10 Non Sequitur Fallacy Examples

The term ‘non sequitur’ comes from Latin and translates as “does not follow.” A non sequitur occurs if the premises don’t justify the conclusion.

A simple non sequitur fallacy example would be: “All trees are tall, all tall things are yellow, therefore, all trees are green.”

More specifically, the term non sequitur refers to those invalid arguments that can not be classified in a precise way (for example, affirming the consequent or denying the antecedent).

Definition of the Non Sequitur Fallacy

The Latin words non sequitur mean “[it] does not follow.” An argument that commits the non sequitur fallacy makes an unwarranted leap in logic.

The point is that the conclusion of such an argument does not follow from the premises. In extreme cases, the conclusion has nothing to do with the truth or falsity of the premises.

The standard logical structure of such arguments might look something like the following:

1. If A is true, we should do B.
2. A is true.
3. Therefore, we should do C.

Or:

1. A is B.
2. B is C.
3. Therefore, C is D.

Or:

1. If A, then B.
2. A.
3. Therefore, C.

The problem with these arguments is that even if the premises were true, the conclusion would never follow.

The conclusion could conceivably be true for other reasons, but the argument would still be invalid.

With the logical structure of non sequitur arguments in mind, here’s a list of 10 hypothetical arguments which commit this fallacy.

10 Non Sequitur Fallacy Examples

1. Non Sequitur about Pythagorus

1. If the Pythagorean theorem is correct, it is always possible to find the length of the hypotenuse of a right triangle when we know the lengths of the other two sides.
2. The Pythagorean theorem is correct.
3. Therefore, the length of the hypotenuse is equal to the sum of the lengths of the other two sides.

This argument commits the non sequitur fallacy because the conclusion does not follow from the premises.

The conclusion continues the theme of the premises and is also concerned with the length of the hypotenuse of a right triangle, but it makes an erroneous leap in logic.

Even if premises (1) and (2) were correct (which they are), the conclusion would still be false, and the argument fallacious.

2. The Color of Trees

1. All trees are tall.
2. All tall things are yellow.
3. Therefore, all trees are green.

This argument commits the non sequitur fallacy, but in contrast to the previous example, its premises are also false.

The fallacious nature of the argument, however, does not depend on the truth or falsity of the premises. Rather, the fact that the argument is fallacious stems from its logical structure: it is a formally invalid form of argument.

In this argument, even if premises (1) and (2) were correct (which, of course, they are not), the conclusion still wouldn’t logically follow from them. The conclusion introduces a completely new and contradictory quality to the argument.

3. Non Sequitur about Socrates

1. If Socrates is a man, then so am I.
2. Socrates is a man.
3. Therefore, you are a man.

In this argument, premises (1) and (2) are sound, but the conclusion is unwarranted. You may well be a man, but this argument would not logically prove that.

The argument commits the non sequitur fallacy because the conclusion does not follow from the premises, even if the premises are completely true.

If the conclusion was: “Therefore, I am a man,” the argument would be formally valid, and if the premises were true, the conclusion would follow. In this case, however, it does not.  

4. Alice is more Healthy than Bob

1. Exercising regularly improves physical health.
2. Alice exercises regularly.
3. Therefore, Alice is more physically healthy than Bob.

This argument might seem reasonable because its premises and conclusion are fairly intuitive, but it is formally invalid.

The argument commits the non sequitur fallacy because it makes an unwarranted leap in logic. The conclusion does not deductively follow from the premises.

Even if premises (1) and (2) are correct, the conclusion that Alice is more healthy than Bob does not follow from them. Maybe Bob also exercises regularly, maybe Bob is naturally very healthy, and so on. The argument does not address any of this.

5. Bicycles are bad for the Environment

1. Cars are bad for the environment.
2. Bicycles and cars are used for transportation.
3. Therefore, bicycles are bad for the environment.

This argument commits the non sequitur fallacy because it makes an erroneous assumption.

Namely: because bicycles and cars are similar in some way, they must share all properties (in this example, being bad for the environment).

In this case, even if premises (1) and (2) were correct (which they are), the conclusion still makes an unwarranted leap in logic. If the first premise was “Everything that is used for transportation is bad for the environment,” the argument would have been valid.

