Non sequitur (logic)

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Non sequitur (Latin for "it does not follow"), in formal logic, is an argument in which its conclusion does not follow from its premises.[1] In a non sequitur, the conclusion can be either true or false, but the argument is fallacious because there is a disconnection between the premise and the conclusion. 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.

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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 direct 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.

Two examples include:

  • "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.)
  • "I hear the rain falling outside my window; therefore, the sun is not shining." (The conclusion is a non-sequitur because the sun can shine while it is raining.)

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 is not 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:

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 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 holds 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:

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