What is inconsistency?  





The topic of inconsistency is at the heart of logic. If you say, "Everyone left the room," and I say, "John is someone who is still in the room," then I've said something inconsistent with what you've said. Noticing an inconsistency is a wake-up call to resolve the conflict. One or both of the conflicting claims must not be true.

Because the study of inconsistency requires you to know what the words "true" and "truth" mean, it might help you to have a definition. Here it is: The truth is a lie that hasn't been found out.

I got that definition from my favorite intelligence service (spy organization). Just kidding.

Resolving an inconsistency can be at the heart of deep issues. For example, theologians recognize that they have a burden of resolving the apparent inconsistency between divine foreknowledge and human free will. Some philosophers of religion argue that the two are inconsistent because God knows what you are going to do, so you are not free to do otherwise than the way God has foreseen. Yet presumably the ability to do otherwise than you do is the essence of your free will. If there's an inconsistency, then you can't have it both ways. Other philosophers of religion say there is no inconsistency, but we won't go further into this thicket of dispute.

Inconsistency between what we expect and what we get is at the heart of many jokes. Here are some examples:

"I didn't attend the funeral, but I sent a nice letter saying I approved of it." -- Mark Twain

"I feel so miserable without you, it's almost like having you here." -- Stephen Bishop

Let me tell you a story about the second time Candace lost her virginity. It was a dark and stormy night. Meanwhile, walking up the lane toward her was a tall man with a dog.... By now you are suspcious of what I am saying because you were alert to the fact that this remark is inconsistent with our common sense knowledge that people can lose their virginity only once.

We have now discussed some different kinds of inconsistencies. They can be put into categories (intellectual boxes). There are logical inconsistencies (or analytic inconsistencies) in which the very meaning of the words requires one of the claims to be false. Example: {Everyone left the room. John is someone who is still in the room.} This is the kind of inconsistency we will pay most attention to in our course.

There are inconsistencies with our expectations as in Mark Twain's joke about approving of the funeral.

There are inconsistencies with accepted facts as when we say say she lost her virginity twice. It's not a violation of logic to lose your virginity twice, just a violation of the principles of biology. A factual inconsistency is a logical inconsistency with the facts.

Here's a sample question. Are these two sentences (or statements) inconsistent?

  • Almost everyone in the room is an Arab.
  • He's in the room, but he's no Arab.

No, they are consistent. If you were to change "Almost everyone" to "Everyone," then they'd be inconsistent.

The notion of inconsistency can get more complicated. These two statements can be said to both consistent and inconsistent:

  • Everybody left the room.
  • John is still in the room.

They are inconsistent with the assumption that John is a person, but they aren't consistent as presented, because John could be a teddy bear in the room. However, if you made these two statements to people without them knowing John was a teddy bear, then you'd be tricking them and violating the normal rules of conversation which say that ordinary names of people refer to people unless the speaker says otherwise.

So, the moral about the complication is that consistency questions can depend crucially on what else you are assuming.

To explore this complication a bit more, consider the relationship between these two statements.

  • Abraham Lincoln is currently the president of the United States.
  • Abraham Lincoln is a Sumo wrestler.

Would you say the two are

a. consistent
b. inconsistent
c. none of the above

Answer: You can't tell if the answer is a or b. None of these sentences are true. They both are inconsistent with the facts (and thus are factually inconsistent), but they are not logically inconsistent with each other and so are logically consistent. If "b" means "factually inconsistent," then the answer is b. If "b" means "logically inconsistent," then the answer is not b. People are notoriously ambiguous when they ask about inconsistency.

Another way to describe inconsistency is to say that two or more statements are inconsistent with each other if they couldn't all be true. Now the ambiguity is embedded in what the word "could" means. Does it mean "could" as far as the meaning of the words are concerned, or "could" where it is assumed that we are not allowed to change any of the current facts of the world? Here's a way to make the point.

Could eggs grow naturally on trees? They couldn't if they have to obey the laws of biology, but they could so far as what those words mean. That is, the sentence "Eggs could grow naturally on trees" violates biology but not grammar. So, we say the sentence is factually inconsistent but not logically inconsistent. The statement that Abraham Lincoln is your mother could be true but in fact is false. Here we are using "could" in the sense of possible so far as grammar and meaning are concerned.

More on that word "could." Most false statements (sentences) could be true, as far as grammar or meaning is concerned. Similarly, most true statements could be false. But there are exceptions. Here's one. The statement "If it's raining and cold, then it's cold" is true, but it could not be false. Statements like this that can't be false without violating what words mean are said to be analytically true. The statement that it's cold at the North Pole is true but not analytically true.

As you deal with problems of consistency in real life, you want to be alert to what people mean rather than just to what they say. For example, suppose Jack says, "Nobody got an A on that test, but she did. Wow, is she smart." What Jack said literally was self-contradictory. If you called him on it, Jack would probably say not to take him so literally because what he really meant was "Nobody (other than her) got an A on that test." What he meant is not self-contradictory.


Yogi Berra, a catcher for the New York Yankees, once complained that a certain famous New York restaurant was no longer popular with his friends. He said this by remarking, "Nobody goes there anymore--it's too crowded." Now, think about that remark. If the restaurant is so crowded, then there must be people going there, so why did Berra say nobody goes there? Well, he was speaking sloppily and shouldn't be taken so literally. What he meant was that the people he would like to associate with don't go there anymore because the restaurant is now crowded with other sorts of people. So, to get what he intends, you need to overlook the inconsistency.

Let's work on some sample questions. Are these three sentences consistent?
  • Lincoln is taller than Jones.
  • Jones is taller than Shorty.
  • Shorty is taller than Lincoln
No. The three are logically inconsistent with each other. Understanding this inconsistency is all part of understanding the term "taller than." If a person couldn't see that the three sentences were inconsistent, we'd have to wonder whether they really understood what "taller than" meant.

Very often, people will use the terms "inconsistency" and "contradiction" as synonyms, but technically they aren't synonyms. A contradiction between two statements is an especially strong kind of inconsistency between them, such that one must be true and the other must be false. Do the following two statements contradict each other?

  • The house is all green.
  • The house is not all green.

Yes, these two contradict each other; one of the two must be true and the other must be false. This is so for any house. Do the following two statements contradict each other?

  • The house is all green.
  • The house is all blue.

No, both could be false; the house might be white. So, the two statements do not contradict each other, although they are inconsistent with each other. This inconsistency is the weaker kind of inconsistency that we call being "contrary."

When you leave the logic classroom and go out onto the street, you'll find that people use our technical terms "contradiction," "inconsistent," and "contrary" in a sloppy manner; sometimes the three terms are mean to be synonyms and sometimes they are not. And few people are careful to distinguish factual inconsistency from logical inconsistency. So, you have to be alert to this and try to get at what they mean rather than just what they say.