Rigid Designation and Semantic Value

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Rigid Designation and Semantic Value Colin McGinn The Philosophical Quarterly, Vol. 32, No. 127. (Apr., 1982), pp. 97-115. Stable URL: http://links.jstor.org/sici?sici=0031-8094%28198204%2932%3A127%3C97%3ARDASV%3E2.0.CO%3B2-J The Philosophical Quarterly is currently published by The Philosophical Quarterly.

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THE

PHILOSOPHICAL

QUARTERLY

VOL. 32 No. 127

APRIL 1982

R I G I D DESIGNATION AND SEMANTIC VALUE It is sometimes supposed that the distinctive semantic function of names is captured in the remark that names, unlike definite desoriptions, are rigid designators. Part of my aim in this paper is to show how misleading this remark is. I shall distinguish two notions which are often confusedly run together under the label 'rigid designation', and explore their significance and their connexions with other notions. My reason for labouring the topic is not that I think it is more important and interesting than has been appreciated; it is, rather, that it is less interesting than has been supposed - but it is interesting why it is less interesting. Besides, there is a lot of confusion surrounding the topic, and it would be good t o dispel some of it.1

I Kripke says that a rigid designator is an expression which designates the same object with respect to any possible world in which the object exists.2 (The ontology of possible worlds invoked in this definition seems inessential: we could say simply that a rigid designator is an expression which is such that no object distinct from its actual referent could be designated by it it necessarily designates what it actually designates.) It is customary, within the tradition of possible worlds semantics, t o put this by saying that associ'The conflation I inveigh against in this paper was alluded to in my review of Meaning, Reference and Neceaaity, ed. Simon Blackburn (Cambridge, 1976), in Philosophical Review, 86 (1977), 106. Since then I have had sight of David Kaplan's (unpublished) Denaonatrativea, in which the distinction I am concerned to stress is very clearly articulated: in what follows I have adopted some of his terminology and apparatus - though I do not know whether he would a t all points approve of the use I make of it. nSee Saul Kripke, Naming and Neceaaity (Oxford, 1980), esp. p. 48.

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ated with a rigidly designating expression is an intension which is to be identified with a constant (partial) function from possible worlds t o extensions: given any possible circumstance as argument the function yields the same object as value. A flexible designator, by contrast, is associated with a function on possible worlds which yields different objects as value with respect to different possible worlds. Such functions are intended to represent the semantical characteristics of expressions, and indeed intensions are commonly identified with senses. Having thus defined the concept of referential rigidity, Kripke proposes that we recognise an expression as rigid by means of an "intuitive test": we substitute the candidate expression into the schema t might not have been t and ask ourselves whether there is any true reading of the result - if there is, the term is flexible, if not, it is rigid.3 I n effect, this is a test for the constancy of the function associated with the term in question. Now the &st thing we should notice about this definition of rigidity is that it covers two very different sorts of case: it counts as rigid both proper names and certain d e h i t e descriptions, e.g., 'the successor of 3' and 'the father of Abel' (granted the necessity of origin). The fact that the notion of rigidity covers both sorts of case already shows that it is wrong to take rigidity as distinctive of names. And this suggests that if we wish t o capture the "Mill-Russell" view of names -the idea that names are, in Kaplan's terminology, "directly referential" - we cannot do so in terms of the apparatus of constant functions on possible worlds. We evidently need t o draw a semantical distinction between names (and indexicals) on the one hand, and rigid descriptions on the other - and t o explain in what the distinction consists. A clear example of the conflation in question is provided by Christopher P e a ~ o c k e .He ~ undertakes t o define the notion of rigid designation without appeal t o possible worlds, and proposes a (non-modal) criterion of what looks more like genuine reference: once we separate the two ideas we shall not be tempted to suppose Kripke's and Peacocke's definitions to be attempts a t capturing the same phenomenon. Kripke belatedly drew the distinction we are after as follows: he speaks of "de jure rigidity" as characterising cases in which "the reference of a designator is stipulated t o be a single object, whether we are speaking of the actual world or of a counterfactual situation"; and he contrasts this concept with that of "defacto rigidity" which characterises cases "where a description 'the x such that Fx' happens t o use a predicate 'F' that in each possible world is true of one and the same unique object (e.g., 'the smallest prime' rigidly designates the number two)". He adds: "Clearly my thesis about names is that they are rigid de jure, but in the monograph I am content aThis is a tidied up formulation of what Kripke says at pp. 48-9 of Naming and Necessity. 4C. Peacocke, "Proper Names, Reference and Rigid Designation", in Meaning, Reference and Necessity, 109-32.

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with the weaker assertion of rigidity."= (It is hard t o know what t o make of Kripke's remark last quoted, since plainly he was not, in the original monograph, claiming that names are of the same semantical kind as rigid definite descriptions!) Kripke is surely gesturing at something intuitively right here, something he had blurred over before, but the distinction could stand further articulation. As a preliminary characterisation, let us (following Kaplan) express the distinction as follows: a & facto rigid designator has constant reference with respect to all possible worlds in virtue of expressing a condition which attributes a certain individual essence t o an object, so that its rigidity traces to extra-linguistic modal facts; a de jure rigid designator, on the other hand, has constant reference in virtue of the semantical rules of the language, so that it does not merely turn out that the term is rigid. Kaplan brings out the semantic difference by considering what are the constituents of the "structured proposition" expressed by sentences in which the two types of rigid designator occur: in the former case, the proposition contains an individual concept which picks out the same individual in any possible circumstances of evaluation; in the latter, the semantical rules introduce the object itself into the proposition, with the consequence that there can be no further task of evaluating the term in a possible world once the semantical rules are fixed. (This bears on the issue of whether transworld identities are rightly seen as stipulative: presumably Kripke's real position is that they are when we are using a de jure rigid designator, since the expressed proposition contains the referent as a constituent; whereas the question is substantive and not merely stipulative when the rigidity is de facto, since the identity of the proposition does not settle that of the referent.) This picture of the semantic difference between the two types of rigidity should make us wary of talk of constant functions. De facto rigid designators can be conceived as expressing functions sensitive t o possible circumstances; but de jure rigid designators are associated with such functions only in a Pickwickian sense, since there is no question of our having to compute the function with respect t o each world with a view to determining its value in that world - the reference of such an expression is simply independent of the distribution of objects and properties in possible worlds. To say that rigid designators correspond t o constant functions misleadingly conflates the very different semantic features of the two types of expression: it fails t o register the different ways in which terms come to be rigid.

