Ever since Epimenides the Cretan (7th century B.C.) declared that All Cretans are liars, the notion of self-reference became synonymous (and often erroneously) with that of paradox. However, most ubiquitous self-reference which happens each time somebody says "I", is harmless. Following are a few gems from Metamagical Themas.

1. Thit sentence is not self-referential because "thit" is not a word.
2. If this sentence didn't exist, somebody would have invented it.
3. This is not a complete. Sentence. This either.
4. This sentence will end before you can say "Jack Rob
5. Does this sentence remind you of Agatha Cristie?

Raymond Smullyan lists what he calls self-annihilating sentences from a collection by Saul Gorn "S. Gorn's Compendium of Rarely Used Cliches." :

1. Before I begin speaking, there is something I would like to say.
2. I am a firm believer in optimism because without optimism, what else is there?
3. Half the lies they tell about me are true.
4. Every Tom, Dick, and Harry is called John.
5. Having lost sight of our goal, we must redouble our efforts!
6. I'll see to it that your project deserves to be funded.
7. I've given you an unlimited budget, and you have already exceeded it!
8. A preposition must never be used to end a sentence with.
9. This species has always been extinct.
10. Authorized parking forbidden!
11. If you're not prejudiced, you just don't understand!
12. Inflation is an economic device whereby each person earns more than the next.
13. Superstition brings bad luck.
14. That's a real step forward into the unknown.
15. You've outdone yourself as usual.
16. Every once in a while it never stops raining.
17. Monism is the theory that anything less than everything is nothing.
18. A formalist is one who cannot understand a theory unless it is meaningless.

David Wells asks the following questions:

I placed his answers at the bottom of the page. However, on my part, I can't help wondering whether one can possibly ask the same question with different objects.

From the wonderful Beyond Numeracy I gleaned the following two pearls

1. There is the case of the voter who when asked by a pollster what were the reasons for the ignorance and apathy of the American public, responded, "I don't know and I don't care."
2. What is the question that contains the word cantaloupe for no apparent reason?

Lest you form a self-defeating impression that thinking up self-referential sentences is an exclusive pastime of self-indulgent mathematicians, I'll cite from a small book by William Safire

1. Don't use contractions in formal writing.
2. Do not put statements in the negative form.
3. Avoid run-on sentences they are hard to read.
4. Verbs has to agree with their subjects.
5. Avoid trendy locutions that sound flaky.

A subtlety from the Littlewood's Miscellany:

The following comes from A Whack on The Side of The Head by R. von Oech

Paul R. has suggested a similar one:

It took me longer than I originally planned to get to the Hofstadter's Law (D. Hofstadter's Godel, Escher, Bach):

A friend of mine found the following in the Omni magazine:

There is a devilish shade of self-reference in a Piet Hein's grook, isn't there?

M.Minski's passage from the jacket of The Mind's I by D.Hofstadter and D.Dennett unfailingly maneuvers one's mind into reflective mood:

Here is another one from the Littlewood's Miscellany:

Krishna Kumar reminded me of the following:

Here are some self-referential statements that I came across recently. Break every rule. All generalizations are misleading. If somebody loves you, love them back unconditionally. Computers are like lynxes in the sense that I cannot think of a suitable analogy for either of them right now. (The last one is by Scott Adams in one of his Dilbert books.)

Robert Arthur quoted from Desmond MacHale's "Comic Sections". Said he, one of the cleverest things I have ever seen in a book went something like this. Page 347 was devoted to ERRATA and consisted of the following

John Allen Paulos opens his book Mathematics and Humor with a paragraph that contains a story of a friend of his who took a speed-reading course. The friend noted this in a letter to his mother. His mother responded with a long, chatty letter in the middle of which she wrote, "Now that you've taken that speed-reading course, you've probably already finished reading this letter."

A superb site IMPOSSIBLE OBJECTS (which I no longer find accessible) defined Impossible objects as

Now think of it. Is it possible to put anything together in an impossible way?

Lew Lefton's gem is quoted by John de Pillis (777, p. 156):

A story is told by Steven Krantz in his Mathematical Apocrypha (p. 23):

Camiel Feij from the Netherlands sent me a delightful philosophical observation with a probable attribution to Isaac Bashevis Singer:

An insert on self-reference appeared in Mathematics Magazine Vol 78, No 1, February 2005:

But now come to think of it: when else but previously a book might or might not have been published? Is this specification not redundant?

Additional examples can be easily found on the Web. I came across the following at the David's Profession Jokes web site:

Another site quotes Milton Berle:

In the September 2005 issue of Math Horizons the readers were asked to submit questions that contained their own answers. The results of the competition have been published in the April 2006 issue. Following are a few samples:

As reported by BBC, US President George W Bush was twice the man at the White House Correspondents' Association annual dinner on Saturday, 29 April, 2006. Playing up to his public persona, Mr. Bush sent himself up alongside impersonator, Steve Bridges. At some point Mr. Bridges volunteered for the president:

And here is a piece of wisdom from Afred E. Neuman [What the Numbers Say, p. 128]:

Now returning to the origin of all the troubles, Epimenides the Cretan, you have probably heard of the island where each person is either a Knight (and speaks only truth) or a Knave (and hence always lies). Does it follow that Epimenides could not possibly live in such a place?

1. Blinking page with errors
2. Apparent paradox
3. Set of all subsets
4. An Impossible Page
5. Russell's paradox
6. An Impossible Machine
7. A theorem with an obvious proof

References

1. B. Bollobas, Littlewood's Miscellany, Cambridge University Press, 1990
2. W. Dunham, The Mathematical Universe, John Wiley & Sons, NY, 1994.
3. D. Fomin, S. Genkin, I. Itenberg, Mathematical Circles (Russian Experience), AMS, 1996
4. M. Gardner, aha! Gotcha. Paradoxes to puzzle and delight, Freeman & Co, NY, 1982
5. D. R. Hofstadter, Metamagical Themas, Basic Books, Inc., 1985, Chapter 16.
6. D. Hofstadter and D. Dennett, The Mind's I, Basic Books, 1981
7. D. Niederman, D. Boyum, What the Numbers Say?, Broadway Books, 2003
8. S. Krantz, Mathematical Apocrypha, MAA, 2002
9. J. A. Paulos, Beyond Numeracy, Vintage Books, 1992
10. J. de Pillis, 777 Mathematical Conversation Starters, MAA, 2002
11. W. Safire, Fumblerules, Doubleday, 1990
12. R.Smullyan, 5000 B.C. and Other Philosophical Fantasies, St. Martin's Press, NY, 1983
13. R. von Oech, A Whack on The Side of The Head, Warner Books, 1990
14. D.Wells, The Penguin Book of Curious and Interesting Puzzles, Penguin Books, 1992

Copyright © 1996-2007 Alexander Bogomolny

Four. The sentence contains three spelling mistakes, plus the false claim that it only contains one mistake, making a total of four mistakes.

The second question, paradoxically, cannot be answered. It contains only two spelling mistakes but claims to contain three mistakes; therefore that claim is wrong and it actually contains three mistakes - except that if it contains three mistakes then the claim that it contains three mistakes is correct, and so it only contains the two spelling mistakes, in which case...!

Here is a remark by Richard Bissell

A response came from Italy:

Here's a reaction to Rita's letter: