2.1. Against static semantics

^{Clapp (2008)} argues that only dynamic semantics can explain how utterances of negative existential constructions manage to be true and informative. This is so because, if one accepts static semantics, “there are only two general strategies of response” (^{Clapp, 2008: 1423}). These are labeled “Meinong’s strategy” and “Russell’s strategy”. Unfortunately for static semantics, both such strategies fail. Before considering Clapp’s objections against these strategies, it is important to note that there is a third general strategy of response that friends of static semantics may follow. These are the so-called “metalinguistic strategies”, suggested by ^{Stalnaker (1978)} and proposed by ^{Walton (2000)}, with different versions developed by ^{Sainsbury (2005)} and ^{Everett (2003)}.² I will consider these strategies in section 5.

Meinong’s strategy claims utterances of negative existential constructions are to be interpreted literally, as predicating the property of nonexistence or inexistence to the referent of the noun phrase ‘X’ (e.g., ‘Hamlet’). On this view, such uses express something true if the referent is in fact nonexistent or inexistent, and false if it is an existent entity. There are multiple reasons one might have for rejecting this strategy, its lack of parsimony being a prominent one. ^{Clapp (2008)} offers a different “fundamental” objection. For him, utterances of negative existential constructions are simply “not about, and make no reference to esoteric entities” (^{Clapp, 2008: 1424}).

Russell’s strategy claims that negative existential constructions are quantificational in nature. On this view, utterances of negative existential constructions deny that there is a unique thing satisfying the descriptions associated to the noun phrase ‘X’. This quantificational interpretation is meant to avoid the esoteric entities problem of Meinong’s strategy, since there is only quantification and no reference (denotation) on this view. ^{Clapp (2008)} identifies another “fundamental problem”, this time having to do with the presuppositional commitments of Russell’s strategy. The problem is, according to ^{Clapp (2008)}, “that definite descriptions, like all NPs, carry presuppositions.” These are either familiarity or referential presuppositions (or both). If this is so, then Russell’s strategy predicts that all utterances of negative existential constructions that, intuitively, convey something true in fact suffer from presupposition failure. This is so because, by definition, any context where such an utterance may be true is a context that does not satisfy either of these presuppositions.

Briefly put, Russell’s strategy fails not because of its reference to esoteric entities, but because even though they may be quantificational expressions, definite descriptions carry presuppositions that cannot be satisfied by the context where a negative existential is uttered. If so, then all uses of negative existential expressions are bound to be infelicitous (at best) or simply lack a truth-value (if the unsatisfied presupposition turns out to be semantic in nature).

In what follows I will assume that ^{Clapp (2008)} is correct about the above-mentioned static strategies. Let me now present ^{Clapp’s (2008)} own dynamic strategy.

4.1. I do not exist

Consider the following scenario. Harry is a rather peculiar person. He enjoys working as a Santa Claus impersonator for the holidays at different public venues. Every now and then a remarkably obnoxious child appears, causing Harry to reconsider his goals. When such a thing happens, Harry feels the need to be honest and tell the truth. One day he is dealing with a rather stubborn and smart girl. After Harry has told her explicitly that Santa is nothing more than fiction, the girl replies with (4).

Harry feels cornered, so he goes straight to the point by uttering (5).

In so doing, Harry has managed to convey p by simply uttering (6).

p: Santa does not exist.

The reading of (6), as conveying a true informative content similar to p, is clear and intuitive within the context of Harry’s utterance. Harry’s use of ‘I’ must involve some semantic shift; it cannot refer to the speaker of the utterance (i.e., Harry) for it would otherwise be false.³ Accounts of how this shift might take place abound (see above). In this case in particular it seems clear that the speaker manages to refer to the contextually salient fictional character Santa.

Can the dynamic semantics account offered by ^{Clapp (2008)} explain how Harry’s utterance of (6) manages to be both true and informative? For this to be the case, it must be that the acceptance of Harry’s utterance reduces the common ground (i.e., it is informative) and that the resulting common ground accurately represents Harry’s belief state (i.e., it is true). As I will show, Clapp’s proposal can only meet the first goal, as it does show how the common ground is reduced, but the resulting common ground fails to accurately represent Harry’s belief state.

