Non Sequitur

When a conclusion is supported only by extremely weak reasons or by irrelevant reasons, the argument is fallacious and is said to be a non sequitur. However, we usually apply the term only when we cannot think of how to label the argument with a more specific fallacy name. Any deductively invalid inference is a non sequitur if it also very weak when assessed by inductive standards.

Example:

Nuclear disarmament is a risk, but everything in life involves a risk. Every time you drive in a car you are taking a risk. If you're willing to drive in a car, you should be willing to have disarmament.

The following is not an example: "If she committed the murder, then there'd be his blood stains on her hands. His blood stains are on her hands. So, she committed the murder." This deductively invalid argument commits the fallacy of affirming the consequent, but it isn't a non sequitur because it has significant inductive strength.

Invalid Reasoning

An invalid inference. An argument can be assessed by deductive standards to see if the conclusion would have to be true if the premises were to be true. If the argument cannot meet this standard, it is invalid. An argument is invalid only if it is not an instance of any valid argument form. The fallacy of invalid reasoning is a formal fallacy.

Example:

If it's raining, then there are clouds in the sky. It's not raining. Therefore, there are no clouds in the sky.

This invalid argument is an instance of denying the antecedent. Any invalid inference that is also inductively very weak is a non sequitur.

Formal

Formal fallacies are all the cases or kinds of reasoning that fail to be deductively valid. Formal fallacies are also called logical fallacies or invalidities.

Example:

Some cats are tigers. Some tigers are animals. So, some cats are animals.

This might at first seem to be a good argument, but actually it is fallacious because it has the same logical form as the following more obviously invalid argument:

Some women are Americans. Some Americans are men. So, some women are men.

Nearly all the infinity of types of invalid inferences have no specific fallacy names.