1. Introduction

Empty names pose one of the principal problems for Millian views of meaning and reference. Kripke, first in a paper he describes as a dry run for his Locke Lectures, and then in the lectures themselves, tackles this problem as it arises for fictional names.¹ (He discusses also mythical names (Poseidon) and names for “failed posits” (Vulcan), as well as fictional common nouns (bandersnatch). I will mostly lump the whole lot together.) Kripke considers four types of statement in which empty names can occur without the disastrous results seemingly predicted:

The problem in each case is that you’ve got a claim that looks meaningful, and even true, but should not be either if Mill is right about the meanings of names. A seemingly fatal combination for Millians is empty-name with evaluable-proposition, especially trueproposition. Or, since names even for the Millian might occasionally be used in non-standard ways, the fatal combination is empty name, standard use, and evaluable proposition.

One has to show in each case why the fatal combination does not obtain. How does Kripke propose to do this? His take on the first three cases is fairly clear. But the fourth will need further discussion, since the fatal combination still at least threatens. Kripke holds roughly that

To begin with (1), Holmes wrote a monograph on cigar ash, as it occurs in the story, is only pretended to be true; it is not “really” true.² The question of how it manages, despite the emptiness of the name, to be true simply does not arise.

The question also does not arise with Holmes is the most famous fictional detective ever, although the sentence is true. For this time the name is not empty. It stands for an abstract artifact created by Doyle in the act of pretending to describe a detective of that name.

A fictional character [. . . ] is an abstract entity. It exists in virtue of more concrete activities of telling stories, writing plays, writing novels, and so on, under criteria which I won’t try to state precisely, but which should have their own obvious intuitive character. It is an abstract entity which exists in virtue of more concrete activities the same way that a nation is an abstract entity which exists in virtue of concrete relations between people. (^{Kripke 2013, ch. 3})

About reportorial uses, Kripke says less than one might hope. He thinks it genuinely true that Holmes wrote a monograph on cigar ash, according to the story. How can it be true, in the absence of a proposition attributing the monograph to Holmes for the story to endorse? Kripke’s solution appears to be that the proposition’s nonexistence does not prevent the story from endorsing “it”, if it exists according to the story.

‘The story has it that Sherlock Holmes is a great detective’. What is it that the story has it that? There is supposed to be no such proposition as that Sherlock Holmes is a great detective which the story has it that. I said of this, [. . . ] that one should speak of a kind of proposition which is being asserted to exist and to be true. The story has it that there is a true proposition about Sherlock Holmes, namely that he is a great detective. (^{Kripke 2013, ch. 6})

This seems only to push the question back a step. Why, if the name’s emptiness makes trouble for the alleged proposition that HOLMES IS A GREAT DETECTIVE, does it not make trouble too for the proposition that THERE IS A TRUE PROPOSITION ABOUT HOLMES TO THE EFFECT THAT HE IS A GREAT DETECTIVE. Kripke gestures in reply at a difference in how the names are used. ‘Holmes’ occurs in the first sentence in a regular old extensional context. But not in the second sentence, after ‘about’. “The phrase ‘about Holmes’” has, he says, “a special sort of quasi-intensional use”.

2. About Holmes

What is Kripke’s idea here? We can approach it in stages, starting with the phrase proposition about Holmes. This is an intensional transitive construction, like memory of Vienna, fear of Houdini, or fascination with aliens. Intensional transitives are marked by referential opacity -both in the substitutivity-failure and existenceneutrality senses- and the property, emphasized by Quine, of admitting both specific and non-specific readings. Wanting a sloop can be wanting this sloop, or wanting relief from slooplessness.³

Fear of Houdini is not simply fear of the referent of Houdini; it is not the same as fear of Harry Weiss. Similarly for a proposition to be in the special quasi-intensional sense about Hesperus, it needs to do more than attribute properties to the referent of Hesperus. Kripke wants to distinguish for certain purposes propositions about Hesperus from propositions about Phosphorus, or about Venus. How and when to do this is controversial, but Kripke is alive to the issue and discusses it elsewhere.⁴ A proposition about Hesperus might be expected to incorporate, say, a preference for evening-based tracking across epistemic alternatives over morning-based tracking, where the two come apart.⁵ Let us say, to have a word for this, that names are used evocatively in certain constructions, not (or not only) referentially.

