Non sequitur (logic)

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Non sequitur is Latin for "it does not follow." In formal logic, an argument is a non sequitur if the conclusion does not follow from the premise. It should be stressed that in a non sequitur, the conclusion can be either true or false, but the argument is a fallacy because the conclusion does not follow from the premise. All logical fallacies are actually just specific types of non sequitur. The term has special applicability in law, having a formal legal definition.

Here are two types of non sequitur of traditional noteworthiness:

1) Any argument that takes the following form is a non sequitur:

If A is true, then B is true.
B is stated to be true.
Therefore, A must be true.

Even if the premises and conclusion are all true (see 1.5), the conclusion is not a necessary consequence of the premises. This sort of non sequitur is also called affirming the consequent.

1.5) An example of a non sequitur where the premises and conclusion are all true would be:

If I am a human (A) then I am a mammal. (B)
I am a mammal. (B)
Therefore, I am a human. (A)

"I" could be another type of mammal without being a human. While the conclusion may be true, it does not follow from the premises. This argument is still a fallacy even if the conclusion is true. It is a non sequitur (note that it is the exact same argument form as in example 1 - the form is always a non sequitur).

2) Another common non sequitur is this:

If A then B. (e.g. If I am in Tokyo, I am in Japan.)
Not A. (e.g. I am not in Tokyo.)
Therefore, not B. (e.g. Therefore, I am not in Japan.)

The speaker could be anywhere else in Japan. This sort of non sequitur is called denying the antecedent.

(If either of the above examples had "If and only if A, then B" as their first premise, then they would be valid and non-fallacious but unsound.)

Many other types of known non sequitur argument forms have been classified into many different types of logical fallacies. In everyday speech and reasoning, an example might be: "If my hair looks nice, all people will love me." However, there is no real connection between your hair and the love of all people. Advertising typically applies this kind of 'deduction'.