From On Quine, Paolo Leonardi & Marco Santambrogio, eds. Cambridge UP 1993 Paolo Leonardi, Ca' Foscari, Venezia Ernesto Napoli, Università di Padova On naming1 1. Quine on names and variables. 2. Names and variables revisited. 3. Naming. What is reference? What are the basic referential devices? Reference, we surmise, is a relation holding between two objects, one of which is a sign standing for the other in virtue of the fact that the relation holds. Our main interest is in reference, not in the form of the expression or the nature of the entity referred to. This relation is, we believe, best exemplified by ordinary proper names. Quine thinks otherwise. Part of his philosophical programme is "the elimination of singular terms other than variables",2 in particular the elimination of ordinary proper names. We shall be concerned with two distinct questions regarding Quine's position, namely the feasibility, not to say, the desirability of the elimination of names, and whether variables have referential status. 1. Quine on names and variables. 1 We wish to thank Joseph Almog for his painsgiving criticisms. This research has been made possible by the grants: CNR 89.0225508 & 90.03603.08; MPI60% "Predicazione e predicazione di atteggiamento" (M. Mignucci, 1989); MPI40% "Il concetto di predicazione" (P. Giaretta & P. Leonardi, 1989). 2 "The Variable and Its Place in Reference", in Philosophical Subjects, Z. van Straaten ed. Oxford at the UP 1980, 172. 1.1. Russell had already eliminated definite descriptions, and Quine, in a prima facie analogous way, explains away names. Quine's elimination of names is achieved as follows: Chief among the omitted frills is the name. This again is a mere convenience and strictly redundant, for the following reason. Think of 'a' as a name, and think of 'Fa' as any sentence containing it. But clearly 'Fa' is equivalent to '(Ex)(a=x.Fx)'. We see from this consideration that 'a' needs never occur except in the context 'a='. But we can as well render 'a='always as a simple predicate 'A', thus abandoning the name 'a'. 'Fa' gives way thus to '(Ex)(Ax.Fx)', where the predicate 'A' is true solely of the object 'a'. (Philosophy of Logic, Englewood Cliffs, NJ, Prentice-Hall 1970, 25.) The above passage makes it evident that the procedure of predicate introduction works in a way analogous to the introduction of quotational names. Just as there is a morphological rule to form the quotational name, say 'Grass is green', from the original expression, Grass is green; there is a morphological rule to form the new predicate – say, aristotelize – from the original name, Aristotle. Grass is green is not part of its quotational name, nor is Aristotle part of aristotelize – the name, as Quine says, is covert in the predicate.3 The similarity is a mere trifle; we could use F-ize instead of aristotelize, G-ize instead of pegasize, provided that F-ize and G-ize are not already predicates of the language. Given a sufficient stock of new predicates, any correlation would do. The procedure has to satisfy only one weak constraint: it must correlate with the name a predicate whose extension is a set whose sole member is the name's original referent. The procedure is not meaning preserving, since it transforms a semantic value, the referent, into a surrogate for one, the extension. The morphological rule is enough to warrant the effectiveness of the procedure. What makes the elimination desirable as a matter of theoretical principle?4 Its virtues are alleged to be multifarious: "it exposes the basic apparatus of reference;" "simplifies the rules of the logic of quantification;"5 permits a clear distinction between ontology (what there is, according to the language) and ideology (what can be said in the language about what there is); confines reference to pure reference, i.e. to reference "unencumbered with descriptive or identificatory offices"; and finally rids us of vacuous names. 3 "The Variable and Its Place in Reference", in Philosophical Subjects, cit., 173. 4 Quine himself has stressed that the elimination of names has a merely theoretical point. Without names many assertions even in highly theoretical languages would become cumbersome to the point of unmanageability. Cf. "The Variable and Its Place in Reference", in Philosophical Subjects, cit., 172. 5 "The Variable and Its Place in Reference", cit., 172. Quine explicitly claims that his elimination of names is remiscent of Russell's elimination of definite descriptions. 'Fa' is treated as an abbreviation of 'Ex(Ax.Fx)',6 where 'A' is the predicate being 'a' or 'a-ize'. Quine's elimination of names is, however, rather different from Russell's elimination of definite descriptions. Russell works on the structure of complex functional terms, such as "the King of France", and when he explains away ordinary (as opposed to logical) proper names he takes them to be abbreviations for functional terms, for instance 'Louis XIV' for 'the most famous king of France'. Quine, on the contrary, directly explains away simple terms. That is, names are not seen as abbreviations of (a set of) definite descriptions. They are directly eliminated by introducing altogether new predicates, actually a new and peculiar breed of predicates. There is another substantial difference between Russell's elimination and Quine's. Russell is concerned with definite descriptions, which according to him do not constitute a proper semantic unit. The elimination is then nothing other than the recognition, made evident, of this fact. Quine instead is concerned with names, which according to anybody do constitute a proper semantic unit. So the elimination is prompted by an altogether different semantic consideration -the thesis that names, qua names and not qua abbreviations of