The fallacy of division is one of the many smokescreens that are used to cover the fact that the reasoning is based on one of the three fallacies of Agrippa's trilemma. Whenever a logical fallacy is committed, the fallacy has its roots in Agrippa's trilemma. All human thought (without Divine revelation) is based on one of three unhappy possibilities. These three possibilities are infinite regress, circular reasoning, or axiomatic thinking. This problem is known as Agrippa's trilemma. Some have claimed that only logic and math can be known without Divine revelation; however, that is not true. There is no reason to trust either logic or math without Divine revelation. Science is also limited to the pragmatic because of the weakness on human reasoning, which is known as Agrippa's trilemma. This is a fallacy that superimposes another level of fallacy on top or one or more of the three fallacies of Agrippa's trilemma.

The logical fallacy of division occurs when someone assumes that what is true for the whole must be true of the individual parts.

“Sandy goes to church every Sunday, so I know that he follows Christ.”

This may not, at first, seem like there is any attribute of a whole that is being projected onto the parts of the whole. The whole is all of the people who go to church every Sunday. Then, there is the fact that many people who go to church every Sunday are actually Christ-followers. There is no reason to believe that Willy has ever acknowledged Christ’s leading and guidance in his life or ever once obeyed Christ just from the fact that Willy goes to church.  There is an old expression that says, “Going to church doesn’t make you a Christian any more than going to your garage makes you a car.”

“Universities are dominated by people with an evolutionary mindset. Bill goes to the University. Bill is dominated by the evolutionary mindset.”

While an organization may be dominated by a certain mindset, that doesn’t mean that a certain person is dominated by that same mindset.

“The Catholic Church has been guilty of sexual abuse, and I have neighbor who is a Catholic.”

There are severe problems with this argument, which was actually adapted from something that was on an Atheist website. First, it personifies that Catholic Church as if it were a monolithic thing, almost making it into a person. It is an organization. Second, it applies the actions of some priests (actions which were against the stated precepts of the organization) to the entire Catholic Church. This is the logical fallacy of composition. You will often find that one fallacy leads to another. The conclusion is not stated but implied that you can apply the generalization about the entire organization to a person in the organization.  You cannot.

On the other hand, there are some common traits that you may be able to guess might be true if your neighbor were a member of the Catholic Church. You would have to verify them, though, since each member is an individual who may or may not follow the teachings and trends found in the Church. In the same way, you would probably not serve pork to someone who told you they were Jewish. That doesn’t mean that you can deductively reason that they don’t eat pork.