Speak univocally, not equivocally

What's wrong with the following argument?

Mad men should be put in mental asylums. Annie's dad is mad--he just berated her for one full hour for taking money from his wallet without asking permission. Therefore, Annie's dad should be carted away in a straitjacket and locked up in a mental institution. (example is adapted from Introduction to Logic and Critical Thinking, 3ed., by Merrilee H. Salmon, Harcourt Brace, 1995, p.47)

If that made you chuckle, then you hit the nail on the head intuitively. In the first sentence (statement) "mad" is used in the sense of "insane" / "mentally disturbed" / "demented". However, in the second statement "mad" is used in the sense of "angry." Because Annie's dad was angry and not insane, the conclusion (the last statement) simply does not follow. If you say that the conclusion does follow from the preceding statements then you're mad! (no, not angry, but nuts and off your rockers).

The use of the same term but with different meanings within the argument is known as the fallacy of equivocation. Professors of logic Copi and Cohen tell us that equivocation is an:

informal fallacy in which two or more meanings of the same word or phrase have been confused. If used with one of its meanings in one of the propositions of the argument but with a different meaning in another proposition of the argument, a word is said to have been used equivocally (p.688)

Equivocal arguments are always fallacious. (p.192)

[Irving M. Copi & Carl Cohen, Introduction to Logic, 10th ed., Prentice-Hall, 1998]

As we've seen from the (facetious) example above the premises (1st and 2nd statements) have nothing to do with one another given that the same word "mad" was used to mean quite different things. The Philosophy Pages tells us that: "The inferential relationship between the propositions included in a single argument will be sure to hold only if we are careful to employ exactly the same meaning in each of them," in other words, if the terms are used univocally--with only one meaning--and not equivocally--several meanings.

As with other logical errors, equivocation is sometimes used in humor. Lewis Carroll, for instance, employs it in Through the Looking Glass:

"Who did you pass on the road?" the King went on, holding his hand out to the messenger for some hay.
"Nobody," said the messenger.
"Quite right," said the King; "this young lady saw him too. So of course Nobody walks slower than you."

(quoted in Copi & Cohen, p.192)

Moving on to more serious examples.

It's the duty of the press to publish news that's in the public interest. There is great public interest in UFOs. Therefore the press fails in its duty if it does not publish articles on UFOs. (Theodore Schick, Jr. & Lewis Vaughn, How to Think About Weird Things: Critical Thinking for a New Age, 2ed., Mayfield, 1999, p.286)

Did you catch how "public interest" shifted in meaning? From meaning "welfare of the public" in the first statement it changed to "what the public wants to read about" in the second.

Here's one that's requires some prior scientific understanding. It's also an example that has an ethical side to it:

[A] sugar advertisement ... argued for increased consumption of sugar on the grounds that "Sugar is an essential component of the body ... a key material in all sorts of metabolic processes." (Howard Kahane & Paul Tidman, Logic and Philosophy: A Modern Introduction, Wadsworth, 1995, p.311)

It is true that sugar is an essential component of the body. But this "sugar" is glucose. On the other hand, the "sugar" which the advertisement is promoting is sucrose--table sugar. While both glucose and sucrose are examples of sugars (i.e., saccharides), using "sugar" to mean glucose in one part of the advert and "sucrose" in another part (even if just implicitly) is a blatant commission of equivocation. Given that this is an ad, it is almost certain that the ad makers were fully aware of what they were doing and intentionally took advantage of the equivocal meaning of "sugar" in an attempt to mislead and dupe the consumer (perhaps to counter the prevailing notion that table sugar in one's diet should be reduced to a minimum).

Now that wily, deceitful ad appropriately segues to an example of equivocation by a member of the sect/cult Jehovah's Witnesses (JW) who had the temerity of locking horns with an atheist using illogic and absurd claims. Like the above ad, his argument misleads readers by resorting to the equivocal use of a pivotal term.

This JW made the following argument:

The gods in the religion of the atheists are the atheists themselves. The atheists deny the existence of all gods. But the atheists believe that they are gods. So they idiotically deny their existence.