I1 I think we can gain more insight into the de factolde jure distinction by considering how it might be generalised beyond the category of singular term. Kripke explicitly extends the notion of rigid designation t o variables, and indeed substituting a (free)variable into the schema that tests for rigidity 5These sentences are from n. 21 to p.21 of the new "Preface" to Naming and Necessity.

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gives a positive result.6 Furthermore, we should presumably take variables t o be de jure rigid; the value of a variable under an assignment attaches to the variable by way of the semantical rules for the interpretation of variables, and the proposition thus (temporarily) expressed will contain the value as a constituent. Indeed, this semantic feature of variables seems an immediate corollary of the corresponding thesis about names, since the value of a variable is precisely what is denoted by a name when it is substituted for the variable. (We might think of a name, i.e., individual constant, simply as what happens t o a variable when you freeze it t o an assignment.) Somewhat less self-consciously, Kripke applies the idea of rigid designation t o general terms, notably natural kind terms (op. cit., pp. 116 ff.). This extension of the idea has occasioned some perplexity: first, because general terms are thought not t o be properly designators; secondly, because it is unclear what they are t o be taken as rigidly designating. The first worry seems to me groundless, but the second points up what looks like a confusion on Kripke's part. Let us take the second question first. Plainly, we cannot say that a natural kind term rigidly designates its extension, since with respect t o other worlds its extension will vary, and so would come out a flexible designator on this choice of designatum. We should rather say that a term like 'tiger' or 'water' designates a property, where we think of the species or substance t o which an object belongs as a property of that object. Kripke is somewhat inexplicit about what he takes the reference of predicative rigid designators t o be, but he does say that 'pain' is a "rigid designator of the type, or phenomenon, it designates", adding that "it seems absurd t o suppose that pain could have been some phenomenon other than the one it is."? Thinking this way, a natural formalisation of the rigidity claim for such predicates would employ lambda abstraction to form terms for the properties thus rigidly designated, as in 'water' rigidly designates (Ax) (x is ~ a t e r ) . ~ Once this is done, however, it is evident that we could say the same about any (primitive) predicate, e.g., 'bachelor', 'desk', 'prime', etc. Nothing other than the properties actually expressed by these predicates are relevant t o evaluating the truth of sentences in which they occur. I suspect that Kripke fails t o notice (or a t any rate t o mention) this because he is not careful enough about distinguishing being connotationless from being rigid; as we have seen, an expression can have descriptive meaning and yet be rigid. The peculiarity of predicates like 'bachelor' is that they have nominal definitions and are a t the same time de jure rigid: it does not merely turn out that 'bachelor' expresses the property of being a bachelor but it is laid down in @"Freevariables can be used as rigid designators of unspecified objects." (Naming and Necessity, p. 49, n. 16.) 'Naming and Necessity, pp. 148-9. See also Keith Donnellan, "Substances as Individuals", The Journal of Philosophy, 70 (1973), 711-2. 8This method of formalisation is meant t o accompany the decision to treat mass terms (or species names) as predicates in logical form, as suggested by, e.g., Tyler Burge, "Truth and Mass Terms", The Journal of Philosophy, 69 (1972), 263-82.

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the semantical rules of the language. There are also de facto rigid designators of properties, as in (given some essentialist assumptions) 'liquid composed of H,O'; and flexible designators too, as in 'species found in locale 1'. Thus, nominalising the predicate, we can try the intuitive test: is there a true reading of 'The species found a t locale 1 might not have been the species found a t locale l'? The answer is affirmative, since we have picked out the kind property by way of a contingent feature of it. Kripke's contrast between 'heat' and 'what causes the sensation of heat' provides another example of a flexible predicate. I n view of the intuitive basis of the distinctions so drawn, it is hardly to be supposed that we are somehow semantically or logically debarred from expressing the notions a t play: if we are t o be puritanical about the word 'designates', we can speak (as I did above) of predicates as expressing properties - and if we don't like reifying talk of properties a t all we can (as I will below) formulate the claim of rigidity in terms of the modal status of the axioms and theorems of a disquotational truth theory. There is a further reason for allowing Kripke the extension to predicates. If we are willing to permit second-order quantification, where the values of predicate variables are properties, then we will need to bring t o bear the apparatus needed t o deal with fist-order quantification into modal contexts t o give an account of such second-order quantification, as in 'There is some property such that Fido necessarily has it'. Thus we shall want to consider assignments to the predicate variable that are de jure rigid (directly referential), and we shall have need of a criterion of intersubstitutivity of predicates in modal contexts analogous to that needed for singular terms -the class of predicates that rigidly designate or express (possibly de facto) the property thus quantified over. Making sense of second-order quantification into modal contexts thus seems to require us (if the quantification is not to be substitutional) t o make sense of an analogue of singular term rigidity for predicates. So far I have considered modal rigidity, but we can sensibly introduce notions of rigidity along other dimensions, in particular that of time. We may thus speali of designators which are temporally rigid or flexible. (This requires that there exist terms which are neutral as t o time, so that we can evaluate them with respect t o different times with the prospect of coming up with distinct designata. If terms were always temporally indexed, there could be no flexible designators along this dimension, rather as worldindexing rigidifies definite descriptions.) The notion of temporal rigidity will then naturally be explained in terms of functions from times to designata: a temporally rigid designator is associated with a constant function from times to objects, a flexible one with, a function whose value varies from time to time. It is important to be sure that the inconstancy of the function does not reflect indexicality rather than flexibility: the issue of rigidity arises only after the context has done its bit in conferring an interpretation on the

