I.

In 1905 Bertrand Russell published a solution to what may seem a minor problem in the philosophy of language, a problem concerning improper descriptive phrases like 'the golden mountain.' How can a sentence beginning with that phrase be meaningful, given that there is nothing in the world answering to the description? Russell's solution was, as well known, breathtakingly simple: the question does not arise because, quite generally, a definitely descriptive phrase is not a means of reference to its descriptum, A sentence whose subject or object term is a definite description has nothing to say about the entity, if any, which fits the description.

The fate of Russell's discovery in the history of this century philosophy is quite remarkable. It was almost unanimously declared a paradigm of the analytic approach, only to be unanimously ignored by almost all analytic philosophers. Theorist after theorist takes it for granted that George Bush, for example, can be referred to as 'The American president' and feels no obligation to stop and consider exactly what, if anything, is wrong with Russell;s argument to the contrary. The argument has been set aside not because it has been found wanting but because its conclusion offends prejudice.

I shall speak of the view that a descriptive phrase does not refer to its descriptum as Russell's Thesis. What was Russell's argument for it? Well, suppose that the noun phrase 'the American president' were a name of George Bush. Then someone who said ' George Gush is the American president' would be saying that Bush is himself. Although Bush undeniably is himself, this is hardly the message conveyed by the sentence, for Bush would be himself even if what the sentence says was false. Similarly, someone who said, mistakenly, ' Michael Dukakis is the American president' would be saying that Dukakis is Bush. Although the utterance undeniably betrays a misconception on the speaker's part, the misconception is hardly as gross as all that.

It is interesting to note that in one place Frege argued for a thesis which in spirit is very close to Russell's. He argued that a sentence like ' All whales are mammals' has nothing to say about any particular animal. Even if we imagine that a particular whale, say Shamu, is right in front of us, the sentence tells us nothing about him because it leaves it open whether Shamu is a whale. Of course, if we know that Shamu is a whale and add this information to that conveyed by the sentence, we can learn something about Shamu, namely that he is a mammal. But it is the conjunction of the two sentences, ' Shamu is a whale' and ' All whales are mammals', which yields this information. The latter sentence by itself is powerless to tell us anything about that or any other beast.

Now it is readily seen that the sentence ' The smartest whale is a mammal' lends itself to exactly parallel line of reasoning. For suppose that Shamu is the smartest whale and is right in front of us. The

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sentence tells us nothing about Shamu because it leaves it entirely open whether Shamu is a whale, let alone one which outsmarts all other whales. Of course, if we know that Shamu is the smartest whale and add this information to that conveyed by the sentence we can learn something about Shamu, namely that he is a mammal. But it is the conjunction of the two sentences, 'Shamu is the smartest whale' and 'The smartest whale is a mammal' which yields this information. The latter sentence by itself is powerless to tell us anything about that or any other beast.

Frege failed to appreciate this parallel and insisted that a descriptive phrase like ' the smartest whale' or ' the American president' is a name of whatever object answers to the description, I shall refer to the view as Frege's Thesis.

Frege's Thesis is so deeply ingrained in conventional philosophical wisdom that it takes some effort to see it for the debatable piece of semantic theorizing that it is. But once the effort is made so many counterarguments suggest themselves that it is hard to know where to start. If 'the American president' designated George Bush then each of the sentences

(1) Dukakis wanted to be the American president

(2) Fred thinks that the American president is a Republican

(3) The American president exists

would say something about Bush. What could that possibly be? (1) certainly does not say that Dukakis wanted to be Bush. (2) does not imply that Fred has any view concerning Bush or that he is even acquainted with, or aware of him. (3) certainly does not ascribe existence to Bush. Indeed one can understand the three sentences perfectly well without having an inkling that the term is in any way connected with Bush. But how can one understand a sentence without knowing what it is about?

On the other hand, from each of the three sentences one learns something about American presidency, the office: From (1) one learns that Dukakis wanted to hold it, from (2) that Fred thinks that it is held by a Republican, and from (3) that it is not vacant. Yet, if the term ' the American president' refers to Bush, there is nothing left to refer to the presidential office. How is it possible that one can acquire information concerning an item from sentences in which that item is never mentioned?

