Making Sense of Names
W. Zachary Wolff 2002

In 'On Sense and Reference' (1892) Gottlob Frege discusses the relation of equality and the meaning of equality statements. He uses this as an introduction to a more general discussion of the meaning of singular terms. The standard interpretation of 'On Sense and Reference' has Frege rejecting the view that equality statements are meta-linguistic statements. However, following Thau and Caplan (2001), I hold that Frege endorses a meta-linguistic interpretation of equality statements and uses his sense and reference distinction to answer a possible objection to this position. Frege's position that a proper name has a sense, given by a definite description, has been attacked, particularly by Saul Kripke (1980). I argue that a proper name does have a sense, though not exactly as Frege proposed. Instead I endorse the Nominal Description Theory (NDT) of Kent Bach (1987).

In the opening paragraph of 'On Sense and Reference' Frege discusses two possible interpretations of equality statements. The first, henceforth the object response, holds that equality is a relation on objects. Frege quickly rejects the object response on the grounds that equality statements are all trivial under this view. 'A = B' would mean the same thing as 'A = A', provided 'A = B' is true. The second view, henceforth the name response, holds that equality is a relation on names, such that 'A = B' means "'A' and 'B' co-refer". This view has the advantage of analyzing 'A = A' as trivial and 'A = B' as cognitively significant. Frege has previously endorsed this view in his 'Begriffsschrift' (1879).

Frege then raises an objection to the name view. If equality statements are analyzed in this meta-linguistic manner, they are no longer about their purported subject matter. Instead, they are about the names in question. Frege writes:
In that case the sentence a = b would no longer refer to the subject matter, but only to its mode of designation; we would express no proper knowledge by its means. But in many cases this is just what we want to do. If the sign 'a' is distinguished from the sign 'b' only as object (here, by means of its shape), not as sign (i.e., not by the manner in which it designates something), the cognitive value of a = a becomes essentially equal to that of a = b, provided a =b is true. A difference can arise only if the difference between the signs corresponds to a difference in the mode of presentation of that which is designated (1892, 1).

Under the standard interpretation, Frege abandons the name response at this point in favor of a position I am unable to understand. Thau and Caplan argue at length that this interpretation is incompatible both with the text of 'On Sense and Reference' and with much of Frege's later writing. Following Thau and Caplan, I see Frege's sense and reference distinction as a brilliant reply to the objection he has just raised to the name response. In defining the sense of a sign, Frege writes:

It is natural, now, to think of there being connected with a sign (name, combination of words, letter), besides that to which the sign refes, which may be called the reference of the sign, also what I should like to call the sense of the sign, wherein the mode of presentation is contained (1892, 1).

In the first piece of quoted material, Frege says that 'a difference can arise only if the difference in the signs corresponds to a difference in the mode of presentation' and in the second piece of quoted material he provides a name for the property of a sign 'wherein the mode of presentation is contained'. The sense of a sign is its mode of presentation, the manner in which it refers. Because we associate a sense with each sign in our language, equality statements, interpreted meta-linguistically, do touch their subject matter. A sentence of the form 'A =B' means "'A' and 'B' co-refer", but it communicates more than a fact about language because the hearer already has a sense associated with each 'A' and 'B'. What is communicated is that the mode of presentation associated with 'A' picks out the same object as the mode of presentation associated with 'B'.

For Frege, the sense of a name can be given by a definite description, or a conjunction of definite descriptions. Frege also holds that names refer in virtue of their senses. Thus 'Superman is Clark Kent' means "'Superman' and 'Clark Kent' co-refer" which in turn means something like "'The superhero from Krypton who wears the red and blue suit and flies around saving people' picks out the same individual as 'the nerdy reporter for The Daily Planet who wears glasses and has a crush on Lois Lane'".