definite descriptions, characterize their referent. Russell's main theoretical interest is in reference, in the nature of the link between language and the world. A semantic link cannot depend upon how things turn out to be. The referent of an expression is fixed by the very introduction of the expression. There is no check to perform, no patience to exercise, no discovery to make. But if the definite description had as its meaning the object which satisfies it, the referent of the description would not be fixed by its very introduction. In other words, the meaning would be attendant on the result of empirical investigations. Quine, on the contrary, is not just concerned with reference and its modes. His semantic thesis is that reference is pure only when the referring expression does not characterize the referent. Quine pursues the programme of limiting reference to pure reference, with bound variables as its only vehicle. The result is a language expressing only general statements. The programme of reparsing all singular terms but the bound variable as general ones is somehow obscured by the fact that Quine provides an amalgam of criteria for distinguishing a singular from a general term, which fall short of a clearcut distinction. The criteria are: (i) grammatical features: a general term admits the definite and indefinite article and the plural ending; a 6 See Philosophy of Logic, cit. 26. singular term acts as antecedent of 'it'.7 (ii) semantical features: it is tentatively suggested that "a singular term names or purports to name just one object, ... while a general term is true of each, severally, of any number of objects."8 (iii) roles in predication: predication joins a general term and a singular one to form a sentence that is true or false according to whether the general term is true or false of the object, if any, to which the singular term refers.9 The amalgam of criteria is theoretically unsatisfactory, and we face many problems when we try to put it to work. One is the following: it is false that singular terms, individuated as such by criteria (i) and (ii), cannot occur in positions other than subject ones, and false that general terms can only occur but in predicate position, as criterion (iii) requires. Some examples: "Man is rational", "Water is H2O" and "Our body is mostly water". 10 The reparsing of singular terms but bound variables as general must, according to Quine, satisfy at least two constraints. The first constraint is that only singular terms occurring in purely referential position are reparsed as general terms -a term is in a purely referential position if it can be substituted salva veritate by another one having the same semantic value. Modal, propositional attitude, quotational contexts are not purely referential, in that substitution of a term for another with the same semantic value may fail to preserve truth value. The elimination of singular terms is partial, pending a reparsing of singular terms in not purely referential contexts, or a dismissal of such contexts. The second constraint limits the reparsing to those singular terms that have no internal structure, or no internal structure we want to preserve, i.e. to simple singular terms, so as not to introduce new problems of analysis of general terms.11 Because of these two constraints, the general programme of the elimination of singular terms reduces to the elimination of names occurring in purely referential position. Supposing that the above limitations are overcome, or not operative, as for example in a first order extensional language endowed with non-logical constants, the question arises whether there are any referential expressions left. Predicates are not, for Quine, good candidates, since they are not, on his account, names of properties or relations, but general terms true of a number 7 A sentence such as "The lion is a mammal. It is now found in Africa and South Asia." suggests that this characterization of singular terms cannot be taken at face value. About the grammatical features, cf. Word and Object, Cambridge MA M.I.T. Press 1960, 90 and 119. 8 Word and Object, Cambridge MA M.I.T. Press 1960, 90-1. 9 Cf. Ibid. 96. 10 A classical variant of (iii) would take care of the last criticism. According to the variant, a term is singular if it can never occupy a predicate position, or better if it can never be a verb phrase, though it can be part of one. This idea can be traced to Frege's "On Concept and Object", Russell's Principles of Mathematics, Strawson's "Singular terms and Predication". 11 Word and Object, cit. 180. of objects. Quine would not consider operators good candidates either, since he takes them to be syncategorematic. Variables, then, are the only possible candidates. Bound variables, in fact. The occurrence of a free variable in an otherwise interpreted formula prevents it from being either true or false, and this rules out any question of the referential status of the free variable. Quine does not consider the possibility of a free variable having a semantic value under an assignment. Quine stresses repeatedly the analogy between variables and pronouns, to the point of claiming that they are indeed pronouns. Then, he attributes to the variable two distinct roles. The variable is a place holder or a position marker, a means of coindexing; but it is also the vehicle of pure reference.12 In the first role, the variable is not more referential than an index, that is, evidently non-referential. In the second role, the variable has an irreducibly referential use, which may or may not entail that it is a referential expression. Hence we are justified in holding that the bound variable is the only candidate for a referential expression, as the following quotations seem to suggest. "Were it not for the irreducibly referential pronoun, or some idiom to the same effect, any distinction between designative words and others would be idle and arbitrary ..." ("The Variable and Its Place in Reference", cit., 167.) "Designation by singular terms hinges thus on the pronoun or variable which is basic to reference." (Ibid., 168.) 