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term. As Kaplan emphasises, we must carefully distinguish dependence of interpretation on context from sensitivity of semantic evaluation to circumstances, or else we shall confuse the quite distinct ideas of indexicality and flexibility. I n fact, Michael Dummett appears t o make exactly this confusion when discussing the introduction of names by means of indexi~als.~ I n the light of this crucial distinction, it looks doubtful that there are any genuine cases of spatial flexibility: alleged cases generally turn out to hinge on unobvious indexicality; but the matter is not easily decided. Note that if (what is false) all definite descriptions 'the P' were equivalent t o 'the actual P', then their apparent flexibility would turn out t o be (on certain views about the function of 'actual') mere indexicality: all definite descriptions would become rigid designators. My actual view of 'the actual F' is that it is de jure rigid but not indexical; 'the present F' is also de jure rigid - as are all the other indexicals. And again, we shall want to distinguish between the de facto and the de jure temporally rigid designators, and to insist upon the deep semantic difference between them; it is obvious that a term may be temporally rigid simply in virtue of the facts of history and not beoause the semantical rules stipulate a constant reference - and talk of constant functions will only serve to obscure the semantical distinction. The distinction is shown, inter alia, in the fact that a de jure rigid designator will be associated with a constant function with respect to any dimension or point of evaluation, just beoause its reference is precisely independent of the circumstances of evaluation; whereas i t will always be a further question whether a de facto rigid designator which is constant with respect to one dimension will be constant with respect t o all - it might be temporally rigid and modally flexible, say. Once we have introduced the idea of temporal rigidity we can consider two directions of generalisation: we can ask of expressions of yet other categories whether they are modally or temporally rigid, and whether the rigidity is de facto or de jure. Let us consider sentences. To formulate our question in application t o this semantic category we need something t o serve as the analogue of the designatum of a singular term. To this end, let me make use of the notion of the semantic value of an expression; this will consist in whatever it is that must be assigned to an expression in order t o fix its contribution to truth conditions. For heuristic purposes we can conceive semantic value in something like the way Frege explained his notion of Bedeutung: each well-formed expression is assigned a "reference" as that which determines its contribution to the truth-value of sentences in which it occurs. Here I am following Dummett's explanation of the notion of semantic value (except that I let the semantic value of a predicate be the property it expresses rather than the set of objects of which it is true).1° It should be remembered Wee the "Preface" to Truth and Other Enigmas (London, 1978), pp. xlvi ff. losee "Frege's Distinction between Sense and Reference", Truth and Other Enigmas, pp. 120 ff.

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that this notion of semantic value does not correspond exactly with the usual conception of semantic property, since (as Dummett notes) the semantic value of many expressions depends (in part) upon extra-linguistic facts. The semantic value of a sentence, then, will consist in its truth-value; so we can say that a sentence designates (in this special sense) its truth-value. Granted this way of speaking, we can enquire whether sentences may designate rigidly - and if so, whether they do so de facto or de jure. With respect to modal rigidity the answer is obvious: necessary truths (or falsehoods) rigidly designate their actual truth-value, while contingent sentences do so flexibly. More familiarly, necessary sentences, unlike contingent ones, are associated with constant functions from worlds to truth-values. I s this species of rigidity de facto or de jure? The answer seems to be that if the sentence is a synthetic necessity it is de facto, since it is an extra-linguistic matter whether the corresponding intension is a constant function; thus I would say that 'Water is H,O', and '7+5=12', being synthetic, are rigid de facto their necessity is not owed to semantic stipulation.ll (The examples I cite are not intended to beg any questions about the status of arithmetical truths: if you happen to think (misguidedly) that these are analytic, then change the example.) With respect to temporal rigidity our answer will depend upon whether propositions can be temporally neutral: if they can, then an eternal sentence will be temporally rigid, while a sentence whose truth-value fluctuates over time will be temporally flexible. If rigidity for sentences is thus definable, it ought to be possible to devise an "intuitive test" for whether a sentence has this property analogous to that proposed by Kripke for singular terms. And indeed it is: we can either formulate the test in a Regean manner - we ask whether the truth-value of a sentence S might not have been the truth-value of S (yes if S is contingent, no if S is necessary) -or we insert S into the schema . . . and possibly not . . . and check the result. Frege held that connectives have reference; they refer to first-level functions (concepts). Allowing ourselves, for the moment, to speak with Prege we can ask whether, say, 'and' and 'not' are rigid designators of the corresponding truth functions. That is, do connectives have their semantic value rigidly - and if so, is their rigidity de facto or de jure? It appears obvious that they are rigid and that their rigidity is de jure: in evaluating sentences formed from connectives with respect to possible circumstances we need only consider the semantic value the connective has with respect to the actual world -the corresponding truth function is a constituent of the expressed proposition. This is because the semantical rules directly assign those truth functions to the corresponding connectives as fixing their contributions t o truth conditions; there is no semantic indirection in the selection 11Striotly speaking, the claim that synthetic neoessities are always rigid de facto has to be qualified in view of points made in § IV (a) about identity sentences: the qualification should he obvious enough.