Turning a name into a definite description is extremely useful, as it allows one to make use of Bertrand Russell's (1905) powerful theory of definite descriptions. This theory of definite descriptions is well known for its ability to avoid three famous puzzles about names: the puzzle of vacuous names, the puzzle of identity sentences, and the puzzle of existence sentences. The application to identity sentences is discussed above, and provides the clearest example of the theory's power. The most widely accepted theory of names is the Rigid Designator Theory of Saul Kripke (1980), which is a descendant of John Stuart Mill's (1872) theory that proper names denote directly. This theory is unable to deal with the above puzzles.

In 'Naming and Necessity' (1980), Saul Kripke presents two arguments that purport to undermine any description theory of names: the modal argument and the argument from ignorance and error. While these arguments are very effective against most description theories, I hold that they fail in the case of the Nominal Description Theory of Kent Bach (1987). Kripke offers a third argument, directed specifically at NDT, which I hold fails as well. NDT proposes that the sense of a name 'N' is "the bearer of 'N'".

Bach provides the following schematization of Kripke's modal argument, which he borrows from Loar (1976):
(a) If 'N' meant 'the F', then 'N might not have been the F' would be false.
But,
(b) 'N might not have been the F' is true.
Therefore,
(c) Therefore 'N' does not mean 'the F'.

Let us apply this argument to NDT:
(a)NDT. If 'N' meant "the bearer of 'N'", then "N might not have been the bearer of 'N'" would be false.
But,
(b)NDT. "N might not have been the bearer of 'N'" is true.
Therefore,
(c)NDT. 'N' does not mean "the bearer of 'N'".

It seems that (b)NDT is false. There is an interpretation under which it is true, but under this interpretation, the argument is not logically valid. The difference in the two possible interpretations of (b)NDT, and therefore of the entire argument, requires careful attention to matters of wide and narrow scope. As I understand it, the interpretation under which (b)NDT is true, requires that 'N' take a different scope with respect to 'might' in (b)NDT than it does in (a)NDT. Changes of scope are not allowed in a logically valid argument, so the argument is destroyed. On an intuitive level, I think we all sense that there is an important difference in the way in which 'Aristotle might not have been the teacher of Alexander the Great' is true and the way in which "Aristotle might not have been the bearer of 'Aristotle'" is true.

Kripke's argument from ignorance and error holds that for any description proposed as the meaning of a name a speaker can be ignorant or even mistaken as to who satisfies the description, but still use the name to refer to that individual. This shows that the description does not determine the reference of the name. For most descriptions this seems intuitively true. I can use 'Aristotle' to refer to Aristotle without knowing that he was Plato's student, or Alexander the Great's tutor, or born in Stagira, or any other number of potential descriptions. I can even use 'Aristotle' to refer to Aristotle if I think that he was Plato's brother, or Alexander the Great's father, or born in Athens. However, the description offered by NDT fares differently. It does not seem possible that I can use 'Aristotle' to refer to Aristotle if I do not know that he is the bearer of 'Aristotle' or if I think that he is not the bearer of 'Aristotle'.

Kripke may have realized that the above two arguments were not sufficient for dealing with NDT, as he offers a third argument directed not at description theories in general, but at NDT in particular. He argues that NDT is viciously circular. Essentially, he seems to object to the meaning of a name being given in terms of the name itself. I fail to see the force behind this objection. Bach argues that Kripke sees circularity only because he confuses a name's meaning with its use to refer. NDT does not purport to be a theory of reference, which Bach holds can only be given by Speech Act Theory. NDT does not analyze 'Aristotle studied under Plato' trivially as 'The person I am referring to studied under Plato' as Kripke seems to hold. It analyzes it as 'The bearer of 'Aristotle' studied under Plato'. Based on the assumption that the hearer already has some thoughts about the bearer of 'Aristotle', this can be used to communicate.

In summary, the Nominal Description Theory stands strong as the best analysis of proper names. The Fregean sense of a name 'N' is "the bearer of 'N'". This theory has the advantages long known of Russell's theory of definite descriptions: it solves the semantic puzzles associated with names. Its widely accepted competitor, Rigid Designator Theory, is unable to do this. At the same time it cleverly dodges Kripke's attacks against description theories in general. No other theory possesses these merits.