This means that the conclusion would logically follow from the premises (even if the premise was false). In this case, however, the argument is a non sequitur. 

6. Illogical Color Assumptions

1. All houses are blue.
2. All books are red.
3. Therefore, all paintings are yellow.

The conclusion has nothing to do with the premises. This argument, therefore, is an extreme case of a non sequitur fallacy.

Even if premises (1) and (2) were true (which they are not), that would not make the conclusion true.

The conclusion introduces paintings and the color yellow, neither of which were mentioned in the premises.

It assumes that just because A is blue and B is red, then C must be yellow. None of this follows from premises (1) and (2).

7. Lawyers Play Sports

1. Some lawyers are rich.
2. Some sports players are rich.
3. Therefore, some lawyers play sports.

The argument commits the non sequitur fallacy because the conclusion does not follow from the premises.

The premises and the conclusion seem reasonable. I would argue that all of these are true, but that does not change the fact that the argument is formally invalid.

Let’s assume that premises (1) and (2) are correct. Would that make the conclusion (3) also correct?

Could we not imagine a world in which some lawyers and some sports players share some property (being rich in this case) but don’t overlap?

This is, of course, logically possible. The argument, therefore, is not deductively valid because the truth of the premises does not guarantee the truth of the conclusion.

8. The Creature is a Raven

1. All birds have wings.
2. That creature has wings.
3. Therefore, that creature is a raven.

This argument is not logically valid because it commits the non sequitur fallacy. Even if the argument concluded that the creature in question is a bird, it would still be formally invalid.

This is because the statement “all birds have wings” is not logically equivalent to the statement “all creatures that have wings are birds.”

The argument above, however, assumes that these two statements are the same. It further assumes that the creature is not just a bird but a raven (something absent from the premises).

9. The Usefulness of Literature

1. Philosophy is useful in everyday life.
2. Math is useful in everyday life.
3. Therefore, literature is useful in everyday life.

This argument commits the non sequitur fallacy because it makes an unwarranted leap of logic in its conclusion.

Even if the premises were true, the conclusion would not follow. The conclusion may itself be true, but the argument would still be formally invalid.

It assumes that because A and B have property D, then C must also have property D.

10. Clarence owns a Large House

1. Clarence is a basketball player.
2. Basketball players are rich.
3. Therefore, Clarence owns a large house.

The argument commits the non sequitur fallacy. It equates being rich with owning a large house, which is not stated by the premises.

Formal vs Informal Fallacies

A formal fallacy, deductive fallacy, or logical fallacy refers to a formally invalid argument. A non sequitur is a formal falacy.

The errors of such arguments can be traced to a flaw or flaws in the logical structure of the argument (Gensler, 2010 & Barker, 2003).

These types of arguments are deductively invalid, which means that a formally fallacious argument could have true premises and a false conclusion.

Aristotle was the first to define most of the usual formal fallacies in his works On Sophistical Refutations (Aristotle, 1955) and Prior Analytics (Aristotle, 1938).

Formal fallacies differ from informal ones in that they never have a valid logical form.

An informal fallacy, on the other hand, could have a valid form yet be unsound because one or more of its premises are false. Read more about informal fallacies here.

Conclusion

The Latin words non sequitur translate as “[it] does not follow.” The non sequitur fallacy is formal. It bears a superficial resemblance to valid forms of inference, but the truth of its premises does not guarantee the truth of the conclusion (Hansen, 2020). The non sequitur fallacy occurs when the conclusion of an argument does not follow from its premises or, in extreme cases, has nothing to do with them.

References

Aristotle. (1938). Prior Analytics (H. P. Cooke & H. Tredennick, Trans.) [Data set]. Harvard University Press. https://doi.org/10.4159/DLCL.aristotle-prior_analytics.1938

Aristotle. (1955). On Sophistical Refutations (E. S. Forster & D. J. Furley, Trans.) [Data set]. Harvard University Press. https://doi.org/10.4159/DLCL.aristotle-sophistical_refutations.1955

Barker, S. F. (2003). The Elements of Logic. McGraw-Hill.

Gensler, H. J. (2010). The A to Z of Logic. Rowman & Littlefield.

Hansen, H. (2020). Fallacies. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Summer 2020). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/sum2020/entries/fallacies/