Article: Fallacies of Ambiguity (Dr. Van Cleave)

By Matthew Van Cleave

Equivocation

Consider the following argument:

This is a silly argument, but it illustrates the fallacy of equivocation.  The problem is that the word “headache” is used equivocally—that is, in two different senses.  In the first premise, “headache” is used figuratively, whereas in the second premise “headache” is used literally.  The argument is only successful if the meaning of “headache” is the same in both premises.  But it isn’t and this is what makes this argument an instance of the fallacy of equivocation.  

Here’s another example:

In this example, the word “argue” and “argument” are used equivocally.  Hopefully, at this point, you recognize the difference.

The fallacy of equivocation is not always so easy to spot.  Here is a trickier example:

The term “law” is used equivocally here.  In the first premise it is used to refer to societal laws, such as criminal law; in the second premise it is used to refer to laws of nature.  Although we use the term “law” to apply to both cases, they are importantly different.  Societal laws, such as the criminal law of a society, are enforced by people and there are punishments for breaking the laws.  Natural laws, such as laws of physics, cannot be broken and thus there are no punishments for breaking them.  (Does it make sense to scold the electron for not doing what the law says it will do?) 

As with other informal fallacies, equivocation can only be identified by understanding the meanings of the words involved.  In fact, the definition of the fallacy of equivocation refers to this very fact: the same word is being used in two different senses (i.e., with two different meanings).  So, unlike formal fallacies, identifying the fallacy of equivocation requires that we draw on our understanding of the meaning of words and of our understanding of the world, generally.

Composition

Consider the following argument:

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:

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:

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:

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:

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.

Division

The division fallacy is like the composition fallacy and they are easy to confuse.  The difference is that the division fallacy argues that since the whole has some feature, each part must also have that feature.  The composition fallacy, as we have just seen, goes in the opposite direction: since each part has some feature, the whole must have that same feature.  Here is an example of a division fallacy:

This is clearly a fallacy.  Just because the whole house costs 1 million dollars, it doesn’t follow that each part of the house costs 1 million dollars.  However, here is an argument that has the same form, but that doesn’t commit the division fallacy:

In this example, since we seem to be referring to one plane crash in which all the members of the team died (“the” plane crash), it follows that if the whole team died in the crash, then every individual on the team died in the crash.  So this argument does not commit the division fallacy.  In contrast, the following argument has exactly the same form, but does commit the division fallacy:

It can be true that the whole team played its worst game ever even if it is true that no individual on the team played their worst game ever.  Thus, this argument does commit the fallacy of division even though it has the same form as the previous argument, which doesn’t commit the fallacy of division.  This shows (again) that in order to identify informal fallacies (like composition and division), we must rely on our understanding of the concepts involved in the argument.  Some concepts (like “team” and “dying in a plane crash”) are such that if they apply to the whole, they also apply to all the parts.  Other concepts (like “team” and “worst game played”) are such that they can apply to the whole even if they do not apply to all the parts.