The use of quotation marks.

Throughout the present text, we are repeatedly making statements about other statements, and by the above dictum (that a statement about something must contain a name of that thing, rather than the thing itself) the statements which we make must contain names of the statements about which we are speaking. For a word or statement, one standard procedure for constructing a name is to enclose the word or statement in quotation marks. Thus one writes:

"Georgia is a southern state" contains "Georgia."

This is a statement about the statement "Georgia is a southern state" and the word "Georgia," and so contains names of the statement and the word, to wit, the statement and the word together with surrounding quotation marks.

I think the typesetters goofed up here. Clearly, the period in "Georgia." (above) belongs outside the quotation marks. After all, the name isn't "Georgia . ", it's "Georgia". Right? I have the same beef with the trailing comma in the following sentence. These may seem like small nits to pick, but Dr. Nick Riviera tells me that current technological applications suffer from such lack of attention to detail and (mis)interpretation of WHAT'S ACTUALLY WRITTEN. Email Dr. Nick for more details (you've got to go back to my index page and read the skit about him to find his address).

If one wishes to talk about a name of a statement or of a word, one must use a name of this name. This becomes rather awkward as in the final words of the preceding paragraph, or in the statement:
The name of "Georgia" is " 'Georgia'. "
In writing the above statement, we are making a statement about a word and a name of the word, and so must actually use a name of the word and a name of the name of the word. Thus we have to use the awkward double quotation marks to make the simple statement about the particular word "Georgia" that, if one has a word without quotation marks, one forms its name by enclosing it in quotation marks.

Such awkward situations arise only when one is discussing names of words or statements (as we are doing now).  Throughout most of the study of logic we make statements only about other statements and not about names of other statements.  Thus we have to USE names of statements (requiring use of single quotation marks), but we do not have to discuss names of statements (and so have no need for quotation marks within quotation marks).  One place where one does have to discuss names of statements is in the proof of Godel's theorem that a consistent logic adequate for mathematics is incomplete.  In this proof we have to use names of names of statements in order to discuss the names of statements.  Failure to comprehend this point is one of the major causes of difficulty in comprehending the proof of Gödel's theorem.

[I was lucky enough to have this logic course before I came across Gödel's theorem.  If you understand this 'naming' business, you're way ahead of the pack.]

Can you think of an area of MATHEMATICS where confusion might arise from failure to distinguish between an object and its name?  .
 

Okay, I've thought about it . . .  TAKE ME THERE!!!!