DIRECT, RIGID DESIGNATION AND A POSTERIORI
NECESSITY: A HISTORY AND CRITIQUE
INTRODUCTION
Quentin Smith
Published in: (eds. James Fetzer and Paul Humphreys), The New Theory of Reference: Kripke, Marcus and Its Origins. Kluwer Academic Publishers: Synthese Library Series 1998, pp. 137-178.
This paper aims to accomplish two interdependent goals, one historical and philosophical. First, I aim to present a partial history of the theories of direct, causal or rigid reference as they appear in the New Theory of Reference, an account additional to that presented in [Smith 1995a, 1995b]. Second. I aim to critically assess and further develop these theories.
The historical part of the paper mostly centers on the largely unknown contributions made by Peter Geach and Ruth Barcan Marcus (that is, contributions additional to the ones discussed in my [1995a] and [1995b] One of my main theses is that Geach [1969], not Donnellan [1970] originated the causal or “historical chain” theory of names. I also argue that Marcus is not correct when she recently writes [1993: xiii-xiv] about her earlier article, [1961], that in this article “proper names are not assimilated to what later came to be called ‘rigid designators’ by Saul Kripke ...“. I shall argue that in her [1961] Marcus does assimilate her proper names to rigid designators. I shall also argue that she does not correctly characterize the relation of her referential definite descriptions in her [1961] to those of Donnellan [1966]. In the course of this argument, I shall put forth the view that the standard history of the New
Theory of Reference is mistaken in attributing the origin of’ the referential! attributive distinction regarding definite descriptions to Donnellan.
The most important philosophical (as distinct from historical) aspects of the paper lie in the development and evaluation of two different definitions of rigid designation, what I call the “direct reference definition” and the world definition”. The “world definition” is commonly associated wilh Kripke and the “direct reference definition” with Kaplan. I shall argue that only the definition based on Kripke’s early work [1971; 1972] is sound.[1]
DIVISION ONE: DIRECT REFERENCE AND CAUSAL REFERENCE
- The referential use of definite descriptions in Marcus
One inaccuracy in the “standard” history of the New Theory of Reference’s arguments against the Frege-Russell descriptional theory is that the first landmark publication appeared with Keith Donnellan’s “Reference and Definite Descriptions” [1966] Two other inaccuracies are that the first articulations of the theory of causal reference appeared in Donnellan’s “Proper Names and Identifying Descriptions” [1970] and Saul Kripke’s “Naming and Necessity” [1972] and that the first presentation of the concept of rigid designation appeared in Kripke’s “Identity and Necessity” [1971]
The “standard” view is well represented by one of the recent historical studies of these theories, Tyler Burge’s “Philosophy of Language and Mind:
1950-1990” [Burge 1992]. Burge writes about “a completely different picture of reference” that emerged with Donnellan’s 1966 article: “In 1966 Donnellan pointed out that there is a use even of definite descriptions in which their meaning — the conditions laid down by the definite descriptions — does not fix the referent” [1932: 23]. Burge is mistaken, since this fact about definite descriptions was first pointed in 1961 by Marcus, as I shall show shortly.
Burge proceeds to claim that “the decisive further move was made in 1970 by Kripke and Donnellan, independently of one another”, namely, that the
referent of a name is usually fixed by a historical “chain of uses of the name” I [24]. But in fact this “decisive further move” was first made by Peter
Geach in his “The Perils of Pauline” [1969] as I shall show below.
Burge then identifies Kripke’s essays as the first “account of names [in terms of] a theory of necessity. He counted names as ‘rigid designators’ — expressions that maintained a certain constancy of reference through variation in the possible worlds by reference to which modal sentences might be evaluated” [1992: 25]. However, these ideas about names and rigid designators were not presented first by Kripke, but earlier presented by Plantinga [1967], Føllesdal [1961] and Marcus [1961]. Furthermore, a theory of rigid names was presented independently of Kripke’s and in the same year by Kaplan (in a talk, “Dthat”, in the Fall of 1970 at Stanford University). I shall discuss Plantinga’s [1967] and Føllesdal’s [1961] in my [1998b] and shall focus on Geach, Marcus, Donnellan, Kripke and Kaplan in this paper.
Let us begin with the idea that Tyler Burge claimed first introduced this new picture of reference, the idea that uses of some definite descriptions are referential rather than attributive.
The virtually universal belief is that the distinction between attributive and referential uses of definite descriptions is original with Donnellan [1966]. But, Donnellan at best only discovered one species of this distinction. Another species and the summum genus, so to speak, was discovered by Marcus in her
[1961].
Donnellan argued that some definite descriptions in a given natural language can be used at some times by some individuals in a referential way, and can be used at other times by these or other individuals in an attributive way. For example, I may use “the man in the corner who is drinking a martini” in a
referential way to directly refer to that man (regardless of whether or not he is
drinking a martini) and at a later occasion I may use it attributively to refer to whatever x has the property of being the only man in the corner who is drinking martini.
But Marcus earlier introduced into the New Theory of Reference another species of the referential/attributive distinction and thereby introduced the genus (whoever introduces the first species ipso facto introduces the genus). Marcus’ species is the conversion of an attributively used definite description into a referentially used definite description that occurs over a time and among the users of a given natural language as a whole, For example. “the evening star” may at first be used in our culture in an attributive way to refer to whatever has the property of being the first heavenly body to be visible in the evening. But at a later time, this definite description may come to be used by language-users in a purely referential way, to refer to that individual, regardless of whether or not it has the property of being the first heavenly body visible in the evening. In these cases, the referentially used definite description comes to be used as a directly referential name of the object. Using the expression “tag” for what later came to be called a “directly referential name”, Marcus writes:
In fact it often happens, in a growing, changing language, that a descriptive phrase conies to be used as a proper name — an identifying tag — and the descriptive meaning is lost or ignored. Sometimes we use certain devices, such as capitalization and dropping the definite article, to indicate the change in use. “The evening star” becomes “Evening Star”. “the morning star” becomes “Morning Star”, and they may come to be used as names for the same thing. ... One might even devise a criterion as to when a descriptive phrase is being used as a proper name. Suppose through some astronomical cataclysm, Venus was no longer the first star of the evening. If we continued to call it alternatively “Evening Star” or “the evening star” hen this would be a measure of the conversion of the descriptive phrase into a proper name [1961: 309].
In this passage we find the idea, later to become central to The New Theory of Reference, that the reference of a locution is not routed through a descriptive sense that the locution expresses; the reference is direct.[2] Marcus herself
comments on her distinction between referential and attributive uses of definite descriptions. In her 1981 article “A Proposed Solution to a Puzzle About Belief” she writes that this distinction was present in her 1961 article:
I also note that a description can come to be used purely referentially and say on p. 309. ‘in fact it often happens, in a growing, changing language, that a descriptive phrase comes to be used as a proper name — an identifying tag — and the descriptive meaning is lost or ignored.’ I note that sometimes we use certain devices such as capitalization and dropping the definite article to mark the shift in use (a foreshadowing of Donnellan’s ‘Reference and Definite Descriptions’ Philosophical Review 75 [1966]: 284-304) [Marcus 1981: 509, n. 2].
Marcus correctly characterizes the sort of referential descriptions that are discussed in her [1961], but it is not strictly correct to say that her referential descriptions foreshadow the sort of referential descriptions in Donnellan’s [1966]. In fact, if this passage is taken to suggest that Marcus’ distinction is the same species as Donnellan’s, it is false (there is no prior discovery of his species). But if we interpret the “foreshadowing” relation in a very broad sense, then we can read the passage as correctly implying that Marcus first discovered the genus “referential use of a definite description.”
The relevant genus/species distinction is demonstrably present in this referential/attributive distinction. The genus is the referential use of a definite description (the use of it to refer directly to something, not necessarily the object that meets the descriptive conditions belonging to the description). One species has for its specific differentia: using referentially a definite description D constantly and by all language users, such that D used to he normally used attributively by earlier generations of language users. A second species has for its specific differentia: using referentially a definite description D on some occasions by some people, such that on many other occasions, many people also use D in an attributive way.
However, I believe in the end we must reject this species/genus distinction, since Donnellan’s alleged species is not a genuine species. Kripke has made a plausible case in “Speaker’s Reference and Semantic Reference” ([1977, reprinted in [Martinich, 1985]) that Donnellan’s species is not a genuine semantic case, since his examples can all be accounted for by the speaker’s reference/semantic reference distinction. Kripke writes; “Suppose I come upon Smith foully murdered. The condition of Smith’s body moves me to say, ‘Smith’s murderer is insane’,” [Martinich, 1985; 251]. This would be an attributive use of “Smith’s murderer”; but if someone uttered the same sentence “while observing the wild behavior of the defendent at the dock” [ 251], this definite description would be used referentially to refer to the person who, in fact, is sitting in the dock, regardless of whether or not he has the property of being Smith’s murderer. Kripke notes that the distinction between the two cases is not due to a semantic ambiguity of the definite description, but is a pragmatic distinction dependent on the speech acts.
Given this, Donnellan’s distinction does not count against Russell’s theory that the semantic content of definite descriptions is captured by treating them as referring in a descriptional or attributive way. It does not amount to a “direct reference” semantics, but is consistent with the traditional descriptivist theory of the semantic reference of expressions.
This interpretation of Donnellan’s article is consistent with a remark that Donnellan himself makes. He writes: “ ... whether the description is used referentially or attributively ... [is not due to] ... an ambiguity in the meaning of the words; it does not appear to be semantically ambiguous. (Perhaps we could say that the sentence is pragmatically ambiguous: the distinction between roles that the description plays is a function of the speaker’s intentions.)” [1966]; Martininch, reprinted in [Martininch, 1985: 236-248, see p. 244].
Accordingly. if Kripke is right (and I think he is) Donnellan’s theory about the “referential use” of definite descriptions is not a new semantic theory since it is not a semantic theory; it retains the old Frege—Russell semantic theory and adds to it a new pragmatic theory about definite descriptions. By contrast, the change of “the little corporal” (as attributively used) to “the little corporal” used as a directly referential name of Napoleon is a semantic distinction (Marcus’ example). This expression first has the semantic content express-ed by “the person who has the property of being the one and only little corporal [in the regiment x at time t]” and later has a new semantic content. namely, the content that consists solely of its direct referent. Napoleon.
Thus, there are not two semantic species of’ “referential uses of definite descriptions”, Marcus’ species and Donnellan’s species, but only one. Only with Marcus’ distinction do we have a semantic theory of the direct reference of some uses of definite descriptions.