2. Names and variables revisited. Concerning Quine's elimination of names, there are two problems: is an elimination of names desirable, i.e. what is its point? Is the elimination suggested by Quine acceptable? Of the many alleged virtues of the elimination we have listed above, at most the last two have a clear semantical import, and so we will limit our attention to them. The elimination of proper names is a significant move towards the confinement of reference to pure reference only on the assumption that names characterize what they refer to. This assumption is rooted in an honoured tradition, still prevailing at the time of Quine's speculation on the issue. Yet, if one thinks, as we do, that there are very good reasons not to embrace it, one need not be much impressed by this alleged advantage of the elimination. Nor need one be impressed by the other alleged advantage. In fact, empty names can also be taken care of by 12 "The Variable and Its Place in Reference", in Philosophical Subjects, cit., 167 and 172. non-eliminative means. Furthermore, if the elimination of names is an advantage, it is one achieved at the price of renouncing a tenable account of their semantical role. So, the desirability of the elimination is not obvious. We believe that the answer to the second question is in the negative. As we have already seen, the peculiarity of Quine's elimination is its mechanical character. Given a name, there is the predicate which is a surrogate for it. So no criticism can be levelled against the effectiveness of the procedure. Misgivings are in sight from another angle: because of its very effectiveness the procedure results in an untenable conception of what semantically a predicate is. The predicate is gotten from the name via a morphological rule. That's why, presumably, the predicate contains "" the name – "the name disappears into a notationally atomic predicate."13 So far so good. Actually not so good. The problem is to understand what "covertly" means here. Does the predicate contain the name or not? What Quine is after is a new predicate inheriting various traits of the name lurking in the background, more precisely a predicate having as its extension the set whose sole member is the referent of the name. It should be asked how the predicate is going to have such a nice feature. There are but two options, either the predicate contains the name or it does not. If the morphological rule led to a "predicatization" of the name, then the predicate would surely inherit some traits of the name, because it would overtly contain the name. The occurrence of "Plato" in "platonize" would be like the occurrence of "red" in "redness", rather that of "can" in "canine".14 Hence, names would not be eliminated. So little would they be, that the interpretation of the new predicate has to abide by the following constraint: the extension of the predicate is the singleton of the referent of the name. If the predicate contains the name only as a string of letters rather than as a semantic unit, any structural connection between the referent of the name and the extension of the predicate is lost. It is only by chance that the predicate could have as its extension the set whose sole member is the referent of the name. Nothing short of a convention would warrant the correlation. On the first option the interpretation of the predicate depends on that of the name. For this reason, predicates would be no real surrogate for names. If one is ready to pay the price of dependency, it is possible to design a new predicate with the singleton of the name as extension. For, quite clearly the predicate "being Aristotle" has as its extension the singleton containing Aristotle, considering that Aristotle is the referent of "Aristotle". The 13 "The variable and its Place in Reference", cit. 173. 14 It would, that is, modulo morphological arrangements. "Aristotle" does not occur in "aristotelize". extension of the predicate is not itself a result of design, i.e. conventional, but it is connected to, or determined by, the referent of the name, which is obviously conventional.15 The extension of the predicate is a descendant of the referent of the name, it is the referent of the name gone bracketed. It is, so to speak, conventional at one remove. On the second option, the problem of the interpretation of the predicate is acute, not to say hopeless. The predicate is a new one, created ex nihilo, introduced not as a proxy for an entity, but just to mimic a linguistic string, the form of a name. One cannot say: no problem, the interpretation does not matter in the least. All that is needed is the extension of the predicate, and this much we can easily get by fixing it conventionally. The fact is that no predicate has the extension it has by convention. (A predicate which is conventional at one step removed is not conventional in the least.) Whether a predicate is satisfied by anything, and what satisfies it, if something does, is not a matter an arbitrary decision can settle. By contrast, a predicate has the meaning it has by convention. That something is red or is a wooden table are matters of fact. That 'being red' stands for being red, rather than being made of wood, is a matter of convention. But, once 'being red' stands for being red, that which is red is not red by convention, but by nature or by artifice. This fact could be also expressed by saying that a sentence cannot be