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© Copyright 1996, Jim Loy
Click here to read about Self-reference & Circular Reference. Wait, don't click on that. It just goes to the top of this article.
The following is a self-referential statement, in other words a statement that mentions itself:
This sentence contains five words.
And, we see that it is true, while the following is false:
This sentence contains six words.
This is a self-referential statement.
By the definition of a self-referential statement, we see that above sentence is true. The following sentence is self-referential, and false:
This statement is not self-referential.
Any statement of fact can be either true or false, including self-referential ones. But, sometimes a self-referential statement causes problems with its own truth value:
This statement is false.
This is a self-referential statement. Further, it contradict itself. A study of it shows that it is neither true nor false. If it is true, then it is false, and if it is false it is true. So we have an apparent statement of fact that is neither true nor false. This is much different from a statement like "My dog has fleas." In that case, you will have to track my dog (Baskerville) down and examine him, to see if it is true or false. The fact that I have no dog, further complicates the matter, but the sentence is not self-referential. More about my dog:
All dogmatic statements are false.
This sentence (which I made up) is, of course, false, since some dogmatic statements are true (or are they?). Does the fact that my statement is false mean that all dogmatic statements are true? On the contrary, it means that "Not all dogmatic statements are false." But, my dogmatic statement, above, illustrates a literary device of making a false statement, with some truth in it, to illustrate a point. An example of this is "All roads lead to Rome." This is false, and always was. And yet, there is plenty of truth to it. The fact that it is stated so dogmatically as to be false, makes a person stop and think about it.
This statement is true.
While related to the earlier sentence ("This statement is false"), the above is not as interesting, as it does not contradict itself. It too has no truth value, but there is no logical problem with considering it either true or false.
We can have two (or more) statements that are not self-referential, but refer to each other. This situation can lead to the same logical problems that self-referential statements can, but the situation can be very complicated:
#1: Statement #2 is true.
#2: Statement #1 is false.
Assume statement #1 is true. Then statement #2 is true. But, statement #2 says that #1 is false, which is a contradiction. Therefore, statement #1 is false. That makes statement #2 false. But, statement #2 says that #1 is false, which is true, which is a contradiction. There is a circular reference going on here. These two statements contradict each other, and are neither true nor false.
Do you actually believe that? Well, let's state: "Statement #2 is neither true nor false." Therefore statement #1, which says that #2 is true, is in fact false. So, it does have a truth value, after all. But, statement #2 actually says that statement #1 is false, which it is. Therefore statement #2 is true. So, both statements have truth values. Then we get right back into the circular reference: Statement #1 actually says that statement #2 is true, so it too is true, but it says that #1 is false... What I'm saying is that saying that either (or both) of the two statements has no truth value (true or false), leads to a contradiction, just as we do when we say that both do have truth values. And so, these two statements not only have no truth value, but they cannot even be examined with the tools of logic!
And We can get even more complicated, by having many statements, referring to each other in a vast web.
I would like to mention self-referential songs. Three of them come to my mind:
1. Song Sung Blue, which Neil Diamond actually did sing with a "cry" in his voice. So, it was a little bit blue (not very).
2. You're So Vain (I'll bet you think this song is about you), sung by Carly Simon. Even though the guy really is vain, that song really is about him.
3. The Song That Doesn't End, by Norman Martin, sung on the Sherry Lewis & Lambchop Show. It's a delightfully simple song, which should give little children plenty to think about, maybe more than their parents think about.
Here's a self-referential statement, that I just thought up:
I find it ironic that this sentence contains no irony whatsoever.
Errata: The word "errata," at the left, should be "erratum."
Addendum:
I was amused to find the book, How To Write a How-To Book.
The word "car" is not a car. The word "word" is a word. The word "big" is not big. The word "small" is rather small. The word "diminutive" is not diminutive. Do you think the word "appropriate" is appropriate, in this sentence? I don't think that it is inappropriate, unless "inappropriate" is appropriate.
Things to do:
Things not to do:
I made a list of things not to do, and then I checked them off as I didn't do them.
Also see Fractals and Self-Similarity.
Definition of self-reference: See self-reference.
I think that abbreviate or abbreviation should be spelled abbrev.