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of negation, say, as that which is relevant to evaluating 'not p' in a world. Again (permitting ourselves some grammatical licence) we can apply the Kripkean intuitive test: can we find a true reading for, e.g., 'Negation might not have been negation'? Clearly not. So far as I can tell natural language contains neither flexibly designating connectives nor de facto rigid ones, but I see no reason why such connectives might not be coherently introduced into some possible language. I n the case of names (identified syntactically) we can distinguish four methods of description-based introduction: (i) we fix the reference of the name with a flexible description; (ii) we fix the reference with a rigid description; (iii) we give the meaning (supply a synonym) by stipulating that the "name" shall abbreviate a flexible description; (iv) we stipulate a meaning equivalence with a rigid description. Only in case (iii) does the "name" thereafter behave flexibly. It seems to me that these four possibilities should be open t o us in the case of connectives. Thus I might fix the reference of a connective symbol by declaring that it is t o express the truth function first introduced in Principia Mathernatica (case (i) ). Or I might stipulate that a connective shall refer to the truth function definable from certain other truth functions in such and such a way (case (ii) ). Since the stipulation in these two cases is reference-fixing in intent, we get de jure rigidity. But suppose I stipulate a meaning-equivalence (of sorts) between the introduced connective and some flexible designator of a certain truth function: then it appears that the connective will take, as its semantic value with respect to a possible world, the truth function which meets that contingent condition in that world; in other words, we shall have introduced a flexibly designating connective. No doubt such a connective would be very different from our own well-behaved conventionally rigid connectives, but I cannot see why such a thing could not be stipulated (case (iii) ). Lastly, I might stipulate such a synonymy relation between some connective and a de facto rigid designator of a certain truth function; and then the semantical evaluation of the connective from world to world would be constant, though the semantic value of the connective was genuinely sensitive t o the facts of each world (case (iv) ). So long as we are able to make it a semantical rule that sentences containing a connective C are to be evaluated with respect to a world according t o which truth-function in that world meets a certain condition, which may be contingently satisfied by a given truth function in the actual world, then it is logicalIy possibIe to introduce connectives with de facto semantic value. (The interaction of such connectives with modal operators might even have some theoretical interest, though as natural language stands there seems no call for consideration of the semantics of such expressions.) It should now be obvious how to generalise the concept of rigidity to other parts of speech, e.g., quantifiers and adverbs. I n these cases too ure have rigidity de jure, though presumably we could construct logical possibilities analogous to those just mentioned in connexion with connectives.

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I n all these cases we have semantical rules that determine the composition of the structured propositions that get expressed by sentences of various kinds of logico-semantic structure. I n fact we may hazard the generalisation that if an expression is semantically primitive then it has its semantic value de jure rigidly. (The converse, of course, does not hold.)

I11 Before we can be satisfied that the generalisations I have suggested are legitimate, we need to eliminate their dependence on the Fregean semantic apparatus in terms of which the generalisation has thus far been formulated. It should be said, at the outset, that it seems hardly likely that the semantic intuitions I have called up should somehow resist articulation within a semantic framework we find philosophically acceptable; given that we have indeed identified a significant pattern of linguistic phenomena, the question can only be what sort of theory we shall use to represent those phenomena - failure to find such a theory should not make us repudiate the intuitions we started with. I shall suggest that we can capture the generalised notion of rigidity within a more or less standard truth-theoretic semantics. First, let us transpose Kripke's criterion of rigidity for singular terms into a truth-theoretic framework. The intuitive idea is that of a term which necessarily denotes a certain object; so the natural criterion will be whether an axiom of the form t denotes x can be necessitated. A little reflection shows that where t is a flexible designator of x the necessitation will be false, whereas it will be true if t is rigid. I am, of course, taking the language parameter as read. so that the necessitation will not be false because of the possibility that t might mean something else.12 Note that the metalinguistic specification of the referent of t must itself be a rigid designator -either a rigid (closed) singular term such as a name, or a variable bound by a description outside the scope of t,he necessity operator. (In fact this restriction is implicit in Kripke's official criterion too.) What about predicates? We saw (in effect) that they would come out flexible if we tried necessitating an axiom assigning an extension t o the predicate; but if we treat predicates in the usual disquotational way I think we can achieve what we want. Thus, for example, we can necessitate the axiom An object satisfies 'tiger' iff that object is a tiger so 'tiger' is declared rigid. If we replaced 'tiger' with 'of a species found at locale 1' on the left hand side, then the necessitation would be false, since tigers are not necessarily found a t locale 1. And we could get the same contrast with other types of predicate too. The rigidity of connectives can be explained in the same way: the usual recursion clauses assign a semantic value t o the connectives in such a way that they may be necessitated, as lasee, e.g., C. Peaoooke, "Necessity and Truth Theories", Journal of Philosophical Logic, 7 (1978), 473-600.

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brief inspection shows. By contrast, this cannot be done with the nonstandard flexible connectives introduced in the last section, since with respect to some worlds the connective used on the right side of the biconditional will not express the truth function which the object-language connective "designates" in those worlds. The situation here is essentially similar to that of (syntactic) names stipulated t o be synonymous with a flexible description; we could not necessitate a reference-specifying clause for such a "name" (assuming the metalanguage employed a rigid designator of the object denoted by the object-language expression). I t should now be apparent how other parts of speech (quantifiers, adverbs, etc.) may have their rigidity expressed in a standard semantical framework. The case of sentences is somewhat special. Normally, a truth theory specifies the truth condition of a sentence, this being always a de jure semantic property of the sentence; but there is no difficulty about expressing rigidity in respect of truth-value without reliance on the Fregean apparatus -we simply apply the truth predicate to the candidate sentence and see whether we can necessitate the result, as in Necessarily '7 5 = 12' is true. I n short, since we can assign semantic values to all the expressions we have considered without taking them to be genuinely referential, we can always ask whether the assignment holds necessarily - and this is the question of rigidity. Parallel remarks can be made about temporal rigidity. We introduce an operator with the sense of 'omnitemporally' and prefix it t o assignments of semantic value, taking care that the metalanguage uses temporally rigid expressions in the assignment of semantic properties. And the same kinds of distinction will arise between the rigid and the flexible - e.g., we might introduce temporally flexible connectives.

