Theory of Descriptions - Definite Descriptions

Definite Descriptions

Russell analyzes definite descriptions similarly to indefinite descriptions, except that the individual is now uniquely specified. Take as an example of a definite description the sentence "the current Emperor of Germany is gray". Russell analyzes this phrase into the following component parts (with 'x' and 'y' representing variables):

1. there is an x such that x is an emperor of Germany.
2. for every x and every y, if both x and y are emperors of Germany, then y is x (i.e. there is at most one emperor of Germany).
3. anything that is an emperor of Germany is gray.

Thus, a definite description (of the general form 'the F is G') becomes the following existentially quantified phrase in classic symbolic logic (where 'x' and 'y' are variables and 'F' and 'G' are predicates - in the example above, F would be "is an emperor of Germany", and G would be "is gray"):

∃x

Informally, this reads as follows: something exists with the property F, there is only one such thing, and this unique thing also has the property G.

This analysis, according to Russell, solves the two problems noted above as related to definite descriptions:

1. "The morning star rises in the morning" no longer needs to be thought of as having the subject-predicate form. It is instead analyzed as "there is one unique thing such that it is the morning star and it rises in the morning". Thus, strictly speaking, the two expressions "the morning star..." and "the evening star..." are not synonymous, so it makes sense that they cannot be substituted (the analyzed description of the evening star is "there is one unique thing such that it is the evening star and it rises in the evening"). This solves Gottlob Frege's problem of informative identities.
2. Since the phrase "the current Emperor of Germany is gray" is not a referring expression, according to Russell's theory it need not refer to a mysterious non-existent entity. Russell says that if there are no entities X with property F, the proposition "X has property G" is false for all values of X.

Russell says that all propositions in which the Emperor of Germany has a primary occurrence are false. The denials of such propositions are true, but in these cases the Emperor of Germany has a secondary occurrence (the truth value of the proposition is not a function of the truth of the existence of the Emperor of Germany).