- Geach ‘s causal theory of reference
Following Tyler Burge’s order of presentation of the ideas in the New Theory of Reference, the second major step is supplying the idea of referential uses of expressions with a “mechanism” that explains how they directly refer. It is questionable if this second step is necessary, since Marcus. Kaplan, Salmon. Almog, Wettstein and other proponents of the direct reference theory take the direct reference relation as primitive. Nonetheless, Kripke. Donnellan. Devitt and Putnam believe it important and the causal theory of reference they propounded is often associated with one of the “new” ideas of the New Theory of Reference. But did this new idea really come from the standard list of characters, as Tyler Burge and others claim?
I have elsewhere said that “the most serious and widespread error in the history of recent analytic philosophy” is the belief that Kripkc. not Marcus. originated the theory of rigid designation, the modal argument for direct reference, etc. Another candidate for “the most serious and widespread error” is that Donnellan and Kripke originated the causal theory of reference, also known as the historical chain theory of reference. The remark by Tyler Burge that I quoted (that the second major step, after Donnellan’s distinction, is the Donnellan-Kripke causal theory of reference in l970-72) is similar to (literally) hundreds of other such remarks that can be found in journals and books.
Nathan Salmon’s Reference and Essence develops a number of new and significant ideas and in addition presents what is perhaps the best and even the “classic” presentation of the standard history of the New Theory of Reference; my work builds upon and refines his achievement, rather than rejects it. Indeed, I based part of my history on Salmon’s [1981] in my [1995a] and [1995b]. But one problem with Salmon’s work is that he repeatedly refers to the causal theory as Donnellan’s and Kripke’s; e.g.. “Donnellan [1972] and [1974] and Kripke [1972] provide accounts of proper name denotation by means of such historical chains of communication.” [1981:31]. Even Michael Devitt’s important study, “Against Direct Reference” [1989], which presents one of the most accurate histories of the New Theory of Reference (e.g., he recognizes the origin of the theory of rigid designation in Marcus), attributes the causal theory to Donnellan and Kripke: Deviti writes The Causal Theory: This theory is the one that really is ‘new’. It was discovered by Kripke [1980] and Donnellan [1972] ...“ [1989: 210]. (Of course, Devitt is referring to the 1980 reprint of Kripke’s [1972]; he is not thinking Kripke first published his theory in 1980.)
Tyler Burge, Nathan Salmon and Michael Devitt are to be credited with a piece of historical knowledge many other philosophers lack: Many people mistakenly think that Kripke discovered this theory. These three authors are careful to co-attribute it to Donnellan and Kripke. But are Salmon’s and Devitt’s sentences correct in referring to the [ reprinting of Donnellan’s [ giving it the same date as Kripke’s [ David Kaplan [ 602, n. 86] writes more exactly that the notion of a historical chain of acquisition by which a name is passed from user to user:
“first appears in print in Keith Donnellan’s ‘Proper Names and Identifying Descriptions”, Synthese 21(1970): 335-58; reprinted in Semantics of Natural Language ed. D. Davidson and G. Harman (D. Reidet Publishing Company 1972). It then appears in Kripke’s Naming and Necessity, which coincidentally, was first published in the same collection in which Donnellan’s article is reprinted (Semantics of Natural Language). Kripke notes, ‘the historical acquisition picture of naming advocated here is apparently very similar to views of Keith Donnellan’ (addenda to Naming and Necessity, p. 164).”
(Kaplan’s reference is to [Kripke, 1980], but his addendum also appears in the original text [Kripke, 1972: 769]. Kaplan is right about Donnellan’s theory appearing in print before Kripke’s, but is wrong about this historical chain theory “first appearing in print” with Donnellan’s work. Donnellan was ten months too late: Peter Geach’s article, first presenting the causal theory of reference, appeared in “The Perils of Pauline”, The Review of Metaphysics Vol. XXIII, No. 2, December 1969, pp. 287-300, and Donnellan’s appeared in October, 1970. Thus, contrary to the prevalent consensus of opinion, the historical chain theory of reference of names is neither “Kripke’s theory” nor “Donnellan’s theory”, nor “the Donnellan-Kripke theory”. It is “the Geach theory” of reference.
Geach writes:
I do indeed think that for the use of a word as a proper name there must be in the first instance be someone acquainted with the object named. But language is an institution, a tradition; and the use of a given name for a given object, like other features of language, can be handed on from one generation to another; the acquaintance required for the use of a proper name may be mediate, not immediate. Plato knew Socrates, and Aristotle knew Plato, and Theophraatus knew Aristotle, and so on in apostolic succession down to our own times; that is why we can legitimately use ‘Socrates’ as a name the way we do. It is not our knowledge of this chain that validates our use, but the existence of such a chain; just as according to Catholic doctrine a man is a true bishop if there is in fact a chain of Consecrations going back to the Apostles, not if we know that there is. When a serious doubt arises (as happens for a well-known use of the word ‘Arthur’) whether the chain does reach right up so the object named, our right to use the name is questionable, just on that account. But a right may obtain even when it is open to question. ... I introduced the use of the proper name ‘Pauline’ by way of the definite description ‘the one and only girl Geach dreamed of on N-night’; this might give rise to the idea that the name is an abbreviation for the description. This would be wrong. [1969; 288—89].
I refer the reader to the rest of Geach’s article for the other aspects of his theory, but instead of comparing its details with Donnellans [1970] and Kripke’s [1972] (see my [1998b] for a comparison), I should note that Michael Devitt has some reason to be listed with Geach. Donnellun and Kripke as one of the early developers of this theory. Devitt developed the most comprehensive causal theory of reference in his unpublished 1972 doctoral dissertation at Harvard, The Semantics of Proper Names. A Causal Tlieori of Reference and in a series of publications in the l970s, l980s and l990s. beginning with his [1974].
In addition to the historical chain theory of reference, we see in Geach’s 1969 article another principal idea of “The New Theory of Reference’: the distinction between a directly referential name and a reference-fixing description (“I introduced the use of the proper name ‘Pauline’ by way of the definite description ‘the one and only girl Geach dreamed of on N-Night’”). a distinction later made famous by Kripke [1972]
Apart from Geach, HP, Grice also had the theory of a refdrence-fixing description for a directly referential name earlier than those to whom it is
commonly attributed, Grice writes [ 144]:
A name a may be introduced either so as to be inflexibly tied, as regards the truth-value of utterances containing it, to a given definite description d, or so as to he not so tied (d being univocally employed); so the difference between the two ways of introducing a may reasonably be regarded as involving a difference of sense or meaning for a; a sense in which a may be said to he equivalent to a definite description and a sense in which it may not.
It is, then, not arbitrary so to design Q [the languagel that its individual constants are to he regarded as representing, among other linguistic items, names with one of their possible kinds of meaning. namely that in which a name is not equivalent to a definite description.
Did Geach, Donnellan and Kripke develop the causal theory of reference independently of each other or were there relations of influence among two or more of them? The scanty published evidence seems to suggest an independent development. In Kripke’s addendum to “Naming and Necessity’ that Kaplan quoted (see my above quotation from Kaplan), Kripke mentions a similarity (but no relations of influence) between Donnellan’s statement of the theory and his own statement of the theory, There is a sentence about Geach that is not present in the relevant footnote in the original version of “Naming and Necessity” [1972: 342: n. 2] but which is added to the 1980 reprinting [Kripke, 1980: 23, n, 2], This is the footnote where Kripke mentions the various philosophers who held similar views and in the 1980 reprinting he added the sentence: “I also recall the influence of early conversations with Albritton and with Peter Geach on the essentiality of origins’. [Kripke 1980: 23. n. 2]. This may suggest the Geach-Kripke interchanges did not involve the causal theory of reference (but only the theory of the essentiality of origins). Geach does not in his publications discuss the relation of his theory to Kripke’s or Donnellan’s. Donnellan writes about the relation of his theory to Kripke’s: “I believe that Saul Kripke has a very similar position, at least insofar as denial of the prevalent theories go. And, indeed, I think I may owe one of my counter- examples to him through a second hand source (although I did not understand the relevance until much later).” [1970: 357]. Donnellan indicates in a later footnote the second hand source is Rogers Aibritton [ 1970: 358, n. 18]. Neither Donnellan nor Kripke mention Geach’s earlier statement of the causal theory of reference. Given this limited evidence, it appears reasonable to conclude that the three accounts of the causal theory were developed independently, lithe three accounts of the theory (by Geach, Donnellan and Kripke) were developed independently and roughly simultaneously, then we should refer to it either as Geach’s theory or as the Geach—Donnellan—Kripke theory (analogously to the Armstrong- theory that laws are relations among universals, which was developed independently and roughly simultaneously by these three philosophers). Given these facts, virtually every single mention of the causal theory of reference in the philosophical literature for the past 25 years or so is false, inasmuch as it is mentioned as the Donnellan and/or Kripke theory. The same holds for the Geach doctrine of reference-fixing descriptions, which is implicit in Marcus [ but explicit in these three writers.
For purposes of clarification of my account of the causal theory, we may examine whether the recent characterization of Kripke’s presentation of this theory in [Burgess 1996] is accurate. Burgess writes that Kripke has “a positive alternative theory, the historical chain account, on which a name is bestowed on a thing spec by description, and on each subsequent occasion is used with the intention of continuing to refer to what it used to refer to, so that the circumstances of the earliest uses ma soon be forgotten, though the name still succeeds in designating what it does only through a chain of usage extending back to the initial bestowal of the name” [1996: 20, my emphasis]. But this is not Kripke’s theory; Kripke repeatedly insisted in [1972] that in most cases of bestowing a name, the name is not bestowed on a thing specifled by a description. For example, Kripke writes that in some cases the name is bestowed by a description but that in general this picture of how a name is bestowed fails. The name is usually bestowed by ostension:
There may be some cases where the description picture is true, where some man really gives a name by going into the privacy of his room and saying that the referent is to be the unique thing with certain identifying properties ... Or he points to a star and says, ‘That is to be Alpha Centauri’. So he can really make himself this ceremony: ‘By ‘Alpha Cerstauri’ I shall mean the star right over there with such and such coordinates’. But in general this picture fails ... A rough statement of a [causal] theory might be the following: An initial baptism takes place. Here the object may be named by ostension, or the reference of the name may be fixed by a description.” [1972: 301—302, my italics].
Kripke’s theory (like Geach’s and Donnellan’s) is that in some cases the name is bestowed by means of a description, but that in general it is bestowed by ostension.
As I indicated, the second published account of the causal theory of reference appeared in Donnellan’s October 1970 paper. ‘Proper Names and Identifying Descriptions”. He offers an example that is supposed to show that reference is determined by a historical chain rather than by descriptions. Suppose that Aristotle’s and Herodotus’ uses of ‘Thales” are connected he a historical chain to a man who never held that ‘al is water and did not possess other identifying properties normally ascribed to him (e.g.. falling into a
while looking at the stars). Suppose this man call was a well-digger with a reputation for saying wise things and who once exclaimed “I wish everything were water so I wouldn’t have to dig these damn wells’. Suppose further that there was some other ancient Greek hermit, unknown to Aristotle and Herodotus, who did hold that all is water and who fell into a well while looking at the stars. Now there is an historical chain connecting the well-digger to Aristotle’s and Herodotus’ use of the name “Thales” and an historical chain connecting Aristotle’s and Herodotus’ use of “Thales” to our use. According to Donnellan, Geach and Kripke, this shows that the person o e refer to he “Thales” is the well-digger and not the philosopher.
