Formal fallacies

Denying the antecedent

This 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.

This argument has the form of the fallacy, denying the antecedent. We know that this argument is invalid even if we don’t 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 don’t really understand the meanings of the sentences in the argument.

Affirming the consequent

This fallacy has the following form:

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

Here’s an argument which uses silly, made-up words from Lewis Carrol’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.

This argument has the form of affirming the consequent. We know that the argument is invalid, even though we haven’t got a 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.