From page xli of the CPBR volume 5 - in a letter of 13 June 1905 to Lucy Donnelly BR wrote:
"For a long time I have been at intervals debating this conundrum: If two names or descriptions apply to the same object, whatever is true of the one is true or the other. Now George IV wished to know
whether Scott was the author of Waverly. Hence, putting "Scott" on the place of "the author of Waverly", we find that George IV wished to know whether Scott was Scott, which implies more interest in
the Laws of Thought than was possible for the First Gentleman of Europe. This little puzzle was quite hard to solve; the solution, which I have now found, throws a flood of light on the foundations
of mathematics and the whole problem of the relation of thought to things."
The solution was published on "On Denoting".
From "On Denoting" - page 423 of CPBR volume 4, BR wrote:
'According to the view which I advocate, a denoting phrase is essentially part of a sentence, and does not, like most single words, have any significance on its own account.
If I say "Scott was a man", that is a statement of the form "x was a man", and it has "Scott" for its subject". But if I say "the author of Waverly was a man", that is not a statement of the form "x
was a man", and does not have "the author of Waverly for its subject. ... , we may put, in place of "the author of Waverly was a man" the following: "One and only one entity wrote Waverly, and that one
was a man".
... And speaking generally, suppose we wish to say that the author of Waverly had the property F, what we wish to say is equivalent to "One and only one entity wrote Waverly, and that one had the property F."
... "Scott was the author of Waverly" (i.e. "Scott was identical with the author of Waverly") becomes "One and only one entity wrote Waverly, and Scott was identical with that one"; or reverting
to the wholly explicit form: "It is not always false of x that x wrote Waverly, that it is always true of y that if y wrote Waverly y is identical with x, and that Scott is identical with x."