If you're a bit nonplussed as to how and why he can make the claim that atheists are gods, he offers the following idiosyncratic definition of "god":

A god can be the true God, can be any powerful being, any person with power in high position or anyone can be a god over a group of people under him, anyone makes himself a god if he denies the true God, a god can be also a thing like money, sex, idol, etc.

Going back to his argument about atheists, let's number the sentences/statements therein:

1. The gods in the religion of the atheists are the atheists themselves.
2. The atheists deny the existence of all gods.
3. But the atheists believe that they are gods.
4. So they idiotically deny their existence.

In #1 since atheists are human beings, natural (not supernatural) phenomena, we know that he uses "gods" in the sense he has defined it.

In #2 however, "gods" can only pertain to supernatural entities since that is what atheists don't believe in, that is what "gods" mean when atheists declare "I/We do not believe in gods". It cannot be in the sense that this JW has defined it since needless to say atheists believe in the existence of powerful persons in high positions, in the existence of other humans beings, in the existence of sex, money, and idols (presumably he means that sex, money and other objects in the world can be idolized, i.e., inordinately valued by some people to the point of obsession, reverence, etc.). This JW cannot of course claim that "gods" in #2 refer to a subset of the "gods" as he has defined it since he tells us that "atheists deny the existence of all gods" (emphasis added). Insisting that "gods" here is the same as in #1 would mean that premise #2 is false, pretty obviously so, thus pulling the rug from his argument.

In #3,ostensibly, he uses "gods" in the sense as he does in #1.

Given that this JW uses "gods" in two different senses, his argument commits the fallacy of equivocation.

#4 is the conclusion. But as we've seen and learned above this conclusion cannot legitimately follow from the premises because the word "gods" has been used equivocally.

In order to further see more clearly how the above argument in fact commits the fallacy of equivocation here is an example that uses "God" (capitalized) equivocally:

Some religious arguments can also include equivocations, for example:

It is not possible for the universe to exist without a cause, therefore there must have been a First Cause, which we can reasonably call "God." I already believe in the God of the Bible, and now you have no excuse for not doing so as well.
...

[W]e can see that God is being used in two entirely different ways. In the first sense, God is simply being used as a convenient term to describe a First Cause of the universe, with no particular attributes beyond that which is necessary to cause a universe. But in the second sense, the term God is used for something much more specific and with many more attributes: a traditional Christian conception of God.

(Fallacies of Ambiguity: Equivocation)

In logic, a deductive argument is said to be valid if it contains no fallacies. In a valid argument the conclusion logically and necessarily follows from the premises. An argument is said to be sound if the argument is valid and all the premises are known to be or have been shown to be true. Given a sound argument the conclusion therein must necessarily be true.

It is important to stress that the premises of an argument do not have actually to be true in order for the argument to be valid. An argument is valid if the premises and conclusion are related to each other in the right way so that if the premises were true, then the conclusion would have to be true as well. We can recognize in the above case that even if one of the premises is actually false, that if they had been true the conclusion would have been true as well. Consider, then an argument such as the following:

All toasters are items made of gold.
All items made of gold are time-travel devices.
Therefore, all toasters are time-travel devices.

Obviously, the premises in this argument are not true. It may be hard to imagine these premises being true, but it is not hard to see that if they were true, their truth would logically guarantee the conclusion's truth. It is easy to see that the previous example is not an example of a completely good argument. A valid argument may still have a false conclusion. When we construct our arguments, we must aim to construct one that is not only valid, but sound. A sound argument is one that is not only valid, but begins with premises that are actually true.

(Validity and Soundness)

Given this primer on validity and soundness, is the argument by the JW a valid argument? No, since it contains at least one logical fallacy.

Is it a sound argument? No, since it is invalid. And we don't even need to ask if the premises are true (a necessary condition for an argument to be valid), because an invalid argument can never be sound (validity is also a necessary condition for an argument to be sound).


The lesson: Make sure you use terms consistently. You can preclude equivocation by defining your terms precisely and in detail at the very beginning and double checking that every instance of the term is consistent with how it has been defined. Remember: the existence of equivocation renders an argument invalid. And sometimes, if flagrant, it may make it rather silly too.