I wanted to make a few additional comments about the Fallacies of Composition and Division. In particular, there are some challenges that arise in correctly applying these two fallacies. As I noted previously, it is clearly an example of Composition if one argues that, "Each piece of this machine is inexpensive, therefore the whole machine is inexpensive." This is clearly fallacious because the quality of 'inexpensive' does not clearly transfer from parts to whole. But what about this very similar argument, "Each piece of this machine is very expensive, therefore the whole machine is expensive"? Here it does appear that 'expensive' is a quality that would transfer from parts to wholes. If we go in reverse, "The whole machine is expensive, therefore each part is expensive," we have a clear example of the Fallacy of Division. However, "The whole machine is inexpensive, therefore each part is inexpensive," does appear to be a legitimate inference.
So, what is going on here? The simple answer is that words are tricky. A more complex answer is that there are some kinds of attributes that do transfer from parts to wholes but not vice versa, and some kinds of attributes that transfer from whole to parts, but not vice versa. The key take away from all this is that one must exercise care in applying and labeling fallacies. In the case of these informal fallacies, one can't just identify a certain argumentative form and automatically identify any argument that has that form as fallacious. One can't just say, "you made an inference from parts to wholes, therefore your argument is fallacious." Instead, one must look more deeply into the actual content of the argument and explore what exactly is being asserted before one can identify it as a fallacy. In effect, one must be sensitive to the language used, what that language means, and how it functions in a particular context.