Formal vs. Informal Fallacies

A fallacy is simply a mistake in reasoning. Some fallacies are formal and some are informal. In chapter 2, we saw that we could define validity formally and thus could determine whether an argument was valid or invalid without even having to know or understand what the argument was about. We saw that we could define certain valid rules of inference, such as modus ponens and modus tollens. These inference patterns are valid in virtue of their form, not their content. That is, any argument that has the same form as modus ponens or modus tollens will automatically be valid. A formal fallacy is simply an argument whose form is invalid. Thus, any argument that has that form will automatically be invalid, regardless of the meaning of the sentences. Two formal fallacies that are similar to, but should never be confused with, modus ponens and modus tollens are denying the antecedent and affirming the consequent. Here are the forms of those invalid inferences:

Denying the antecedent

p ⊃ q

~p

∴ ~q

Affirming the consequent

p ⊃ q

q

∴ p

Any argument that has either of these forms is an invalid argument. For example:

1. If Kant was a deontologist, then he was a non-consequentialist.
2. Kant was not a deontologist.
3. Therefore, Kant was a not a non-consequentialist.

The form of this argument is:

1. D ⊃ C
2. ~D
3. ∴ ~C

As you can see, this argument has the form of the fallacy, denying the antecedent. Thus, we know that this argument is invalid even if we don’t know what “Kant” or “deontologist” or “non-consequentialist” means. (“Kant” was a famous German philosopher from the early 1800s, whereas “deontology” and “non-consequentialist” are terms that come from ethical theory.) It is mark of a formal fallacy that we can identify it even if we don’t really understand the meanings of the sentences in the argument. Recall our Jabberwocky argument from chapter 2. Here’s an argument which uses silly, made-up words from Lewis Carrol’s “Jabberwocky.” See if you can determine whether the argument’s form is valid or invalid:

1. If toves are brillig then toves are slithy.
2. Toves are slithy
3. Therefore, toves are brillig.

You should be able to see that this argument has the form of affirming the consequent:

1. B ⊃ S
2. S
3. ∴ B

As such, we know that the argument is invalid, even though we haven’t got a clue what “toves” are or what “slithy” or “brillig” means. The point is that we can identify formal fallacies without having to know what they mean.

In contrast, informal fallacies are those which cannot be identified without understanding the concepts involved in the argument. A paradigm example of an informal fallacy is the fallacy of composition. We will consider this fallacy in the next sub-section. In the remaining subsections, we will consider a number of other informal logical fallacies.

4.1.1 Composition fallacy

Consider the following argument:

Each member on the gymnastics team weighs less than 110 lbs. Therefore, the whole gymnastics team weighs less than 110 lbs.

This arguments commits the composition fallacy. In the composition fallacy one argues that since each part of the whole has a certain feature, it follows that the whole has that same feature. However, you cannot generally identify any argument that moves from statements about parts to statements about wholes as committing the composition fallacy because whether or not there is a fallacy depends on what feature we are attributing to the parts and wholes. Here is an example of an argument that moves from claims about the parts possessing a feature to a claim about the whole possessing that same feature, but doesn’t commit the composition fallacy:

Every part of the car is made of plastic. Therefore, the whole car is made of plastic.

This conclusion does follow from the premises; there is no fallacy here. The difference between this argument and the preceding argument (about the gymnastics team) isn’t their form. In fact both arguments have the same form:

Every part of X has the feature f. Therefore, the whole X has the feature f.

And yet one of the arguments is clearly fallacious, while the other isn’t. The difference between the two arguments is not their form, but their content. That is, the difference is what feature is being attributed to the parts and wholes. Some features (like weighing a certain amount) are such that if they belong to each part, then it does not follow that they belong to the whole. Other features (such as being made of plastic) are such that if they belong to each part, it follows that they belong to the whole.

Here is another example:

Every member of the team has been to Paris. Therefore the team has been to Paris.

The conclusion of this argument does not follow. Just because each member of the team has been to Paris, it doesn’t follow that the whole team has been to Paris, since it may not have been the case that each individual was there at the same time and was there in their capacity as a member of the team. Thus, even though it is plausible to say that the team is composed of every member of the team, it doesn’t follow that since every member of the team has been to Paris, the whole team has been to Paris. Contrast that example with this one:

Every member of the team was on the plane. Therefore, the whole team was on the plane.

This argument, in contrast to the last one, contains no fallacy. It is true that if every member is on the plane then the whole team is on the plane. And yet these two arguments have almost exactly the same form. The only difference is that the first argument is talking about the property, having been to Paris, whereas the second argument is talking about the property, being on the plane. The only reason we are able to identify the first argument as committing the composition fallacy and the second argument as not committing a fallacy is that we understand the relationship between the concepts involved. In the first case, we understand that it is possible that every member could have been to Paris without the team ever having been; in the second case we understand that as long as every member of the team is on the plane, it has to be true that the whole team is on the plane. The take home point here is that in order to identify whether an argument has committed the composition fallacy, one must understand the concepts involved in the argument. This is the mark of an informal fallacy: we have to rely on our understanding of the meanings of the words or concepts involved, rather than simply being able to identify the fallacy from its form.