In “On Denoting” Bertrand Russell responds to Gottlob Frege’s system of categorizing names and descriptive phrases as being meaningful within the boundaries of Sinn and Bedeutung, often translated “sense” and “reference.” Russell translates and alters Frege’s Bedeutung as “denotation.” Though Russell does not define precisely what he means by this term, from the examples he gives it can be ascertained that by “denoting phrases” he seems to mean, more or less, quantitative descriptions. By his definition, then, names acquire their meaning quantitatively from the denoting phrases attached to them or associated with them and both names and denoting phrases have meaning within the limited context of the sentence. Within the framework of the problems and examples he presents in “On Denotation,” (e.g. “Scott wrote Waverley, and it is always true of y that if y wrote Waverley, y is identical with Scott.”) this makes sense, and solves a few problems Frege’s system could not explain.
Russell’s view on names as getting their meaning from quantitative descriptions rather than what they refer to (“refer to” in the minds of the people hearing/speaking) could present a few problems if applied to the real world, however. Consider the example “Columbus was the man who discovered America.” This is a statement that is seemingly true; we all learned this in grade school. Not only is it factually true, but according to Russell’s system it denotes one and only one person: the definite article “the” not only implies but insists upon the quantitative value of this statement equaling one and only one. Since Columbus was a real person, this statement is also logically true: the quantitative ONE (Columbus) is not ZERO (a non-entity in the real world).
Russell would not say here that this description is equal to Columbus—he was not interested in proving that x = x. Rather, he was interested in the parameters that define x, in the context of their descriptions, which should be factually true in order to equate to a truthful statement. Again, it is safe to say that most people would regard “Columbus was the man who discovered America” to be factually true. In a sense, we know this based on Russellian definitions. None of us have met Columbus, or know people who knew Columbus and have described his freckles, scars, his bearing, stench, or his quotidian mannerisms to us. What we know of Columbus we have learned by rote, by scholastic description. We do know Columbus, primarily, as “the man who discovered America.”
However, suppose it is one day concretely discovered that Leif Eriksson discovered America, long before Columbus convinced the Spanish court to supply him with ships and a bevy of sailors for the pecuniary conquest of the Far East. Suppose I forget to pick up the newspaper the day this information is dispersed. Suppose my friends are too busy doing laundry, grading freshmen papers, cooking ramen and potatoes and writing their own essays to bring this topic up. A week later, I casually refer to Columbus as “the man who discovered America.” My friends laugh. They say: “Yeah, airhead, you’re behind the times. Leif Eriksson discovered America.”
Suddenly, my textbook definition is thrown into turmoil. By Russell’s framework, what I previously knew to be true: “Columbus was the man who discovered America” could have been described in a Russellian framework as “Columbus discovered America, and it is always true of y that if y discovered America, y is identical with Columbus.” Now, I hear Leif Eriksson discovered America. According to this definition, Leif Eriksson should just be another name for Columbus. Obviously, however, this is not the case; Leif Eriksson died before Christopher Columbus’ grandmother was born; these are separate men with separate stories.
Russell might have countered that in this circumstance the definition would automatically change to “Leif Eriksson was the man who discovered America,” and the previous definition would become immaterial. This would certainly reflect what is known to be factually true in the world. However, Russell’s focus was not on sense but on denotation. If people’s names are meaningful only in the context of their definite descriptions, then, in theory, given that my textbook definition is all I really know of Columbus, and that “it is ALWAYS true of y that if y discovered America, y is identical to Columbus” and given that suddenly my new knowledge is “Leif Eriksson discovered America,” and this is all I know of Leif Eriksson, I could, quite easily, assume that Leif Eriksson is Christopher Columbus.
Again, this seems like a ridiculous conclusion. To say it is ridiculous, though, requires at least some appeal to the real people Leif and Christopher, as they were, in their glories and failures, in what we know of them and do not know of them, in their great feats and quotidian mannerisms. It requires an appeal to meaning, or sense, or to the humbling realization that I really know very little about either one of these men. It requires that I refer to them and not just to their names in the context of the sentence.