Second, the evocative aspect might sometimes be dominant. There might indeed be claims that do not draw in any serious way on the referential aspect at all, and do not “mind” if that aspect goes missing.⁶ The truth-value of A proposition about Jack the Ripper is about a presumed killer does not depend very much on the identity of the referent, or whether a referent exists. The same goes, perhaps, for A proposition about Holmes, to the effect that he is a great detective, both exists according to the stories and is true according to the stories.

This is more than Kripke himself says about “about Holmes”, and more, I imagine, than he would be comfortable saying. His main comment about quasi-intensional uses is that they are “a little obscure to me, and perhaps to you” (^{Kripke 2013, ch. 6}). A theme he does return to, however, again and again, is that his proposals in Naming and Necessity are directed at non-epistemic contexts, and that the question of names in epistemic contexts remains wide open.

[T]here need be no contradiction in maintaining that names are modally rigid, and satisfy a substitutivity principle for modal contexts, while denying the substitutivity principle for belief contexts. The entire apparatus elaborated in Naming and Necessity of the distinction between epistemic and metaphysical necessity, and of giving a meaning and fixing a reference, was meant to show, among other things, that a Millian substitutivity doctrine for modal contexts can be maintained even if such a doctrine for epistemic contexts is rejected. Naming and Necessity never asserted a substitutivity principle for epistemic contexts. (^{Kripke 2011a, p. 158})

He does not, in other words, want to insist that “codesignative proper names are interchangeable in belief contexts salva veritate” (^{Kripke 2011a, p. 158}). He himself knows of no good way of explaining substitution failures along Millian lines. But this makes him wary rather than skeptical; he is just unsure how to proceed. (“[W]e enter into an area where our normal practices of interpretation and attribution of belief are subjected to the greatest possible strain, perhaps to the point of breakdown” (2011a, p. 158).)

Philosophers are less pessimistic nowadays about explaining (quasi-) intensionality in a way that treats names’ semantic contribution as purely referential (note 5). If his special quasi-intensional use can be squared with Millianism, Kripke ought presumably to welcome this, counting a claim like Holmes is a great detective according to the story true just if the story has it both that there is a proposition about Holmes attributing great-detective-hood to him, and that this proposition is true.

Our concern in this paper is less with reportorial uses of Holmes than existential uses, in statements like Holmes does not exist. Kripke gives the outlines of his proposal in a famously enigmatic passage:

What gives us any right to talk that way [to deny that Holmes exists]?⁷

I wish I knew exactly what to say. But the following is a stab at it. We can sometimes appear to reject a proposition, meaning that there is no true proposition of that form, without committing us to mean that what we say expresses any proposition at all. (^{Kripke 2011b, p. 71})

Where reportorial claims turn on the existence within the story of a certain sort of true proposition about Holmes, nonexistence claims turn on the (non)existence outside the story of another sort of true proposition about Holmes. Call this the NO TRUE PROPOSITION account of nonexistence claims. A statement purportedly denying Holmes’s existence is really, it seems, not about Holmes at all. Its real topic is propositions about Holmes, in the special quasi-intensional sense that does not require Holmes to refer:

NTP: The truth of Holmes does not exist reflects only that there are no true propositions about Holmes to the effect that he does exist.⁸

That Kripke is not entirely thrilled with this suggestion is apparent from the summation that follows. He begins by reviewing the results he has reached about internal, external, and reportorial statements, reminding us for instance that “questions of the existence of fictional characters, and other fictional objects, are empirical questions like any other, and sometimes have affirmative or negative answers” (^{Kripke 2011b, p. 72}). Eventually we are left with “a residue of questions that appear to involve genuinely empty names and real assertions of nonexistence” (2011b). Rather than restating for us his position on nonexistence claims, he remarks simply that “These have just been discussed”.

3. Taking a Stab

Why does Kripke say he is only taking a stab at the nonexistence problem? And why is he not happier with the stab he takes? One can think of several possible reasons. The first he raises in connection with common rather than proper nouns, but the point seems general. “How can the statement that unicorns exist not really express a proposition, given that it is false?” Kripke seems to be assuming here a kind of grounding or dependence principle:

DEP: A sentence’s truth-value depends on what it says, the proposition it expresses.

Evaluation turns essentially on what is said; it cannot get off the ground without that proposition as input. And so there is something worrisome about assigning a truth-value in the absence of such a proposition, indeed in recognition of the proposition’s absence: “[A] certain sentence about bandersnatches seems to have a truth-value, but this does not mean that sentences containing ‘bandersnatch’ express ordinary propositions. And this I regard as a very substantial problem (^{Kripke 2011b, p. 65}).”

