In their papers On Sense and Nominatum, and On Denoting, Frege and Russell each address the epistemological question of defining meaning. Frege proposed that there are two elements to meaning, while Russell took an entirely different approach to defining meaning.
In On Sense and Nominatum, Frege poses the question, “Is sameness a relation between objects or between signs of objects? (Frege, 217)” He concludes that sameness is a relation between objects, however this idea gives rise to the main question of his paper: how is a statement which indicates sameness information, or is the statement ‘pecunia’ is money’ informative? It is a problematic question; it is akin to asking why ‘Bruce Wayne is Batman’ is informative and ‘Bruce Wayne is Bruce Wayne’ is not. In order to solve this riddle he proposes that there are two aspects of meaning, Nominatum, hereby referred to as reference, and sense. The former refers to the thing in a world which is referred to; the reference of, ‘Professor Fiocco’s sandals’ would in fact be the pair of objects which Professor Fiocco often wears to class. The sense of a phrase or term is how one regards the term. To say, “Bruce Wayne is Batman” indicates that the sense of Bruce Wayne is the same as the sense of Batman. If the sense of Bruce Wayne is ‘the playboy billionaire of Gotham city’ and the sense of Batman, ‘the dark knight,’ then the statement “Bruce Wayne is Batman” is informative because it equates the sense of each term. Frege uses the analogy of “the shadings and colorings which poetry seeks to impart to the sense (219)” to differentiate between sense and reference. The pictures associated with the words are to be ignored, but the poetry is said to express its sense and designate its reference. However, not all linguistic expressions have a sense. He discounts propositions on account of them being abstract and do not fit the definition of a linguistic expression. However, individual terms all have a sense since all individual terms express something (224). Reference differs from sense in that not all terms have it. A phrase such as ‘the greatest integer’ has no reference since there is in fact no greatest integer but since it is a comprehendible statement which conveys some meaning, it has a sense. Frege’s account of meaning is relatively understandable and comprehensive but is challenged by Russell in his paper, On Denoting.
Russell wrote his account of meaning in response to Frege. Both wrote using the same definition of a denoting phrase but Frege proposes that all things have a sense and reference while Russell proposes that a denoting phrase is meaningless unless they occur in a sentence. His theory relies on propositional functions and variables. He treats a denoting phrase as a variable and a sentence, sans a denoting phrase, as a propositional function. If one were to say, “this shirt is white,” then the variable would be ‘this shirt’ and the propositional function ‘____ is white.’ Russell distinguishes between three of the most basic variables: everything, nothing, and something. In a propositional function, the variable everything indicates that the function is always true while nothing indicates that the proposition is always false. The variable something is more problematic as it means that the proposition is sometimes true. He stresses that among these variables and any propositional function that they are a part of are meaningless except in context provided with them. Russell describes three linguistic puzzles which his theory answers. They are the puzzles of identity, the law of excluded middle, and negative existential claims. The identity puzzle asks how a comparative sentence can be informative. Russell notes that Scott is the author of Waverley. King George the IV wanted to know if Scott was indeed the author of Waverley; since Scott and ‘the author of Waverley‘ are interchangeable, one can say that George IV wanted to know if Scott was in fact Scott (Russell, 233). The law of excluded middle, or LEM, is the second puzzle. The LEM states that every proposition has a determined truth value. The problem arises when there is a statement with a variable that does not refer to anything. Russell uses the example of the present king of France. To say that the present king of France is bald is a confusing statement; there is not king of France so it is difficult to state the truth value of the sentence. The third puzzle is of negative existential claims, which are claims about things which do not exist. The problem arises when one tries to make a statement about something which does not exist. Russell uses the example of a round square. It cannot be the subject of a predicate so it is essentially meaningless. Russell’s theory answers these puzzles and has become a subject of great debate for modern philosophy.
Each, Frege and Russell, have a differing but equally valid theory of meaning. Frege uses a two part system of sense and reference to communicate meaning while Russell proposes the use of variables and propositional functions.
Martinich, A.P.. The Philosophy of Language. 5th Edition. New York: New York: Oxford University Press, 2008.