true or false by convention.16 In other words, the extension of a predicate cannot be the meaning, i.e. the referent, of the predicate. Reference is conventional; extension is not. Actually, what belongs to the extension of a predicate depends on what has the referent -a property, relation, or whatever -of the predicate. If 'being a flower in my room' has for its extension a set of three objects, it is because three objects have the property of being a flower and being in my room. Let us turn now our attention to the variable. Quine acknowledges two roles for the variable: it is a device of coindexing (which comes down to coreference, when there is a referential antecedent), and it is a device of reference. Quine makes strong pronouncements in favour of the variable in this capacity: the variable is the essence of the referential idiom, the vehicle of pure reference, has an irreducibly referential use, and finally it is in virtue of the variable that the distinction between designative 15 Nota bene, conventional rather than explicitely stipulative. For in the latter case we would be trapped in a vicious regress. If words were not conventional proxies, then is either reference were magic, or it would a natural link rooted in the nature of words and things. 16 Quine would agree, we surmise, on this point and also on the fact that the extension of a predicate is not stipulative. words and others is neither idle nor arbitrary.17 Nonetheless nowhere does he exactly assert that the variable is a referential expression. We must confess our uneasiness. Maybe the best clue to Quine's views is the well trodden path of the parallel between variables and pronouns. In the philosophical literature the variable has, most often, been considered as the formal counterpart of vernacular pronouns. As we have seen, Quine goes as far to say that variables are pronouns. Indeed, pronouns seem to embody both the coindexing and the referential role. But one must be careful. Not all pronouns are variables. Standardly, pronouns are considered not to work as variables if they are: a) indexicals and demonstratives, b) anaphoric to proper names, c) anaphoric to what Strawson has called identifying descriptions. c) includes lazy pronouns and E-type pronouns; the difference being that the former are anaphoric to a description actually occurring, while the latter are anaphoric to a description recoverable from the text. What the above restrictions amount to is that variables are pronouns when pronouns are variables. We do not seem to have a better understanding of variable-like pronouns than of variables. In fact, it seems that to understand a variable-like pronoun requires an understanding of the variable. If anything, it is by recourse to the variable that an account is given of certain pronouns, rather than the reverse. Moreover, the parallel between variables and pronouns does not provide us with reasons to ascribe a referential status to the variable. To be sure, pronouns and variables alike are instruments of coindexing. Coreference is reference inherited by coindexing, and coindexing amounts to coreference only provided that there is at least one referential item. An anaphoric (or cataphoric) pronoun selects via the associated linguistic rules, or character, a referential expression (its antecendent), from which it inherits its reference. A variable does nothing like that. An anaphor is characteristically implemented by coindexing an expression to another referential expression, and not to another occurrence of the same expression. But in the case of a variable coindexing holds not between different variables but between different occurrences of the same variable. Can this position's index have a referential value? As we have seen, variables are neither pro-nouns nor pro-phrases. The only further possibility is that they are pro-objects. This seems to be Quine's idea when he says that the variable is the vehicle of pure reference: it reaches for the objects directly, i.e. without any linguistic or conceptual mediation. It looks as if the variable were a harpoon for things. 17 "The variable", cit. 168; "A Logistical Approach to the Ontological Problem", 1939, printed in The Ways of Paradox, New York Random House 1966, 65. Here our intuitions seem to conflict. On the one hand, there is no difficulty in the idea of a tool to pick up objects which is not something which refers to the object. For example, a stick with pliers at the end is a tool for lifting cans from upper shelves, but it surely does not refer to any can. If, however, the variable is a tool, it is no doubt a linguistic tool and the temptation is strong then to say that it is a referential expression. There would be nothing wrong with this but for the fact that for an expression to be referential it is required that it picks up not just an object but a specific and predetermined one. Names, for example, could not be referential if it were not for our ability to tell one object from another and hence to focus on it as the referent of the name. Quine, though, thinks of variables as non-discriminating instruments of reference. In fact, as we have already hinted, his main grounds for dissatisfaction with names as vehicles of reference rests on their characterizing and hence individuative role. The problem is that if he is right, then variables are, according to Quine, instruments of reference which, according to us, are not referential. As we have just said, it is tempting, to hold that the variable, a tool of reference, is a referential expression. More than tempting, mandatory. For how could the variable, a linguistic tool of reference, fail to be a referential expression? It seems that either we stop characterizing the variable as a tool of (pure) reference or we are forced to characterize it as a referential expression. If with Quine we stick to the idea that the variable is a tool of reference, is there any way of making sense of the referential status of the variable? The problem in a nutshell is to determine what it refers to. We see two options. (a) The first option is one which will look, as we have had the opportunity to verify, outrageous to most. To give it a name let us call it the multiple distributive reference view. According to this view, a bound variable refers, whatever the determiner, neither to the class or collection of the many objects which there are in the domain, but to each and all of them severally, to their plurality. 