Non sequitur (logic)

Non sequitur (Latin

Latin

Latin is an Italic language originally spoken in Latium and Ancient Rome. Through the Roman conquest, Latin spread throughout the Mediterranean and a large part of Europe...

 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

Formal fallacy

In philosophy, a formal fallacy or a logical fallacy is a pattern of reasoning which is always wrong. This is due to a flaw in the logical structure of the argument which renders the argument invalid...

 are special cases of non sequitur. The term has special applicability in law, having a formal legal definition.

Non sequitur (Latin

Latin

Latin is an Italic language originally spoken in Latium and Ancient Rome. Through the Roman conquest, Latin spread throughout the Mediterranean and a large part of Europe...

 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

Formal fallacy

In philosophy, a formal fallacy or a logical fallacy is a pattern of reasoning which is always wrong. This is due to a flaw in the logical structure of the argument which renders the argument invalid...

 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

Advertising

Advertising is a form of communication used to influence individuals to purchase products or services or support political candidates or ideas. Frequently it communicates a message that includes the name of the product or service and how that product or service could potentially benefit the consumer...

 to trigger an emotional purchase

Impulse purchase

An impulse purchase or impulse buy is an unplanned or otherwise spontaneous purchase. One who tends to make such purchases is referred to as an impulse purchaser or impulse buyer....

.

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
  Pet food
  Pet food is plant or animal material intended for consumption by pets. Typically sold in pet stores and supermarkets, it is usually specific to the type of pet .-Industry:...
  
  , you are neglecting your dog." (Premise and conclusion are once again unrelated; this is also an example of an appeal to emotion
  Appeal to emotion
  Appeal to emotion is a potential fallacy which uses the manipulation of the recipient's emotions, rather than valid logic, to win an argument. Also this kind of thinking may be evident in one who lets emotions and/or other subjective considerations influence one's reasoning process...
  
  .)
• "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
  Sunshower
  A sunshower or sun shower is an unusual meteorological phenomenon in which rain falls while the sun is shining. These conditions often lead to the appearance of a rainbow, if the sun is at a low enough angle. The term "sunshower" is used in the United States, Canada, Australia, New Zealand, Ireland...
  
  .)

Fallacy of the undistributed middle

The 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 isn't distributed. It is thus a syllogistic fallacy...

 is a logical fallacy that is committed when the middle term

Middle term

The middle term is the term that occurs in both premises of a categorical syllogism. The other two terms, called the end terms are the major term and minor term, which do appear in the conclusion.Example:...

 in a categorical syllogism is not distributed

Distribution of terms

A categorical term is said to be distributed, if all individual members of that category are accounted for. In a statement like "All A are either B or C", the term A is distributed, because all elements of the set A are pinpointed...

. It is thus a syllogistic fallacy

Syllogistic fallacy

Syllogistic fallacies are logical fallacies that occur in syllogisms. They include:Any syllogism type :*fallacy of four termsOccurring in categorical syllogisms:...

. 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

Co-premise

A co-premise is a premise in reasoning and informal logic which is not the main supporting reason for a contention or a lemma, but is logically necessary to ensure the validity of an argument...

 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

Soundness

In mathematical logic, a logical system has the soundness property if and only if its inference rules prove only formulas that are valid with respect to its semantics. In most cases, this comes down to its rules having the property of preserving truth, but this is not the case in general. The word...

. 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. All men are human.
2. Women are human.
3. Therefore, women are men.

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

Affirming the consequent

Affirming the consequent, sometimes called converse error, is a formal fallacy, committed by reasoning in the form:#If P, then Q.#Q.#Therefore, P....

.

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

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

Denying the antecedent

Denying the antecedent, sometimes also called inverse error, is a formal fallacy, committed by reasoning in the form:The name denying the antecedent derives from the premise "not P", which denies the "if" clause of the conditional premise....

.

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 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 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.

See also

• Modus tollens
  Modus tollens
  In classical logic, modus tollens has the following argument form:...
  
  
• Modus ponens
  Modus ponens
  In classical logic, modus ponendo ponens is a valid, simple argument form sometimes referred to as affirming the antecedent or the law of detachment...
  
  
• Post hoc ergo propter hoc
  Post hoc ergo propter hoc
  Post hoc ergo propter hoc, Latin for "after this, therefore because of this", is a logical fallacy which states, "Since that event followed this one, that event must have been caused by this one." It is often shortened to simply post hoc and is also sometimes referred to as false cause, ...
  
  
• Regression fallacy
  Regression fallacy
  The regression fallacy is an informal fallacy. It ascribes cause where none exists. The flaw is failing to account for natural fluctuations...
  
  
• Fallacy of many questions
  Fallacy of many questions
  Loaded question, also known as complex question, presupposition, "trick question", or plurium interrogationum , is an informal fallacy or logical fallacy. It is committed when someone asks a question that presupposes something that has not been proven or accepted by all the people involved...