Several students have asked what quotation marks do. The relevant part of our textbook is pages 60-62 (although it uses single quotes where the professor uses doubles).

The brief answer to the question is that we mean for the addition of quotation marks to create a new word, sign or expression, just like adding the prefix "un-" to "controlled" yields the new word "uncontrolled". The resulting new word, sign or expression has a different meaning from the original one. Regardless of whether the original word is a noun, verb, adjective or whatever, the new word will be a noun. This noun will refer to the original word, sign or expression. THUS, LOGICIANS USE QUOTATION MARKS TO CONSTRUCT NAMES FOR PARTICULAR EXPRESSIONS WITH WHICH THEY CAN TALK ABOUT THEIR PLACE IN LANGUAGES.

After checking through an English grammar book, I can see why this is so confusing. The way logicians use quotes isn't even mentioned! The only uses the grammar book mentions for quotation marks are (1) for dialogue, (2) for minor titles, and (3) to enclose words meant in a special or ironic sense. As an example of the third case, it gives

         His "castle" was a cozy little rattrap.

Which the book says may be paraphrased as

         His so-called castle was a cozy little rattrap.

Thus, according to the grammar book,

         "5" is a number.

can only mean

         What is called "5" is a number.

(Which is true.) However, what professor Rauti means by it is

         The expression "5", which refers to the number 5, is itself a number.

(Which is false -- Expressions and numbers are two different kinds of things; had the evolution of language proceeded differently, "6" might have referred to the number 5 and "5" to the number 4, but this would not have changed the fact that 5 + 5 = 10 -- we would have expressed this fact as "6 + 6 = 10".)

In short, the dialect of English used by our textbook and throughout the logic literature is so different from that described in the grammar book that you would end up with different answers if you didn't realize that we are using a special dialect.

In our dialect, the first word of the sentence in question is ""5"", which is 3 characters long and refers to an expression rather than to the same thing as that expression. The thirteenth word of the sentence immediately previous to this one is """5""", which is 5 characters long. It refers to the word for the word for the number 5. This goes on and on ad infinatum as we expand English to refer to itself.

I hope this helps!

Chris Lang