Identity Puzzle

• To lead up to the theory of sense, it helps to understand how Frege used identity puzzles to create the theory. We can create our own identity puzzles to illustrate this. Take the statement "Dr. Seuss is Theodore Geisel," which is a true statement in the form "a=b." But this statement is different from "Dr. Seuss is Dr. Seuss," which is an "a=a" statement and is automatically true. To ascertain the validity of an "a=b" statement such as "Dr. Seuss is Theodore Geisel," you must examine the world to see if those two individuals are indeed the same.
  
  

Resultant Problem

• However, if both "a=a" and "a=b" are true, and if both of them are true in the same way (Dr. Seuss is identical to Dr. Seuss and Dr. Seuss is also identical to Theodore Geisel), then there needs to be some way of distinguishing the two types of statements. To clarify this difference, take another one of Frege's puzzles, involving the Principle of Identity Substitution. To continue with our previous example, the sentence "John believes that Dr. Seuss wrote 'The Cat in the Hat'" is true, as is the statement "Dr. Seuss is Theodore Geisel." However, the following conclusion ("John believes that Theodore Geisel wrote 'The Cat in the Hat'") is not necessarily true. Thus, the logic of substitution in language comes into question.
  
  

Conundrum

• Knowing that Dr. Seuss was Theodore Geisel's literary pseudonym and that "The Cat in the Hat" was indeed published by a man wishing to call himself Dr. Seuss, the statement "John believes that Dr. Seuss wrote 'The Cat in the Hat'" can easily be said to be false. But if all that has occurred is a substitution of one valid and true name for another, why would the sentence have a different meaning than "John believes that Theodore Geisel wrote 'The Cat in the Hat'?" Out of this, the need for a distinction between sense and reference arises.
  
  

Sense and Reference

• The names "Dr. Seuss" and "Theodore Geisel" refer to the same person, but each name expresses a different sense. Thus the "a=a" and "a=b" substitution conundrum is explained. Since "a" has a different sense from "b," the sense of the entire expression "a=a" is different from the sense of the expression "a=b." When this idea is taken one step further, you can see how the usage of "a" for "b" in a propositional attitude statement like "John believes that Theodore Geisel wrote 'The Cat in the Hat'" can result in an untrue statement; in this example, "Theodore Geisel" and "Dr. Seuss" have different references as well as senses, as "Theodore Geisel" refers to a man who could be said to not have written any books.
  
  

Terminology

• The most important concept to grasp from Frege's Theory of Sense is that a name's meaning is imprecise unless it is analyzed in terms of sense and reference. "Reference" is the exact object indicated by a name, and "sense" is the meaning of a name or noun independent of its reference. Frege called sense "Sinn," but other scholars have used "meaning," "intention" or "content" to explain it; for "Bedeutung" or "reference," scholars have used "denotation," "nominatum" and "designatum."