# Recognizing Fallacies/Formal Fallacies

## Formal Fallacies

Formal fallacies are patterns of reasoning that are invalid because they use an invalid logic structure. In formal fallacies, the conclusion is always invalid, regardless of the truth of each premise. It is possible for the conclusion to be true, even if the conclusion is invalid.

### Affirming the consequent

It may be helpful to begin this section by viewing this Khan Academy video on the fallacy of Affirming the Consequent.

Affirming the consequent is a formal fallacy of inferring the converse from the original statement. It is the fallacy of inferring the truth of the antecedent (what comes after the “if”) of a conditional statement from the truth of the conditional and its consequent (what comes after the “then”).

Other names for this fallacy include: fallacy of modes ponens, converse error, fallacy of the converse, or confusion of necessity and sufficiency.

The corresponding argument has the general form:

If P, then Q.
Q.
Therefore, P.

An argument of this form is invalid, i.e., the conclusion can be false even when both premise statements are true. Since P was never asserted as the only sufficient condition for Q, other factors could account for Q (while P was false).

This is the fallacy of modes ponens; it gets the P and Q mixed up. Valid use of modes ponens asserts P and concludes Q. This invalid use asserts Q and then concludes P.

Consider these simple examples:

If it's raining then the streets are wet.
The streets are wet.
Therefore, it's raining

This is invalid because the streets can become wet as a result of some cause other than rain.

If Bill Gates owns Fort Knox, then he is rich.
Bill Gates is rich.
Therefore, Bill Gates owns Fort Knox.

Owning Fort Knox is not the only way to be rich. Any numbers of other ways exist to become rich.

If she's Brazilian, then she speaks Portuguese. Hey, she does speak Portuguese. So, she is Brazilian.

But people not from Brazil, for example from Portugal, speak Portuguese and they are not from Brazil.

### Denying the antecedent

It may be helpful to begin this section by viewing this Khan Academy video on the fallacy of Denying the Antecedent.

Denying the antecedent, is a formal fallacy of inferring the inverse from the original statement. This fallacy occurs when we mistake the direction of a conditional. This is the fallacy of inferring the falsehood of the consequent (what comes after the “then”) of a conditional statement from the conditional and the falsehood of its antecedent (what comes after the “if”).

Other names for this fallacy include: fallacy of modes tollens, inverse error, or fallacy of the inverse.

The corresponding argument has the general form:

If P, then Q.
Not P.
Therefore, not Q.

An argument of this form is invalid, i.e., the consequent can be true even when both premise statements are true. Since P was never asserted as the only necessary condition for Q, other factors could account for Q being false even while P is false.

This is the fallacy of modes tollens; it gets the P and Q mixed up. The valid form of modes tollens denies Q and concludes the falsehood of P.

Consider these simple examples:

If it is raining, then the grass is wet.
It is not raining.
Therefore, the grass is not wet.

The argument is invalid because there are other reasons for which the grass could be wet (being sprayed with water by a hose, for example).

Another example:

If Queen Elizabeth is an American citizen, then she is a human being.
Queen Elizabeth is not an American citizen.
Therefore, Queen Elizabeth is not a human being.

That argument is intentionally bad, but arguments of the same form can sometimes seem superficially convincing.

### Assignment

1. Become alert for fallacies while listening to rhetoric, reading persuasive materials, or discussing and debating with others.
2. Identify a specific instance of a formal fallacy in the arguments being presented.
3. Name the specific formal fallacy that is being used.
4. Identify the premise and the conclusion if they exist. Identify the evidence for each premise, if any. Cast that argument in the form of the specific fallacies of relevance studied here.
5. Identify the missing information that would be required to make a valid argument. Recast the argument in a valid form, if possible.