What is the Fallacy of Division?

Fallacies of Ambiguity

In critical thinking, we often come across statements that fall victim to the fallacy of division. This common logical fallacy refers to an attribution placed onto an entire class, assuming that each part has the same property as the whole. These can be physical objects, concepts, or groups of people. 

By grouping elements of a whole together and assuming that every piece automatically has a certain attribute, we are often stating a false argument.

This falls into the category of a fallacy of grammatical analogy. It can apply to many arguments and statements we make, including the debate over religious beliefs.

Explanation of the Fallacy of Division

The fallacy of division is similar to the fallacy of composition but in reverse. This fallacy involves someone taking an attribute of a whole or a class and assuming that it must also necessarily be true of each part or member.

The fallacy of division takes the form of:

X has property P. Therefore, all parts (or members) of X have this property P.

Examples and Discussion of the Fallacy of Division

Here are some obvious examples of the Fallacy of Division:

The United States is the richest country in the world. Therefore, everyone in the United States must be rich and live well.

Because professional sports players are paid outrageous salaries, every professional sports player must be rich.

The American judicial system is a fair system. Therefore, the defendant got a fair trial and was not executed unfairly.

Just as with the fallacy of composition, it is possible to create similar arguments which are valid. Here are some examples:

All dogs are from the canidae family. Therefore, my Doberman is from the canidae family.

All men are mortal. Therefore, Socrates is mortal.

Why are these last examples valid arguments?

The difference is between distributive and collective attributes.

Attributes which are shared by all members of a class are called distributive because the attribute is distributed among all members by virtue of being a member. Attributes which are created only by bringing together the right parts in the right way are called collective. This is because it is an attribute of a collection, rather than of the individuals.

These examples will illustrate the difference:

Stars are large.

Stars are numerous.

Each statement modifies the word stars with an attribute. In the first, the attribute large is distributive. It is a quality held by each star individually, regardless of whether it is in a group or not. In the second sentence, the attribute numerous is collective. It is an attribute of the entire group of stars and only exists because of the collection. No individual star can have the attribute "numerous."

This demonstrates a primary reason why so many arguments like this are fallacious. When we bring things together, they can often result in a whole which has new properties unavailable to the parts individually. This is what is often meant by the phrase "the whole is more than the sum of the parts."

Just because atoms put together in a certain way constitutes a living dog does not mean that all atoms are living - or that the atoms are themselves dogs, either.

Religion and the Fallacy of Division

Atheists often encounter the fallacy of division when debating religion and science. Sometimes, they may be guilty of using it themselves:

Christianity has done many evil things in its history. Therefore, all Christians are evil and nasty.

One common way of using the fallacy of division is known as "guilt by association." This is clearly illustrated in the example above. Some nasty characteristic is attributed to an entire group of people - political, ethnic, religious, etc. It is then concluded that some particular member of that group (or every member) should be held responsible for whatever nasty things we have come up with.

They are, therefore, labeled guilty due to their association with that group.

While it's uncommon for atheists to state this particular argument in such a direct manner, many atheists have made similar arguments. If not spoken, it's not unusual for atheists to behave as if they believed this argument were true.

Here is a slightly more complicated example of the fallacy of division which is often used by creationists:

Unless each cell in your brain is capable of consciousness and thinking, then the consciousness and thinking in your brain cannot be explained by matter alone.

It doesn't look like the other examples, but it is still the fallacy of division - it's just been hidden. We can see it better if we more clearly state the hidden premise:

If your (material) brain is capable of consciousness, then each cell of your brain must be capable of consciousness. But we know that each cell of your brain does not possess consciousness. Therefore, your (material) brain itself cannot be the source of your consciousness.

This argument presumes that if something is true of the whole, then it must be true of the parts. Because it is not true that each cell in your brain is individually capable of consciousness, the argument concludes that there must be something more involved - something other than material cells. 

Consciousness, therefore, must come from something other than the material brain. Otherwise, the argument would lead to a true conclusion.

Yet, once we realize that the argument contains a fallacy, we no longer have a reason to assume that consciousness is caused by something else. It would be like using this argument:

Unless each part of a car is capable of self-propulsion, then self-propulsion in a car cannot be explained by the material car-parts alone.

No intelligent person would ever think to use or accept this argument, but it's structurally similar to the consciousness example.