Second, one has to explain not only why Holmes does not exist seems true, but also why Holmes exists seems false. (NTP) as written accounts at best for the first. It tells us that ¬ Eh is true, or counts as true, for lack of a true proposition expressed by Eh. But that Holmes exists fails to express a truth hardly suggests it should strike us as false, any more than nonsense sentences strike us as false.⁹

A third worry is overgeneration. There is no true proposition either to the effect that Holmes fails to exist, or attributing to him a certain blood type. But we are not in the same way tempted to deny that he fails to exist, or has that blood type.

Fourth, we want a unitary account -not, one for empty names, another for full. If Pegasus does not exist says that there is no true proposition of a Pegasus-exists sort, then Trump does not exist should say the same of Trump-exists-type propositions. Whereas surely it says of Trump himself that there is no such person.

Fifth, (NTP) comes uncomfortably close to a theory that Kripke explicitly rejects: the metalinguistic theory. This takes the cash-value of Holmes does not exist to be that there is no object of a certain sort, viz. referred to by ‘Holmes.’ Kripke points out that to hypothesize counterfactually that Socrates does not exist is NOT to hypothesize that the name lacks a referent; he could exist with another name, or no name at all. A similar problem would seem to arise for the no-trueproposition theory. To hypothesize counterfactually that Socrates exists, or fails to exist, is not to hypothesize that a certain sort of proposition exists, or fails to. He could exist without the proposition, and the proposition can on some views exist without him.

4. Counting As False

Some of these objections are directed at a view Kripke does not in fact maintain. Kripke nowhere asserts that Holmes exists is false in the strict sense of having a false proposition as its literal content. He allows that we may, in rejecting the sentence, be finding it false in an extended sense that involves the falsity of some other, related, proposition, that is not the literal content: “It is natural, extending our usage, so to speak, to use ‘There are no bandersnatches’ to say ‘There is no true proposition that there are bandersnatches (in the Arctic, or even on the whole earth)’ (^{Kripke 2013, ch. 6}).”

Here it seems the felt falsity of ‘There are bandersnatches’ reflects the genuine falsity, not of the proposition that there are bandersnatches, but the higher-order proposition that among the truths is a proposition of the sort just alluded to.

CAF: S may count for us as false not because “the proposition that S” is false, but due to the falsity of a proposition suitably related to S.

Let’s pursue this idea a little in its own terms, bracketing for the moment Kripke’s specific proposal about what the suitably related proposition might be: a higher-order proposition about the nonexistence of other propositions. For there is at least a kind of case where (CAF) seems enormously plausible.

Suppose that there is no such thing as the proposition expressed by S. S’s expressive ambitions are to that extent not fully realized. Ambitions that are not fully realized might still, however, be partly realized. If a sentence said something false, that would seem to explain its intuitive falsity, and depending on our other views might even suffice to make it false. Rather than S owing its false appearance to its failure to express a truth, as in (NTP), maybe the problem is its success at expressing inter alia a falsehood.

SFP: An unevaluable S that succeeds in saying something false counts as false; its negation counts as true.

This kind of view -the SOME FALSE PROPOSITION view- should in principle be attractive to Kripke. First, it respects supervenience. The sentence’s falsity, or seeming falsity, does derive from a proposition it expresses, just one not describable as “the” proposition that Holmes exists.¹⁰

Second, Kripke suggests himself that S’s potential for falsity, in particular, does not require a full-fledged proposition that S.¹¹ (SFP) agrees; there is no such thing as the proposition that S. It expresses if you like a partly-fledged proposition with the potential only to confer falsity, not truth.

Third, the idea of a “bad” sentence evaluated on the basis of something it says is not unknown to Kripke. He relies in his work on truth on the Strong Kleene valuation scheme. P&Q is false, on the Strong Kleene scheme, if either conjunct is false. This condition may be met even if the other conjunct expresses no proposition. Snow is black & This conjunct is false says in part that snow is black, and that is enough to make it false, even if the Liar conjunct does not succeed in saying anything. Likewise Snow is black & KERPLUNK, where the second conjunct is pure nonsense.