+

IV I turn now to discuss three issues concerning rigid designation: rigidity and identity sentences; rigidity and understanding; rigidity and scope. Our earlier reflections should help to put these issues in a clearer light. (a) Rigid designation and identity sentences. Let us assume (what seems pretty safe) that the identity relation is non-contingent, so that the identity predicate expresses a relation that holds necessarily when it actually holds. Then we can ask which singular terms are such that, when they are inserted into this predicate, a necessarily true sentence results, and what the ground of this necessary truth is. The orthodox answer is that the resulting identity sentence is necessarily true just if the inserted terms are rigid designators. This seems t o me obviously correct, but I think it is worth distinguishing among the cases, according to whether the rigidity is de facto or de jure. When the rigidity is de facto the identity sentence is necessary because it happens that one and the same object satisfies the expressed conditions

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in every possible world; the designators express individual essences of the same object. Since the designatum is determined only after the semantioal rules are fixed, it is no constituent of the proposition expressed by such an identity sentence; it merely turns out that the propositional components corresponding t o each designator yield the same object in any world. I n view of this we should say that identity sentences formed from de facto rigid designators are necessary de facto - not as the direct upshot of the semantical rules governing expressions occurring in the sentence. Thus, for example, 'The successor of 3 = the (positive) square root of 16' is necessary de facto. On the other hand, when the designators are rigid de jure the necessary truth of the identity sentence has a different source; for in those cases the terms are simply stipulated to have a given designatum, and the designata are the same. Thus it is with names and variables as they occur combined with the identity predicate. Here it is determined by the semantical rules that the terms are coreferential; the designata are thus constituents of the expressed proposition. I n view of this it seems correct to say that such identity sentences are necessary de jure, in the sense that their truth follows directly from semantical rules (and the fact that the identity relation is non-contingent). I n other words, the necessary truth of the sentence rests (in part) upon a semantic stipulation. But notice that the necessity involved is not ordinary analyticity; so we must allow that there are sentences whose necessary truth results from semantic conventions yet which are synthetic. This arises, I think, because the rules that assign semantic value serve only t o fix the reference; the stipulation determines that a certain object shall be the propositional component, not that the condition expressed by the reference-fixing description shall be. We therefore need to distinguish two ways in which a sentence can be "true in virtue of meaning", and hence two ways in which a sentence may be a de jure rigid designator of its truth-value. More accurately, we should distinguish two kinds of syntheticity: the kind where the sentence is not in any sense true solely in virtue of meaning, and the kind where it is, yet the sentence is true a posteriori. This distinction arises because there are (I think) two aspects t o the meaning of an identity sentence: its truth condition and its cognitive significance. My point is that the truth condition of a true identity sentence formed from de jure rigid designators contains the same object twice over, so that which proposition is expressed already suffices t o settle truth-value. But in addition we have t o reckon with the cognitive value of each singular term, from which the truth of the sentence is not deducible. The difference between 'a = b' and 'a = a' is thus that the former is true (when it is) in virtue of one component of its total meaning, viz., the truth conditional component, whereas the latter is true in virtue of both components, since it is a priori inferable that the sentence is true on the basis of the cognitive value of the contained names.13 lSFor further elucidation of these (no doubt opaque) remarks see my paper, "The Structure of Content", in Thought and Object, ed. A. Woodfield (Oxford, 1982).

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I should also add that I do not wish t o subscribe t o any reductive conventionalism about necessary truth: from the fact that we do not need t o appeal to anything beyond the proposition (truth condition) expressed by a sentence to fix its truth-value it does not follow that the truth of the sentence results from or reduces to human convention or decision. (b) Rigid designation and semantic understanding. Is rigidity a properly semantic feature of an expression, in the sense that it is a necessary condition of understanding an expression that you appreciate whether it is rigid or flexible? I shall argue that it is not. If I am right, it will follow that we make no contribution toward explicating the sense of an expression, say a proper name, by remarking that the expression is a rigid designator -for that will be a remark about what is strictly an extra-semantical property of the expression. The question bifurcates, according as the expression is rigid de facto or de jure. I n the former case the answer seems to me fairly obvious: it is not a necessary condition of understanding, say, 'the father of Abel' that one appreciate its rigidity - for you can know what is said in the use of this expression and not know that origin is essential. This is because the source of the constancy of the associated function lies in the modal facts, not in the sense of the words. I am not saying that we know the rigidity of this description a posteriori; on the contrary, I think we know it a priori but not simply by knowing what 'father' means. Someone might challenge this claim by insisting that unless you know that origin is essential you do not really understand 'father' -and there may indeed be some sense in which the necessity of origin is comprised in the concept of paternity; but it seems to me very implausible t o hold that one who has never thought about essentialism or rejects the necessity of origin literally does not know what is said when 'father' is used. So I conclude that the de facto rigidity of an expression is not part of what is understood when its sense is grasped; indeed this seems true by definition, since de facto rigidity is precisely rigidity which is not laid down by the semantical rules of the language. The point is yet more obvious in application to sentences: if a sentence is synthetically necessary, it would be very implausible to claim that grasping its meaning required knowledge of its necessity. And this already shows that the general notion of rigidity is non-semantic, in the strict sense correlative with understanding. Kripke appears to hold that the constant function associated with any rigid designator constitutes its sense (op. cit., p. 59, n. 22). We have just seen that this is implausible for the de facto case, but the de jure case seems more promising for Kripke because there the rigidity follows from semantical rules. He says, of 'Aristotle was fond of dogs', that a "proper understanding of this statement involves an understanding both of the (extensionally correct) conditions under which it is in fact true, and of the conditions under which a counterfactual course of history, resembling the actual course in some

