Mediated Reference Theory - Bertrand Russell

Bertrand Russell

A paradigm example of an indirect theory of reference is that of philosopher Bertrand Russell. In his direct reference theory, Russell first distinguished between a "logical subject" and a "grammatical subject." The former is the thing in the real world - the referent; while the latter is a description or concept. He then claimed that in logic a "feeling for reality" had to be maintained in order to save discussion from a whole host of troubles. And since the logical subject was made up only of reference, tied together in strings by propositional functions, in logic there was no meaning except reference.

Russell was also quite alive to the topic of descriptions. His particular interest was in "definite and indefinite descriptions." Definite descriptions have the form of "the such-and-such", and indefinite descriptions have the form of "a such-and-such". Russell then made a surprising argument: that "descriptions had meaning only if they were put into bigger statement(s)." This is because his method of translating sentences necessitated that they be rewritten in logical notation, and an isolated description cannot be effectively captured by any such notation.

Take the sentence, "The king of France is bald", for instance. For Russell, what it really translates as (in a reformed, better English) is:

There is at least one x such that: x and nothing else is a King of France, and x is bald.

In this newer, better form, the word "the" no longer appears; it is diffused throughout the rest of the logical translation. This, for Russell, is why the definite description "the king of France" is not meaningful on its own; the word, 'the', doesn't work unless it appears in the context of a full sentence.

Furthermore, the above can be expressed in a more strict logical form (where K(x) means "x is the king of France", B(x) means "x is bald", the bullet means "and", and the arrow means "if-then"):

Which says: "there is an x such that: x is bald and x is a king of France; and for every y that is a king of France, x is y; and every z that is a king of France is bald". This is a very long way of stating that something is uniquely both king of France and bald.

For Russell, this logical form would provide the speaker of a language with metaphysical insight as to what they are actually speaking about.