Fourth, the idea of a sentence S reckoned false on the basis of something it says (short of the proposition that S) is also not unknown to him qua theorist of reference. He alludes to it in remarks on Strawson at the 1973 conference where he gave “Vacuous Names” (^{Kripke et al. 1973}). There is no such thing for Strawson as the proposition expressed by a King-of-France sentence. But we do often find such sentences evaluable. The King of France is bald & the Queen of England is bald has a falsehood-expressing conjunct right there on the surface. (SFP) tries in a way to generalize this to “deep” conjuncts, aspects of a sentence’s overall commitments that do not appear on the surface. Strawson suggests a number of examples, for instance, The lodger next door offered me twice that sum!, when there is no lodger next door, and The King of France and I had breakfast this morning. Here is Kripke’s example:

Where someone puts this question in a form like ‘Is the present king of France bald?’ the informant may be puzzled and not say ‘No’. But if you put it to him categorically, say first specifying an armament program to make it relevant and then saying ‘The present king of France will invade us’, the guy is going to say ‘No!’, right?¹²

The ‘No!’ is licensed by (SFP) on the assumption that ‘The present king of France will invade us’ says in part that a French king will invade us, or that we will be invaded.¹³ The sentence gets something wrong, and that is enough.¹⁴

Granted, Kripke is talking in this passage about a description (‘the present King of France’). And our problem is to do, in the first instance, with names. Does Kripke ever suggest that an empty-name claim seems false because it inter alia misdescribes something? He comes close: “Without being sure of whether Sherlock Holmes was a person,. . . we can say ‘none of the people in this room is Sherlock Holmes, for all are born too late, and so on’; or ‘whatever bandersnatches may be, certainly there are none in Dubuque’ (^{Kripke 2011b, pp. 71-72}).”

Holmes is here in this room seems false, because what it says about the inhabitants of this room is false. Likewise Holmes is in NY State, etc. If we keep going in this way, eventually we reach Holmes is in the universe, which seems pretty close to Holmes exists. Alternatively let “US”, or “EVERYTHING”, be you and me and all the other existing things. It is a fact about US, presumably, that Holmes is not of that happy number. Holmes exists seems false, maybe, because it misdescribes US.

5. Topic and What Is Said

This idea of S counting as false because it misdescribes something is tantalizing, but a little obscure. Before we start charging S with describing X incorrectly, one should ask whether S takes descriptive aim at X in the first place. Linguists distinguish a sentence’s “topic” -what it purports to describe- from its “focus” or “comment” -the information it purports to provide about the topic. (Theme vs rheme is another distinction in this neighborhood.) Strawson took the view that a King-of-France sentence is especially likely to strike us as false if we can find another topic for it than the king of France -like ourselves in The KoF will invade us.

Suppose we call a notion semantic if it bears, or can bear, on truth-conditions. Then topic is a semantic notion. I only breathe when I’m meditating can go from true to false, for instance, as the topic shifts from meditating to breathing. It is true that I do nothing but breathe when I’m meditating, false that I avoid breathing except when meditating.

But if topic is semantic in its effects, it is, or can be, pragmatic in its causes. A sentence’s topic depends in many cases on the discourse context, for instance on the question under discussion when it is produced. I only breathe when I’m meditating is about meditating, uttered in response to What do you do when meditating? It says of meditation-time that nothing but breathing is done then. Given in response to When do you breathe? it says of breathing that it is not done at other times.¹⁵ This according to Strawson is why The King of France is bald sounds false in response to Who are some bald notables?¹⁶ Its topic in the aftermath of that question is the bald notables, a group it misdescribes as including a French king.

Two things follow. First, the notion of “what S says” in (SFP) will have to be topic-sensitive, and so discourse-context-sensitive. Why does The King of France is bald count as false when its topic is the bald notables? Because it is only then that the sentence says in part that that group includes a French king. Second, an utterance of S in such and such a context may say in part that X is F, even if S considered in isolation does not mention X (as The King of France is bald does not mention the bald notables).

Take again Holmes exists. It is a fact about EVERYTHING that Holmes is not of that number. Granted, it is not clear as yet what kind of fact this could be, given that there is no such individual as Holmes. The point for now is just that an utterance of Holmes exists may be about EVERYTHING, though the sentence considered in isolation does not mention EVERYTHING. If The King of France is bald can count as false by virtue of what it says about the bald notables, when the extent of that group is under discussion, why should not Holmes exists count as false by virtue of what it says about EVERYTHING, when the extent of that larger group is under discussion?¹⁷

The Millian will as usual complain that (i) whatever it is that Holmes exists says about EVERYTHING will have to derive somehow from the meaning of Holmes, and (ii) there is no more to the meaning of Holmes than that it’s an empty name. This was already answered in section 2, when we observed that the particular name employed is, like the pointing behavior accompanying a demonstrative, a feature of discourse context like any other, and capable in that capacity of influencing what is said.