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respects but not in others, would be correctly (partially) described by [that sentence]" (p. 6). I n effect, this is to claim that t o understand a sentence containing a name you must associate a constant function with the name as its sense, i.e., know that in any world the corresponding intension gives the same value. Now we should be suspicious of this claim in the light of an earlier point, namely that such constant functions are, in a certain sense, idle in determining the semantic value of a directly referential expression (where they are not idle, as with de facto rigid designators, they are clearly non-semantic). No computation of the function with respect t o possible worlds is needed t o work out that the term always takes the same object as designatum. But I wish to make the stronger point that understanding a name does not constitutively require deployment of modal concepts. The point is not easy to establish, but here are my reasons for suspecting it is true. Kripke's conditions for understanding appear tantamount t o the idea that t o grasp the sense of a name you have to know how it will behave in modal contexts - you have, in particular, to know the result of the ICripkean intuitive test. Kripke says that the rigidity of names in simple sentences is "equivalent to the thesis that if a modal operator governs a simple sentence containing a name, the two readings with large and small scopes are equivalent" (p. 12, n. 15), i.e. the name passes the intuitive test. That is, you have to appreciate that an operator which takes you to counterfactual circumstances does not alter the evaluation of the name. It therefore seems that Kripke is making tacit appeal, in his account of the understanding of atomic sentences, to our understanding of certain complex sentences, namely those formed with modal operators. Now the blunt way t o state my misgivings about this conception of name understanding is just that it does not seem impossible for someone t o grasp the sense of names (or indexicals), as they occur in atomic sentences, and yet have no complex modal sentences in his language - so that we could not represent understanding of the former as dependent upon understanding of the latter. We might make a parallel point about temporal rigidity: should we say that understanding a name constitutively involves grasp of its behaviour in tensed sentences? If we did insist on these necessary conditions, there would be the question why those modes of sentence formation have been selected from among the many other kinds of complex sentence we find in language. The only principled way I can see t o defend such a view of name understanding would be t o opt for a rather strong holism about understanding: that atomic sentences containing names were somehow understood derivatively from the whole range of complex sentences in which they may occur. There is no evidence that Kripke has any such holism in mind, and I myself would prefer to see understanding as proceeding from the simple t o the complex: we should be credited with a perfectly good understanding of atomic sentences ahead of their appearance in complex (including modal) contexts. Our grasp of the truth conditions of modal sentences is a consequence of our grasp of simple

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sentences, not a precondition of it. Quite generally, if someone grasps the sense of a name he will indeed be disposed t o understand complex sentences in a certain way, but it does not follow that his understanding of the name is defective or incomplete until he acquires mastery of these modes of sentence formation. Since direct reference, in contrast t o referential rigidity, is not defined modally, we can acknowledge its presence in simple sentences without needing t o advert t o the properties of complex modal sentences. This conclusion seems reinforced by recalling the generalised notion of de jure rigidity: is our understanding of 'not', 'there is', etc. really dependent on grasp of their behaviour in modal contexts? Implausible, I think. Describing an alternative view of understanding may help strengthen the negative claim of the last paragraph. This is the view -call it the RussellKaplan view -that understanding a sentence consists in identifying the structured proposition expressed by the sentence: that is, t o understand a sentence you have t o be suitably acquainted with the constituents of the expressed proposition. (That understanding a sentence requires acquaintance with the constituents of the proposition it expresses is, of course, not in tension with the idea that words get interpreted by "stipulation": if we agree with something like Russell's acquaintance theory of understanding, ure may make it a condition on stipulations of semantic value that one be acquainted with the items thus stipulatively associated with words. Nothing I say in this paper (immediately) commits me to the claim that genuine directly referential names can be introduced by stipulative description-based dubbing in absentia - though in fact I believe names can be so introduced.) Two things are involved: knowing the (de jure) semantic value of each expression, and knowing the way in which semantic value is determined by the words in the sentence. What this comes t o is appreciating how the structured proposition is determined from the primitive elements of the sentence. This view contrasts with the Kripkean view in that it requires grasp of the manner of semantic valuation and not grasp of the modality of such valuation. If the Russell-Kaplan picture is nearer t o the mark than the Kripkean picture, then we have another reason for doubting that possible worlds semantics offers a satisfactory representation of what sentences express: according to the former view, we do not need to know in which worlds a sentence is true in order t o know what it means. Kripke's claim that understanding involves knowledge of rigidity is thus predicated upon a possibleworlds conception of propositions: if you already reject the latter, then I think you should reject his thesis about names - both tie modality and meaning too tightly together. I t is true, I would agree, that primitive denotation is a rigid relation; but I think this is a reflection that comes when we begin to theorise about our language -it is not something we need to know in order to use language in our ordinary unreflective way. I n this respect the rigidity of semantic relations might be compared with their irreducibility: by reflecting upon our semantic concepts we can, I would

