Formal fallacies

Denying the Antecedent

The denying the antecedent fallacy would have the following form:

1. If P, then Q.
2. Not P.
3. Therefore, not Q.

Consider the following argument:

1. If Kant was a deontologist, then he was a non-consequentialist.
2. Kant was not a deontologist.
3. Therefore, Kant was a not a non-consequentialist.

We know that this argument is invalid even if we do not know what “Kant” or “deontologist” or “non-consequentialist” means. (“Kant” was a famous German philosopher from the early 1800s, whereas “deontology” and “non-consequentialist” are terms that come from ethical theory.) It is mark of a formal fallacy that we can identify it even if we do not really understand the meanings of the sentences in the argument.

Affirming the Consequent

The affirming the consequent fallacy has the following form:

1. If P, then Q.
2. Q.
3. Therefore, P.

Here is an argument that uses silly, made-up words from Lewis Carroll’s “Jabberwocky.” See if you can determine whether the argument’s form is valid or invalid:

1. If toves are brillig then toves are slithy.
2. Toves are slithy
3. Therefore, toves are brillig.

We know that the argument is invalid, even though we have no clue what “toves” are or what “slithy” or “brillig” means. The point is that we can identify formal fallacies without having to know what they mean.