But let us bracket this reply for now and consider the complaint in its own terms. How much of a problem it presents depends on the datum that we are trying to explain. If the datum is simply that Holmes exists is properly counted false in discussions of what there is, then the name’s emptiness may be enough. What after all does Holmes exists say about EVERYTHING? It says that one of US has a certain feature: that of identity with Holmes (λx x = Holmes). And the fact is that everything lacks that feature, given that the name is empty. To put it less metaphysically and more semantically, whether an object o satisfies (falsifies) λx x = Holmes turns on whether there is a p such that (i) o = p, and (ii) Holmes refers to p.¹⁸ But then o always falsifies λx x = Holmes, simply because there is no p meeting condition (ii).¹⁹

6. Cognitive Content (I): A Priori Conditionals

This explains the falsity of Holmes exists when the topic is EVERYTHING. But, falsity is not the only data-point that needs explaining. To learn that Holmes does not exist gives us one sort of information about EVERYTHING. To learn that Vulcan does not exist tells us something quite different. Holmes exists thus apparently misdescribes EVERYTHING in one way, while Vulcan exists misdescribes it in another. Even if the falsity of Holmes exists can be arranged on the basis of the name’s lack of a referent, at least when the topic is EVERYTHING, to understand the information carried by such a claim -its cognitive content- we will need to look elsewhere.

Suppose with Kripke that Holmes and Vulcan are semantically indistinguishable; their referential contribution is exhausted in each case by the failure to provide an object. How is it that Holmes exists and Vulcan exists appear to make different claims, and their negations appear to provide us with different information? In the case at least of Vulcan, Kripke might say that the information derives from an associated reference-fixing description. To learn that Vulcan doesn’t exist is to learn that no single planet explains the advance of Mercury’s perihelion. To learn that Homer doesn’t (didn’t) exist might be to learn that no single person wrote the Iliad and The Odyssey.

This deals with the “different information” problem insofar as m exists will a priori imply a different falsehood than n exists, if there is a difference in the descriptions by which the names’ references are respectively fixed.

But what are we to make of the second premise? It is not clear even for Kripke how n, if it exists, is an F can be known, never mind a priori, when there is no such proposition in the first place. If we are bothered about n exists when the name is empty, we should be bothered as well about If n exists, then. . .

Kripke might reply that that the conditional is not known, a priori or otherwise, unless the name refers. If that is right, then the proposed model of distinctive information collapses. But a second, related, model might be possible. Call S conditionally a priori if we know it a priori, provided it expresses a proposition.

All we can conclude, on this second model, from the would-be implication’s falsity is that n exists fails to express a truth. Kripke would reject “fails to express a truth” as too metalinguistic to capture what is conveyed and learned, but it is otherwise not far from his actual suggestion about the cash-value of n does not exist, namely, that there is no true proposition about n to the effect that it exists. Unfortunately the second model has many of the same problems noted above for this idea: overgeneration, for instance (there is no true proposition, either, portraying Holmes as nonexistent, but we don’t reject his nonexistence).

7. Stories and Antecedents

The problem was to understand how n, if it exists, is the F could be a priori, if it fails to express a proposition. But, why must it fail to express a proposition? Because the name is empty, you say. But this assumes that n is used referentially. And Kripke thinks that names can also be used quasi-intensionally, e.g. in the phrase proposition about Holmes, and the sentence According to the story, Holmes is a great detective. The second does express a proposition for Kripke, the empty name notwithstanding. It is true, more or less, if readers playing along with the story are to imagine both (i) that there is a proposition about Holmes depicting him as a great detective, and (ii) that this proposition is true.

Story-prefixes are not the same as if-prefixes (antecedents). But the two have much in common. S, according to fiction F is often analysed in conditional terms, e.g., by Lewis as If F were told as known truth, then S would be the case.²⁰ An indicative conditional might be preferable to Lewis’s counterfactual, given that S and Actually, S are not interchangeable in the consequents of counterfactuals, whereas they do seem to be largely interchangeable in According to F,. . . contexts (with actually assigned narrow scope).

