Turning then the the Ilya Shapiro article I discussed in connection with Composition, we see Shapiro commit the Fallacy of Division later in the article when he writes:
Similarly, when you tax corporations, you’re taxing the people who ultimately profit from corporate activity: officers, directors, and, most directly, shareholders. Of course, all these people also pay individual income taxes so, in effect, that income is being taxed twice. I’ll leave it to my colleague Dan Mitchell to explain why that might be bad and how otherwise to reform our tax code, but the fact of the matter is that raising corporate taxes does in fact constitute raising taxes on people — which you have to be against if you want to become the Republican presidential nominee.Leaving aside the political calculation and benefits behind making such an assertion, we can see clearly here how Shapiro moves from a claim about the whole corporation to a claim about the individuals that make up that corporation. In effect he argues that because corporations are made up of people, when one taxes a corporation one taxes the individuals who make up that corporation. Again the fallacious reasoning here should be obvious. In particular, it is easy to imagine a situation where the government taxes a corporation, that corporation is unable to pay its taxes so the corporation declares bankruptcy in order to avoid paying or to restructure its tax burden. When this happens, the individuals who make up the corporation do not also declare bankruptcy, and the tax burden of the corporation does not transfer to those individuals. Thus, the claim that taxing corporations amounts to taxing the individuals who make up the corporation is not only factually false, but also an example of the Fallacy of Division.
More generally, it is often the case that as with the article discussed above one finds Composition and Division together. Essentially, both are the result of mereological errors. Very quickly, mereology is the study of the relations between parts and whole. As we have seen above, both Composition and Division arise from a confused or mistaken understanding of this relationship.