Contemporary adherents of Frege's Thesis (and they are legion) have invested a great deal of intellectual energy in fending such obvious counterexamples off. In each of (1)-(3), they tell us, the descriptive term does not refer to what it describes, because it appears in a special kind of context, termed 'oblique', 'opaque', 'non-referential' or 'intensional'. This sounds interesting and makes one anxious to learn how to tell special contexts from others. It turns out, however, that there is nothing to learn: what makes a context special is by definition its failure to conform to Frege's Thesis. The

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defenders of the thesis thus save it from counterexamples by watering it down to a tautology: a descriptive term refers to its descriptum except where it does not.

So attenuated, the thesis is, of course, perfectly compatible with the view that a descriptive term never refers to what it describes, that is, with Russell's Thesis. What saves the opacity doctrine as a whole from the abyss of triviality is the fact that it comes with a sample of contexts which are allegedly non-special (or 'transparent'). There is a universal consensus, for example, that a sentence like

(4) The American president is a Republican

represents such a context. In such a sentence, it is claimed, the term 'the American President' definitely refers to George Bush.

It would ve absurd for anyone who takes this view to maintain the sentence nevertheless asserts nothing about Bush. Surely one would not normally refer to a man if one had nothing to say about him.

Let us then ponder what it may possibly be that the sentence says about Bush. The only conceivable answer seems to be that it ascribes to him the property of being a member of the Republican party. But if this was so then the assertive content of (4) would be no different from that of

(5) George Bush is a Republican.

Both would mention the same man and ascribe the same property to him.

How can this conclusion be squared with the obvious fact that the two sentences express two logically independent facts? For I don't suppose anybody would want to deny that it is perfectly possible for George Bush to be a Republican without the American president's being one, and equally possible for the American president to be a Republican without George Bush's being one.

How can the conclusion be reconciled with the fact that (4) conveys factual information about the American presidential office (implying as it does that the office has a Republican incumbent) while the other does no such thing?

II.

Let us consider again the sentences (1)-(3). As mentioned above, some adherents of Frege's Thesis speak of those contexts as 'non referential'. This is a term that Frege himself would have never used. Frege took the view that referring to something is what a linguistic expression is for, and that a sentence containing an expression which fails to refer is truth-valueless and hence epistemically useless. According to Frege, in (1)-(3) the term ' the American president' refers all right, but not to Bush or any other individual. It refers to what he called a 'sense' and what can be spoken of, more generally, as a determiner.

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A determiner is an entity which determines, or singles out, an object other than itself. A proposition is a typical determiner: it singles out a truth-value, and hence can be called a truth-value determiner. A property is a determiner: it singles out a class of individuals, and hence can be called a class determiner. A physical magnitude (such as the temperature in Karlovy Vary on September 1, 1992) is a number determiner etc. What the phrase 'the American president' stands for in sentences (1)-(3)is, according to Frege, an individual determiner, something which singles out an individual.

The relation between a determiner and its determinee is typically a contingent matter: the identity of the determinee is not intrinsic to the determiner itself, but depends on matters of fact. The determiner which goes with the phrase 'the American president', for example, singles out George Bush, but only happens to do so. Had Dukakis won the last presidential election, the very same determiner would have singled out Dukakis instead. The determiner which goes with the common noun 'Republican' singles out a certain class of individuals, call it C. But it only happens to do so. Had Dukakis thrown in his lot with the Republican Party, the very same determiner would have singled out a class numerically distinct from C. The identity of the determinee also depends on time. The very same determiner which currently singles out Bush, used to single out Ronald Reagan, and will sooner or later single out yet another individual. The class determined by the property of being a Republican changes all the time.

Set-theoretically speaking, a determiner is a function which takes world/time couples to the objects singled out by the determiner in those worlds at those times. The determiner the American President, for example, is best thought of as a function which takes a world/time to the person, if any, who occupies the American presidential office in that world at that time. And the property of being a Republican is best thought of as a function which takes every world/time to GOP membership in that world at that time. Let us call the two functions A and R respectively.