18 Graphically, this case can be depicted as follows. o1 o2 x ... 18 The idea of reference to a plurality seems to suggest the idea of ambiguous reference. Even granted the multiple distributive view according to which the variable refers to a plurality, it cannot be an ambiguous expression. For it refers simultaneuously to the plurality of the objects in the domain and because of this it cannot be disambiguated, i.e. made to refer to one object rather than another. An expression is ambiguous when it refers to one or another of a number of entities, but not to one and another. on (...) The view looks outrageuos, we surmise, because bound variables are not standardly thought of as referential. For, variables aside, one can find clearcut instances of multiple distributive reference in the use of ordinary pronouns. For example, 'you', in its distributive reading, seems to be one. When, in giving a lecture, one says "As you well know", one makes multiple distributive reference to each person in the audience. (When the coach exhorts his team, claiming "You will win the match" his 'you' is on the contrary a collective you, 'you together'.) The variable refers, it can be suggested, along the same lines of the distributive you. (b) The second option is what we will call the multiple assignments view. Here, as in the first option, the end result is that the variable refers. The route by which this is achieved is, though, altogether different. In the one case there is simultaneous reference, and then no variation in the reference; in the second there is a(n apparent) variation of assignment. For what refers is the free variable (under an assignment). The bound variable is a summary of the references implemented by the assignments to the free variable. Each assignment is the assignment of an element of the domain, so the bound variable qua summary of all assignments might improperly be said to refer to the potential satisfiers of the open sentence (of the predicate), i.e. to all the elements in the domain.19 The variation is apparent because all, and not one or other, assignments have to be made.20 The bound variable refers, if it does refer at all, to the potential satisfiers, i.e. the elements in the domain, and definitely not to the actual satisfiers (if any) of the predicate, to the truth makers of the sentence.21 To claim that the reference is to the actual satisfiers, would amount to committing the fallacy already signalled by Buridan, that of making the reference of components of the sentence depending upon the very truth of the sentence. The satisfier, if any, of "x loves a dog" in "There is an x such that x loves a dog" is not the referent of 'x'. Sentences in which one or more bound variables occur are general sentences irrespective of the specific determiner. That is, universally and existentially quantified sentences both say of the elements in the domain, and not of predetermined elements, that all of them, or some of them, have a property or stand in a certain relation. Quantified sentences are general exactly in the sense of not referring to one object rather than another. 19 A. Whitehead e B. Russell Principia Mathematica 19272 p. xx: "We may similarly assert a proposition of the form "(x)Fx" meaning "all propositions of the assemblage indicated by Fx are true". 20 Indeed, Peano, and many after him, may have wanted to express this feature, by qualifying the free variable as "real", and the bound variable as "apparent". 21 A potential satisfier is an entity of the appropriate category, or from the relevant domain. In first order logic a potential satifier is an object. No modality is involved in the notion. Two observations point to the generality and the primitiveness of quantification: (i) when we come to give truth conditions for quantified sentences the quantification recurs at the metalevel. Any account of quant~ifiers uses quantifiers, as is clear in standard truth clauses for quantified sentences, such as "'Something' A is true iff some object satisfies A" or "'All A is true iff all objects satisfy A."22 (ii) A general statement, whether existential or universal, is not reducible to either a disjunction or conjunction of particular (singular) statements. What is needed to get logical equivalence is the extra clause to the effect that the disjunction or conjunction is exhaustive. Significantly, exhaustiveness cannot be expressed except via quantification. x (Fx) and x (Fx) are equivalent to a&Fb... and a... plus the specification that a and b and... are all there is.23 The same cannot be said of the variable. Variables are not indispensable but a very convenient notational device to keep track of cross-reference. It is controversial whether there are any variables in natural languages. In Italian there are Roman names acting in variable-like way, namely 'Tizio', 'Caio', 'Sempronio'. They are commonly used to indicate any person whatsoever, or an undetermined person. "Un tizio ha suonato alla mia porta per vendermi saponette." (Notice the absence of the capital initial and the presence of the