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.

Affirming the Consequent

If you have enough evidence to affirm the consequent of a conditional and then suppose that as a result you have sufficient reason for affirming the antecedent, you commit the fallacy of affirming the consequent. This formal fallacy is often mistaken for modus ponens, which is a valid form of reasoning also using a conditional. A conditional is an if-then statement; the if-part is the antecedent, and the then-part is the consequent. The following argument affirms the consequent that she does speaks Portuguese.

Example:

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

If the arguer believes or suggests that the premises definitely establish that she is Brazilian, then the arguer is committing the fallacy. See the non sequitur fallacy for more discussion of this point.