Chapter 4: Informal fallacies

The division fallacy is like the composition fallacy and they are easy to confuse. The difference is that the division fallacy argues that since the whole has some feature, each part must also have that feature. The composition fallacy, as we have just seen, goes in the opposite direction: since each part has some feature, the whole must have that same feature. Here is an example of a division fallacy:

This is clearly a fallacy. Just because the whole house costs 1 million dollars, it doesn’t follow that each part of the house costs 1 million dollars. However, here is an argument that has the same form, but that doesn’t commit the division fallacy:

In this example, since we seem to be referring to one plane crash in which all the members of the team died (“the” plane crash), it follows that if the whole team died in the crash, then every individual on the team died in the crash. So this argument does not commit the division fallacy. In contrast, the following argument has exactly the same form, but does commit the division fallacy:

It can be true that the whole team played its worst game ever even if it is true that no individual on the team played their worst game ever. Thus, this argument does commit the fallacy of division even though it has the same form as the previous argument, which doesn’t commit the fallacy of division. This shows (again) that in order to identify informal fallacies (like composition and division), we must rely on our understanding of the concepts involved in the argument. Some concepts (like “team” and “dying in a plane crash”) are such that if they apply to the whole, they also apply to all the parts. Other concepts (like “team” and “worst game played”) are such that they can apply to the whole even if they do not apply to all the parts.