determiner.) In English we have 'Tom, Dick and Harry', 'John Doe', 'guy' (a proper name, i.e. "Guy Fawkes", gone common). The English expression which seems to come closer to a variable is the pronoun 'one'. Where artificial languages have variables, natural languages have common nouns or pronouns. (Somebody, anyone, all dogs, etc.) Because of this one could view quantifiers as second order predicates and the variable itself as a predicate to which they apply. The variable would express the property of being (an) 'element in the domain', and it could be substituted by 'element in the domain'. These considerations bring us back to the original question: is the variable referential? Concerning the first option, the multiple distributive reference view, the problem is that even granted the aptness of the analogy with the plural 'you' we do not seem to have a clear understanding of the working of the plural 'you'. We have a sufficiently good grasp of singular reference and of plural reference as a concatenation of singular references, but not of reference to a plurality as such. Some uses of the plural 'you' are quantificational, others are not. "You understand me well" can be either "All of you understand me well" or "The three of you understand me well". 'The 22 Some combinatorial languages can do without both variables and quantifiers. This fact does not tell against the idea that quantifiers are primitive, since when we come to interpret the combinatorial formulae we fall inevitably back on quantifiers. 23 Cf. Russell's The Philosophy of Logical Atomism. three of you' is not a numerical quantifier, and it can be indeed substituted by 'you and you and you' without any further exhaustiveness clause. On the other hand 'all of you' has quantificational force independently of the cardinality of the domain, which can be as small as one likes. Here a concatenation of singular references would not do, without the added clause 'and these are all.' So much for the multiple distributive reference view, according to which it is the bound variable which is referential. In the second option, the multiple assignments view, although it summarizes a multiplicity of references, the bound variable is not in itself referential. The free variable, in spite of occupying a position available to names, is not referential. It is rather the free variable under an assignment, if anything, that is referential. This makes it name-like and no more. A name is a name because it is a name of (a certain individual); but a variable is not a variable because it is assigned to (a certain individual). The variable under different assignments is the same variable; names standing for different objects are different names. Unlike a name, a free variable does not individuate any particular entity in the domain. Reference is to entities qua units (whatever their internal complexity) and it cannot take place unless it is determined to what, unless the entity is given. Quine has qualms about names as referential devices are based on their characterizing role. We think names do not characterize but individuate, and we have qualms about the variable as a referential device precisely because it is inept at individuation.24 3. Naming. We have examined Quine's arguments for preferring variables to names as referential devices. This preference, we have argued, requires the introduction of predicates which are non-standard in having been assigned an extension, which is arbitrary in the sense of being stipulated and is non arbitrary in being the one needed to make them pick out the object named by the name under elimination. Now, this picking out warranted by an explicit stipulation makes this kind of predicate act on all counts as a proper name. In fact, the predicate remains distinct from the proper name only synctatically; 24 It may be interesting to notice in this connection that a name can be empty while a variable cannot. This, by the way, seems to be a likely ground for Quine's notion that names characterize and his preference for the variable as a referential device. Variables are preferable because they are safe, they cannot miss the object. One can take a different attitude toward empty names, and for instance hold that they have the form of a name without being one. So, after all a name too cannot be empty. semantically there is no serious difference between picking out by stipulation a specific individual, and standing for it. Indeed, ordinary names paradigmatically exemplify this standing for, to which reference reduces. Far from characterizing, names are naked proxies. That makes them ineliminable expressions in any ordinary language.25 Once we have provided ourselves with the name 'Aristotle', we can ask questions ad libitum concerning Aristotle: whether he taught Alexander (something which is uncertain), whether he was a pupil of Plato, whether he was called 'Aristotle', etc. Without the name we could not even express our doubts.26 That is, we need names when we want to speak acontextually about specific particulars, without assuming about them anything as true from the start. Names are proxies which select items, and can be used to stand for them. By naming we link a word to an item. To bestow a name nothing more is needed than to have singled out the item to be named. That does not mean to have identified it, or to be able to reidentify it later (in any other circumstances). By naming we either generate the link or exploit it. The naming relation is an unmediated relation between two items which makes one proxy for the other, and consequently makes the first a sign of or an expression for the second. Once we have a name for an item, we can issue judgements concerning it: we judge what kind of item the bearer is, attributing, or