Another reason for focussing on indicative if/then is that, where we evaluate According to F,. . . by imagining ourselves informed of F, we evaluate an indicative conditional by imagining ourselves to have learned the antecedent: “If two people are arguing ‘If P, then Q?’ and are both in doubt as to P, they are adding P hypothetically to their stock of knowledge and arguing on that basis about Q.”²¹

This is the Ramsey test for indicative conditionals P→Q. The element of pretense comes out more clearly in Quine. To decide whether P→Q, we “feign belief in the antecedent and see how convincing [we] then find the consequent” (^{Quine 1960, p. 222}).

An interesting feature of the Ramsey test for our purposes is the connection it suggests between reportorial claims and claims of (non)existence. Let us suppose with Kripke that we can ask, within a fictional pretense that assigns Holmes a referent, whether Holmes is a great detective; and that it is our affirmative answer within the fictional pretense that licenses us in saying, outside of it, that according to the stories, Holmes is a great detective. Shouldn’t we then also be able to ask, having feigned acceptance à la Ramsey of a factual hypothesis (Holmes really exists) that assigns Holmes a referent, whether Holmes lived in the 19th century? And whether Vulcan is closer to the Sun than Mercury, having feigned acceptance of Vulcan really exists?

Now Holmes presumably did, from the perspective of one who has added This Holmes fellow turns out to really exist hypothetically to his stock of knowledge, live in the 19th century. This is why we judge unconditionally that he lived in the 19th century if he exists. Likewise we judge unconditionally that Mercury is not the closest planet to the Sun, if Vulcan exists, because we take Vulcan to be closer to the Sun than Mercury on adding Vulcan after all exists hypothetically to our stock of knowledge. From this it seems a short step to singular negative existentials. Judging that Vulcan exists→Q, where Q is understood to be false, is not far from judging that Vulcan does not exist.

8. Cognitive Content (II): A Posteriori Conditionals

Two models were sketched in section 6 of the cognitive content of non-existence claims, both relying on reference-fixers. Kripke would reject these models. It is the rare name, he thinks, that has its reference fixed by a description in the strong sense there supposed.²²

If n exists, it is an F is almost never a priori in his view, not even conditionally so. But then the cognitive content of n does not exist cannot be cashed out in terms of properties that the referent must possess as an a priori matter.

One option at this point would be to switch to properties that the referent as an a priori matter cannot possess. You might think it a priori, for instance, that Holmes, if he exists, is not a black and white dog born in 2005. The cognitive cash-value of Holmes does not exist could be that EVERYTHING has properties which Holmes, if he exists, as an a priori matter lacks. This is not a million miles from what I am going to suggest. But if the data point is simply that n does not exist carries distinctive non-metalinguistic information, the carrying does not have to take the form of a priori implying distinctive non-metalinguistic conclusions.

Suppose I know, somehow or other, that If P, then Q.²³ Call Q in that case an indicative consequence of P (for me, at the time in question). A P and P* that do not express distinct propositions, perhaps because they do not express propositions at all, can still differ cognitively by virtue of their distinct indicative consequences.²⁴The realization that some of P’s indicative consequences fail may lead us to reject P while we continue to hold out hope for P*.²⁵

I appear to know that if Vulcan exists, then there are planets closer to the Sun than Mercury. I do not need to know it a priori, for the conditional to figure in an explanation of what transpires at an informational level, when I learn that Vulcan does not exist. Leverrier might have left the door open to Vulcan being further from the sun than Mercury and acting on it by anti-gravity. In that case my knowledge of the conditional turns in part on empirically grounded doubts about anti-gravity. This does not stop it from investing Vulcan does not exist with distinctive informational content. I appear to know that if Holmes exists, he lived in the 19th century, and hence that he is not one of us, since none of us was alive back then. Crucially I do not know it on account of having fixed the reference of Holmes so that it can only stand for someone alive when Doyle was. I am open in principle to the possibility that Doyle, a lover of the occult, had precognition of the still unborn Holmes at some seance. If that is how Doyle made Holmes’s acquaintance, then a story written before any of us were born might still be about one of us. It is just that I don’t believe that any such thing occurred.²⁶ We have then a third model of the distinctive information carried by n does not exist.