4.2. First Problem: The Indexical Negative Existential

Recall the two-step account of utterances of negative existential constructions. Prior to Harry’s assertion of (6), there is a shared set of presuppositions. Harry wants to opt out of this conversation by asserting ‘I do not exist’. To do so, first step, he makes use of ‘I’ referentially, thus adding the presupposition that ‘I’ has a referent and the presupposition that the speaker exists. Now, if Harry is to follow ^{Clapp’s (2008)} two-step correction he should make sure that the presupposition that Santa exists is part of the common ground. So far it only seems to be part of his’ audience’s presuppositions. How can Harry do this?

Here is a rather intuitive, just-so, explanation of how Harry could do so. Harry is aware that his audience does presuppose that Santa exists. So he cooperates with that presupposition and (somehow) signals that he shares such presupposition precisely by means of using ‘I’ referentially while making it clear that he intends to refer to Santa with his use. So let us say that, first step, by making a clear and obvious use of ‘I’ to refer to Santa, Harry manages to accommodate the presupposition that Santa exists. Now the common ground does include a presupposition that Harry wants to correct away.

But let us not be hasty with this dynamic semantics. We should pause and ask how it is that Harry manages to presuppose that Santa exists by using ‘I’ to refer to Santa if not by also presupposing that Santa is the speaker of the assertion? In other words, unless Harry also agrees to play along and presuppose that he, Harry himself, is Santa, it seems impossible for him to merely (i.e. directly) presuppose that Santa exists. Harry’s audience, the obnoxious child, shares this latter presupposition too. She pretty clearly insists that Harry is Santa, and she makes this clear when she utters (4) prior to Harry’s assertion of (5).

Now we have a complete picture of the common ground prior to Harry’s assertion of the negative existential construction ‘I do not exist’. The common ground does include the presupposition that Santa exists, the very presupposition that Harry aims at with his correcting speech act by uttering the negative existential construction. But it does not only include this presupposition. It also includes some other presuppositions, like the presupposition that Harry is the speaker, the presupposition that Harry is Santa, and thus the presupposition that Santa is the speaker. It is against this set of shared presuppositions (i) to (iv) that the assertion of the negative existential construction is meant to do its work by reducing it.

Set of Presuppositions of (5):

The problem for dynamic semantics should be obvious by now. Harry wants to correct the common ground, and so he utters ‘I do not exist’. If his assertion is accepted, second step, the resulting common ground will exclude presupposition (i). This is something that Harry wants. But there will be more reduction, as many other presuppositions are tied to (i). Presupposition (i) gets excluded from the common ground once the assertion of (5) is accepted only because the common ground already includes both presupposition (i) and (ii). Yet (ii) is already part of the common ground in virtue of the fact that, again prior to the assertion of (5), presuppositions (iii) and (iv) are also included. It is this latter presupposition (iv) that is both essential and problematic for dynamic semantics. It is essential because without it Harry simply cannot refer to Santa by using the indexical expression ‘I’ and, hence, cannot achieve his goal of eliminating (i) from the common ground by uttering ‘I do not exist’. It is problematic, and seriously so, because it ties presuppositions (i) and (iii) together. If presupposition (iv) (i.e., that Harry is Santa) is part of the common ground, then whatever happens to Santa must happen to Harry as long as (iv) is still in the common ground.

More specifically, if the common ground excludes presupposition (i) (i.e., that Santa exists) then it must also exclude presupposition (iii) (i.e., that Harry exists), because (iv) (i.e., that Harry is Santa) is part of the common ground. This is clearly a bad result. The goal of Harry’s assertion is to modify the common ground so that it rejects the presupposition that Santa exists, not the presupposition that the speaker exists, much less the presupposition that Harry exists. The resulting common ground does not offer an accurate representation of Harry’s belief state. So, according to dynamic semantics, Harry has not managed to assert something true, even though it may be informative-after all, the common ground has been reduced.

Notice that this bad result would be avoided if the common ground was to include presuppositions (i) and (iii) only-i.e., that Santa exists and that Harry exists. If such were the case, the speaker could easily get rid of one of them without the other; e.g., she could get rid of the presupposition that Santa exists while keeping the presupposition that Harry exists. Unfortunately, as I said before, such a common ground is simply not one where the speaker can reject (i) by uttering ‘I do not exist’, for that to happen we need to presuppose that Santa is the speaker -i.e., Harry in the present example.⁴

4.3. Second Problem: The Demonstrative Negative Existential

To make sure that this is not an exceptional case against dynamic semantics, let me further elaborate the example so that it includes demonstrative expressions. The result, as will be clear, is the same. Suppose that, as part of the same conversation with Harry, the obnoxious child insists in defending her pro Santa views. So right after Harry’s assertion of (5), the child replies by uttering (7) while pointing at Carl, who happens to be dressed as an elf and enjoys impersonating Alabaster Snowball.

