. Joan jumped out of an airplane traveling 300 mph at 10,000 ft without a parachute.
2. Therefore, Joan fell to her death.
• Even this is invalid because there are conceivable scenarios (like landing in a net or being caught by someone with a parachute) where Joan could survive.

5. Application of Validity:

• Example:
1. A person can be President of the United States only if they were born in the United States.
2. Obama is President of the United States.
3. Kenya is not in the United States.
4. Therefore, Obama was not born in Kenya.
• This is valid because if the premises are true, the conclusion must be true.
• Counter Example:
1. A person can be President of the United States only if they were born in Kenya.
2. Obama is President of the United States.
3. Therefore, Obama was born in Kenya.
• Despite the false premises, the argument is valid because the conclusion logically follows from the premises.

### Exercise 5: Validity Test

Determine the validity of the following arguments and provide counterexamples if invalid.

1. Katie is a human being. Therefore, Katie is smarter than a chimpanzee.
2. Bob is a fireman. Therefore, Bob has put out fires.
3. Gerald is a mathematics professor. Therefore, Gerald knows how to teach mathematics.
4. Monica is a French teacher. Therefore, Monica knows how to teach French.
5. Bob is taller than Susan. Susan is taller than Frankie. Therefore, Bob is taller than Frankie.
6. Craig loves Linda. Linda loves Monique. Therefore, Craig loves Monique.
7. Orel Hershizer is a Christian. Therefore, Orel Hershizer communicates with God.
8. All Muslims pray to Allah. Muhammad is a Muslim. Therefore, Muhammad prays to Allah.
9. Some protozoa are predators. No protozoa are animals. Therefore, some predators are not animals.
10. Charlie only barks when he hears a burglar outside. Charlie is barking. Therefore, there must be a burglar outside.

Use the informal test of validity to evaluate each argument, ensuring a clear understanding of whether the premises logically necessitate the conclusion.

4.7: Validity is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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