When I posted the video lecture on chapter 3 of the Critical Thinking textbook, I neglected to discuss the fallacies of composition and division. Both involve attributions of properties with regard to wholes and their parts.

There are some properties such that, if the parts of something have those properties, then the whole thing will also have them. An example is weighing more than ten pounds. If every piece of a wall weighs more than ten pounds, then the entire wall must weigh more than ten pounds. On the other hand, weighing less than ten pounds is not like that. If each part weighs less than ten pounds, there is no guarantee that the whole weighs less than ten pounds. When we attribute a property of the parts to the whole, and that property is not one that can be so attributed, then we commit the fallacy of composition.

The fallacy of division involves wrongly attributing properties of the whole to the parts. Our previous example, weighing more than ten pounds, can be used to commit the fallacy of division.