Falacias: Non sequitur

Non sequitur (Latin for "it does not follow"), in formal logic, is an argument in which its conclusion does not follow from its premises. 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.

 

Non sequitur in normal speech

Derailment (thought disorder)

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, it is possible to 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.)
• "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

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:

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 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:

1. Men are human.
2. Mary is human.
3. Therefore, Mary is a man.

Affirming the consequent

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 true.
3. Therefore, A is 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)

While the conclusion may be true, it does not follow from the premises: I could be another type of mammal without also being a human. The truth of the conclusion is independent of the truth its premises - it is a 'non sequitur'.
Affirming the consequent is essentially the same as the fallacy of the undistributed middle, but using propositions rather than set membership.

Denying the antecedent

Denying the antecedent

Another common non sequitur is this:

1. If A is true, then B is true.
2. A is false.
3. Therefore, B is 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.

Affirming a disjunct

Affirming a disjunct

Affirming a disjunct is a fallacy when in the following form:

1. A is true or B is true.
2. B is true.
3. Therefore, A is not true.

The conclusion does not follow from the premises as it could be the case that A and B are both true. This fallacy stems from the stated definition of or in propositional logic to be inclusive.
An example of affirming a disjunct would be:

1. I am at home or I am in the city.
2. I am at home.
3. Therefore, I am not in the city.

While the conclusion may be true, it does not follow from the premises. For all the reader knows, the declarant of the statement very well could have her home in the city, in which case the premises would be true but the conclusion false. This argument is still a fallacy even if the conclusion is true.

Denying a conjunct

Denying a conjunct

Denying a conjunct is a fallacy when in the following form:

1. It is not the case that both A is true and B is true.
2. B is not true.
3. Therefore, A is true.

The conclusion does not follow from the premises as it could be the case that A and B are both false.
An example of denying a conjunct would be:

1. It is not the case that both I am at home and I am in the city.
2. I am not at home.
3. Therefore, I am in the city.

While the conclusion may be true, it does not follow from the premises. For all the reader knows, the declarant of the statement very well could neither be at home nor in the city, in which case the premises would be true but the conclusion false. This argument is still a fallacy even if the conclusion is true.

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