Are Geach, Donnellan and Kripke right? How shall we evaluate the “semantic argument for direct reference”, as Salmon calls it? Nathan Salmon calls the semantic argument “the strongest and most persuasive of the three kinds of argument for the primary thesis of the direct reference theory” [1981: 29], the other two kinds being the modal and epistemic arguments. It seems to me this is not the case, for the semantic argument is inconclusive due to the fact that it does not elicit the linguistic intuition that its proponents believe it elicits.
The example regarding Thales does not elicit the linguistic intuition that the well-digger is the referent of our use of “Thales”: nor does it elicit the contrary intuition that the hermit philosopher is the referent. Rather, it elicits the intuition that the reference of “Thales” is ambiguous. Our linguistic intuitions are best expressed as a reflection of this ambiguity: “I thought that ‘Thales’ referred to the philosopher who held that all is water, but I also thought that ‘Thales’ referred to the person that Aristotle’s and Herodotus’ use of ‘Thales’ was connected to by a historical chain; now the situation is confused and in the future it needs to be made clear as to whom we are referring by ‘Thales’.”
This ambiguity is consistent with the descriptional theory of reference, for the descriptivists may explain the ambiguity by the ‘act that the descriptions pick out two different people; the descriptive sense the philosopher who said all is water refers to the hermit unknown to Aristotle, but the descriptive sense the
person to whom Aristotle’s use of “Thales”is causally connected refers to the well-digger.
Likewise, in Geach’s example, he makes a plausible case only as long as he makes only one description of Pauline inaccurate. But if most of the important descriptions are inaccurate, then it seems that a good explanation of why “communication” [1969: 289] breaks down is that the semantic content of the name is not unambiguously determined.
Thus, I do not believe the “semantic argument for direct reference” is conclusive. As I argued in [1997] the modal argument for direct reference is not conclusive either, since it does not refute the rigid descriptivist theories. And I argue in [ that the epistemic argument for direct reference is unsound. If this is indeed the case, the result would seem to be that the evidence underdetermines the direct reference and rigid descriptivist theories.
DIVISION TWO: RIGID DESIGNATION
3. Kaplan on the origins of the rigid designation theory
Following Tyler Burge’s order of presentation of ideas, the next important idea is supposed to be the interconnection of names and modality. Tyler Burge follows the standard history and claims that Kripke originated this idea; Burge writes that Kripke’s essays are the first “account of names [involving] a theory of necessity. He counted names ‘rigid designators’ — expressions that main tained a certain constancy of reference through variation in the possible worlds by reference to which modal sentences might be evaluated” [1992: 25].
The origin of very few theories has been so widely misunderstood as the origin of the theory of rigid designation. As is well known, the theory that names are rigid designators was presented by Kripke in his January, 1970 lectures at Princeton University, published as [1972]. It is less well-known that (i) a theory that names, indexicals and other expressions are rigid designators was developed independently and presented by Kaplan in a talk, “Dthat”, in the Fall of 1970 at Stanford University (see Kaplan, [1989a: 487], (ii) a theory of the rigid/nonrigid distinction was presented by Plantinga in seminars given in 1963 and later at Wayne State University, stated in final form in a section of a manuscript written in 1965, submitted to a publisher in 1966 and published in [1967: 1277-183][3] and (iii) this distinction was presented earlier by Hintikka in an August, 1962 talk attended by Marcus, Montague, Prior, Kripke, Geach and others (published as [1963]; see Marcus [1993: 89] for the date of his talk), (iv) this distinction was also presented by Føllesdal [1961; 1967] and (v) presented by Marcus in [ I discuss Plantinga’s, Hintikka’s and Føllesdal’s theories in [ and shall concentrate here on the theories of Kaplan, Kripke and Marcus.
Most philosophers think Kripke originated this theory in his 1971 and 1972 articles, which are transcriptions of talks he gave in January 1970 at Princeton University [1972] and later that year at New York University [1971]. Although David Kaplan’s works are almost as widely known and discussed as Kripke’s, it is rarely if ever remarked that Kaplan independently developed a .theory of rigid designation and presented his theory in the same year, 1970, in a Fall talk at Stanford University. (See my quotes below from [Kaplan, 1989a: 487]. Kaplan’s 1970 talk, later published as “Dthat” in 1978 (Syntax and Semantics, Vol. 9, ed. P. Cole [New York: Academic Press]), laid out the apparatus of singular propositions, direct reference, possible world semantics. etc. and the argument that proper names, indexicals and other locutions are rigid designators. Kaplan refers to his 1970 talk as his 1978 publication “Dthat”, which is reason to think there are no differences between the two. In Kaplan’s own words, he says: “In fall 1970, 1 wrote for a conference at Stanford. a paper ‘Dthat’.” [1989a: 487]. He appends to this sentence a footnote reading: “David Kaplan, ‘Dthat’, in Syntax and Semantics, vol. 9, ed. P. Cole (New York: Academic Press, 1978); reprinted in Martinich, op. cit.”) [Kaplan, 1989a: 487. n. 5]. Readers of Kaplan’s “Dthat” will see that he argues that proper names, as well as indexicals, are rigid designators. (But Kaplan did not use the phrase “rigid designators’.)
The reason people do not co-credit Kaplan and Kripke with the rigid designation theory is that Kaplan’s article was not published until 1978 and Kripke’s talks were published years before in [1971] and [1972] Kripke gave his lectures on “Naming and Necessity” from January 20- 29. 1970. and Kaplan gave his lecture on “Dthat” in the Fall of 1970, but Kaplan had not read a transcript of Kripke’s talk until after his own talk on “Dthat”. Kaplan explains this and other facts about his 1970 theory in the following sentences from [1989a: 487]; my inserted comment is in italics and brackets,
“In fall 1970, I wrote, for a conference at Stanford, a paper ‘Dhat. Using Donnellas’s ideas as a starting point, I tried to develop the contrast between Fregean semantics and the semantics direct reference .., In Spring 1971, I gave a series of lectures at Princeton on the semantics of direct reference. By this time I had seen a transcript of Naming and Necessity and I tried to elate some of my ideas to Kripke’s. [In a footnote to this sentence, Kaplan writes]: ‘Although the central ideas of my theory had been worked out before I became familiar with Naming and Necessity, I have enthusiastically adopted the ‘analytical apparatus’ and some nic of the terminology of that brilliant work.” [Kaplan: 487., n. 6)
Given these facts, it seems that, at the very least, the rigid designation theory should be called the Kripke-Kaplan theory.
In my [1995a], I mistakenly included Kaplan among those who had not recognized Marcus’ earlier statement of the rigid designation theory and origination of the basic ideas of the New Theory of Reference. First of all. I misinterpreted his sentence that Kripke uses the term “rigid designator” in connection with Kripke’s “controversial, though, I believe, correct claim that proper names ... are rigid designators” [Kaplan: 1989a: 492], In my [1995a] I interpreted this sentence as Kaplan attributing the origin of the theory of rigid designation to Kripke. But (as I now realize) this sentence does not mean, imply or suggest that Kripke originated this idea. It merely states that Kaplan endorses this claim, a claim that Kaplan himself independently developed at least as early as 1970 and prior to his reading “Naming and Necessity”.
Second, I mistakenly said that in his published articles that Kaplan did not attribute the theory of rigid proper names to Marcus. In Kaplan’s [1986]. he does just this. In Kaplan’s discussion of modal contexts in his [1986], he says that when we quantify into modal contexts, we can use as surrogates for values of variables “proxy names (closed singular terms)” and that either Marcus’ tags or Kripke’s rigid designators can serve as these modally stable closed singular terms. Kaplan continues: “Something like the intuitive idea of a tag [Marcus 1961] or a rigid designator [Kripke 1971, 1972] may guide out choice of proxy names.” [1986: 253].
Third, Kaplan wrote a summary of Marcus’ contributions to contemporary philosophy that includes a recognition of her priority in founding the New Theory of Reference. An excerpt from this appears on the back cover of the paperback edition of Marcus’ Modalities. The excerpted parts on the book cover read: “Marcus is a brilliant, original, learned, tenacious, and productive scholar, many of whose early out-of-fashion ideas have now come into fashion and have largely swept the competition away... The topics to which Marcus has contributed are high on the agenda of philosophers throughout the world”.
Apart from the mistaken account of Kaplan’s views I gave in [1995a], I did not realize in my [1995a] and [1995b] that Michael Devitt had stated in his [1989: 210] that Marcus originated the theory of rigid designation. This was a major omission from footnote 1 of my [1995a] since I there attempted to list the philosophers who recognized to the greatest extent Marcus’ contributions, and it turns out that (apart from Kaplan), Devitt has recognized this to the greatest extent. Devitt wrote in [1989: 220]:
THE RIGID DESIGNATION THEORY
The Rigid Designation theory has much more claim to be considered “new” though it is, in effect, to be found in Ruth Barcan Marcus (1961). Kripke is famous for urging the theory (1971, 1980).
I am grateful to Devitt for pointing this out to me in 1995, although he now reports (private communication of January 1997) that he has worked out a new and different theory of rigid designation and a new history. In his new theory [Devitt, forthcoming], Devitt distinguishes two main parts of the rigid designa tion theory, the rigid reference in modal contexts (which he argues was originated by Marcus) and the rigid reference in simple sentences (which he argues was originated by Kripke).
Hintikka and Sandu [1995] have also recently. pointed out that Marcus discovered the rigid designation theory, e.g., after noting that Marcus developed the necessity of identity thesis about variables in 1947, they say; “This Marcus did years before she formed the rigid designation idea in 1961.” [1995: 271].
Recently, these facts are becoming more widely known, as is evinced by the entry for Marcus in the 1996 Encyclopedia of Philosophy.’ Supplement, which reads in part: “She also proposed that ordinary proper names are contentless tags [Marcus, 1961]. In so doing, Marcus rejected earlier ‘descriptivist’ accounts, often associated with Gottlob Frege and Bertrand Russell, and laid the cornerstone of the so-called new theory of reference later elaborated .by Saul Kripke, Keith Donnellan, David Kaplan, and others.” [Raffman and Schumm, 1996: 322].