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hold, come t o see that they cannot be reduced to, say, physical concepts, but no such philosophical awareness is pre-requisite t o the ordinary understanding of names.14 (c) Rigid designation and scope. It is sometimes suggested, notably by Dummett, that there is no more to the Kripkean notion of rigidity than considerations of scope: that is, the linguistic intuitions Kripke represents in terms of rigidity are better explained in terms of a (tacit) convention t o assign maximum scope t o the expression in question.15 I n other words, the suggestion is that no term is, so t o speak, intrinsically rigid; it is just that we tend t o give intrinsically flexible designators wide scope. To assess this suggestion we must, as always, take it in two parts: as a thesis about de facto rigidity, and as a thesis about de jure rigidity. The suggestion is surely incredible in respect of de facto rigidity. We judge a definite description rigid because we recognise that it expresses an individual essence; it could scarcely be maintained that such modal intuitions rest upon a tendency t o give the corresponding description wide scope! It would be similarly preposterous to hold tha,t we judge a sentence necessarily true because we have a convention to give it (the sentence) wide scope with respect t o some modal operator! Similarly, there is no plausibility in the suggestion that de facto temporal rigidity derives from a convention to award maximum scope with respect to tense operators. The absurdity of a scope interpretation of de facto rigidity is shown by considering the result of abrogating such a convention. Imagine that we have a language in which there is an explicit scope indicator assigning wide scope to all descriptions, including those Kripke would declare flexible. Now imagine cancelling the convention, so that descriptions can now fall within modal operators. Since there would then be a distinction between, say, 'the inventor of bifocals' and 'the father of Franklin' on the score of constancy of reference across possible worlds, it cannot be that in the original language with the wide scope convention all the designators were rigid; and this is just to say that rigidity is a matter of semantic evaluation within the scope of modal operators. The scope suggestion is usually offered by way of defending the description theory of proper names; their behaviour in modal contexts is not, on this defence, due t o intrinsic rigidity but to a convention to give the underlying description wide scope. By this manoeuvre it is hoped to avoid the objection that the description theory renders flexible what is in reality rigid. Kripke makes two objections t o such a view (op. cit., p. 13): (i) that we have an intuition of rigidity for names even in simple sentences, where there are no modal operators around t o generate scope interactions; (ii)that 141allude to the issue raised by Hartry Field in "Tarski's Theory of Truth", The Journal of Philosophy, 69 (1972), 347-74. 1Vee M. Dummett, B'rege (London, 1973), Appendix to Chaptor 5, § 2; and Truth and Other Enigmas, pp. xlv ff.

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if the two scope readings are really present in modal sentences containing names, why are we unable t o recover the narrow scope reading - why can we not flout the convention and hear the blocked reading? I am sympathetic t o both Kripke's objections, but I doubt their power to convince the opposition. About objection (i) it might be said that our intuitions in regard t o simple sentences really reflect our grasp of how names would behave in complex sentences; we see that the wide scope convention would apply as soon as a modal operator came on the scene. Indeed, it might well be said, ad hominem, that this claim of Kripke's and his doctrine about understanding are dubiously consistent: for what substance is there to the idea that we understand a simple sentence by knowing how t o evaluate it in counterfactual circumstances but the thought that we implicitly grasp its behaviour in complex modal sentences? Recall the earlier discussion of rigidity and understanding. Once rigidity is connected with behaviour in complex modal sentences, Dummett will be offered the chance t o claim that what looks like equivalence of distinct scope readings is really the effect of the automatic operation of the wide scope convention. (Perhaps this tension results from Kripke not distinguishing adequately between rigid designation and direct reference: we do have a direct intuition of the latter in simple sentences, but then the content of that intuition is not to be explained in modal terms.) About objection (ii) some explanation might be produced (though I cannot myself produce one) for why the wide scope convention is inviolable, i.e., for why we cannot as things are hear the blocked reading. (Note that we would need an explanation, not just of the existence of such a convention, but also of its infrangibility. Dummett himself offers no explanation of the "ad hoc convention" he invokes: but it is necessary to provide one if Kripke's objection is to be overcome.) And then it might be held that if, per impossibile, we managed t o revoke the convention, then we would treat the small scope reading just as we would the syntactic names we stipulate t o abbreviate definite descriptions. The case might be compared with an analogous issue concerning Russell's theory of descriptions. It is a familiar point that Russell's analysis commits us t o a pair of readings for negated sentences containing definite descriptions, corresponding to whether the description has primary or secondary occurrence, which we have difficulty finding in the sentences concerned; in particular, we cannot hear the reading on which the negation operator includes the existential clause of the analysis in its scope - we automatically take the 'not' in 'the P is not a' t o apply t o 'G'. A defender of the Russellian theory will claim that the apparently unavailable scope reading is present in the meaning of the sentence, but that there is some sort of convention which blocks its appearance. Since there is plausibility in this move for the case of the semantics of definite descriptions, it would appear open to the scope theorist about de jure rigidity t o plead analogy; so Kripke's second objection, though a genuine challenge, is not knockdown.

