We use quotation marks for (among other things) mentioning words. In other words, we quote words in order to indicate that we are talking about the word, phase, or sentence occurring within the quotes, and not what what that word, phrase, or sentence refers to. Thus:

Red is a color and "Red" has three letters are true while Red has three letters and "Red" is a color are false.

With this in mind we can see that "Red" names red. is true while each of Red names red and "Red" names "Red" are false.

In addition, we can add multiple pairs of quotes to talk about a word, phrase, or sentence that itself contains quotes. For example ""Red"" takes five keystrokes to type and ""Red"" names "Red" are true.

With this in mind, what is the least number of pairs of quotation marks that need to be added to the following poem to make it true, non-redundant, and not nonsense?

According to W. Quine
Whose views on quotation are fine,
Boston names Boston
and Boston names Boston
But 9 doesn't designate 9.

[Note: "Designates" is understood to be synonymous with "names".]

(In reply to re: More by Penny)

The examples in the problem include "Red names red" as an example of a false statement .. meaning that the first part of a "names" relationship, true or false, need not have quotes around it for the statement to make sense.

Thus, "9 doesn't designate 9" is a true, sensical statement even without the quotes, and (aside from trivial solutions involving one pair of quotation marks) four pairs of quotes are sufficient to complete the problem.

Posted by DJ on 2004-02-16 18:35:10