Formal and informal fallacies

A formal fallacy is a violation of the rules of formal logic. Let me give you an example. This is a syllogism in formal logic called modus tollens.

* If P, then Q.
* Not Q.
* Therefore, not P.

In the first premise, there are two parts. The first part is called the antecedent because it comes before the second part. The second part is called the consequent because it is the consequence of the first part.

The second premise denies the consequent. This is a valid rule of a logic. If your argument follows this pattern, then it's formally valid. But now look at this argument:

* If P, then Q.
* Not P.
* Therefore, not Q.

Notice in this case that instead of denying the consequent, the second premise denies the antecedent. This is a logical fallacy. It makes the syllogism invalid. The conclusion doesn't follow from the premises. The name of this fallacy is the fallacy of denying the antecedent. Another related fallacy is called affirming the consequent. It looks like this:

* If P, then Q.
* Q.
* Therefore, P.

This syllogism is also invalid. There is a valid syllogism that affirms the antecedent, though. It goes like this:

* If P, then Q.
* P.
* Therefore, Q.

That's a valid syllogism called modus ponens.

So basically there are two kinds of valid hypothetical syllogisms. Modus tollens denies the consequent, and modus ponens affirms the antecedent. There are two fallacies to screw these syllogisms up--affirming the consequent and denying the antecedent. You don't have to memorize these because it's plainly evident just by looking at the syllogisms whether they are valid or not. Thankfully, God created us with minds capable of grasping the basic laws of logic merely by introspection. It just requires careful thought and consideration.

These fallacies I just explained are called formal logical fallacies. They differ from informal logical fallacies. The major difference is that there are no exceptions when it comes to formal logical fallacies, but almost all informal logical fallacies have exceptions. There are informal fallacies without exceptions (like the straw man fallacy), but most of them have exceptions. I want to give just two examples.

One informal logical fallacy is called the fallacy of composition. This is a mistake in reasoning where you say something like, "Since all the parts have property X, it follows that the whole thing has that same property." For example, if somebody said that because every part of the car is inexpensive, it follows that the whole car is inexpensive. That's a mistake. However, there is an exception to the fallacy of composition. Here's an example of an argument from composition that is not a fallacy. "Every pixel on the screen is red; therefore, the whole screen is red." That's obviously not a fallacy.

Another informal logical fallacy is called the argument from silence. This is a mistake in reasoning where you say that because such and such isn't evident it follows that such and such isn't the case. For example, suppose I say, "I don't see a spider in this room; therefore, there's no spider in this room." That's a mistake because spiders are very small, and there may be lots of places a spider could be hiding. But suppose I said, "I don't see an elephant in the room; therefore, there's no elephant in the room." Well, that's not a mistake. So what's the difference? The fallacy of argument from silence is only committed when there is no reason to expect that if something were the case, then it would be evident. If there is reason to expect that if something were the case then it would be evident, then one can draw the conclusion that it is not the case based on lack of evidence without committing a fallacy. Since I should expect to see an elephant if it were in the room, but there's no reason to expect that I'd see any spider that was in the room, I can make a valid argument from silence about the absence of an elephant in my room, but if I make the same argument about a lack of spiders, then I've committed an informal fallacy.

The reason I'm making this post is because I see a lot of people learning informal fallacies, then throwing them around willy nilly without recognizing that there are exceptions to them. If something follows the basic pattern, they'll name the fallacy and pretend like they've won the argument. We'd all like to improve our critical thinking skills, and learning about informal fallacies can help. However, if you don't also have an understanding that there are exceptions to informal fallacies, then learning their names without knowing when exception apply will actually make you a more sloppy thinker.

There are some people who intentionally use informal fallacies in their arguments because they're counting on the other person not to understand these subtleties. So understanding the exceptions to informal fallacies can also prevent you from being duped.

Most of the web sites I've found on line about informal fallacies do explain the exceptions, but a lot of them don't. There are two books on informal fallacies that are both good in explaining these fallacies, but one of them talks about the exceptions and the other doesn't. Logically Fallacious by Bo Bennett discusses the exceptions but The Fallacy Detective by Nathaniel and Hans Bluedorn doesn't. The good thing about Bluedorn's book, though, is that it's easier for beginners since it's written for kids. Bennett's book can be pretty dry and tedious. One problem with Bennett's book is that there are so many informal fallacies that nobody could possibly remember them all, and Bennet doesn't divide his book up into "common fallacies" and "obscure fallacies."

If every mistake in reasoning a person could make had a name, I suppose you'd end up with a book like Bennett's. I mean we don't really need to have names for mistakes in reasoning at all. It's just that some mistakes in reasoning are very common. It's useful to have names for the common ones. That's why there is such a thing as an informal fallacy. It's just a way of being able to identify a common pattern of mistaken reasoning so that we can recognize it when it happens, point it out in a succinct way without having to explain it, and so we can avoid making the mistake ourselves. But we don't need to have a name for every single mistake in reasoning that a person can make, and I think that's the problem with Bennett's book.

Of course another problem with the Bluedorn book is that it doesn't use the common names to the fallacies. There's an advantage to using common names to them. It's so we can communicate with each other about them and so if you want to read about the same subject from another source, it's easier to see when two people are talking about the same thing.