Fallacy Friday: Division and Composition

Today I want to look at two fallacies, the fallacy of composition and the fallacy of division. These two fallacies are related in that they both mistakenly confuse what is true of the parts with what is true of the whole.

The Fallacy of Composition
M&MsThe fallacy of composition involves mistakenly reasoning that what is true of all the parts of something is therefore true of the whole of that thing. Some obvious examples would be reasoning that because every track on a CD is 10 minutes long the whole CD is ten minutes long; or arguing that because atoms are colourless, and m&ms are made up of atoms, it follows m&ms are colourless. These are examples are fairly obviously cases of invalid inferences.

However, some examples are less obvious. In some versions of the Cosmological Argument for God’s existence, or at least in some apocryphal versions of the argument, it is mistakenly argued that because every item in the universe has a prior cause, the universe as a whole has a prior cause. This is mistaken. If the universe is infinite in time, i.e. it has no beginning, then it is possible for the whole universe to be uncaused while every part is caused by a prior part. Hence, what is true of each individual part of the universe will not be true of the whole. Of course, not all forms of the cosmological argument make this mistake but those that do commit the fallacy of composition.

The Fallacy of Division
Just as the fallacy of composition mistakenly infers what is true of the parts is true of the whole, the fallacy of division mistakenly reasons that what is true of the whole is true of the parts. This would occur, for example, if someone reasoned that because the All Blacks score multiple tries in a game, it follows that every member of the All Blacks scores multiple tries in a game; or that because a particular wall is fragile and breakable, every single brick that makes up the wall is fragile and breakable.

Our Schist Flagstone FireplaceThe problem with both these fallacies is that they mistakenly assume that the whole and the parts that make up the whole have the same properties. Madeleine and I have a beautiful flagstone fire-place in our lounge. It is made up of a series of different sized, shaped and coloured pieces of schist rock, plastered together in flagstone formation to make a single rectangle panel. Merely looking at the fire-place gives a visual illustration that the parts can have different properties to the whole. The individual flagstones are a variety of shapes and not very rectangular yet the whole fire-place is rectangular. Some of these rocks are grey, others are brown,  some have amethyst and teal tones to them but the whole panel is not grey, nor is the whole panel brown, amethyst or teal. This visual picture shows, quite nicely, that what is true of the parts is not always true of the whole and vice-versa.

Conflating Collective & Distributive uses of General Terms
Apart from the straight-forward mistake of confusing what is true of a part with what is true of the whole, there are more subtle versions of this kind of fallacy. The most common is where a person conflates what is true of a groupdistributively and what is true of it collectively. This is less technical than it sounds; consider the following two propositions which can be sensibly said to be true:

1) Cats have roamed the earth longer than humans.

2) Cats have a natural life span of around 15-20 years.

1) is a statement about cats collectively; it is a statement about cats as a group. This type of animal has been roaming the earth since before humans came on the scene. On the other hand 2) is true of cats distributively; it is a  about a property possessed by every individual cat.

Felis takes a break from all the earth roamingIf a person does not pay attention to the differences between distributive and collective uses of general terms one can make fallacious inferences that may sound correct but which are not. An example will illustrate, our children have a cat called Felis who  is around 5 years old. Suppose, however, that I were to reason:

1) Cats have roamed the earth longer than humans;

2) Felis is a cat;

Therefore:

3) Felis has roamed the earth longer than humans.

This argument superficially looks valid.  Yet  premises 1) and 2) are true and the conclusion is clearly false. Why? Because there is a subtle fallacy in the inference: 3) is true of cats collectively; it is true of cats as a group that they have roamed the earth longer than humans but it is not true of cats distributively – no individual cat has been alive this long. The conclusion  3) follows only from 2) and 1) if 1) was meant to be read in the distributive sense.  The person who makes this inference confuses a collective claim about cats, which is true, with a distributive claim about cats that is false.

You might think all this seems silly, a little unnecessarily technical and somewhat obvious; however, there are examples with important social implications, which often arise in our society. Sometimes racists commit this kind of fallacy; they argue that because a certain ethnic group commits more crimes than Pakehas[1] that it follows that individual persons of that ethnicity commit more crimes than individual Pakeha persons.

This involves inflating collective and distributive ways of talking about a group. Racists take a claim which might be true of a ethnic group collectively and infer that it is true of that group distributively – which is what they need to do to justify treating individual members of that group as criminal.

Less noticed is that the same kind of inference can also be used to justify giving certain benefits to particular individuals. When I was at University I attended a meeting where it was argued that every individual Pacific Island student should be entitled to gain a certain benefit on the grounds that Pacific Islanders need more economic help than Pakehas. Again, the arguer infers from something that is true of Pacific Islanders, collectively, to a conclusion which assumes it is true distributively. One only needs to compare the Pacific Islander who is a CEO of a major company with the Pakeha who cleans toilets  for a living to see that the conclusion being drawn is false.

A similar line of argument was sometimes pushed by the student unions at the universities Madeleine and I have studied at. As  a criticism of government policy they would point out that “students owe billions of dollars of student loan debt”. Now, this is true of students collectively, students as a whole do owe a vast sum of money in student loans, but it is false of students distributively, no single student has a personal student loan debt in the billions. Often when the claim was made, it was made to claim or insinuate that individual students were crippled by debt but such reasoning is fallacious. What is true of the class distributively is not necessary true of it collectively and vice versa.

Exceptions
As a final point, someone might want to argue that there are times when making part to whole inferences are valid. Take the following inference, all parts of my car are blue, therefore the whole car is blue. This seems to be a case where inferring from parts to whole would lead to a correct conclusion. Similarly, if my whole car is blue then every part is blue. Again we seem to infer from the whole to the parts in a manner that leads to the correct conclusion.

These examples tell us that sometimes what is true of the parts is true of the whole and vice-versa but note the word sometimes here; sometimes this is true and sometimes it is not. As I noted in Assessing Arguments, a valid argument is one where it is impossible for the premises to be true and the conclusion false. The fact that sometimes an inference gets a true conclusion from true premises and sometimes it does not shows that the argument is invalid.

The fact that sometimes what is true of the parts is true of the whole and vice-versa and sometimes it is not, suggests that when making inferences of this sort one needs to ascertain what kinds of properties this is the case with and what kinds of properties it is not. A valid inference will not merely move from part to whole or whole to part, instead it will argue that properties of a certain type are such that the whole and the part share them and it will add, as a  further premise, that the property in question is of the correct type so that the inference works. But this means the argument is no longer merely a parts to whole argument but that it involves additional premises and hence is not a version of the composition or division fallacy.

[1] For overseas readers, the word Pakeha is the Maori term for people of European descent which is commonly used in New Zealand.

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