The English language associates with every descriptive phrase a particular determiner or office. As Frege often emphasized, to understand such a phrase means to be acquainted with the corresponding determiner (or 'sense' as he called it) and not necessarily with what the determiner singles out. What I have been calling Frege's Thesis can thus be restated as follows:

Special contexts aside, a descriptive phrase does not refer to the determiner linguistically associated with it but to the object (if there is one) which the determiner singles out.

III.

Frege introduced his distinction between sense and reference in the course of his celebrated discussion of identity statements. He asked himself how a sentence like

(6) The American president = the husband of Barbara Bush

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differs semantically from

(7) The American president = the American president.

The insight that the English terms 'the American President' and 'the husband of Barbara Bush' are associated with two distinct determiners and that no adequate semantic account of (6) can be given without invoking those determiners, is Frege's lasting contribution to the philosophy of language. Yet, despite its popularity, Frege's putative solution of the identity problem fails. It fails because of what I have been calling Frege's Thesis.

According to Frege, the above sentences are of different 'cognitive import' because in (6) George Bush is referred to once through the determiner A and once through a distinct determiner, B, while in (7) he is referred to twice through the same determiner, A.

What is cognitive import? 'Cognitive import' is not a systematic term of semantic theory,not even of Frege's own. But presumably two statements have different cognitive import if they impart two different pieces of knowledge. Hence the questions to ask are, Do the sentences convey two different messages? Do they record two distinct facts?

If the messages are about Mr Bush, as they must be if Frege's Thesis is correct, the question can be put like this: do the two sentences ascribe to Mr Bush two distinct properties? On Frege's theory the answer is clearly No. Given that in both sentences the only individual mentioned is Mr Bush and the only attribute mentioned is the identity relation, both sentences say that Bush is identical with Bush. The paradox is still with us.

Now nobody would want to deny that (6) and (7) are true in virtue of two different facts. Let us call two determiners congruent if they happen to determine one and the same object. Then (6) is true by virtue of the fact that A happens to be congruent with B, while (7) is true because A happens to be congruent with A. The reason Frege's followers find his theory satisfying is because they tacitly, or subconsciously, think of the two sentences as records of these two distinct facts. But the Fregeans are understandably reluctant officially to admit that this is what they take the master's solution of the identity puzzle to be. For the circumstance that A is congruent with B is a fact concerning the determiners A and B; and the fact that A is congruent with A is a fact concerning the determiner A. Neither fact is anything to do with Bush. Had Dukakis married Barbara and won the 1988 election to boot, we would have had the very same two facts to live with: A's congruence with B and A's congruence with A.

So if they owned up to this esoteric interpretation of Frege's 'solution' the proponents of Frege's Thesis would have to face the fact that on their theory sentence (6) says something about the determiners A and B although it never mentions them, and contains not one but two names of George Bush although it has nothing to say about him. This is an embarrassing contention to have to defend. No wonder that subscribers to Frege's Thesis tend to be allergic to the very notion of aboutness and dismiss it as a 'confused intuition.'

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IV.

Frege's Thesis, as formulated at the end of section II., makes a descriptive phrase what may be called a contingent designator. It designates something not by (linguistic) necessity or fiat, but only by courtesy of some contingent facts. The phrase 'the American President', for example, stands for George Bush, but only because Americans chose to act in a certain way at the last election. Had they acted differently, the very same phrase would have designated Dukakis. Frege's thesis makes a descriptive phrase a contingent designator in the sense of designating at each world/time whatever object (if any) is singled out by the corresponding determiner in that world at that time. Those objects will often be different at different world/times.

