Russell On Denoting
-- ShaughanLavine - 29 Aug 2005
Russell says he is advocating a theory about denoting, but he never mentions a central fact about his theory: his theory provides a way to translate what we say using denoting phrases into formal logic. He analyzes all denoting phrases in terms of one "is always true," and he understands that in the same way he understands the universal quantifier.
What is a proposition for Russell? He never got the distinction between use and mention. Therefore, what a proposition is always has the structure of the sentence, but, for example, if the subject of a sentence is a name, then the reference of the name turns out to be a constituent of the proposition. A sentence with a definite description replaced by a variable is a "propositional function" Sometimes that is a function that, given a name, yields the sentence obtained by plugging in the name, sometimes it is a function from objects to truth values, and sometimes it seems to be both.
His theory only considers phrases that are replaceable by names, not, for example, predicates.
Only an animal can bray;
ergo Socrates is an animal, if he can bray.
But any animal, if he can bray, is a donkey.
Ergo, Socrates is a donkey.
Geach, p. 143, Reference and Generality, 3rd ed, Cornell U.P., 1980.