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.

Denying the Antecedent

You are committing a fallacy if you deny the antecedent of a conditional and then suppose that doing so is a sufficient reason for denying the consequent. This formal fallacy is often mistaken for modus tollens, a valid form of argument using the conditional. A conditional is an if-then statement; the if-part is the antecedent, and the then-part is the consequent.

Example:

If she were Brazilian, then she would know that Brazil's official language is Portuguese. She isn't Brazilian; she's from London. So, she surely doesn't know this about Brazil's language.