The Fallacy of Division 101

Have you ever argued with someone and said something like “well, you’d think that wouldn’t you, you’re a [insert group/affiliation]”?

The implication here is that by belonging to a particular ‘group’, they automatically have the same characteristics (rightly or wrongly) attributable to the group as a whole.

This erroneous reasoning makes us more open to biases that negatively affect our decision-making.

The question to answer then becomes; can the whole really be more than the sum of its parts, and if so, how do we know when that is and isn’t the case?

Let’s find out…

What is the Fallacy of Division?

The Fallacy of Division is a common logical fallacy we fall prey to when assuming that because a group (of people, objects, etc.) has a certain characteristic, all of its parts (or members) must also have the same characteristic.

The simplest way to illustrate this fallacy is with water. When we combine two gases (molecular hydrogen and oxygen) we get water. We cannot then turn around and say: Water is liquid, so H2 and O2, its constituent parts, must also be liquid.

Example

Now, it is not inherently wrong to assume that a characteristic of a group applies to all its individual members. Sometimes that could be the case, and because sometimes it is the case, it is easy NOT to question such a claim when it is made… even when it is incorrect.

So, for example, the following set of reasoning is true:

“Elephants are herbivores”. AND “Nelly is an elephant”. SO “Nelly is a herbivore”

The characteristic “herbivore” is actually an inherent, individual characteristic that applies to all elephants. This is why it can safely be reverse-applied from a group of elephants to any individual elephant.

But a characteristic that applies to the group as a whole AND is only valid because of the grouping, cannot then be deduced to the individual members.

For example:

“Elephants are endangered”. AND “Nelly is an elephant”. SO “Nelly is endangered”

Some more daily examples are probably colloquially known as prejudice… (I wasn’t going to go there, BUT… I’m gonna go there!):

– “Republican Party is pro-life” AND “Julie is a Republican” SO “Julie is pro-life.”

– “The Left control the media.” AND “John is Left-Wing.” SO “John controls the media.”

– “Muslims are terrorists.” AND “Muhammad Ali was a Muslim.” SO “Muhammad Ali was a terrorist.”

Overcoming the Fallacy of Division

The easiest way to expose this fallacy is to do what I did above with sentence structures. When you hear someone (or yourself) say “B has property X”, break that statement down to check its underlying assumptions.

In this case, structurally, that means we expose all the beliefs that have led us to conclude that B has property X:

– A has property X, and

– B is a part/member of A,

– therefore, B has property X”.

E.g.,

– Harvard produces smart young people.

– Bob went to Harvard

– Bob is a smart young man.

By exposing the underlying assumptions, it is much easier to think critically about the individual premises and recognise whether they are true or false and if they are true and false all the time, vs some of the time.