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The point I would press is that the scope interpretation only postpones recognition of de jure rigidity as a sui generis linguistic phenomenon. The scope theorist wishes to see names as functioning rather as quantifiers do: they both involve binding variables across modal operators.la This means that the variables bound by the underlying description occur both outside and inside the modal operator; and we have seen that variables are almost the paradigms of de jure rigid designation. So the scope theorist has eliminated one kind of rigidity only t o introduce another. Nor could it be suggested that the variables are really equivalent t o definite descriptions of their several values which in turn automatically take wide scope; for this launches us on a regress. But now since variables are just "temporary names" of their values under an assignment, there can surely be no logical obstacle t o freezing them into individual constants - and then won't these look just like our familiar names? If these constants behaved just as our names do, the scope theorist would find himself in a weak arguing position. The inescapability of de jure rigidity is also evident from our generalisation of the notion. If the case of names is semantically analogous t o that of predicates, connectives and other semantic primitives, then we can ask why the scope theorist does not extend his theory t o these other expressions: whenever we have what looks like de jure rigidity we say that there is an underlying description taking wide scope. Such a view is, of course, absurd; indeed the modal operators themselves would have to be given a scope interpretation of their de jure rigidity. But if the scope theorist is reluctant t o apply his suggestion thus generally, there is the question what motivation he has for holding t o this view for the case of names - a t the least he must deny the analogies of semantic function we have tried to bring out. I myself cannot see any principled way in which the scope interpretation of the rigidity of names can be sustained. Taking a step back, I would suggest that Kripke's attack on the description theory of names somewhat invites the sort of response the scope theorist makes. Kripke concentrates his attack on the alleged consequence of the description theory that names wrongly come out flexible designators; the description theorist then tries by various stratagems to repair this defect in the classical theory. But the original Millian intuition about names is that they are non-descriptive labels for their bearers. If that is the basic objection t o the description theory, then the trouble is not so much that the theory makes names jlexible; it is that it makes their means of designation de facto - and the scope interpretation does nothing to lessen the unattractiveness of this aspect of the description theory. (This observation is not offered as a conclusive refutation of the description theory; I am merely suggesting that the focus on the behaviour of names in modal contexts mislocates the crucial disagreement between the rival conceptions of the semantics of names.) l6See e.g., Dummatt, Frege, p. 114.

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There is another, quite different, question about the relation between rigidity and scope which requires comment: this concerns the proper interpretation of the claim that rigid designators are "scopeless". We must consider this claim in two parts. I n the de facto case we find that a modal operator does not have the effect of shifting the designatum of the term from world to world; this is because such a description expresses an individual essence of the designatum. Consequently, both scope readings of The P might not be the F where 'the F' is de facto rigid, come out necessarily equivalent. Now this just means that variations in the scope of a de facto description do not affect truth-value, and in that sense the de facto rigid designator is scopeless. But I would say that the sentence in question is not unambiguous with respect t o scope: it is semantically ambiguous because the rigidity of the description is de facto. One who failed t o appreciate its rigidity would assign different truth-values t o the two readings, and this would betray no linguistic incomprehension. Put differently, the necessary equivalence of the two scope readings is due to the constancy of the associated function, but this constancy is not a semantic matter, and so the sentence is genuinely ambiguous. The de jure case is quite different; here I would say that there is no ambiguity. (That is, we have mere "constructional" ambiguity, corresponding to no semantically distinct readings.) The reason for this is that directly referential terms introduce their designatum into the proposition expressed; so they could give rise to scope ambiguities only if operators could alter the very meaning of expressions lying in their scope. To understand a de jure rigid designator you have t o appreciate how it contributes to fixing what is said, and this implies that you appreciate that modal operators cannot generate scope ambiguities with such designators - on pain of changing their sense. I n view of this difference between the scopelessness of the de fwto and the de jure, we should note that Kripke's intuitive test really taps two quite distinct kinds of intuition - intuitions about essential properties of objects, and intuitions about language. If we confuse these, we shall not get a proper account of the semantic distinction between names and descriptions.

v The impression is sometimes given that rigidity is a rather special semantic property enjoyed by only an Blite minority of expressions; and that there is some mystery about how an expression can come to have this property. If what I have been saying in this paper is right, this impression is mistaken. A language will be capable of de facto rigid designation just as long as it can express essential traits of the world; if our metaphysics will allow us such essentialism, our semantics can hardly refuse to go along with it. De jure rigidity is unsurprising for a different reason. We saw that this species of rigidity is a matter of the upshot of stipulative semantical

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rules assigning a specific contribution to truth conditions. Such rules may be pictured as determining the composition and structure of the propositions the language is capable of expressing. Russell applied this model to predicates (they introduce universals) as much as to (logically) proper names, but did not (because of his logical atomism) extend the model t o expressions of other categories (except, waveringly, negation).l' (Latter-day Russellians about names do well to remember that Russell's doctrine on logically proper names was part of a general theory of the significance of expressions of all categories.) It seems to me that we should view each (primitive) expression as introducing some constituent into the proposition by dint of semantical rules, if we wish to say that any do. If this is the right way to look a t the matter, then a certain conception of proper names, which we have been schooled to see as extraordinary, will come t o seem almost banal. Names are said to "reach right out to reality", unmediated by concepts interposed between them and their bearers; that is, they make their bearers the propositional constituent.l8 But this prehensile feat will seem less extraordinary (and alarming) if we see it as just a special case of stipulating what is to be the semantic value of an expression: if we can stipulate semantic values for other types of expression, then why should we not make it a semantical rule that names have their bearers as semantical value? I n other words, if what distinguishes names from descriptions is their de jure rigidity, this does not make them different from a wide range of other expressions - so we commit ourselves to nothing very astonishing in making a name's bearer its semantic value. From this point of view the debate about the correctness of the Mill-Russell conception of the semantics of names will take on a different complexion: those opposing the view as somehow semantically incoherent will seem t o be questioning a linguistic phenomenon that is widespread and anyway inescapable; while those who uphold the view will be maintaining a less bold and interesting thesis than they perhaps supposed. That the bearer of a name "enters the truth conditions" of sentences in which the name occurs begins t o seem scarcely more surprising than that the truth function of negation enters the truth conditions of sentences containing 'not'?

University College London

':See Russell, Problems of Philosophy, Ch. 5; and The Philosophy of Logical Atomism, passzm. '8The phrase 'reaching right out to reality' is John McDowell's (echoing Wittgenstein) from his review of Naming and Necessity, in The Times Literary Supplement, January 16, 1981, pp. 61-2. '9Acknowledgement is due t o Anita Avramides, W. D. Hart, Ian McPetridge, Christopher Peacocke and various members of the 1981 Keele conference on the philosophy of logic and language.