Logical Fallacy #14: Non-Sequitur

Literally this means not in sequence, which is usually written as “does not follow”. This fallacy has a conclusion that is not connect to the premise. There are several types of disconnect – common, undistributed middle, affirming the consequent, denying the antecedent, affirming a disjunct and denying a conjunct. The commonality of all of these is that the argument A is not properly related to the conclusion B, thus B in not valid, or that assuming B cannot give validity to A.

– Common Non-Sequitur

This is simply where one thing has nothing to do with the other.

“The apple in the fridge is red, so the bee cannot pollinate the flower.” This can commonly be found being spouted by ‘gurus’ who are pretending to have depth, or by people who really do not understand how things are connected and attempt to make a connection that should be clearly not made.

– Affirming the Consequent

This non-sequitur assumes a bi-directionality of the consequences – what goes one way must go the other. On the surface this seems reasonable, yet when you consider how this looks in a Venn Diagram, where all of one circle is inside another, you can clearly see that this is not true.

Affirming the consequent
Venn Diagram used to understand non-sequitur’s

Here we have two categories, Red A and Green B. Let us say that A is animals with a vertebrae, and let us say that B is humans. All humans have a vertebrae (that is all of B is a member of A). Daisy has a vertebrae, therefore Daisy is a human. This seems true and accurate, yet when we realise that Daisy is a cow, we realise the mistake. Not all creatures with vertebrae are human.

 

– Denying the Antecedent

Another bi-directional error is denying the antecedent (first part) because the consequent is false.

Consider our diagram above – Green B is now people who have brown skin and Red A is people who have brown eyes.

The argument is this “If I have brown skin, then I have brown eyes” – this may be quite true. The non-sequitur is to then say “I do not have brown skin, therefore I do not have brown eyes”. This does not follow, because having brown eyes does not require you to have brown skin.

Another way to look at this is mathematically: If Alpha is true, then Beta is true. Beta is not true, therefore Alpha is not true. The second statement was not defined by the first statement, so it is not necessarily true – Beta can be false and Alpha can still be true.

– Affirming a Disjunct

This is an error in understanding the meaning of the word “or”. This error is usually cleared up in programming by the use of “or” which is inclusive, or “xor” which is exclusive.

Let us have two items A and B. If the statement is “A or B is true” and we are inclusive, then:

* A is true and B is false = True

* A is false and B is true = True

* A is true and B is true = True

* A is false and B is false = False

Where as if the “or” is exclusive, then

* A is true and B is false = True

* A is false and B is true = True

* A is true and B is true = FALSE

* A is false and B is false = False

Note the difference in the third phrase. By Affirming the Disjunct one is using an exclusive form of the “or” when an inclusive version is expected. This can also be seen as a false dichotomy, trying to create only one true answer.

So let us get rid of the maths and go with English.

“I am nice or male – I am male therefore I am not nice” – the or is ‘inclusive’, but the argument is using an exclusive version.

vs

“I am either male or I am female  – I am male therefore I am not female” – the ‘either’ is exclusive, so the statement is valid. I know that some people are defined as neither or both, yet on government forms in Australia, the logic is you are either male or female, and you must tick one, not both nor neither.

– Denying a Conjunct.

In this case, the statement is that both statement A and B cannot be true (exclusive or). The following statement “A is false therefore B must be true” is in error because B can still be false (check the chart above for exclusive or/xor).

An example of this could be “It is not the case that I am in a lake and at home”. This can be useful. The follow up statement “I am not in a lake, therefore I must be at home” is in error because I may be in an aeroplane, or driving. The statement is only useful if one of the statements is true, thus if I am in a lake, I am definitely not at home, and if I am at home, I am definitely not in a lake. I cannot, however, conclude that because I am not in a lake I must be at home.