denying, to it properties and relations. Notice that, (a), in giving an item a name, its specific nature is irrelevant. (b) It does not usually matter how we introduce the naming link -how the baptism is performed. (c) Lacking the ability to identify and reidentify the bearer of a name, of course, impairs the possibility of tracing the entity, and hence the ability to use the name; the name, as it were, a dead end. Yet, semantically, this is irrelevant. Many ways of conceiving of names derive from two possible confusions -one between semantics and ontology, the other between semantics and cognition. Semantics and ontology. The entity referred to by a name, a, has properties and relations, and it would have them even if it had no name. We can mistake its being the entity that has such, or some such, properties and relations, as the meaning of the name. We attribute to it, rightly or wrongly, or recognize it 25 May be they share company with certain common nouns and certain predicates standing for sensory properties. In any case, to start a language names have to be introduced not via an explicit stipulation, which presupposes language, but via some implicit convention. 26 Unless it were the case that in correspondence of any ordinary name there is a condition free of names uniquely satisfied by the referent of the name. has, any such property or relation, not by naming the entity but by judging it. Of course, if the entity were the only one to be or have F, by 'the one which is or has F' we would pick it out as well as by its name -but in a very different way: by the description because it would be true that a is or has F, by 'a', because that is its name. If naming characterized an entity as having some property or relation, then just by naming we would make true the entity having those properties and relations. Any description of the entity characterizes it rather than expressing the meaning of its name. Semantics and cognition. The descriptions we deem true of an individual amount to our cognition of it -our knowledge of it being limited to the descriptions actually true of it. We can mistake such descriptions, or at least some of them, for the meaning of its name. Yet, our cognition of an entity can change, and be augmented as well as revised, a fact we can express only if we can say that it is nonetheless cognition of the same individual, for instance by using a name of it. But if those descriptions were the meaning of the name, this could not happen. A change in our cognition would induce a change in the meaning of the name. If the name of an individual had a (set of) description as its meaning, then by knowing the name of an entity we would know a number of things about it -at least implicitly. Of course, what we say about a thing, we say on the background of our cognition of it, and anything we hear about an individual affects our cognition of it. A name stands for the entity it stands for independently of the knowledge on the part of any particular speaker about what it is proxy for. To be competent in the use of a name, all that is required is to have singled out which entity it is proxy for. One need not know what is the entity which the name is proxy for. Any ontic involvement concerning the nature of the entities comes up only later, when judging, which is always judging the what or the how of the entity. What the name is proxy for is conventional and there is no investigation of the world which could settle the matter. Things are different with quantified expressions and quantified sentences, neither of which pick out, properly speaking, any entity. The entities are picked out by the predicates occurring there. The selection effected by the predicate is non conventional but depends on the world, which makes the sentence either true or false. A definite description, the F, in "The F is or has G", denotes an object on the proviso that there is one, and just one, individual that F s. That can be made explicit, by the sentence "There is one, and just one, entity that Fs", and the definite description 'the F' can then be substituted by the pronoun 'that', as follows, "There is one thing, and only one, that it is or has F. That is or has G". A definite description acts as a name without being one. For it is capable of being a subject of predication, but the entity it singles out is not its (conventional) referent. In this way some entities are picked out via a judgment that something in the circumstances is true of them, and not because a linguistic expression has been constituted as a proxy for them. Because, the relation between quantified expressions and the entities they pick out is mediated, it is not reference. By naming we link a word to an entity, and to introduce a name we need do nothing more than single out the entity to be named. "But there are vacuous names", someone may immediately protest. Indeed, there are: does this refute our view? 