Okay. I realize that I opened this thread a rather long time ago, but other things distracted me from finishing Russell's On Denoting. So I am back at it once again. Unsurprisingly, I have some new questions, but let us first read an excerpt:
If we say "the King of England is bald," that is, it would seem, not a statement about the complex meaning "the King of England," but about the actual man denoted by the meaning.
What I find somewhat perplexing about this quote is when he says "about the complex meaning." What exactly is meant by "complex" in this setting; does it refer to another sentence such that it means "the King of England?" Also, notice that he says "but about the actual man denoted
by the meaning. [emphasize added]" In this section, he seems to be arguing against Frege's view in Sense and Reference (and theories akin to it). Does Frege actually hold a view like this? I didn't get the impression that Frege held
the meaning (sense) to denote something, while reading Sense and Reference. What Russell is saying here appears rather subtle, but perhaps I am wrong and it is straightforward. I'll let you be the judge of that!
Now, in the paragraph containing this quote, and the one following it, Russell seems to be arguing against theories that posit that every denoting phrase must have a meaning and denotation (sense and reference) by considering a few examples. The first of these is about the King of France. The examples that follow this are the ones that confuse me, namely, the one about the unit class and the King's only son. Let's first look at the unit class.
The unit class example is, like the King of France example, suppose to show that statements can have meaning
and truth value despite having no denotation (referent). Here is what he says concerning this example:
Or again consider such a proposition as the following: "If u is a class which has only one member, then that one member is member of u," or, as we may state it, "If u is a unit class, the u is a u." This proposition ought to be always true, since the conclusion is true whenever the hypothesis is true. But "the u" is a denoting phrase, and it is the denotation, not the meaning, that is said to be a u. Now if u is not a unit class, "the u" seems to denote nothing; hence our proposition would seem to become nonsense as soon u is not a unit class.
First of all, I do not see how "If u is a class which has only one member, then that one member is member of u" and "If u is a unit class, the u is a u" say the same thing, particularly the conclusions of the two conditional statements.
However, just focusing on the latter conditional statement, I am somewhat confused at what he says about it. I grant that the conditional is always true, because the conclusion "the u is a u" appears to be a tautology. Moreover, I grant that "the u" is a denoting phrase, where, presumably, "u" is a variable that ranges over all classes/sets. What perplexes me is that the denoting phrase "the u" has no denotation once "u" is not a unit class. Why couldn't "the u" denote whatever "u" is? I find this remarkably confusing. Is he stipulating that it refers solely to unit classes? If that's the case, how could it ever denote anything but a unit class, so that his worry seems groundless? Why does he think this is true? I don't see how the proposition becomes nonsense as soon as u is anything besides a unit class.
I'll leave it at that. Once we have resolved these issues, we can move on to the example about the King's son.