More generally the cognitive cash value of n does not exist lies in its indicative implications. These will typically be different for distinct empty names.²⁷

“But what is your semantics for indicative conditionals?” I am tired of ducking this question, so let me just say the following. One doesn’t need a semantics to know that the truth-values it assigns had better respect the cognitive differences between receiving n exists in testimony for distinct names n. A semantic scheme that allowed the name employed (Vulcan, Holmes) no influence over a truthrelevant parameter -a “triggered information” parameter, say, or one for epistemic counterpart relations- has no hope of assigning the right truth-values. Names have got to make a non-referential contribution in indicative conditionals, or else the Ramsey test is completely confused. Though not a semantic contribution if Mill is right, it is a contribution nevertheless.²⁸

9. Uniformity

The suggestion is that Vulcan does not exist conveys distinctive information by conveying of EVERYTHING -of each o- not that it lacks λx x = Vulcan, but that it possesses λx (x 6= Vulcan, even if Vulcan exists). What makes the information distinctive is that the properties militating against an identification of o with Vulcan, if Vulcan exists, are nothing like the properties militating against an identification with Holmes, if Holmes exists.

What would Kripke think of this proposal? On the plus side, it makes use of basically Kripkean materials. He never doubts for a moment that we can pretend, imagine, or suppose that Holmes exists. He ought to be happy, then, with the idea of specifying the cognitive content of nonexistence-claims in terms of how the supposition of his existence bears on to the characteristics of things that truly do exist. What Holmes does not exist tells us is that the supposition of his existence sits ill with the characteristics of EVERYTHING, in that EVERYTHING has features that reveal it not to be identical to this supposed individual.

That Holmes is not one of US, if he exists, is meant to be without prejudice to whether Holmes does, or did, exist. Kripke is evidently not so optimistic. For right around the passage just quoted, where it is observed that Holmes is not in this room even if he exists, he returns to his earlier worry that there are two claims we might be making in excluding someone from the room -claims that can be brought under the same verbal umbrella only using the “no true proposition” device: “one should, strictly speaking, once again say ‘There is no such true proposition as that Sherlock Holmes is in this room’, where I understand the purported name ‘Sherlock Holmes’ and can therefore refer to this alleged proposition by a ‘that’ clause (^{Kripke 2013, ch. 6}).”

Reflection on conditionals like If Holmes exists, he is anyway not in this room leaves Kripke still thinking that “in some sense the analysis of a singular existence statement [e.g., Holmes exists] will depend on whether that statement is true. And this, of course, seems in and of itself to be absolutely intolerable: the analysis of a statement should not depend on its truth-value (2013, ch. 6).”

Does this kind of worry apply to our proposal as well? Not yet, it doesn’t. Our proposal concerns, not the analysis of (non)existenceclaims, but their cognitive content, what we convey by them and learn from them. To the extent that we have an analysis of n does not exist, it is the one given long ago by Stalnaker: EVERYTHING has λx ¬(x = n). It is the same analysis whether we are talking about Neptune or Vulcan.

But one might think that existence-claims should have the same cognitive content whether true or false, not only the same analysis either way. That content for us is given by conditionals like Holmes is not Yablo, even if Holmes exists. Does this hold for the same reasons whether Holmes exists or not? It seems not. If Holmes exists, then the conditional holds because two existing things (Holmes and Yablo) are distinct. Whereas if Holmes does not exist, it holds because Yablo is a poor candidate for the Holmes role, quite apart from whether the role is occupied.

But does the conditional not also hold, on the hypothesis that Holmes exists, because Yablo is a poor candidate for the Holmes role, quite apart from whether the role is occupied? Its truth is overdetermined, in other words. One reason Holmes is not Yablo, if Holmes exists holds is that its antecedent and consequent are both true; Holmes does exist and he and Yablo are just two different items.²⁹Another reason for the truth of Holmes is not Yablo if Holmes exists is that Yablo has properties that count, regardless of whether Holmes exists, against such an identification. We may grant that Holmes is not Yablo, even if Holmes exists does not hold for exactly the same reasons in either case, while still insisting that it is true in both cases for a shared reason, namely that Yablo has properties (e.g. that Doyle never wrote about him) that unsuit him for the role.

So much for conditionals like Holmes is not Yablo, even if he exists. The proposal was that Holmes does not exist -if the topic is EVERYTHING (for short, US)- conveys as a cognitive matter something like a conjunction of, or generalization over, these nonidentity conditionals, with a conjunct, or instance, for every one of US. The generalization holds whether Holmes exists or not, and for similar reasons whether Holmes exists or not. This is our reply to the uniformity worry.

10. Turning Out to Exist

Kripke proposes a NO TRUE PROPOSITION account of singular existentials. But he gestures as well in the direction of a SOME FALSE PROPOSITION account, which is what we have been trying to develop here. Some features of the account should be noted in closing, and some problems and open questions pointed out.