Given this and what Burgess has called the “very wide publicity” [1996: 1] that has been given to the claim that Marcus’ [1961] included the idea that names are directly referential rigid designators, we should say by the present time (say, May 7, 1997) there is no longer a widespread belief that this theory was originated by Kripke. But there does remain one thing, namely, to present a more detailed argument than is present in the above-mentioned works (including my [1995a] and [1995b] that Marcus’ [1961] includes the concept of rigid designation. This is especially important in the light of the fact that Marcus, in her own recent interpretations of her [1961] denies that her proper names are rigid designators. She states that in her 1961 article “proper names are not assimilated to what later came to be called ‘rigid designators’ by Saul Kripke ...“ [Marcus, 1993: xiii—xiv].
Furthermore, the main argument for the thesis that Marcus’ names are rigid designators, presented in Devitt’s [ is unsound, as I argue in [Smith, 1997]. Devitt also no longer believes his [1989] argument is sound (private communication), but for different reasons than the ones I present in [Smith, 1997]. It appears, then, ifwe are able to have an accurate history of the concept ofa rigid designator, a considerable amount of work remains to be done. In the following, I will endeavor to present an argument that Marcus’ 1961 names are in fact rigid designators and that Marcus’ own (recent) interpretation of her [1961] is mistaken, After I do this, I will compare Marcus’ theory with the two most well-known theories of rigid designators, Kripke’s and Kaplan’s. I will also, in the sections on the world-definition and direct-reference definition of rigid designation, develop or make explicit the rigid designation theory beyond what is in the texts of Marcus, Kripke and Kaplan, and argue that only one of these definitions is correct, the one based on Kripke’s work. This requires three tasks, two historical and one philosophical.
First, I shall remove an obstacle created in some people’s mind that prevents them from seeing the notion of rigid names in Marcus. (This is not the obstacle that prevents her from seeing that her names are rigid I discuss her argument later.) I am now talking about the “real doubt” that some people have about whether her tags or names are meant to belong to natural languages or instead to an artificial language. If she is not talking about natural languages, then she is not introducing a main idea of the New Theory of Reference, that names in natural languages are direct rigid designators.
Second, I will show that in Marcus’ [1961] “necessity” is not an epistemo logical notion, but a logical/metaphysical notion. If “necessity” is defined to mean a priori, as in Ayer and others, then rigidity (which involves the notions of possibility and necessity) is an epistemological notion and has little relevance to rigidity defined in terms of possible worlds, which is how this notion is defined in the New Theory of Reference. I shall show Marcus defines necessity and rigidity in terms of possible worlds,
Then I will construct a “complete theory” of rigidity in a technical sense I shall explain. This complete theory involves giving two definitions, with several elements in each definition, and comparing the two definitions to determine which is the most satisfactory. This “complete theory” will be the most substantive philosophical part of this paper, whereas the other sections belong in large part to the history of philosophy.
4. The discussion of natural and artificial languages in Marcus’ [1961]
Marcus introduced the notion that names in natural languages are rigid designators only if.she discussed natural languages. Is there a “real doubt” that she is discussing names in natural languages, as Scott Soames [1995] and John Burgess [1996] have maintained?
At some points of her 1961 paper, Marcus is talking about artificial languages (e.g., in the entire section called “Semantic Construction”), and at other points she is talking about natural languages, such as the following passage, which is a continuous text in Marcus’ [1996: 309-10]:
“In fact it often happens, in a growing, changing language, that a descriptive phrase comes to be used as a proper name — an identifying tag — and the descriptive meaning is lost or ignored. Sometimes we use certain devices such as capitalization and dropping the definite article, to indicate change in use. “The evening star” becomes “Evening Star”, and they may come to be used as names for the same thing. Singular descriptions such as ‘the little corporal’, ‘the Prince of Denmark’, ‘the sage of Concord’, or ‘the great dissenter’ are as we know often used as alternative proper names of Napoleon, Hamlet, Thoreau and Oliver Wendell Holmes. One might even devise a criterion as to when a descriptive phrase is being used as a proper name. Suppose through some astronomical cataclysm, Venus was no longer the first star of the evening. If we continued to call it alternatively ‘Evening Star’ or ‘the evening star’ then this would be a measure of the conversion of the descriptive phrase into a proper name. If, however, we would then regard (10) [The evening star eq the morning star] as false, this would indicate that ‘the evening star’ was not used as an alternative proper name of Venus. We might mention in passing that although the conversion of descriptions into proper names appears to be asymmetric, we do find proper names used in singular descriptions of something other than the thing named, as in the statement ‘Mao Tse-tung is the Stalin of China’, where one intends to assert a similarity between the entities named.
That any language must countenance some entities as things would appear to be a precondition for language. But this is not to say that experience is given to us as a collection of things, for it would appear that there are cultural variations and accompanying linguistic variation as to what sorts of entities are so singled out. It would also appear to be a precondition of language that the singling out of an entity as a thing is accompanied by many — and perhaps an indefinite or infinite number — of unique descriptions, for otherwise how would it be singled out? But to give a thing a proper name is different than giving a unique description. For suppose we took an inventory of all the entities countenanced as things by some particular culture through its own language, with its own set of names and equitable singular descriptions, and suppose that number were finite (this assumption is for the sake of simplifying the exposition). And suppose we randomized as many whole numbers as we needed for a one-to-one correspondence, and thereby tagged each thing. This identifying tag is a proper name of the thing. In taking our inventory we discovered that many of the entities countenanced as things by that language-culture complex already had proper names, although in many cases a singular description may have been used. This tag, a proper name, has no meaning. It simply tags. It is not strongly equitable with any of the singular descriptions of the thing ...“
Several comments about this passage are in order. (a) Obviously, if any philosophy of language is about natural language, this passage exhibits such a philosophy. (b) Obviously, the example of randomized whole numbers being used as tags is used to illustrate the idea that tags or proper names in natural languages have no meaning at all and differ in this respect from descriptions. (c) The main evidence that Soames and Burgess have presented as “real doubts” that Marcus is talking about names in natural language is quoting the sentence about “randomizing whole numbers” out of context. Here is how Burgess [1996] produces this doubt, where (A) contains a quote from Marcus:
“Accordingly, Marcus invites us to contemplate the following imaginary scenario:
(A) For suppose we took an inventory of all the entities countenanced as things by some particular culture ... And suppose we randomized ss many whole numbers as we needed for a one-to-one correspondence, and thereby tagged each thing.
When she continues, ‘This identifying tag is a proper name of the thing.’ What is being celled a ‘name’ is thus not a name in the ordinary sense, or even a linguistic expression, but a serial number.’ [ Burgess, 1996: 3-4, my emphasis]
By these textual manipulations, Burgess has managed to create a doubt in the mind of some of his readers who are unfamiliar with Marcus [1961] about whether or not Marcus’ theory of tags is a theory of proper names in ordinary language. Note that: (i) Burgess omits all the preceding sentences where it is evident that she is talking about natural language, and replaces them by his misleading introduction to the quote, where he says “Marcus invites us to contemplate the following imaginary scenario”. Note also (ii) the ellipses in Burgess’ quote, which consist of omitted material (present in my above, long quotation) that show she is talking about natural language, and (iii) Burgess misleadingly concludes about this passage that Marcus’ serial numbers were not introduced as illustrations of the fact that names in natural languages have no meaning, and instead presents this illustration as all that she means by a name — a name is just a serial number in a non-natural language.
I conclude, then, that Burgess and Soames have failed in their attempt to establish a “real doubt” as to whether Marcus is talking about names in natural languages.
5. Necessity in Marcus’ 1961-1962 theory
What does Marcus mean by “necessity”? Does she hold that “necessary” means knowable by an analysis of its linguistic meaning along? Or does she mean obtains in all possible worlds?
There is no controversy about whether she characterizes certain classes of statements, e.g., identity statements involving names, as “tautologies”, “analytic truths”, “logical truths”, “logically necessary truths”, “necessary truths” and “not contingent truths”. The question, rather, is what she means by these terms.
Since her main discussion is about quantified modal logic, it is reasonable to assume that by a “logical truth” or a “logically necessary truth” she is talking about “logic” in the sense pertinent to quantified modal logic (her semantic construction on pp. 319ff. is in terms of QS4). In fact, she begins her discussion of identity statements by saying precisely that:
“In the light of the previous remarks I would like to turn specifically to the criticisms raised against extended modal systems in connection with identity and substitution. In particular, I will refer to my extension of Lewis’ S4 which consisted of introducing quantification in the usual manner and the addition of the axiom…” [she then states a version of the Barcan formula}.
It is uncontroversial that she takes identity statements such as “Venus is Phosphorus” to be logical truths (in the sense pertinent to QS4), so we will move on. In her discussion of theorems of QS4 and its “logical truths” on pages 307-308, she uses “tautology” to mean a logical truth; e.g., she says the fact that “alb” is a “tautology” “is precisely the import of my theorem (8)” [1961: 308], where theorem (8) is a theorem of QS4 stating:
where the box ‘ٱ’ is the modal symbol for logical necessity”. [1961: 308].
The use of “tautology” for theorems of quantified modal logic is not new with Marcus; in Kripke’s [1959] he called the logical truths of S5 tautologies. In this article, Kripke says a statement true in every possible world is a “universal logical validity’ [1959: 3] and adds: “Using these observations it is easy to prove that for formulas of S5 our notion of tautology coincides with our notion of universal validity”. [1959: 11] “... All axioms of S5 are tautologies” [1959: 12]. A formula “A is said to be universally valid if and only if A is valid in every non-empty domain”, [1959: 2]. The point here is not that Kripke’s semantics for modal logic and conception of tautologies are the same as Marcus’; they are not. Rather, the point is that the use of the word “tautology” does not ipso facto mean that one is not talking about statements true in all possible worlds and does not mean one is writing in the tradition, say, of Al Ayer.
Marcus also calls “alb” or “Venus is Hesperus” an “analytic” truth; she writes: “What I have been arguing in the past several minutes is, that to say of an identity (in the strongest sense of the word) that it is true, it must be tautologically or analytically true”. The question now is: what does Marcus mean by “analytic”?
The word “analytic” is standardly used in many different senses, sometimes in a linguistic sense to mean a sentence that is transformable into a logically true sentence by substitution of synonyms for synomyns, sometimes in an epistemic sense to be knowable a priori, by reflection on linguistic meaning alone, sometimes in a conceptual sense to mean a thought where one concept contains another concept as a part, and sometimes in a logical sense to mean a logically necessary truth. In what sense does Marcus use it? The preceding quotations suggest that “analytic” means tautological and that tautological means logically necessary (in the sense of QS4). Is there any further evidence that she means “analytic” in the sense of (modal) logical necessity?
In the subsequent discussion of her paper [Marcus et al. 1962: 140. my emphases] she distinguishes between a narrow and broad sense of “analytic”:
“Necessary attributes would correspond to analytic functions in the broader sense of analytic. These may be thought of as a kind of essential attribute, although necessary attribute is better here. For these are attributes which belong necessarily to every object in the domain, whereas the usual meaning of essentialism is more restricted, Attributes like mathematician and cyclist do not correspond to analytic functions”.
