Non sequitur (logic)

Non sequitur (Latin for "it does not follow."), in formal logic, is an argument where its conclusion does not follow from its premises. 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 formal fallacies are special cases of non sequitur. The term has special applicability in law, having a formal legal definition. Many types of known non sequitur argument forms have been classified into many different types of logical fallacies.

Non sequitur in normal speech

The term is often used in everyday speech and reasoning to describe a statement in which premise and conclusion are totally unrelated but which is used as if they were. An example might be: "If I buy this cell phone, all people will love me." However, there is no actual relation between buying a cell phone and the love of all people. This kind of reasoning is often used in Advertising to trigger an emotional purchase.

Other examples include:

* "If you buy this car your family will be safer." (While some cars are safer than others, they will most likely decrease instead of increase your family's overall safety.)
* "If you do not buy this type of pet food you are neglecting your dog." (Premise and conclusion are once again unrelated, this is also an example of an appeal to emotion.)
* "Our product is so good, it was even given away in celebrity gift bags." (True, perhaps, but not relevant to the quality of the product)

Fallacy of the undistributed middle

The fallacy of the undistributed middle is a logical fallacy that is committed when the middle term in a categorical syllogism isn't distributed. It is thus a syllogistic fallacy. More specifically it is also a form of non sequitur.

The fallacy of the undistributed middle takes the following form:

  1. All Zs are Bs
  2. Y is a B
  3. Therefore, Y is a Z

It may or may not be the case that "all Zs are Bs," but in either case it is irrelevant to the conclusion. What is relevant to the conclusion is whether it is true that "all Bs are Zs," which is ignored in the argument.

Note that if the terms were swapped around in either the conclusion or the first co-premise or if the first premise was rewritten to "All Zs can only be Bs" then it would no longer be a fallacy although it could still be unsound. This also goes for the following two logical fallacies which are similar in nature to the fallacy of the undistributed middle and also non sequiturs.

An example can be given as follows:

  1. All men are human
  2. Ann is a human
  3. Therefore, Ann is a man

Affirming the consequent

Any argument that takes the following form is a non sequitur

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

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

An example of affirming the consequent would be:

  1. If I am a human (A) then I am a mammal. (B)
  2. I am a mammal. (B)
  3. 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.

Denying the antecedent

Another common non sequitur is this:

  1. If A is true, then B is true.
  2. A is stated to be false.
  3. Therefore B must be false.

While the conclusion can indeed be false, this cannot be linked to the premise since the statement is a non sequitur. This is called denying the antecedent.

An example of denying the antecedent would be:

  1. If I am in Tokyo, I am in Japan.
  2. I am not in Tokyo.
  3. Therefore, I am not in Japan.

Whether or not the speaker is in Japan cannot be derived from the premise. He could either be outside Japan or anywhere in Japan except Tokyo.

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