Logic is a good thing. It helps to have a working knowledge of logic and the use/misuse/abuse of it. One of the most beneficial studies you can make is to understand "logical errors." There are certain things that people say within the argument that makes the argument invalid. Their position is defeated because of the fallacy being made. A fallacy is a "mistake," therefore a logical fallacy is a mistake made in your logic.
One such fallacy is to engage in a "category mistake." What is a category mistake? Let me give a very real and relevant example.
A certain phrase has been appearing a lot lately almost to the point of becoming a slogan. That statement is "I'm not a Calvinist. I'm not an Arminian. I'm a Baptist." I heard and read that statement from Ergun Caner. The statement was uttered quite a few times at the recent Southern Baptist Convention. Perhaps it even resonates with you. It shouldn't. It is a nonsensical statement.
It is a nonsense statement because the one who speaks it or writes it makes a "category mistake." It is the same thing as saying, "I am not a Republican. I am not a Democrat. I am a Steelers fan."
Do you see the connection? In the hypothetical statement above, Republicans and Democrats belong in one category (political parties) and Steelers fan belongs in another (sports team devotion). In fact, one can combine the two - a Republican who likes the Steelers or a Democrat who likes the Steelers. Therefore, the statement is unnecessary and does not move the debate along.
In the same way, the "Calvinist/Arminian/Baptist" triumvirate does the same thing. The terms "Calvinist" and "Arminian" belong to a single category (a certain belief about the doctrine of salvation). "Baptist" belongs to a different category, defining how one views issues like church polity/governance, baptism, deacons/elders, mission work and funding, etc.
Also, in the same way with the political football fan, one can be an Arminian Baptist or a Calvinistic Baptist. "Baptist" is not mutually exclusive of the other two terms.
Next time you hear that statement, think it through. You can be sure the one who utters it has not done so.
Logic is a wonderful thing.