It seems here that the broader sense of “analytic” is used in a modal logical sense, rather than an epistemic, linguistic or conceptual sense: a broadly analytic function corresponds to an attribute that belongs necessarily to every object in the domain. This broad sense of ‘analytic” has metaphysical import. for it is defined in terms of every object in the domain. “Domain” is used here in the sense of her earlier “semantic construction”, where all possible worlds
are said to include only objects that belong to the actual world. The “domain of objects” is all actually existing objects. A broadly analytic function corresponds to an attribute that belongs necessarily to every object in every possible world.
This use of traditional terminology to introduce new ideas shows why it is easy to misunderstand Marcus’ theory, as Kripke, Soames and Burgess have done, (But Kaplan [1986] Devitt [1989], Hintikka and Sandu [1995] and others seem to have understood the main points of her theory.) Marcus is trying to express a new idea by adding “broader” to a term that is traditionally used in other senses, just as Plantinga [1970] adds “broader” to the traditionally used “logically necessary” to express a new idea, namely, non-trivial essences, such as being prime, being a number, and world-indexed properties such as being snub-nosed in Kronos, where “Kronos” is a name for the actual world. Plantinga pointed out [1970] that the concept of a broadly logical necessity belongs to metaphysics, not epistemology, and argues that there are logical necessities that are known a posteriori.
The modal-metaphysical import of Marcus’ use of ‘analytic”, “tautologial’ and “logically necessary” is further evidenced by her definition of a logically true sentence, She offers her definition of logical truth in terms of her semantic construction, which she says “corresponds to the Leibnizian distinction between true in a possible world and true in all possible worlds” [1961: 320, my emphasis]. As some other modal logicians do at this time, she uses “possible world” interchangeably with “model”, so that “every model” is synonymous with “every possible world”. Here is her definition of a logically true sentence:
“A logically true sentence is one which would be true in every model”. [1961:
319].
She also talks about counterfactual situations in her discussions of possibility and necessity, further evincing her metaphysical understanding of these notions. John Burgess stated to the contrary that Marcus’ [1961] does not contain a single explicit discussion of a counterfactual comparison (and thus cannot contain the concept of a rigid designator): “there patently is no explicit discussion of rigidity — no explicit discussion of cross-comparison between actual and counterfactual situations, or between one counterfactual situation and another — in Marcus” [1996: 27, my emphases]. In fact, there are many explicit discussions of cross-comparisons between actual and counterfactual situations in Marcus [1961] such as the following, where Marcus is talking about the criteria for deciding whether “evening star/morning star” and “Scott/author of Waverley” are being used as names or contingent descriptions: “... if our decision is that they are not simply proper names for the same thing; that they express an equivalence which is possibly false, e.g., someone else might have written Waverley, the star first seen in the evening might have been different from the star first seen in the morning — then they are not identities”. [1961: 311, my emphases]. Other explicit discussions of cross- comparisons between actual and counterfactual comparisons appear on pages 308,309,311,312,313,315,316,317, and 318 of her [1961].
Burgess and Soames believe that by “necessary” Marcus means “discover able by reflection on linguistic meaning alone”. Thus, necessarily true identity statements involving names are (according to Burgess’ and Soames’ interpreta tion of Marcus) identity statements whose truth can be determined simply by reflecting on their meaning. But this cannot be what Marcus meant, if only for the reason that she denies that names have meaning. “This tag, a proper name, has no meaning. It simply tags”. [Marucs, 1961: 310]. In order for “Hesperus is Phosphorus” to be known to be true by reflection on its linguistic meaning alone, “Hesperus” and “Phosphorus” would have to express concepts or descriptive senses, or some other sort of meanings, grasped by reflection. But with Marcus’ theory, we have no such concepts or “graspable meanings” and we have merely meaningless syntactical entities (the tags), the identity sign, and astronomical bodies millions of miles away — there is nothing here to be reflectively grasped by contemplating the sentence in my “armchair”, to use Burgess’ word [1996: 25].
Soames and Burgess also ascribe to Marcus the view that the name-object relation is a priori, e.g., that it is an a priori truth that the public language name “Hesperus” (rather than “Kansas” or “Beethoven”, for example) refers to Venus. The consequence they draw from this is that “on the view articulated by Marcus, true identity statements involving names are knowable a priori” [Soames, 1995: 205].
This is how Kripke understood Marcus, but Kripke misunderstood and misquoted [1971: 142-3; 1972: 305] her remark in [Marcus et al., 1962: 142]. (See Smith [1995b: 236-37]; the misquotation appears in [Kripke, 1971: 142, n. 7]). Can we use Kripke’s misquotation of Marcus as evidence that Marcus held the name-object relation to be a priori? Burgess asserts this is evidence in his [1996] It is not obvious, however, that if x says “F” and y quotes her as saying “not-F”, that counts as evidence that x did not say “F” but instead said “not F”.
Apart from this issue, how is this theory of an “a priori name-object relation” consistent with Marcus’ remarks that objects can be named ostensively and a posteriori, by inspection? Marcus writes: ‘‘For we can on inspection name the objects to which it applies just as one can on inspection name the members of the class designated by [Venus, Neptune, Mars]”. [1963: 131]. The “it” refers to an abstract that is instantiated by replacing its individual constants by names we assign to objects on inspection. The abstract is
where ‘I’ names the identity relation and u1, u2 . . . un are individual constants”. [1963: 131]. If the name-object relation is a priori, how could there be inspections in which we name objects? How could one “on inspection name the members of the class designated by [Venus, Neptune, Mars]”? [1963: 131, my italics]. If objects had their names a priori. then it would be impossible to name them on inspect ion, for any attempt to name an object on inspection would result in the realization that the object already has a name, prior (a priori) to that inspection and any other possible inspection.
Marcus’ notes that “there are cultural variations and accompanying linguistic variations as to what sorts of entities are so singled out ... [S]uppose we took an inventory of all the entities countenanced as things by some particular culture through its own language, with its own set of names and equitable singular descriptions ...“ [1962: 309-310], The mere fact that the inventory of named entities varies from culture to culture implies that empirical investigation is required to learn a given culture’s inventory of named entities. One has to learn through observations or records of linguistic practices the culture’s inventory of named entities, and, in addition, the very development and compilation of the inventory by members of the culture requires observations of the linguistic practices of the people in that culture. The creators or compilers of that culture’s dictionaries or lexicons are observers of that culture’s linguistic practices.
Once names have acquired an established use in a language. their usage may be recorded and the recording may be consulted to find out if two names have been assigned to the same object [Marcus et al.. 1962: 142]. One way we do find out that the same object has more than one name is to find more than one name listed for the object in a dictionary. For example, Webster’s New World Dictionary (2nd ed., 1974, p. 256) has this entry: “Cic-cr-o, (Marcus Tullius) 106-43 B.C.; Roman statesman, orator, and philosopher”. Merriam Webster’s (1941, p. 466) has for an entry: “Hes’per-us, ii, The evening star: Venus”. Kripke’s theory that recordings of established uses, such as are found in dictionaries or lexicons, represent a priori knowledge has obscured the common sense fact that a paradigmatic way in which we answer empirical questions about the references of names is through reading a culture’s lexicons or recordings of how people in that culture use names.
We “inspect” the objects to which the culture has assigned names only in atypical cases where we suspect the culture has made a mistake about whether two names are co-referring or not. This atypical sort of a posteriori knowledge about identity statements involving names was first discussed by Plantinga [1970]. Marcus’ discussion is only about the typical cases where we assume that the culture’s use of names is accurate and their lexicons give reliable empirical knowledge. In these typical cases, we consult the dictionaries rather than engage in a scientific observation of (say) “Venus’ mass, or its orbit” [Marcus et a!., 1962, p. 142]. Such cases as the case of the Babylonians whose lexicon or established use of names is inaccurate are resolved by resorting to the “naming inspections”, to see where or how people went wrong in assigning names to objects (see [Plantinga, 1970]). If we combine Marcus’ theory with Plantinga’s, then we have a theory of the typical and atypical ways in which we learn a posteriori about the truth of necessary identity statements involving names.
The theory (which Kripke seems to presuppose) that all questions of co reference are resolved in the manner in which they are in fact resolved when the lexicons are assumed to be unreliable fails to take into account the standard or typical case, which is when we assume our lexicons are reliable and that consulting them (rather than the objects themselves) is sufficient to answer our questions.
(Perhaps it goes without saying that we need to use selected cases of famous names in order to talk about consulting dictionaries, since “analogous inquiries” are required for names that are not famous.)
Marcus uses the empirical fact that names, but not contingent descriptions, are listed in lexicons as part of her argument that aggregates of objects are necessarily identical. Her novel argument about aggregates in [ has this structure: the relevant aggregates are necessarily identical since (i) an aggregate can be designated by a set of names, (ii) the identity sign is flanked only by names, (iii) identities are necessary, (iv) lexicons list names but not contingent descriptions, and (v) questions of identity about aggregates (that are designated by different sets of names) can be answered by consulting the cross-listing of co-referring names in a lexicon.
Marcus’ theory has not been widely appreciated as a consequence of Kripke’s misinterpretation of her theory in terms of his false theory of dictionary knowledge as a priori knowledge.
What is dictionary knowledge? David Gurlank and the others who engaged in the empirical research required to determine how English words are used, and to record this usage in Webster’s New World Dictionary [Gurlank, 1974], put such entries in the dictionary as: “Hesperus. the evening star, esp. Venus” [Gurlank, 1974: 658]. I omitted the pronunciation symbols and Greek root from the entry]. If somebody asks me, “Is Venus identical with Hesperus”? and I understand the question and respond that I don’t know the answer, but then proceed to look up the name in the dictionary, I will find the entry on page 658
for “Hesperus” and then learn these two names are co-referring. How is this different from being asked the question, “Is gold identical with the atomic element 79”?, understanding the question, and then proceeding to find out the answer by reading a chemistry textbook? Kripke believes the former procedure is a case of a priori knowledge and the latter a case of a posteriori knowledge. Kripke either has an incorrect theory of the a priori/a posteriori distinction or else does not understand correctly the nature of dictionaries,
Even if, counterlegally, dictionaries do contain a priori truths about name- objects relations, looking up entries in a dictionary would still be a posteriori knowledge. For (as Kripke notes) one can learn a mathematical truth a posteriori by consulting a computing machine, or even by asking a mathematician ... All the cases of the necessary a posteriori advocated in the text [of (Kripke, 1972)] have the special character attributed to mathematical statements ...“ [1972: 765]. The exception Kripke makes for consulting dictionaries is simply a mistake.
It is worth noting that the only place in the philosophical literature where the bizarre thesis that “the ordinary name-object relations reported in dictionaries are a priori” is even mentioned is in the writings of Kripke [1971; 1972: also see his remarks in Marcus et al., 1962], Burgess [1996] and my rebutals in [1995a;
1995b] and the present paper.