In an effort to stay calm while defending his point, Harry utters (8) while pointing at Carl:

Intuitively, Harry has managed to convey q, a true and informative content, while uttering (8).

q: Alabaster Snowball does not exist.

The dynamic semantics account of Harry’s assertion of (8) should be familiar by now. Prior to Harry’s use of the demonstrative ‘He’, the common ground does not include the presupposition that Alabaster Snowball exists. The obnoxious child does believe that such is the case, but Harry does not agree. Harry wants to fix this situation. To do so he first uses ‘He’ to refer to Carl in an attempt to refer to Alabaster Snowball. He succeeds in doing so and in so doing he accommodates the presuppositions that Alabaster Snowball exists, that Carl is Alabaster Snowball, andthat Carl is the demonstrated individual. By adding such presuppositions Harry has managed to prepare the common ground for his corrective goal. He can now go on to assert the negative existential construction in (8), the acceptance of which will get rid of the presupposition that Alabaster Snowball exists, as Harry hopes, but also of the presupposition that Carl exists, given that it is presupposed that Carl is Alabaster. The resulting common ground is not, of course, the one that Harry is aiming at with his assertion of (8), for it dramatically fails to represent his belief set.

5.1. Metalinguistic Pragmatic Reinterpretation

After presenting his two-dimensional pragmatic account of assertion, ^{Stalnaker (1978)} offers an account of negative existential assertions as one more case of a successful application of his two-dimensional pragmatic (or metasemantic) model:

[F]or true negative existential statements, it seems that proper names must play a different role in the determination of the proposition expressed from the role they play in ordinary predicative statements.

Perhaps a negative existential statement says, simply, that there is no individual standing in the right causal relation to the speaker’s use of the name (^{Stalnaker, 1978: 92-93}).

According to ^{Stalnaker (1978)} the metalinguistic interpretation of (1) into something like (1*) is the product of a pragmatic mechanism of reinterpretation (i.e., Stalnaker’s diagonalization procedure). Once we run the traditional static distribution of semantic values to (1) we may realize that the resulting propositions are all pragmatically unacceptable, either because they are trivial (i.e., necessarily false) or ambiguous (i.e., they change from context to context). Thus, reinterpretation is forced upon us. There is one proposition available which is both informative and not-ambiguous, this is the proposition according to which “there is no individual standing in the right causal relation to the speaker’s use of the name”, in this case `Hamlet’.

It is not difficult to see how this view can be extended to account for the answering machine examples in section 4. Consider the indexical negative existential in (5) and its metalinguistic interpretation in (5*).

Take the assertion `I do not exist’ in (5), according to static semantics, the proposition it expresses is necessarily false. All uses of ‘I’ refer to the speaker, and the speaker must exist in every context of use for there to be such use. Thus, the proposition determined by the static semanticsof ‘I do not exist’ is pragmatically unacceptable. An interpretation is forced upon the audience. Now, we will fail if we reinterpret the speaker’s use of ‘I’ as referring to Santa, for such interpretation would take the speaker to presuppose that Santa exists and, hence, the resulting proposition would still be necessarily false. Given that the context includes the presupposition that the speaker is Santa, there is an alternative proposition available in the context. This is the proposition according to which there is no individual standing in the referential relation with the name ‘Santa’. This proposition is informative, and it gets the truth-conditions right for the speaker’s use of (5).

5.2. Existence as Metaphor for Referential Success

^{Walton (2000)} proposes a different account. On this view, it is the predicate ‘exists’ that is special in that it does not predicate a property of an object, but success or a lack of it to certain attempts to refer:

To say that Neptune or Falstaff exists (…) is to say that attempts to refer of a certain kind are successful. To say that Neptune or Falstaff does not exist is to say that such referring attempts do not succeed. (…) The impression that Falstaff and Neptune are what we speak of is explained by the fact that we are pretending that this is so-or rather, we pretend to refer successfully by means of the names and to attribute properties to the referents.

In pretending to refer by means of the names, the speaker displays, shows, demonstrates, the kind of attempted reference she is talking about. In attaching the predicate “exists” or “does not exist”, she declares the kind of attempted reference indicated by the use of the name to be successful or unsuccessful; she avows or disavows attempts to refer of that kind (^{Walton, 2000: 82}).

