Determining the truth value of a statement - Essay Example

In this light, meaning is not limited to the reference of a term; rather, it involves the aspects of both sense and reference. Furthermore, Frege claims that in the context of a sentence, the sense is its “thought” while the reference is its “truth-value.” Herein, Frege clarifies how the sense of a given term should relate to its reference. Frege claims that a term that has a reference necessarily has a sense, but a term that has a sense need not have a reference. Hence, phrases such as the “King of France” are still meaningful, for they do have a sense.

However, Frege contends that in the context of a sentence, such as “The present King of France is Bald,” it does not have a truth-value, i.e. it is neither true nor false. But doesn’t this manner of explicating non-referring terms lead to a rejection of the law of excluded middle? Russell’s Theory of Definite Descriptions Unlike Frege, Russell basically maintains a referential theory of meaning, for he believes that the difficulties attributed to this theory are results of the failure to distinguish between the grammatical structure and the logical structure of language.

According to Russell’s theory, a linguistic expression, because of its grammatical form, may be taken as a referring expression. And because it is so taken, we may think that for it to be meaningful, it is necessary that it should have a reference, such that if that reference cannot be found in this world, it must be of another world. The point of Russell is that this referring expression, once analyzed logically, may not turn out to be a referring expression at all; and being such, the necessity of attributing a reference to it, to account for its meaning, simply vanishes.

Definite descriptions are linguistic expressions that are taken as referring expressions in their grammatical form, but in their logical form, they are predicate expressions. They are of the form “the so and so;” they begin with the definite article “the” which makes them identify one and only one entity in the world. Moreover, Russell analyzes certain logical puzzles to show that ordinary grammar is a poor guide when it comes to determining what exists in the world. In this essay I shall discuss one of the puzzles raised by Russell.

The Puzzle: The Present King of France is Bald? The puzzle concerns the following statement: “The present King of France is bald.” If we ask whether this sentence is true or false, since there is at present no King of France, the most natural thing to say is that it is false. But supposing we negate it; thus: “The present King of France is not bald.” Still this is false by virtue of the fact that there is at present no such “King of France.” But how can a statement and its negation both be false at the same time?

Consider another statement, “The cat is on the mat.” If this is false, then surely its negation, “The cat is not on the mat,” is true. But it seems that this does not work in the former statement. If we translate the original statement “The present King of France is bald” into its logical form; thus: “There is at least one x, such that x is the present King of France, and X is bald,” we can clearly see that we can negate the statement in the following manner: “There is at lea