Our account does not purport to identify a fixed, context-insensitive piece of information that one is always conveying in saying that Holmes does not exist. One is saying in effect that every o is, in a weak, a posteriori sense, disqualified; o is not Holmes even if he exists. But the disqualifying properties are not explicitly stated and may differ from speaker to speaker, according to the indicative conditionals they accept about Holmes’s properties should he exist.

What if Holmes really does exist? Then not everything is disqualified, for he himself is not disqualified. One can imagine two ways this might play out. Perhaps there are more entities than we thought -Holmes, if he exists, is a further entity- or perhaps one of US was Holmes all along.

The second scenario brings out a possible problem with the account. Why should there not be individuals who, although failed candidates as we now see it, are “good enough” on the hypothesis that Holmes exists? He has to be squeezed in somewhere, and a good enough existing candidate may provide a more plausible destination than unoccupied-looking space off to the side. The worry is that although Holmes does not exist, there is an existing o (Prince Albert, say) such that Holmes is o if he does exist.

To get the worry into perspective, we need to look more deeply at the circumstances under which Holmes turns out to really exist. One should not assume these are circumstances in which the stories turn out to be true! They are circumstances rather in which Doyle turns out to have been writing, inaccurately in all likelihood, about someone real (perhaps he didn’t realize it himself). I am just repeating here what Kripke says about unicorns: “I of course acknowledge that it might turn out that there really are unicorns, but one shouldn’t regard this question as simply a question about whether there is an animal matching the description in the myth (2013, ch. 2).”

Similarly bandersnatches exist if Carroll was writing, unbeknownst to his readers, about genuine animals, quite possibly misdescribed in the poem. Kripke actually mentions this possibility:

I once read a hypothetical story about Lewis Carroll in which it turned out that that was the case. Contrary to what we thought, he was writing a straightforward report about bandersnatches. (Actually I didn’t read a story; it was a comic strip.) At any rate this could turn out to have been the case. Suppose we had asked him and he said he was quite surprised that people thought he was talking about imaginary animals here; why, he himself used to be warned to avoid them when he walked through the park as a child, and that is what they were always called in his little region, though apparently the term has passed out of usage. So one could discover that, contrary to what we thought, bandersnatches are real. (2013, ch. 2)

Our worry can now be put like this. Suppose that Carroll came in his childhood across some Tibetan Mastiffs (a fearsome sort of dog used to hunt bears), which he was warned to avoid. These served as inspiration for the poem, but not to the extent that bandersnatches just are fancifully redescribed Tibetan Mastiffs. It might still seem that Tibetan Mastiffs are such excellent candidates for the role that bandersnatches if they exist are Tibetan Mastiffs.

This clearly cannot be the kind of conditional featuring in our theory, if the theory is to predict that bandersnatches do not exist. Therefore more needs to be said about how the intended conditional is meant to work. I myself am attracted to partition- or subjectmatter-sensitive accounts along the lines of ^{Kaufmann 2004}, ^{Khoo 2016}, ^{Yablo 2016}, and ^{Hoek 2018}. The subject matter in this case -US AS WE ARE, call it- would be a partition m that fixes enough of our properties to prevent our turning out to be bandersnatches if the latter exist. Tibetan Mastiffs in particular would have had to be different m-wise to stand a chance of turning out to be bandersnatches.

But then if we hold fixed the world’s m-condition in evaluating Tibetan Mastiffs are bandersnatches, if bandersnatches exist, it will be false in our world. Bandersnatches, if any, will have to be a further thing, over and above the things that actually exist. Which makes it false of US AS WE ARE that one of us is a bandersnatch.

Kripke gets into the neighborhood of these issues when he asks, what exactly is it that we are excluding when we say that bandersnatches do not exist? One thing we are presumably excluding is that bandersnatches turn out to be some of us -Tibetan Mastiffs, or what have you- along the lines just suggested. He hints that Bandersnatches don’t exist may be used to “express the fact that such a discovery hasn’t occurred” (2013, ch. 2).

That goes too far, surely. Bandersnatches’ nonexistence is not a matter of anyone’s discoveries, but how things are in the world. A more charitable reading of Kripke’s idea is this. What we exclude with Bandersnatches do not exist is that things exist -Tibetan Mastiffs, or whatever- whose properties leave the door open to such a discovery. The proposed account of nonexistence claims has them saying in essence that that door is closed. Everything has properties given which, or holding which fixed, it turns out not to be a bandersnatch, even if bandersnatches exist.³⁰