Intro to Language: Russell’s Theory of Descriptions

by Luke Muehlhauser on January 16, 2011 in Intro to Language

Part 4 of my Intro to Language series.

intro_to_language It seems natural that sentences have meaning in virtue of the things to which their words refer. But earlier, we explored why reference alone cannot account for meaning in language, and last time we explored why reference can’t even seem to account for singular terms like “this” and “Charlie Chaplin.” Specifically, we looked at four puzzles that Bertrand Russell addressed with what came to be called his Theory of Descriptions.1 Russell built up his theory around the word “the,” another problematic word for any Reference theory of meaning. (To what does “the” refer?) Consider:

(1) The author of Hamlet was English.

This sentence seems to be the simplest kind of subject-predicate sentence. Its subject refers to a person (William Shakespeare) and predicates something (Englishness) of him. But notice that troublesome word “the.” What are we to make of that if we want to say that sentences mean something because their words refer to things? Russell suggests that “the” is an abbreviation for a set of statements involving quantifiers like “all”, “some”, “most”, “six”, and so on. Russell would say (1) really means all of the following:

(1a) At least one person authored Hamlet. (1b) At most one person authored Hamlet. (1c) Whoever authored Hamlet was English.

And this is what we all mean by saying (1). Each of these three is necessary for the truth of (1), and together they are sufficient for the truth of (1). So Russell seems to be on to something. He has identified the logical form of (1), which is more useful to logicians than its grammatical form. As an illustration of the difference, consider:

(2) I saw Theresa.

(3) I saw nobody.

Grammatically, these sentences have the same form: Subject + Transative Verb + Object. But logically, these sentences work quite differently. “I saw Theresa” entails that I saw somebody, but “I saw nobody” entails the opposite. Logically, “I saw nobody” does not mean that I saw some person we have given the name “nobody.” Instead, it means “It is not the case that I saw nobody.” This “nobody” is not really a singular term, but a quantifier. It means that I saw zero persons.

In the same way, Russell would say that “the author of Hamlet” is not really a singular term as it appears to be, but rather a convenient (though misleading) abbreviation of the three part set of quantifying statements  (1a), (1b), and (1c). Russell says that this apparent singular term “the author of Hamlet” actually “disappears on analysis.” And since the troublesome singular term was the source of the four puzzles we visited in the previous post, we can now solve those puzzles using Russell’s theory. That’s what we’ll do next time.

  1. In the first several posts of this series, I am following along with William Lycan’s superb Philosophy of Language: A Contemporary Introduction. []

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{ 3 comments… read them below or add one }

Alex January 16, 2011 at 3:15 pm

I think you meant “It is not the case that I saw somebody” in the second to last paragraph.

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Xan Bozzo January 17, 2011 at 6:23 am

In the same way, Russell would say that “the author of Hamlet” is not really a singular term as it appears to be, but rather a convenient (though misleading) abbreviation of the three part set of quantifying statements (1a), (1b), and (1c).

Actually, Russell would say that “the author of Hamlet” is an incomplete symbol; in other words, contrary to your comments, “the author of Hamlet” does not represent (1a), (1b), and (1c), at least not in isolation (as you present it). The definite description, “the author of Hamlet,” logically reduces to (1a), (1b), and (1c) only when in the context of a sentence or a proposition. So, your (1).

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Steven R. January 17, 2011 at 9:27 am

Interesting series Luke, I had begun to question how our language worked and here you are starting a mini-course on the topic. Much thanks.

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