Direct reference

    Russell used the four puzzles and (implicitly) his Spot-Check argument to attack the view that ordinary proper names are Millian names, in favor of the Description theory.  In turn, Kripke attacked the Description theory in favor of the claim that ordinary proper names are rigid designators.  But the latter claim does not quite amount to Millianism, for not all rigid designators are Millian names.
    A Millian name, remember, is one that has no meaning but its bearer or referent.  Its sole function is to introduce that individual into discourse; it contributes nothing else to the meaning of a sentence in which it occurs.  If we say "Jason is fat," and "Jason" is a standard proper name, then the meaning of that sentence consists simply of the person Jason himself concatenated with the property of being fat.
    Being Millian certainly implies being rigid.  But the reverse does not hold.  Although Kripke cites Mill and argues that names are rigid, rigidity does not imply being Millian.  For definite descriptions can be rigid.  Suppose we fall in with the prevalent view that arithmetical truths are all necessary truths. Then there are arithmetical descriptions, such as "the positive square root of nine," that are rigid, because they designate the same number in every possible world, but are certainly not Millian because in order to secure their reference they exploit their conceptual content.  Indeed, they seem to Russellize: "The positive square root of nine" seems to mean, whatever positive number yields nine when multipied by itself.  So that description is not Millian even though it is rigid, because it does not simply introduce its bearer (the number three) into the discourse; it also characterizes three as being something which when multiplied by itself yields nine.  Thus, in defending the rigidity of names, Kripke did not thereby establish the stronger claim.  (Nor did he intend to; he does not believe that names are Millian.4).
    However, other philosophers have championed the Millian conception, which has come to be called the "Direct Reference" theory of names.  The first of these in our century was Ruth Marcus (1960, 1961), cited by Kripke as having directly inspired his work.  Subsequent Direct Reference (DR) theories of names built on Marcus' and Kripke's work (for example, Kaplan (1975) and Salmon (1986)).
    The latter theorists have extended DR to cover some other singular terms, notably personal and demonstrative pronouns such as "I," "you," "she," "this," "that," as well as names.  (An obvious problem about extending DR to pronouns is that any normal speaker of English knows what they mean, whether or not the speaker knows whom they are being used to designate on a given occasion; if you find "I am ill and will not hold class today" written on the blackboard in an empty classroom, you understand the sentence even if you do not know who wrote it or on what day.  This problem will be addressed in Chapter 11.)
    Of course, DR must confront the four puzzles, which are generated just as surely by names as they are by descriptions.  And, obviously, The DR theorist cannot subscribe to Russell's solution or anything very like it, for according to DR, names do nothing semantically but stand for their bearers.
    Let us reconsider the Substitutivity puzzle first.  Recall our sentence

(1) Albert believes that Samuel Langhorne Clemens has a pretty funny middle name.
(1) goes false when "Mark Twain" is substituted for "Samuel Langhorne Clemens."  How can DR explain or even tolerate that fact?
    DR theorists employ a two-pronged strategy.  There is a positive thesis and there is a negative thesis (though these are not often explicitly distinguished).  The positive DR thesis is that the names in question really do substitute without altering the containing sentence's truth-value.  On this view,
(2) Albert believes that Mark Twain has a pretty funny middle name.
is true, not false.  At the very least, belief sentences have transparent readings or understandings, on which readings the names that fall within the scope of "believes" really do just refer to what they refer to.
    We naturally think otherwise; (2) does not seem true to us.  That is because when we see a belief sentence, we usually take its complement clause to reproduce the ways in which its subject would speak or think.  If I assert (2), I thereby somehow imply that Albert would accept the sentence "Mark Twain has a pretty funny middle name" or something fairly close to it.  If I say, "Albert doesn't believe that Mark Twain has a pretty funny middle name," I am suggesting that if faced with the sentence "Mark Twain has a pretty funny middle name," Albert would say either "No" or "I wouldn't know."
But the DR theorists point out that such suggestions are not always true, perhaps not ever true.  Consider
(3) Columbus reckoned that Castro`s island was only a few miles from India.
We all know what one would mean in asserting (3); the speaker would mean that when Columbus sighted Cuba he thought that he was already in the East Indies and was approaching India proper.  Of course, being 450 years early, Columbus did not know anything about Fidel Castro; yet we can assert (3) with no presumption that its complement clause represents things in the way that Columbus himself represented them.  The speaker makes this reference to Cuba without at all assuming that Columbus would have referred to Cuba in that way or in any parallel or analogous way.  Or suppose you and I are among the few people who know that our acquaintance Jacques is in fact the notorious jewel thief that has been terrorizing Paris' wealthy set, called "Le Chat" in the popular press and by the gendarmes.  We read in the newspaper after a particularly daring but flawed robbery that police believe "Le Chat dropped the fistful of anchovies as he or she ran."  We say to each other, "The police think Jacques dropped the anchovies as he ran."
    So it seems undeniable that there are transparent positions inside belief sentences, in which the referring expression does just refer to its bearer, without any further suggestion about the way in which the subject of the belief sentence would have represented the bearer.  Singular terms can be and are often understood transparently.  We might even say,
(4) Some people doubt that Tully is Tully,
meaning that some people have doubted of the man Cicero that he was also Tully.  That would perhaps be a minority interpretation of (4), but we can at least hear that as asserting that the people doubt of Cicero that he was Tully.5
    Virtually all the DR literature has been devoted to establishing the positive thesis, that names do have Millian readings even in belief contexts.  But the positive thesis is far from all that the DR theorist needs.  For although we may be persuaded that every belief sentence does have a transparent reading, most of us also remain convinced that every belief sentence also has an opaque reading, that on which some substitutions turn truths into falsehoods: in one sense Columbus believed that Castro's island was just a few miles east of India, but in another, he believed no such thing, for the obvious reason that he had never heard (and would never hear) of Castro.  Similarly, in one sense the police believe that Jacques dropped the anchovies, but in another they do not, and likewise for people doubting "that Tully is Tully."  Yet it seems DR cannot allow so much as a sense in which belief contexts are opaque.  That is DR's negative thesis: that names do not have nonMillian readings, even in belief contexts.
    The problem gets worse:  It is hard to deny that the opaque readings are more readily heard than the transparent readings.  Indeed, that is implicitly conceded by the DR theorists, in that they know they have had to work to make us hear the transparent readings.  The DR theorists must try to explain the fact away as a particularly dramatic illusion.  That is, they must hold that in fact, sentences like (1) - (3) cannot literally mean what we can and usually would take them to mean; there is some extraneous reason why we are seduced into hearing such sentences opaquely.  A few such putative explanations have been sketched, using materials we shall encounter in Chapter 13 (Salmon (1986), Soames (1987), Wettstein (1991), and cf. Marcus (1981)).  But here, in my opinion, the DR theorists have come up short; none of the sketches produced to date has struck me as either plausible or promising.