The reader may well ask why I have used the term 'contingent designator' where most semanticists would nowadays use Kripke's term 'non-rigid designator' in the same sense. The point is that those semanticists have not read their Kripke closely enough. Kripke's non-rigid designators are not contingent designators as I have jest defined them. Note that my definition presupposes that the English language we speak is an abstract object which, like other abstract entities, is a trans-world/time affair. The definition presupposes, in particular, that the English term 'the American president' has the same determiner associated with it, and refers to what the determiner singles out, even in worlds and at times where no one speaks English or any other language linking the determiner with the term. Imagine a world which differs from ours in two respects: (a) Dukakis, rather tan Bush, is the president and (b) everybody speaks English*, a language which is like English except that the word 'president' is missing from its vocabulary and its duty is dome by some other expression: 'presiding person' or some such. In that world, the phrase 'the American president' is never used. Yet the defenders of Frege's Thesis, speaking of our starless English, surely want to say that with respect to that world the phrase 'the American president' refers to Dukakis, thus manifesting its status as a contingent designator. So the tacit assumption must be that in that unactualized world where nobody speaks it, starless English is still sitting in the platonic heaven as it were, its noun phrases idly going about their referring tasks.

This, however, is miles away from the Kripkean picture. Kripke conceives of a language as a social phenomenon, not as an abstract, fact-independent entity. On his view words depend for their reference in a world on the histories of their use in that world. Kripke would say that in the counterfactual world I have just mentioned, the term 'the American president' does not refer to anything at all.

In Naming and Necessity Kripke was at pains to advocate the notion of rigid designator, and one can only infer what a non-rigid designator is supposed to be by contrast to that notion. What is a right designator according to Kripke?

When I say that a designator is rigid and designates the same thing in all possible worlds I mean that, as used in our language, it stands for that thing, when we talk about

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counterfactual situations. ... In describing a world we use English with our meanings and our references.

Thus, unlike the notion of contingent designator discussed above, Kripkean rigidity is nothing to do with the behaviour of a term in alternative possible worlds. What makes a designator rigid is its behaviour in the actual world. A term is rigid if it is unambiguous: if it has the same reference whether we use it (here, in this world) in speaking about the actual world or about counterfactual possible worlds. A non-rigid designator, presumably, is then one which is ambiguous in that its reference depends on the context in which it stands.

Is the term 'the American President' a non-rigid designator in Kripke's sense? Let us see. If we say

(4) The American president is a Republican

it refers allegedly to George Bush. Are there contexts where the term refers to somebody else, say Dukakis ? Consider a world W in which Dukakis is the president and the current membership of the Republican Party is the same as in the actual world, namely C. The following is a sentence which says something about that counterfactual situation:

(8) In W, the American president is not a Republican.

Does the term 'the American president' stand for Dukakis in this sentence? Hardly. If it did then the message conveyed by (8) would be to the effect that in W, Dukakis is not a Republican. But Dukakis is not a Republican in the actual world either; Dukakis' membership of the Republican party is not a matter in which W differs from the actual world. Yet (8) clearly appraises us about an aspect of world W in which it differs from the actual world, not about one in which it agrees with it.

Or consider

(9) In some world, the American president is not a Republican,

surely a context 'where we talk about counterfactual situations.' Who does the tem 'the American President' stand for there? No candidate even comes to mind.

V.

Here is a hypothesis about how the misconceived notion of non-rigid designator came into being.

It is an elementary truism of logic that a set of objects is defined by specifying a definite condition; objects which satisfy the condition are the members of the set and objects which don't aren't. Imagine little Johnie gets this wrong. He forms the idea that a set is defined in such a way that every object is assigned its own distinctive membership condition. Consider, for example, the class C of

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numbers whose sine is positive. Johnie thinks, that the reason the number 30,say, is in the class is not because it, the number 30 itself, satisfies the condition of having a positive sine, but because .5 is positive. And the reason the number 210, say, is not in the class is not because it, the number 210 itself, fails to satisfy the condition of having a positive sine, but because -.5 is not positive. It is clear that Johnie badly needs some instruction in the basics of logic. For otherwise his error is bound to lead to the misconception that the statement '30 is in S' is somehow about the number .5 and the statement '30 is in C' is about the number -.5.

