Russell - Concepts vs Denotation

Question

I understand why definite descriptions like 'The King of England' are denoting phrases, but I am confused by differing between concepts and what they 'denote'.

In Principles of Mathematics:

A concept denotes when, if it occurs in a proposition, the proposition is not about the concept, but about a term connected in a certain peculiar way with the concept. If I say “I met a man,” the proposition is not about a man: this is a concept which does not walk the streets, but lives in the shadowy limbo of the logic-books. What I met was a thing, not a concept, an actual man with a tailor and a bank-account or a public-house and a drunken wife. Again, the proposition “any finite number is odd or even” is plainly true; yet the concept “any finite number” is neither odd nor even.

For example 'a man' seems equivalent to 'one man', why is this treated as denoting anything but the idea of there being a single entity and that entity being of a class 'man'?

For example, I could easily say 'one man lives next door', It is a simply a statement about how many men are next door I do not need to be using 'one man' to refer to any individual, in this case it denotes a concept.

This is different to 'The King of England' where I could argue that 'the king of england' is a person and the idea of what it is to be the king of england is a different entity which needs it's own reference.

Do these phrases have two meanings and what is the difference between the concepts and what they denote? Take 'two' does it have a concept and denotion because it's denotation is a concept?

With 'The king of England', I could suggest that the only 'concept' it gives me is that of the man, the denotation in this case which to me is clearly a particular person.

Clearly I am misunderstanding, but I'd appreciate if anyone could suggest where, and if there is other sources for which I can clear up my confusion.

Answer 1

"The king of England" is not always a denoting expression. In a sentence like "the king of England has always had the power to dissolve Parliament", the phrase "the king of England" does not denote a particular; it's meaning is a concept.

Similarly, the phrase "a man" may denote or may not denote depending on context. In a sentence like "She needs a man", the the phrase "a man" does not denote; there is no particular man that it is referring to. However the phrase still has meaning. You can still look at particulars and say whether a given particular is a man or not. We describe this situation by saying that the meaning (not the denotation) of the phrase "a man" in this context is a concept.

On the other hand, in a sentence like "She went out with a man last night", the phrase "a man" denotes a particular man--the one she went out with last night. In this case, for consistency, we still say that the meaning of the phrase "a man" is still a concept--the concept of being the man she went out with last night--but that the denotation of the phrase is the man himself.

You can't tell from the mere form of a noun phrase whether it denotes or not. For example, some people claim Jesus never existed. If he did exist then "Jesus" denotes. If he did not exist, then "Jesus" does not denote.

But it's worse than that; from the form of a phrase you can't tell even whether it is intended to denote, not even a proper noun. For example, suppose it rains and you say "Mother Nature didn't want us to play baseball today". The phrase "Mother Nature" is a proper noun, but in this context it is not intended to denote.

Furthermore, even if a phrase denotes, the denotation may not relevant to the intent of the speaker in uttering the sentence. This may be the case for "One man lives next door". If your intention is simply to convey the number and sexes of your neighbors, then the phrase "one man" in that context may denote a particular, but the particular is not relevant to the utterance. What is relevant is the concept of being one man, which is the meaning of the phrase, not its denotation.