'Vacuous' qualifies 'name' like 'toy' qualifies 'gun': just as one cannot understand what a toy gun is without grasping what a gun is, to understand what a vacuous name is we have to grasp what a name is. Vacuous names are parasitic on non-vacuous ones. Indeed, our claim that a name does not characterize what it refers to, shows its virtues in suggesting a quite articulated picture of how a name can be vacuous and in distinguishing different cases of emptiness. Naming establishes a (conventional) relation between two entities, one of which is a linguistic expression, the other of which is an entity. Now, one can distinguish many cases, where the second member of the relation is missing. Believing that someone has called us this morning, we can give him the code name 'George'; we can now decide to call 'Newman IV' our fourth son, if we will ever have a fourth son. Both 'George' and 'Newman IV' are conditional names: we have not supplied any second member of the relation constituting the names. Instead, we have offered a description of such an entity, if any. If one entity, and only one, satisfies the description, 'George' and 'Newman IV' will indeed be names. The case of 'Homer' can be viewed as analogous to them. Similar cases are that of 'Neptune' and that of 'Vulcan', names given by Leverrier respectively to the planet beyond Uranus which diverted Uranus's orbit, and to the planet between Mercury and the Sun which diverted Mercury's orbit. Leverrier did not see such planets; he posited them as an explanation of the perturbations, and gave them these "names". Both were conditional names. Since there is a planet perturbing Uranus's orbit, 'Neptune' has indeed become a name; and since there is no planet perturbing Mercury's orbit, 'Vulcan' has not become a name. None of these names is properly speaking vacuous. A different case is that of fictional names. Stories begins usually in this way: once upon a time there was Nama, a princess, who... The same thing happens in novels: "The first time I laid eyes on Terry Lennox he was drunk in a RollsRoyce Silver Wraith outside the terrace of The Dancers." (R. Chandler, The Long Good-Bye, 1, line 1.) Or: "Did you hear me! I said I was Clyde Umney, the lawyer." (R. Chandler, Playback, 7.) Here, names or indexicals introduce an entity, which the story characterizes afterwards. A third case is that instanced by a psychotic who hallucinates a Jack who is persecuting him. Here, again, there is really no one there. The psychotic believes someone is there, and eventually describes him, but he is just mistaken, there is no such Jack. A fourth case is that of Pegasus, Bellerophons' winged horse. Mythical names are partially akin to fictional ones and partially akin to hallucinations, since a myth seems to start claiming literal truth. In these three cases names are indeed vacuous, but in different ways. The psychotic hallucinates, and as a consequence of his being mistaken about the facts, the name he introduces is vacuous. The novelist exploits the fact that names go proxy for things, and by using a name pretends to be introducing an individual. Mythical names seem to be hallucinations which have become fictions. In our picture, descriptions fit in not as expressing the sense of the name, but as claiming to describe the entity the name-word is supposed to stand for.27 Proper names are words standing for objects; are there expressions standing for properties and relations? 'Red' does not characterize the property red. To radiate waves of length between approximately 7.500 and 6.450 Ångstrôm is not the meaning of 'red'.28 'Red' stands for the colour red, and the colour red can be characterized as radiating waves of length between approximately 7.500 and 6.450 Ångstrôm. To conceive of simple nouns, verbs and adjectives as standing for properties or relations, does not attribute to these objecthood: to claim a property is an object is a mistake. To refer to a property or a relation we need only to have singled it out. Quine has forcibly argued that attributes -let us call attributes what predicates stand for -have no clear principle of individuation, and therefore are not entities. If they were not, however, it would not make sense to claim either that two attributes are different or that they are identical. Yet, we do claim that many attributes are distinct. Being a horse is different from being a dog. Indeed, it is easier to confuse two bloodhounds than a dog and a horse. We even have an extrinsic criterion for the distinctness: if two attributes apply to different objects, they are distinct -being a horse and being a dog are different attributes because Blueprint is a horse and not a dog and Hunter is a dog and not a horse. Although extrinsic, difference of extension is a fully reliable criterion for distinguishing between attributes. But we even distinguish between attributes which have the same extension: being rhenate is distinct from being hearted, although any rhenate being, like Blueprint and Fido, is a hearted one. That it is difficult to account for their difference, hence for their individuality, does not imply that they do 27 We have adhered to the current terminology of vacuous (or empty) names. We think though that strictly speaking no name is vacuous, or if you prefer certain names are vacuous only in the sense of lacking a referent of the appropriate or expected ontological category. 28 Similarly, 'wicked' does not characterize the property wicked, nor does it characterize the class of wicked persons. Cf. Methods of Logic, cit., 80. not have one. Indeed, if we could not tell the difference between being a horse and being a dog, it would be hard to claim that being a horse is true of Blueprint and being a dog is not. To characterize things as well as properties and relations, we need a language, and by introducing words for these entities -object-words as well as property-words and relation-words -we start a language.29 Naming constitutes the prototype of the sole semantic relation, i.e. referring. The elimination of proper names in favour of variables and predicates, quite apart from its practicability, is of dubious theoretic value. On the one hand, its supposed desirability depends on a mistaken conception of the semantic role of names; on the other hand, no account of the linguistic role of variables is forthcoming independently of that of names. 29 As the labels indicate there is no denial of differences between proper names and nouns – and other expressions close to nouns as, for instance, verbs and adjectives. They are different already at the surface linguistic level.