    As is implied by example (3), Frege's Puzzle is even worse for the Millian.  According to DR, a sentence like "Samuel Langhorne Clemens = Mark Twain" can mean only that the common referent, however designated, is himself.  Yet such a sentence is virtually never understood as meaning that.  And anyone might doubt that Clemens is Twain, seemingly without doubting anyone's self-identity.  Here again, the DR theorist bears a massive burden, of explaining away our intuitive judgments as illusory.
    The problems of Apparent Reference to Nonexistents and Negative Existentials are if anything worse yet.  If a name's meaning is simply to refer to its bearer, then what about all those perfectly meaningful names that have no bearers?

    We have come to a deep dilemma, nearly a paradox.  On the one hand, in Chapter 3 we saw compelling Kripkean reasons why names cannot be thought to abbreviate flaccid descriptions, or otherwise to have substantive senses or connotations.  Intuitively, names are Millian.  Yet because the original puzzles are still bristling as insistently as ever, it also seems that DR is pretty well refuted.  This is a dilemma, or rather trilemma, because it has further seemed that we are stuck with one of those three possibilites: Either the names are Millian, or they abbreviate descriptions outright, or in some looser way such as Searle's, they have some substantive "sense" or content.  But none of these views is acceptable.
    A few theorists have claimed to find ways between the three horns.  Plantinga (1979) and Ackerman (1979) have appealed to rigidified descriptions (cf. note 3 above).  Devitt (1989, 1996) has offered a radical revision of Frege's notion of sense.  I myself (Lycan (1994)) have offered a much subtler, more beautiful and more effective weakened version of DR, but it would be immodest of me to tout it here.6
 
 

Footnotes

1  In Kripke (1979) he comes back and he uses a variation on the Substitutivity puzzle about referring expressions to refute the Millian view.  His argument there also seems to embarrass his own rigidity thesis, but he does not offer any alternate positive view.
    Kaplan (1975) fashions a made-up word "dthat" (pronounced "that"), which takes an ordinary description like "the man in the corner" and makes it denote its satisfier rigidly rather than flaccidly or attributively.  Thus, "dthat man in the corner" refers at a given possible world, not to whatever man is in the corner at that world, but to the same man who is in the corner in this world.  If I use "dthat man in the corner," you should understand it as talking simply about that person, and my having put in the conceptual content, alluding to manhood and in-the-cornerness, is just a way of calling your attention to that man, as if I were fixing the reference of my own description without fixing its sense.  So "dthat" functions as a rigidifier.  Plantinga (1978) and Ackerman (1979) enlist Kaplan's idea in defending positive theories according to which proper names are rigid but not Millian.

2  Of course, if "Tully" is also a Millian name, that would amount to doubting that the person referred to is that very person.  But this too is a possible understanding of (3).
    Incidentally, the point about transparent readings can also be made regarding pronouns.  Addressing Jacques himself, we could say "The police think you dropped the anchovies as you ran" (Sosa (1970), Schiffer (1979)).

3  Even the paperback edition of Lycan (1994) is expensive, I am afraid, but well worth every penny.