Theory of Descriptions - Indefinite Descriptions

Indefinite Descriptions

Take as an example of an indefinite description the sentence "some dog is annoying". Russell analyzes this phrase into the following component parts (with 'x' and 'y' representing variables):

1. there is an x such that x is a dog.
2. x is being annoying.

Thus, an indefinite description (of the general form 'an D is A') becomes the following existentially quantified phrase in classic symbolic logic (where 'x' and 'y' are variables and 'D' and 'A' are predicates):

∃x

Informally, this reads as follows: there is something such that it is D and A.

This analysis, according to Russell, solves the second problem noted above as related to indefinite descriptions. Since the phrase "some dog is annoying" is not a referring expression, according to Russell's theory, it need not refer to a mysterious non-existent entity. Furthermore, the law of excluded middle need not be violated (i.e. it remains a law), because "some dog is annoying" comes out true: there is a thing that is both a dog and annoying. Thus, Russell's theory seems to be a better analysis insofar as it solves several problems.