As I indicated in [1995b] we do not find in Marcus earls’ writings an explicit discussion of the traditional thesis that the necessary and the a priori are identical or coextensive. Marcus’ theories of direct reference, rigid designation. the necessary of identity between names, the modal argument for direct reference, etc., are explicit in her early writings, but as I maintained [1995b: 235], the argument that necessary identities can he a posteriori is implied by (but not explicitly stated in) her theory. The traditional thesis that “necessity = a priori” was not explicitly addressed and rejected until Plantinga’s October, 1969 talk at Cornell University, later published as [Plantinga, 1970]. It may well be that a later theory that explicitly discusses and rejects the “necessary = a priori” thesis is more historically important than an earlier theory that merely implies this rejection. But this is not the issue here: the point is merely that Kripke, Soames and Burgess are mistaken in ascribing to Marcus the explicit or implicit endorsement of the theory that the ordinary name-object relation is a priori and that “Hesperus is Venus” is necessary in the sense that it is knowable by reflection on its meaning alone, This and the various other considerations I have discussed in this section indicate that Marcus understood “necessity” in a logical—metaphysical sense, not in a linguistic. epistemic or conceptual sense.
This fact is further evinced if we examine the claim that Marcus is not a New Theorist of Reference, and is not writing in the tradition of Kaplan. Kripke.
Putnam, Donnellan, etc., but is instead a Russellian who is merely repeating
Russell’s 1918 doctrines in her 1961 article.
6. Russell and Marcus
One reason both Burgess and Soames do not understand or correctly represent Marcus is that they insist that Marcus is repeating Russell’s theory. For example, Soames writes that Marcus treats proper names as Russellian logically proper names: “However, given Marcus’ treatment of names as Russellian logically proper names, and hence as supporting substitution with out change of meaning in any non-quotational context, (P1 [‘It is knowable a priori that Hesperus = Phosphorus’) is plausible, as are the other steps in the argument” [1995: 207]. And Burgess writes:
“Marcus (1961) endorses the very well known, but at the time not very popular, view of Mill that names have no descriptive meaning, as well as some only slightly less well known views of Russell, including the view that true identity statements involving ‘names’ are ‘tautologies’ [1996: 391].
Burgess’ reference to Mill has some truth to it, but his and Soames’ claim that
Marcus was repeating or endorsing Russell’s theory if false. Burgess and
Soames claim at several points that what Marcus meant by “tautology”,
“identity”, “names”, “necessity”, etc., is the same thing that Russell meant.
This is demonstrably untrue.
First, Russell’s tautologies are theorems in extensional logic, specifically, first order propositional calculus or first order predicate calculus; but Marcus’ tautologous statements are theorems in intensional logic, specifically, quantified modal logic (she uses QS4 in her 1961 semantic construction).
Secondly, Marcus uses “identity” to express a relation different than strict equivalence, material equivalence, and other weaker sorts of equivalence relations, but Russell did not use “identity” to express this strong relation. For Russell, the identity sign can be flanked by a name and a definite description, but a key idea in Marcus’ philosophy is that the identity sign can be flanked only by names. Russell used the word “identity” to express what Marcus calls an equivalence relation weaker than identity. Furthermore, for Russell, identities can be contingent, but for Marcus, identities are necessary. Russell writes: “That illustrates how ‘the author of Waverley’ is quite a different thing from a name. You can prove this point very clearly by formal arguments. In ‘Scott is the author of Waverley’, the ‘is’ of course expresses identity, i.e., the entity whose name is Scott is identical with the author of Waverley” [1918: 245]. Also see Russell [1918: 247]. Here Russell is using “Scott” as an artificial example of a name, since in ordinary usage (according to Russell) it is an abbreviated description and in reality names are demonstratives such as “this” and “that”. But Marcus denied that the “is” in “Scott is the author of Waverley” expresses the identity relation and she denies that identity statements can be contingently true.
Thirdly, by “is necessarily true” Russell means the temporal notion, is always true; for Russell, “necessity” means what is always true in the actual world, not the modal notion of what is true in all possible worlds. (This is Russell’s doctrine in his 1918 essay on the “Philosophy of Logical Atomism”, which Soames and Burgess take Marcus to be repeating.) But Marcus does not use “necessary truth” in a temporal sense but in the contemporary modal sense to mean truth in all possible worlds. Russell says that one may call a propositional function necessary, when it is always true” [1918: 231, my emphasis], but Marcus rejects this temporal definition of necessity and accepts a possible world definition; a necessarily true sentence is one that is “true in all possible worlds” [1961: 320]; she uses “model” as a synonym for “world” and writes in addition: “A logically true sentence is one which would be true in every model”. [1961: 319].
Fourth, Russellian logically proper names are names in a private language for my fleeting sense data with which I have an immediate acquaintance. “The only words one does use as names in the logical sense are words like ‘this’ or ‘that’, One can use ‘this’ as a name to stand for a particular with which one is acquainted at the moment ... [A proper name] seldom means the same thing two moments running and does not mean the same thing to the speaker and to the hearer”, [1918: 210], Indeed, logically proper names are necessarily private:
in a logically proper language “all the names that it would use would he private to the speaker and could not enter in the language of another speaker” [1918:
198]. Russell’s names (a) are in a private language, (b) refer only to a person’s introspected sense data, (c) seldom mean the same thing in two successive moments, (d) are demonstrative words, such as “this” and “that” and (e) are not intersubstitutable in (metaphysical) modal contexts, since for Russell there are no such contexts (for Russell, contexts involving “necessarily”, “possibly” and the like are temporal contexts). But Marcus’ names (a) are in a public language. (b) refer to ordinary things in the universe, such as Venus or Walter Scott, (c) usually have a constant reference across long periods of time. (d) are not demonstratives such as “this” and “that”, but arc what are ordinarily called “names”, e.g., “Scott”, “Venus”, etc., and (e) are intersubstitutable in (meta physical) modal contexts,
Burgess claims that Marcus merely repeats the “views of Russell, including the view that true identity statements involving ‘involving are ‘tautologies’ [1996: 39]. But Russell’s theory that “a true identity statement involving names is necessarily true” is the theory that the true private language statement about my sense data, “this is this’ is always true and expresses a kind of identity relation that can obtain contingently. Marcus’ theory that “a true identity statement involving names is necessarily true” is the theory that a true public language statement about publically observable things in the universe, such as ‘Venus is Hesperus’ is true in every possible world, where “is” expresses her strong relation I of identity (which can never obtain contingently) and where the statement is a “tautology” in the sense of being a theorem of quantified S4 (rather than of the extensional logic of Whitehead’s and Russell’s Principia Mathematica).
The claim that Marcus’ [1961] is a “repetition and endorsement” of Russell’s 1918 theory is as mistaken as any claim about the history of philosophy can possibly be.
Soames and Burgess occasionally recognize (what one would hope to be) the obvious fact that Marcus’ names are not Russellian logically proper names, but they continue to conflate the concepts. This is evident in Soames’ discussion of a thesis (P1) he mis-attributes to Marcus:
(P1) It is knowable a priori that Hesperus = Phosphorus.
Soames says about (P 1): the premise “that it is knowable a priori that Hesperus is Phosphorus, presupposes a prior rejection of the description theory. The basis for assuming this premise is simply a prior acceptance of Millianism”. [1995: 207].
But this is a mistake; the Millian theory of names ia not a prior basis for accepting, and does not imply, the premise that it is knowable a priori that Hesperus is Phosphorus. Kripke, Kaplan, Donnellan, Salmon, Wettstein and others are Millians and they reject the idea that Millianism is a basis for holding that Hesperus is Phosphorus is knowable a priori. Indeed, the fact that Millianism does not imply that such identity statements are a priori is standard orthodoxy among New Theorists of Reference, so one wonders how Soames went wrong here. Reading elsewhere on this page [Soames, 1995: 207], it appears that Soames is conflating Millian names with Russellian logically proper names:
“However, given Marcus’ treatment of proper names as Russellian logically proper names, and hence as supporting substitution without change of meaning in any non-quotational context, P1 [“It is knowable a priori that Hesperus = Phosphorus”] is plausible, as are the other steps in the argument”.
Contra Soames, identity statements involving Russellian logically proper names (“this” and “that”, names of my private sense data) are a priori, but identity statements involving Millian proper names are not a priori. The attribution of both theories to Marcus can only lead to confusion. (The Russell—Mill conflation also underlies Soames’ claim that Smullyan originated all the ideas about names that appear in Marcus [1961]and that it was Smullyan, not Marcus, who is the unacknowledged founder of the basic ideas of the New Theory of Reference (direct reference, the modal argument for direct reference, the rigidity of names, the thesis that identity statements involving names are necessary if true, etc.). Smullyan is a Russellian, but Marcus is not, and Smullyan did not hold any of the above-mentioned ideas, as I argue in my [1998b].)
7. The Marcus-Kripke theory that necessity is logical-metaphysical necessity
Soames and Burgess think that by “necessary truth” Marcus means the episternological notion of being true a priori rather than the metaphysical notion of truth in all possible worlds. They argue that since Kripke means by “necessary truth” a non-logical and metaphysical notion of truth in all possible worlds, Kripke made the decisive advance into the post-1970 New Theory of Reference.
Soames and Burgess identify the transition from logical modalities to metaphysical modalities as the (alleged) major advance made by Kripke from Marcus’ position. For example, Burgess writes:
Marcus can be credited with a version or variant of the stability argument [made by Kripke] only if she can be credited with recognizing that possibility in the metaphysical’ sense of what (is or isn’t but) potentially could have been the case is not to be analyzed as or conflated with possibility in the ‘logical’ sense of what it is not logically or analytically self-contradiction to assert or assume actually is the case.” [Burgess, 1996: 25]
The viewpoint of Burgess and Soames is erroneous since, both Marcrus and Kripke identify possibility in the so-called “metaphysical” sense of what could have been the case with logical possibility.
I have already argued above that Marcus used “tautology, logically true, broadly analytic”, etc., in quantified modal logic senses that that are meant to have metaphysical import about what must be the case, what is the case in all possible worlds. Let us repeat a couple of sentences From Marcus I have already quoted:
the rough outline above [her semantic construction for QS4] corresponds to the Leibnizian distinction between true in a possible world and true in all possible worlds…” [1961: 320. my italics She calls a possible world a model and defines a logically true sentence as follows “A logically true sentence is one which would be true in every in model’, [1961, my italics}. A necessary truth, for Marcus, is defined in modal terms; it is nor defined as a priori truth. She does not write instead: ‘A logically true sentence is one which can be known to be true independent of all experience.” Marcus likewise defines an individual’s necessary possession of a property, not in terms of it being true a priori that the individual possesses the property, but in terms of it being true that the individual possesses the property in every possible world (model). “To say of thing a that it necessarily has a property j(ڤ(ja)) is to say that ja is true in every model. Self-identity would be such a property”. [Marcus et al., 1962: 133].
