Non Sequitur

Non-sequitur: A fallacy committed when a conclusion does not follow logically from its given premise.
Non-sequitur: A fallacy committed when a conclusion does not follow logically from its given premise. Any argument that takes the following form is a non-sequitur: “‘If A is true, then B is true;” “B is true;” “Therefore, A is true.”’

Breaking Down Non Sequitur Reasonings

Non-sequitur (a Latin term for “nonsequential” literally “does not sequentially follow”), is described as a fallacyOpens in new window committed when a conclusion does not follow logically from its given premiseOpens in new window. In this case, non sequitur entails reasoningsOpens in new window or premises that are irrelevant to a conclusion.

Observations in Law — The term is also applicable in lawOpens in new window, where it is important that a legal representative, while preparing for a legal defense, should construct his/her argument in a logical manner.

As Bob L. Johnson et al, opine: “The goal is to convince both judge and jury that: (1) the argument made is valid to the data evidence in the case; and that (2) the conclusions reached by the lawyer logically follow from his or her argument. Success depends on the lawyer’s ability to articulate this logical sequence.

Non sequitur reasoning undermines the probability of success. It is the cardinal sin of rhetoric and debate. In a similar fashion, non sequitur reasoning can lead the decision maker to misinfer. The references reflected in a decision may not logically or sequentially follow from the data that surrounds that decision. It is in this sense that overinferring is misinferring.

To infer that Willie was turned away at the party by the Secret Service because his favorite color was green is to over and misinfer from data givens.” —( Bob L. Johnson, Jr., Sharon D. Kruse, Decision Making for Educational Leaders: Underexamined Dimensions and Issues)

Affirming the consequent — Any argument that takes the following form is a non sequitur:

  • If A is true, then B is true.
  • B is true.
  • Therefore, A is true.

Even if the premise and conclusion are all true, the conclusion is not a necessary consequence of the premise. This sort of non sequitur is also called affirming the consequentOpens in new window. An example would be:

  • Premise A: If Jackson is a human | Premise B: then Jackson is a mammal.
  • Premise B: Jackson is a mammal.
  • Premise A: Therefore, Jackson is a human.

While the conclusion may be true, it does not follow from the premise:

  • Humans are mammals
  • Jackson is a mammal
  • Therefore, Jackson is a human

The truth of the conclusion is independent of the truth of its premise — it is a non sequitur, since Jackson might be a mammal without being human. He might be, say, an elephant.

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:

  • If A is true, then B is true.
  • A is false.
  • Therefore, B is false.

While B can indeed be false, this cannot be linked to the premise since the statement is a non sequitur. This is called denying the antecedentOpens in new window. An example would be:

  • If I am Japanese, then I am Asian.
  • I am not Japanese
  • Therefore, I am not Asian.

While the conclusion may be true, it does not follow from the premise. For all the reader knows, the declarant of the statement could be Asian, but for example Chinese, in which case the premise would be true but the conclusion false. This argument is still a fallacy even if the conclusion is true.

Affirming a disjunct — Affirming a disjunctOpens in new window is a form of fallacy in the following form:

  • A is true or B is true.
  • B is true.
  • Therefore, A is not true

The conclusion does not follow from the premise 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:

  • I am at home or I am in the city.
  • I am at home.
  • Therefore, I am not in the city.

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

Important! — Note that this is only a logical fallacy when the word “or” is in its inclusive form. If the two possibilities in question are mutually exclusive, this is not a logical fallacy. For example:

  • I am either at home or I am in the city.
  • I am at home.
  • Therefore, I am not in the city.

Denying a conjunct — Denying a conjunctOpens in new window is a fallacy when in the following form:

  • It is not the case that both A is true and B is true.
  • B is not true.
  • Therefore, A is true.

The conclusion does not follow from the premise as it could be the case that A and B are both false.

An example of denying a conjunct would be:

  • I cannot be both at home and in the city.
  • I am not at home.
  • Therefore, I am in the city.

While the conclusion may be true, it does not follow from the premise. 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 premise would be true but the conclusion false. This argument is still a fallacy even if the conclusion is true.

Fallacy of the undistributed middle

The fallacyOpens in new window of the undistributed middleOpens in new window is a fallacyOpens in new window that is committed when the middle termOpens in new window in a categorical syllogismOpens in new window is not distributedOpens in new window. It is thus a syllogistic fallacyOpens in new window. More specifically it is also a form of non sequitur.

The fallacy of the undistributed middle takes the following form:

  • All Zs are Bs.
  • Y is a B.
  • 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.

An example can be given as follows, where B=mammals, Y=Mary and Z=humans:

  • All humans are mammals.
  • Mary is a mammal.
  • Therefore, Mary is a human.

Note that if the terms (Z and B) were swapped around in the first co-premiseOpens in new window then it would no longer be a fallacy and would be correct.

Further Readings:
Wikipedia | Non sequiturOpens in new window