Now suppose that instead of S Johnie considers the class P of world-times, at which the American Presidency is occupied by a Republican, that is the proposition that the American President is a Republican. Just as in the previous case, Johnie takes the view that each particular world/time has its own membership condition of P. He thinks, for instance, that the actual world-time is in the class not because the world-time itself is one at which the American Presidency is occupied by a Republican, but rather because George Bush is in the class C. Similarly, he thinks the reason that the couple consisting of W and the present time is not in the class not because the world-time itself is not one at which at which the American Presidency is occupied by a Republican, but because Dukakis is not in the class C. Johnie is making exactly the same logical mistake as in the case of S. To define a set of world/times - that is, a proposition - one has to specify a single condition satisfiable by world/times. World/times which satisfy it are then members of the proposition and those which don't aren't. P is the set of world/times at which the American Presidency is occupied by a Republican. It is this single membership condition, that of being a world/time at which A is occupied by a bearer of R, that defines the set in question.

Let us say that an office distinguishes a property if it is occupied by a bearer of the property. For example, the office of the American president happens to distinguish the properties of being a Republican, of being a golf-player, etc., while back in the late '70s it distinguished the properties of being a Democrat, being a peanut framer etc. Now we can say, more succinctly, that P's membership condition is that of being a world/time at which A distinguishes R. The pair consisting of the actual world and the present moment is a member because it satisfies the condition, and the pair consisting of W and the present moment is not because it does not.

The condition as such is nothing to do with George Bush, Michael Dukakis, or any particular set of individuals. It involves only the functions A and R, as is immediately clear as soon as a the definition is formalized:

(D) <w,t> Î P =_df A(w,t) Î R(w,t)

Thus it is that when we say that the pair consisting of the actual world and the present moment is in P we say nothing about Bush or the set C. All we are saying is that the truth condition, which is nothing to do specifically woth any particular person or set of persons, is satisfied by that pair. The illusion that the statement is also about Bush and C arises only if one shares Johnie's misconception that the

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proposition has a distinctive truth condition - that of George Bush's belonging to C - custom made for that particular world/time pair.

The way Kripke expresses himself indicates very strongly that he indeed shares Johnie's fallacy. On p.10 of Naming and Necessity, for example, he says that a proposition conforms to 'a rule of rigidity'

[if] there is a single individual and a single property such that, with respect to every counterfactual situation, the truth conditions of the proposition are the possession of the property by that individual, in that situation.

On p. 7, discussing the sentence

(10) Exactly one person was last among the great philosophers of antiquity, and any such person was fond of dogs,

Kripke comments:

The actual truth conditions of [(10)] agree extensionally with those mentioned above for [the sentence 'Aristotle was fond of dogs'] ... But counterfactually [the] conditions can vary wildly from those supposed by the rigidity thesis. (Bold added.)

Now unless these statements are not to be taken literally, Kripke's presupposition is that rather than having a single truth condition, a proposition has a whole range of them, a specific one for each possible world. In the case or a 'rigid' proposition those truth conditions may coincide, but in other cases they 'vary wildly'.

Now once one espouses the view that the truth-condition of (4) relative to world W is for Dukakis to be a Republican, and its truth condition relative to the actual world is for Bush to be a Republican, it is no leap to the misconception that when we talk, as in (8),about W, the term 'the American President' refers to Dukakis and when we talk, as in (4), about the actual world, the same term refers to Bush, This, I submit, is how the idea of a non-rigid designator was born.

VI.

But even if one should swallow the quaint idea that a proposition has a separate truth condition relative to each possible world, and draw Kripke's semantic consequences from it, the problem concerning statement like

(9) In some world, the American president is not a Republican,

would still remain unresolved. For in (9), instead of talking about a particular counterfactual situation, we quantify over them all. What does the term 'the American President' refer to in this context ? No story about the behaviour of the term in unactualized possible worlds will answer the question. We want to know what the term refers to 'as used in our language, when we talk about counterfactual

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situations [using] our meanings and our references' in the actual world. Does the term perhaps suddenly lose its status as a designator?