This identification of a logically necessary truth with a truth in every possible world is also made by Kripke.
Kripke’s [1971] and [1972] reiterate Plantinga’s [1970] thesis that the metaphysical distinction between necessity and possibility is not equivalent to the epistemological distinction between a priori and a posteriori. This metaphysical vs. epistemological distinction is made in Kripke’s work, but Soames and Burgess are quite mistaken when they say Kripke also makes a metaphysical vs. logical distinction. In fact, Kripke identified metaphysical necessity with logical necessity. This can be seen from numerous passages, a small number of which I will quote.
First, consider that on the page immediately after the page where Kripke says the distinction between necessity and possibility belongs to metaphysics and not epistemology [1971: 150], he starts talking about logical possibility and necessity (which he takes to be the same thing as metaphysical possibility and necessity). He talks about “performing an infinite number of acts like looking through each number one by one. A vast philosophical literature has been written on this: Some have declared it logically impossible: others that it is logically possible; and some do not know. The main point is that it is not trivial that just because such a statement is necessary it can be known a priori [1971: 151; my emphasis]. This shows that Kripke’s point is to distinguish between a prioricity and logical necessity, not (contra Soames and Burgess) to distinguish between metaphysical necessity and logical necessity.
Examples from Kripke’s [ make this even more clear; at one place he writes that “it is (metaphysically) possible that there should have been animals that resembled tigers but were not tigers” [1972: 330; my emphasis; the parentheses are in the original text]. But he immediately proceeds to say he is talking about logical possibility. He says “the notion of a posteriori necessary truth may still be somewhat puzzling” and represents an objector to his theory as asking “What then can you mean when you say that such eventualities are impossible”? [1972: 331]. Kripke formulates the objection to his theory, and his answer to this objection, in terms of logical possibility. He formulates the objection as follows: “it really is logically possible that gold should have turned out to be a compound, and this table might really have turned out not be made of wood, let alone of a given particular block of wood” [1972: 332, my emphasis]. Kripke answers this objection as follows: “In the case of some necessary a posteriori truths, however, we can say that under appropriate qualitatively identical evidential situations, an appropriate corresponding qualitative statement might have been false. The loose and inaccurate statement that gold might have turned out to be a compound should be replaced (roughly) by the statement that it is logically possible that there should have been a compound with all the properties originally known to hold of gold” [1972: 333; my emphasis].
For yet another example, note that Kripke later phrases his argument about the essence of pain and brain states in terms of logical possibilities; e.g., he writes “it would seem logically possible that B could exist without any sensation with which it might plausibly be identified” [1972: 335; my emphasis]. For a final example I will give (there are many others), I will note Kripke’s famous discussion of the necessity of origins. His discussion of the necessity of origins is framed in terms of “contradictions”; Kripke says there is “no contradiction” [1972: 312, my emphasis] in the announcement that the thing we thought to be the Queen is in fact an automaton, but distinguishes this non-contradictory statement from the (allegedly) contradictory statement that the Queen was born of different parents from the parents from whom she actually came.
In his [1971] and [1972] Kripke consistently makes these equations: logical necessity = metaphysical necessity = obtaining in all possible worlds. He does not maintain that there is a distinction between logical necessity and metaphysical necessity.
In summary, Soames and Burgess are mistaken in holding that Kripke made a major advancement over Marcus by distinguishing logical from metaphysical necessity and they are mistaken in holding that Marcus failed to have the concept of necessary truth as truth in all possible worlds. Both Marcus and Kripke identified logical with metaphysical necessity and both defined logically necessary truth as truth in all possible worlds.
The following sections will further evince that Marcus s not a Russellian— Millian, but a Kripkean But first I will rebut Marcus’ recent thesis that she is not a Kripkean—Millian, i.e., that her ‘proper names are not assimilated to what later came to be called rigid designators’ by Saul Kripke, although they share some features with rigid designators” [Marcus, 1993: xiii xiv]. Marcus seems to hold this view since she believes Kripke “... classifies proper names as ‘rigid designators’ along with rigid descriptions, thereby obscuring the difference in semantic relationship between a proper name and the object named as compared with the relationship between a rigid description and the object described”, [1993: 248. n. 19]. 1 believe she is wrong it’ only for the reasons that Kripke denied that proper names refer descriptively and that Kripke held names are connected with their referents by an historical chain. whereas rigid descriptions are not, Since Kripke’s alleged “assimilation” is the only reason Marcus offers for her denial that her tags are rigid designators, I think it is reasonable to conclude that her denial is based on an incorrect interpretation of Kripke’s theory and that her denial does nothing to impugn the extensive textual evidence that her tags are rigid designators.[4]
8. Necessary identifications and non-trivial essential attributions in Marcus [1961]
A distinction that is present in both Marcus’ [1961] and Kripke’s [1972] is the distinction between necessary identifications and non-trivial essential attributions. “alb” is an identification, whereas (to use Marcus’ symbolism),
may make a non-trivial essential attribution (it attributes the property of being necessarily r to the individual a), Marcus introduces this symbolism in conjunction with her distinction between necessary properties that belong to some objects and necessary properties that belong to every object in the domain of objects in all possible worlds, She presents the following two def3nitions to capture this distinction in item (57) of her [1961]:
The first definition translates as “x instantiates the necessary attribute r = df necessarily, x instantiates the attribute r”. The second de6nition translates as “r is a logically necessary attribute r=df for every x, x instantiates the necessary attribute r”. Marcus makes this definitional distinction or the purposes of distinguishing between properties that necessarily belong to each thing (such as self-identity), which is captured in the second definition, and properties that necessarily belong to some things (such as being rational), which is captured in the first definition. Her point here is to distinguish “necessary properties” in the sense of non-trivial essences, such as being rational (one of the examples she is using in discussing Quine’s argument about being rational. two-legged, a cyclist and a mathematician) from “necessary properties in the sense of properties that of logical necessity belong to each thing. Quine argued that the semantics of quantified modal logic is committed to non-trivial essences, but Marcus counter-argues that this semantics is committed only to logically necessary properties possessed by each thing, such as self-identity.
In these definitions, Marcus is also introducing the notion of “de re necessity” in the sense of necessary properties of things, as distinct from “de dicto necessity”, which pertains to statements or propositions having the property of being necessarily true. For some individual x,
this means x has a necessary property r, such as being rational. By contrast
the definitional equivalent of
states that it is necessarily true that
where “necessity” is an operator that takes a “dictum” as its operand.
Thus, in Marcus’ symbolism, a necessary identification, such as “Necessarily, Venus is Hesperus” appears as
whereas a necessary attribution of a non trivial essence, such as “Socrates is necessarily rational”, appears as a
In Marcus’ 1961 theory, the first statement is defined as meaning it is true in all possible worlds that Venus is Hesperus and the second statement is defined as meaning Socrates instantiates rationality in each possible world. (Marcus has a constant domain in her semantics for modal logic, so it would be redundant to say “Socrates instantiates rationality in each possible world in which he exists”.) I have presented the necessary identity in a de dicto formulation and the necessary attribution in a de re formulation, but both necessities can be given either a de dicto or a de re formulation in Marcus’ [1961] theory.
In my [1995b] I explained the theory of necessary a posteriori identities in terms of object level facts (which are necessary and a priori) and metalevel facts about the relation of statements to the fact stated by them (the metalevel fact being contingent and a posteriori). However, there is a third ingredient in the theory of necessary a posteriori identities that needs to be mentioned. The statement itself, “Hesperus is Venus”, is necessarily true and is a posteriori. (More exactly, it is necessarily true given the actual interpretation of these names, viz., that “Hesperus” and “Venus” both refer to Venus.) On Marcus’ theory, statements of the form alb possess both the property of being necessary and (at least in some cases) the property of being a posteriori. Thus, we have one and the same item (the statement) that is necessary and a posteriori.
Marcus’ introduction and defense of de re necessities marks the first departure in the literature on modal logic from the orthodox view of Carnap, Quine, CI. Lewis, Kanger and others, namely, that the notion of de re necessity is nonsensical and that “necessity resides only in our language, not in things themselves”. This is one of the facts that has gone unrecognized in standard histories of modal logic and the New Theory of Reference.
It should now be evident that Marcus’ [1961] develops ideas that belong to the theoretical framework of Kripke’s and Kaplan’s 1970s writings and that her [ does not consist of repetitions of Russell’s 1918 doctrines. Accordingly, I will now pass to comparing, developing and evaluating the theories of rigid designation that can be found in the works of Marcus, Kripke and Kaplan. In the next section, we will concentrate on Marcus’ theory of rigidity and show how it can be used to develop a “complete concept of a rigid designator.
9. The “complete concept’ of a rigid designator
Neither Marcus nor Kripke nor Kaplan talked about (what I shall call) the complete concept of a rigid designation, so here I am making something more explicit than what is present in any of their texts.
The complete concept of rigid designation contains an informal purl and ii formal part. The informal part belongs to the philosophy of language and is an intuitive explication of the difference between rigid and nonrigid designators in ordinary language. The formal part is a definition of rigid designation in terms of a semantics for modal logic, and embodies the formal notion of the referent of a singular term at a model or possible world. Somebody has the complete concept of a rigid designation if and only if she has both the informal and formal parts.
There are two ways to explicate formally the notion of rigidity, associated with Kripke and Kaplan respectively, and they tire both present in Marcus’ 1961 work (but are not explicitly formulated in any of their works). I shall argue in a later section that the definition associated with Kripke is accurate but the definition associated with Kaplan is not. But before I engage in a discussion of these formal explications, I shall illustrate the in formal explication of the rigid/nonrigid distinction in Kripke’s and Marcus writings.
The informal explication does not require a model-theoretic semantics, the notion of a possible world, or the concept of a singular proposition. The concept of rigid designation can be stated in an informal way using only modal prefixes or adverbs (“possibly”, “necessarily”) and subjuntctives (“might have been”, etc.). In the following few quotations. I am repeating my [1995b], but this is necessary to introduce my more complete account here. Kripke conveys the distinction between rigid and nonrigid designation in “Naming and Necessity” in this informal way. Kripke writes:
One of the intuitive theses I will maintain in these talks is that names are rigid designators. Certainty they seem to satisfy the intuitive test mentioned above; although someone other than the US President in 1970 might have been the U.S. President in 1970 (e.g.. Humphrey might have), no one other than Nixon might have been Nixon ... For example, ‘the President of the U.S in I 970’ designates a certain man, Nixon; but someone else (e.g.. Humphrev) might have been the President in 1970, and Nixon might not have; so this designator is not rigid [1972: 270].