So, according to ^{Walton (2000)}, (1) expresses the speaker’s disavowal of referential uses of ‘Hamlet’. Thus, to say that ‘Hamlet does not exist’ is to say something like d:

d: Hamlet: that was not a successful attempt.

This metalinguistic account certainly has none of the problems identified by ^{Clapp (2008)} against static semantic accounts. It makes no reference to esoteric entities, and it has no presupposition-failure problems, as evidenced in Russell’s strategy. On Walton’s account (2008) the speaker’s use of the name in an existential construction is metalinguistic. It may carry existential and referential presuppositions associated to the referential attempts, but it is presupposed that a name exists and that a given expression (e.g., ‘Hamlet’) refers to it. Both presuppositions are satisfied by the context. The predicate ‘exists’, in turn, expresses either an avowal or a disavowal of such referential attempts. There is no gap in semantic values assigned to `Hamlet does not exist’. It simply expresses the proposition d.

This account offers a straightforward explanation of answering machine cases of negative existential constructions. They directly disavow attempts to refer of the kind of the pretense. When Harry utters (5) I do not exist, he pretends to be Santa and disavows any attempts to refer of the kind Santa. When Harry utters (8) He does not exist either, he pretends that Carl is Alabaster and disavows any attempts to refer of the kind Alabaster Snowball.

5.3 Further Alternatives

Aside from ^{Stalnaker’s (1978)} and ^{Walton’s (2000)} explicitly metalinguistic accounts, recent views on the semantics of empty names may prove to be useful for a static semantic response to the problem of negative existentials. Take, for example, ^{Sainsbury’s (2005}) theory of reference without referents (RWR).

According to RWR all proper names, whether empty or not, have two semantic values (see ^{Sainsbury, 2005: 45-46}). On the one hand, they may (or may not, if empty) have a referent. On the other hand, they all have (and cannot fail to have) what ^{Sainsbury (2005)} calls a “referential condition”. This referential condition states that the given name `N’ refers to its referent o if and only if o is identical to N. On this view, all proper names (whether they have or lack a referent) have at least one level of semantic content, namely, the second level of referential condition. It is in this sense that there can be reference-i.e., meaningful referential use of a name-without referents-i.e., without esoteric entities being referred to by fictional or otherwise empty names.

Even though it is not explicitly presented as such, ^{Sainsbury’s (2005)} account can be viewed as a metalinguistic one. The “referential condition” level of semantic content to which the theory appeals is, explicitly, a metalinguistic one as it states about the relevant name ‘N’ that it has such and such referential condition. It is this semantic level that accounts for the semantic content and, thus, truth-evaluability of assertions involving names without referents on ^{Sainsbury’s (2005)} view, including his account of successful uses of empty names in negative existential constructions such as (1).

Aside from the two levels of referential semantic content for names, ^{Sainsbury (2005)} proposes a double criterion of truth-evaluation for statements involving proper names. According to this criterion, statements involving empty names are false if and only if (i) they fail to have a referent; or (ii) their referent fails to have the property referred to by the relevant predicate. Since all empty names fail to have a referent, all simple (i.e., non-negated) assertions involving empty names are false. Such is the case of positive existential constructions involving empty names such as `Hamlet exists’. The statement itself is meaningful in virtue of the referential condition associated to ‘Hamlet’, yet it is false in virtue of the fact that ‘Hamlet’ lacks a referent.

It should be clear how ^{Sainsbury’s (2005)} proposal explains the truth of a negative existential construction such as (1)

An assertion of (1) is meaningful because it states a metalinguistic referential condition concerning the name ‘Hamlet’, and it is true in virtue of the fact that it is the negation of a false statement, namely the statement that Hamlet exists. Briefly put, an assertion of (1) asserts that `Hamlet’ has such and such referential conditions and that such conditions fail to be met.

This account can also be extended to explain the problematic answering machine cases of negative existential assertions. When Harry utters (5) he pretends and so he is presupposed to be Santa:

(5) H: The truth is, I do not exist. Your parents have consistently lied to you. What you see is just a costume.

On Sainsbury’s view of reference, this use of ‘I’ will be taken to have the same two levels of semantic content that proper names have. Presumably, this use of ‘I’ will state that, for something to be the referent of such use of ‘I’, that thing must be identical to Santa. If so, then an assertion of (5) simply states that such conditions fail to obtain, asserting something like (5**)

(5**) H: There is no individual that meets the referential conditions of my use of ‘I’, namely, no individual that is identical to Santa. Your parents have consistently lied to you. What you see is just a costume.