Philosophy structure definition

Advancements in mathematical logic in late nineteenth century proved to have an important impact on the concept of structure as it was applied within philosophy. First order logic provided philosophers with a rich formal language in which to represent the logical forms of various entities, ranging from sentences to scientific theories, thus allowing reasoning involving these entities to be represented within a logic.

In the philosophy of language, the importance of the concept of structure can be seen in the importance attributed to the representation of sentences by their logical form. Such representation was suggested by Bertrand Russell in his classic paper "On Denoting," which proved to have an enormous impact on the subsequent practice of philosophy.

Russell's paper was motivated by concerns regarding the truth values of sentences that contain empty definite descriptions. As an example, consider the following sentence:

(1) The present king of France is bald.

The truth or falsity of this sentence would appear to depend upon the properties of the referent of the definite description "the present king of France." The logical structure of the sentence appears to be that of

(2) Bk

where 'B' is a once place predicate signifying baldness and 'k' is a constant referring to the present King of France. But of course France does not have a King, and so the referent of 'k' is null and so the truth value of the sentence is undecided. This means that if we propose to determine the meaning of a sentence in terms of its truth conditions, the sentence is meaningless. And this then results in a number of problems.

In "On Denoting," Russell offers a way to avoid these problems through the assignment of meanings to sentences such as (1) via the the assignment of logical forms to these sentences that differ from that of (2). That is, Russell proposes that the logical form of (1) is not provided by its surface grammar. Instead, Russell proposes that the logical form of (1), and of other sentences that include definite descriptions, is instead

(3) For all x (Kx and For all y (Ky then y = x) and Bx)

where 'K' and 'B' are one place predicates stating that an entity is the King of France and is bald, respectively, and states that any individual that satisfies the 'K' predicate is unique. According to Russell, the logical structure of (1) thus differs dramatically from the surface grammar of the sentence. Rather than simply assume the existence of an individual 'k', the sentence instead takes the form of an existence claim. And as there is no individual that satisfies this claim, the sentence is thus false.

The importance of "On Denoting" to philosophy stems from the concept of philosophical practice that is implicit within the movement from (2) to (3). The idea that the logical form of a given sentence might differ from its surface grammar, and that this logical form was in turn important in determining the meaning of the sentence, offered an important task to philosophers, namely that of identifying the logical forms of sentences. Since the publication of "On Denoting," most philosophy has been devoted to this task.