Val(x, "Norma Jeane Mortenson") iff x = Norma Jeane Mortenson. |
iff x lived in a foster home for 7 years, and x was raised by a friend of her mother's, and x married a sailor, who x later divorced, and then y = x. |
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dossiers |
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This chapter develops an explanation for the meaning of proper nouns (names - Albert Einstein, Lake Ontario, Superman) in terms of the mechanisms developed in the previous chapter, especially PC+.
The previous pages follow the book's order rather closely; this page breaks this precedent by concentrating more on the issues raised by the chaper, and less on the particular order in which they are raised.
The crux of this chapter is what to do with all of the things that you know about a given proper noun. It will help to have a specific example, so let us talk about Norma Jeane Mortenson. There is a lot you could know about her: she was born on June 1, 1926, she lived in a foster home for 7 years, she was raised by a friend of her mother's, and she married a sailor, who she later divorced, etc. The question that we will endeavor to answer is whether all of this descriptive material is part of the meaning of 'Norma Jeane Mortenson' or not.
There are two alternatives, (i) it is not part of the meaning of the proper name, but it is important to keep track of it anyway, and (ii) it is part of the meaning of the proper name. The book incorporates the first alternative into our existing theory PC+, but for the second one it proposes a new theory, PC+DN. For the specific case of Norma Jeane Mortenson, the two hypotheses can be contrasted as in the following table:
Val(x, "Norma Jeane Mortenson") iff x = Norma Jeane Mortenson. |
iff x lived in a foster home for 7 years, and x was raised by a friend of her mother's, and x married a sailor, who x later divorced, and then y = x. |
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dossiers |
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PC+ divides its hypothesis of proper noun meanings into three components: semantic theory, concepts & dossiers, and a theory of naming. PC+DN, in contrast, has but a single component, which consists of the semantic valuation from PC+, plus the descriptive material about who Norma Jeane Mortenson that we mentioned above, plus an extra condition on the semantic value. What is important to notice is that PC+ also lists the same descriptive material, but it removes it from the semantic valuation and puts into the dossier for Norma Jeane Mortenson, as you can see by clicking on the Concepts & dossiers link.
There are two main pieces of evidence that the book uses to decide between the two hypotheses, empty proper nouns and coextensive proper nouns.
Empty proper nouns are names like Oz or James Bond that do not refer to any individual in the real world. I am sure that you could think of many other examples of empty proper nouns. [Some of our suggestions are found here.] The reason why they are problematic can be gleaned from examining an example, or actually two, in PC+:
As usual, it is not very revealing to state the condition on the valuation in the same form as the linguistic expression to be analyzed, so let us restate it in the set-theoretic terms of PC+set:
Of course, the whole point of calling these proper nouns 'empty' is that the sets given in the conditions are empty, that is, they evaluate to the null set:
But this leads to a counterintuitive result, once we realize that the null set is equivalent to itself:
In other words, both 'Superman' and 'Wonder Woman' should mean the same thing (the set-theoretic analog of 'nothing'), but they plainly do not. Thus, despite the appealing simplicity of the PC+ analysis, it needs some kind of modification in order to be able to supply a convincing meaning for empty proper names.
Moving on to the second piece of evidence, two proper nouns are coextensive if they refer to the same entity. There are not many good examples of these, because people do not ordinarily give different names to the same thing. The situations in which this does happen are usually rather odd: criminal aliases or mistaken identity, but there is one situation in which this is standard practice: when entertainers take a stage name. In fact, we have already seen just such an instance - did you catch it? Norma Jeane Mortenson was the given name of Marilyn Monroe.
To understand why coextensive proper nouns create a problem for PC+, let us go ahead and analyze our Norma Jeane Mortenson/Marilyn Monroe example in PC+set:
To capture the coextensitivity of these two proper nouns, their semantic conditions should pick out the same set. For clarity, let us call the single member of this set 'njmmm':
This equation says that all three sets are equivalent (Remember, two sets are equivalent if they have the same members.), which predicts that the two proper nouns should have the same meaning. But again, such a prediction would plainly appear to be false, as we can quite readily appreciate by performing the following thought experiment:
Yet these beliefs are contradictory, because they are about the same person. More generally, we may say that the PC+ analysis makes it impossible for us to know different things about two coextensive proper names. Unfortunately, we are clearly able to partition our knowledge in just this manner. So the PC+ analysis needs an additional modification in order to be able to supply a convincing meaning for this bit of data.
The first attempt to modify PC+ to avoid these problems takes a two-step approach: (i) insert the descriptive material on the right-had side of a PC+ condition, as if it were a predicate, and (ii) add an additional condition that ensures that whichever individual meets this description is the semantic value of the proper name. The resulting formula is known as a descriptive name.
Let us consider how the hypothesis of descriptive names applies to our two coextensive names:
Val(x, "Norma Jeane Mortenson") iff x was born on June 1, 1926, and |
x signed a contract with Twentieth Century-Fox as Marilyn Monroe in 1946, and x's first leading part in a serious feature was "Don't Bother to Knock" in 1952, and x married Joe DiMaggio in 1954, and |
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then y = x. |
Twentieth Century-Fox as Marilyn Monroe in 1946, etc, then y = x. |
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Given that there is no statement in these axioms that require them to apply to the same person, it is easy to understand how I could think that they apply to different people, only the first of which do I know from high school.
As for empty proper nouns, let us try Xena:
Val(x, "Xena") iff x was born in Amphipolis, and x is the heroine of a weekly TV series, and |
If you say to me, "Xena called this morning.", the axiom sketched above would lead your sentence to be evalauted as:
This evaluation cannot turn out to be true, because the condition "for some x, ..." cannot be met in the real world.
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