Which of the two following statements is True and which is False ?

The next statement is "False".
The previous statement is "True".

The posted solution is incorrect, at least if we are sticklers about grammar and punctuation.

Quotes, such as those used around the words "False" and "True" in the puzzle, serve three main purposes:

[1] scare quotes, used to indicate that one should take the use of the word with a grain of salt, or that the word is not being used in a perfectly literal sense.

[2] for quoting something said, written, etc. by another speaker, author, etc.

[3] for the purposes of mentioning a word, instead of using it.

Now, given the context (a logic puzzle, or paradox), we can rule out the use of scare quotes, since it is unclear what the intention of the question would then be, and presumably the present context is one in which precision is wanted (and, being charitable, we can assume that the question should be interpreted in a precise way). Second, we can immediately rule out the possibility that the puzzle writer meant to be quoting someone else's use of "true" and "false". As a result, the only coherent way in which to intepret the use of the quotation marks is that of signifying that the words in question are being mentioned, not used.

A bit of clarification: One uses a word when one wants to speak, write, etc. about what the word refers to, while one mentions a word (and uses quotes) when one wants to talk about the word itself. A word without quotation marks is understood always to be used, while (in some instances, see above) a word in quotes is being mentioned. So for example:

Red is a colour.

"Red" has three letters.

are true while:

Red has three letters.

"Red" is a colour.

are false (the first would imply that there is some colour that has three letters, while the second would imply that there is some object that is simultaneously a word and a colour). Thus, realizing that the sentence involved in the puzzle are mentioning the words "False" and "True", we can now see that they are equivalent, respectively, to:

The next statement is identical to the word "False".

The previous statement is identical to the word "True".

Upon inspection, we can see that both statements are false, since neither statement consists of a single word (much less one or the other of the particular words "True" or "False").

Posted by RoyCook on 2003-10-06 13:53:43