Tutorial # 9. Russell. On Denoting. Denoting in "On Denoting"

The subject of denoting is of very great importance, not only in logic and mathematics, but also in the theory of knowledge.

- No general characterization of denoting is given, only a list of “denoting phrases.”

A man,
Some man,
Any man,
Every man,
All men,
The present King of England.

"A phrase is denoting solely in virtue of its form"

+ The notion of a variable is fundamental to the theory of denoting.

A variable x "is essentially and wholly undetermined."

A proposition is always of the form C(x)

A proposition results from replacing the variable with a denoting phrase, as with C(a man).

Russell’s general thesis is that propositions containing denoting phrases are reducible to propositions not containing them.

*The Reduction

C(a man) means C(x) and x is human for some values of x.

"I met a man." means "I met x, and x is human for some values of x."
"All men are mortal” means “If x is a man, then x is mortal for all values of x"

--> “a man” and “all men” are contextually defined:
they have meaning only when embedded in a larger context.

*Definite Descriptions
Denoting phrases preceded by "the" are "by far the most interesting and difficult of denoting phrases."
Like the other denoting phrases, definite descriptions are contextually defined.

- Strict use of a denoting phrase in the sentence “The father of Charles II was executed” involves:

Existence: x was father of Charles II, for some value of x.

Uniqueness: if y was father of Charles II then y is identical with x, for any values of x who was father of Charles II and any value of y.

The Reduction of Definite Descriptions
The definite description "the father of Charles II" may occur in propositions of the form C(the father of Charles II).

The general analysis of C(the father of Charles II) combines existence and uniqueness:

For some value of x, x was father of Charles II, and C(x), and if y was father of Charles II, then y is identical to x, for any value of y

"The father of Charles II was executed” is:
For some value of x, x was father of Charles II, and x was executed, and if y was father of Charles II, then y is identical to x, for any value of y.


*** Consequences for Knowledge


Acquaintance and Description
The theory of denoting has consequences for knowledge.
We know things in two ways:

I) By being acquainted with them,
II) Through descriptions of them.
If we can apprehend (think about) a proposition, then we are acquainted with all its constituents.
If we know an object (say, someone else’s mind) only by description, then our knowledge can be expressed in propositions with denoting phrases, which do not contain the object itself.
We then know only the properties of the object and do not know any propositions
which contain the object itself.