Here the notion of rigid designators is explained in terms of the subjunctive expressions “might have been”, “might not have been”, and no mention of possible worlds or singular propositions is needed. This is also how Marcus introduced the notion in her 1961 article. The rigid/nonrigid distinction between names and contingent definite descriptions is present in the following passage, but with a different terminology:
Let us return now to (10) and (15). [(10) is “The evening star eq the morning star” and (15) is “Scott is he author of Waverley”]. If they express a true identity, then “Scott” ought to be anywhere intersubstitutable for “the author of Waverley”, and similarly for “the morning star” and “the evening star”. If they are not so universally intersubstitutable — that is, if our decision is that they are not simply proper names for the same thing; that they express an equivalence which is possibly False, e.g., someone else might have written Waverley, the star first seen in the evening might have been different from the star first seen in the morning—then they are not identities. [1961: 311][5]
I shall use the conceptual materials in Marcus’ [ to formulate the formal way of explicating the concept of rigid designation. The formal explication is based on the semantics for modal logic and includes notions of individual constants or variables, modal operators, predicates, models (worlds) and related ideas. The formal explication uses these notions to define rigidity in terms of the referent of a singular term at a model or possible world.
Let us see how this explication is based on Marcus’ 1961 model-theoretic construction that “corresponds to the Leibnizian distinction between true in a possible world and true in all possible worlds” [1961: 320]. Her construction embodies the simplifying assumption that there is only one two-place predicate (R). She presents:
a language (L), with truth functional connectives, a model operator (à, or ‘diamond’), a finite number of individual constants, an infinite number of individual variables, one two-place predicate (R), quantification and the usual criteria for being well-formed. A domain (D) of individuals is then considered which are named by the constants of L. A model of L is defined ss a class of ordered couples (possibly empty) of D. The members of a model are exactly those pairs between which R holds. To say therefore that the atomic sentence R(a1a2) of L holds or is true in M, is to say that the ordered couple (b1, b2) is a member of M, where a1 and a2 are the names in L of b1 and b2 If a sentence A of L is of the form ~B, A is true in M if and only if B is not true in M. If A is of the form B1, B2 then A is true in M if and only if both B1 and B2 are true in M. If A is of the form
then A is true in M if and only if at least one substitution instance of B is true (holds) in M. If A is àB then A is true in M if and only if B is true in some model M1.
We see that a true sentence of L is defined relative to a model and a domain of individuals. A logically true Sentence is one which would be true in every model. [1961: 319].
Here the models M, M1, etc. are possible worlds, the individuals in the domain D exist in each world, and these individuals are referents of the individual constants a1, a2, etc. In a later article, Marcus said of her 1961 theory that “in my own sketch of a semantics for modal logic, the domains of individuals assigned to alternative worlds were coextensive. Given that one of the worlds is the actual world, no entities are spawned that are not in this world and no entities of this world are absent in others”. [Marcus, 1993: 195].
Marcus uses the phrase “member of a model” or “member of a world” to refer to any pair of individuals between which R holds; thus the empty world contains no “members” in the sense that it contains no pair of individuals between which R holds.
If one prefers, one could say that the ordered couples are members of a model whereas the individuals in the domain D are present or exist in a model (the “present/absent” terminology conforms to Marcus’ later phraseology in [1993: 195]. The “present in” or “exists in” terminology may he explained in part in terms of the fact that the quantifiers in each model range over the domain D. which is required for her derivation of the Barcan formula. Since the domain D is fixed, Marcus’ worlds differ from one another in that her elation R holds between different individuals in different worlds (or does not hold between any individuals in her empty world). For example, Alice and Ed exist in one world M as related by the relationship of friendship and exist in another world M but not as related by this relation.
This semantics for modal logic contains the notion of a referent of a singular term at a possible world and a dyadic rule of interpretation that connects an individual constant a to an individual b in the domain D. This may be expressed as the rule V (a) = (b), where a is the individual constant and b the individual in the domain. This dyadic rule of interpretation entails the triadic rule of interpretation, V (a, M) = b, which assigns to a the referent b in the model M. This entailment holds since Marcus’ domain of individuals is constant across her models.
The triadic rule of interpretation is the formal semantical notion of a referent of an individual constant at a possible world. This formal semantic notion of rigid designators (be they individual variables or individual constants) is also present in earlier work by Hintikka [1961; 1963], Kripke [1959; 1963] and others. But it does not seem that this idea can he traced hack curlier than the late 1950s. Marcus’ writings in the l940s are the first to display the idea that variables have the formal features of rigid designators. Her thesis [1947] of the necessity of identity for variables,
is the object-language counterpart of the metalanguage statement that individual variables are rigid designators in the formal sense. However, Marcus [1947] does not include a semantics for modal logic and such a semantics is necessary to have the formal semantical notion of rigidity.
But what of Carnap? Marcus notes in her 1961 article that her semantical construction is a variant of Carnap’s in his Meaning and Necessity [1947] which is related to Carnap’s modal semantics in his “Modalities and Quantification” [1946] However, a crucial difference between Marcus’ semantics and Carnap’s is that Carnap’s does not contain the formal or informal explication of a rigid designator. Carnap’s proper names are not directly referential hut have intensions (individual concepts) as well as extensions and in modal contexts Carnap’s names do not refer to their extensions (the relevant individuals in the various possible worlds) but to their intensions. A necessary condition of a name being rigid is that it has the same referent in both extensional and modal contexts, and Carnap’s names, unlike Marcus’s do not meet this condition. In fact, Carnap explicitly rejects the theory of what he calls “the name-relation” [1947: 98], which implies certain theses associated with the theory of rigid designation, most notably, the thesis that co-referring names are intersubstitutable in modal contexts.
Carnap also does not have a formal conception of the rigidity of individual variables, for art analogous reason. Carnap writes: “the values of individual variables in a modal system are not individuals but individual concepts” [1946: 37-38]. In order for individual variables in a modal system to be rigid, their values need to be individuals, not individual concepts.[6]
Accordingly, it seems that Marcus’ [1961] was the first work to contain the complete concept of a rigid designator, since it included both the informal explanation in terms of natural languages and the formal semantical concept of a referent of a singular term at a possible world. In the next section, I shall use her modal semantics to construct the two different ways of defining the formal semantical concept of a referent of a singular term at a possible world, the direct-reference definition and the world-definition.
10. The direct-reference definition of rigidity versus the world-definition of rigidity
The direct-reference definition of a rigid designator is famously associated with Kaplan and he is its main contemporary champion. The direct-reference definition is suggested by Kaplan’s concept of an obstinately rigid designator. A recent presentation of this concept is made in his 1989 “Afterthoughts” [Kaplan,, 1989b]. Kaplan writes:
If the individual is loaded into the proposition (to serve as the propositional component) before the proposition begins its round-the-worlds journey, it is hardly surprising that the proposition manages to find that same individual at all of its stops, even those in which the individual has no prior, native presence. The proposition conducted no search for a native who meets propositional specifications; it simply ‘discovered’ what it had carried in. In this way we achieve rigid designation. Indeed, we achieve the characteristic, direct reference, form of rigid designation, it which it is irrelevant whether the individual exists in the world at which the proposition is evaluated. [Kaplan, 1989b: 571].
This way of explicating the concept of rigid designation logically implies that characteristic rigid designation involves direct reference, since only in cases of direct reference does the relevant expression (e.g., a use of a name or indexical) introduce the entity into the proposition itself. In cases of descriptional reference, where reference is routed through sense, rigid designation is not achieved through loading the referent into the proposition. For example, the modally stable sense expressed by “the largest actual galaxy” does not introduce a galaxy into the proposition, but rather a sense, and this sense denotes whatever galaxy is the largest galaxy in a (where “a” is a name of the actual world) in each possible world in which this galaxy exists.
Marcus’ [1961] semantics provides the conceptual materials for a direct- reference definition of rigidity. The rigid designation of an individual constant a is achieved by loading an individual b from the domain D into the proposition expressed by the sentence (or, in Marcus’ terminology, loading the individual into “what is said” [the singular proposition] by the “statement” [the sentence]).
This Kaplanian distinction between the statement and what is said by the statement was first made by Marcus, as Kaplan and his colleague Joseph Almog wish to remind readers. Almog [1986: 220. n. 8] pointed out that Marcus was the first to introduce the terminology whereby we distinguish the “statement” from “what is said” by the statement, a distinction that was later used to coincide with the distinction between the sentence-token (or use of a sentence) and the singular proposition expressed by (the semantic content of) the sentence-token. Almog writes: “When I say ‘Quine is a philosopher’, a particular individual, Quine, becomes the subject constituent of the proposition I express ... ‘Quine’ names a flesh-and-blood individual: Quine. Thus a proposition with an objectional constituent is generated. what Kaplan calls a singular proposition. This is what I say, when I say ‘Quine isa philosopher’ [1986: 220]. At this point, Almog has a footnote [1986: 220, n. 8] which reads.
In modern times, I think Ruth Marcus was the first to see this, in her “Modalitiers and Intensional Language’’, Synthese, XIII, 4 (December, 1961): 303, 330. She was the first to use the language “what is said” on which (see her p. 308) ‘‘a = a’’ and ‘‘a = b” say the same thing when a is b. She also introduces the old Millian terminology of a name being a simple tag.
Using Marcus’ initial idea and Kaplan’s extensive development of it, we may formulate the direct-reference explication of the rigidity of individual constants as follows. We take an individual constant a1 and assign to it a tagged individual (a direct referent) b1 from the domain D, and we do this prior to our “round the worlds” trip through the different models M1, M2, etc. This is reflected in the fact that the triadic rule of interpretation V (a, M) = b is derivative from the dyadic rule V (a) = b in Marcus’ semantic construction. When I utter a name, I directly dip into domain D and load the relevant individual into what is said (the singular proposition expressed ) by my statement containing the tag. The rigidity of the tag is guaranteed by the actual assignment of b to the tag as the tag’s direct referent, without needing to check whether the tag’s descriptive conditions are met at this or that world (since the tag has no relevant descriptive conditions).
But we cannot proceed here without noting a lacuna that appears in the theories being discussed. I am talking at length about directly and rigidly referential expressions and the associated singular propositions that constitute “what is said”. I have said much about the linguistic expressions, but what, exactly, is a singular proposition? “It is a proposition that includes a thing as one of its constituents, and may be represented as an ordered n-tuple”: Such one- liners are practically all that has been said in the literature, about the parts and structure of singular propositions. Indeed, nothing beyond a few remarks have ever been offered about the parts and structure of general propositions. In an attempt to fill this lacuna, I developed a detailed theory of the parts and structure of both singular and general propositions in Part Two of Language and Time [1993a]. Alan Sidelle [1995: 680-681] seems to be one of the few who has recognized this lacuna and the need to fill it, e.g., he writes about Part Two of Language and Time: “Smith has some interesting discu