Surely not. But the only object which can be, with any plausibility, associated with the term as it occurs in (9) is the function A from worlds to individuals. (I am following Kripke in ignoring the time parameter at the moment.) And the plausibility seems overwhelming. The principle of compositionality requires that A receive reference in the embedded clause, for it is clearly that function, rather than some particular value of it, that one needs to calculate the class of world/times that the clause refers to. (9) obviously conveys something about the office A: it tells us that there are worlds which satisfy a certain condition regarding A, that of being a world in which A fails to distinguish R. The term 'the American president' is the only part of the sentence which can perform the function of referring to that office. Anybody who dogmatically insists that the term serves to designate an individual faces two unanswerable questions: Which individual does the term refer to in (9) ? And how come that (9) tells us something about A but contains no term referring to it?

To admit that the term stands for A in sentence (9), however, is to find oneself on a slippery slope. (9) says that a certain condition is satisfied by some world or other and (8) differs from it only in saying that the condition is satisfied by the specific world W. In both cases, the condition is spelled out by the clause 'the American President is not a Republican', the subject term playing the same role, that of adverting to the office A.

Now what (8) says about world W, the sentence

(11) In the actual world, the American President is not a Republican.

says about the actual world. The embedded clause refers once again to the condition of being a world where the office A fails to distinguish the property R, the subject term serving to advert to that office. (11) is not false, but this is as it should be. As noted above, (8) appraises us of on aspect in which W differs from the actual world. If in the two sentences the embedded clause were to be construed differently, the fact that (8) is true and (11) false would fail to capture this intuitively obvious contrast.

But now note that in the case of (11) the locative adverb is redundant. When it is said, simply, that

(12) The American president is not a Republican

it is understood that the condition in question is claimed to be satisfied by the actual world. The deletion of the superfluous prefix surely does not affect the correct construal of the clause. So in (12) too the term 'the American President' serves to refer to A, and not to Bush. Finally, dropping the 'not' cannot alter the semantics of the term either. Thus in

(4) The American president is a Republican

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too the subject term refers to the office A. We have reached the bottom of the slippery slope.

According to a routine objection, (4) cannot be telling us anything about the presidential office because the office is obviously not a member of the Republican or any other party. The objection, however, is based on the naive principle that the predicate of a statement must invariably be ascribed directly to whatever item the statement mentions. On this principle one could similarly argue that the statement that all whales are mammals cannot be about whaleness, the property, because the property is not the sort of thing that can be a mammal. But, as Frege himself has taught us, the statement is about whaleness. The sentence tells us that the property is related to another property, that of being a mammal, in such a way that every object instantiating it also instantiates the latter property. But the statement leaves it completely open what those instances are and therefore does not refer to any of them. The statement that the American president is a Republican is structurally very similar. It speaks of the American president, the individual-determiner, and the property of being a Republican. What it says is that the determinee of the former instantiates the latter. But it leaves it entirely open who the determinee is, and therefore involves no reference to that individual. This is what sets it apart from sentence (5), which does speak about an individual. There is an individual, George Bush, such that (5) cannot be true unless that particular individual is a Republican. On the other hand, their is no individual such that (4) cannot be true unless that individual is a Republican. For (4) to be true, all that is required is that there be an individual who holds the American Presidential office and is a Republican. But any arbitrary individual will do.

VII.

Summarizing his position, Kripke says that when it comes to determining the semantic role of a designator in a sentence, the question to ask is

whether what is expressed would be true of a counterfactual situation if and only if some fixed individual has the appropriate property. This is the question of rigidity.

Kripke speaks explicitly about designators of individuals, but he does not mean to confine the notion of rigidity to designators of this sort. ('Heat' and 'gold', for instance, are also rigid designators.)

Now if what has been argued above is correct then the term 'the American president' passes the rigidity test with flying colours. There is indeed a fixed individual office, A, such that what is expressed by (4) would be true in a counterfactual situation if and only if that office has the appropriate property, namely that of distinguishing R. There is indeed a fixed individual office, A, such that what is expressed by (6) would be true in a counterfactual situation if and only if that office has the appropriate property, namely that of being congruent with B. And the same office is such that (1), (2), (3) would be true in a counterfactual situation if and only if it has the appropriate properties, namely, that of Dukakis' wanting to occupy it, that of Fred's thinking that it is occupied by a Republican, and that of not being vacant, respectively.

All designators, without exception, are rigid.

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