A contextualist treatment of negative existentials

1 Introduction

In this paper, I want to vindicate the contextualist treatment that is typically applied by artefactualists on fictional entities (ficta) both to general and to singular negative existentials. According to this treatment, the truth value of a negative existential, whether general or singular, changes according to whether the existential quantifier or the first-order existence predicate is contextually used as respectively ranging over and applying to a restricted or an unrestricted domain of beings. In (2003), Walton has criticized this treatment with respect to singular negative existentials in particular. First of all, however, as Predelli (2002) has shown, this treatment can be applied to singular predications in general, independently of the existential case. Moreover, not only does applying it to singular negative existentials explain why we may contextually use the quantifier restrictedly in general negative existentials, but also it accounts for why comparative negative existentials, both singular and general, may have different truth values as well depending on the comparison group they mobilize.

The architecture of this paper is the following. In Section 2, I articulate the contextualist treatment of negative existentials. In Section 3, I present Walton’s criticism to it. In Section 4, I put forward the replies to Walton that a contextualist may provide. Section 5 concludes.

2 The contextualist treatment of negative existentials

There are two main kinds of negative existentials, GNE, i.e., general negative existentials – in particular, those of the form “There is (exists) no x such that Fs”, where “F” may more properly be seen as abbreviating the predicate “is identical with O”, in which “O” is a genuine singular term, briefly: “There is no O” – and SNE, i.e., singular negative existentials – those of the form “O exists”, where “O” is again a genuine singular term.^[1] Many people, typically artefactualists with respect to fictional entities (ficta) – i.e., people who claim that ficta are a kind of abstract entities, mind-dependent created artefacts – say that there is no single answer as regards the question of the truthvalue of any such sentence. For, they add, the answer depends on the context. Starting from the case of GNE, the idea indeed is that if the existential quantifier contextually occurs restrictedly, i.e., as ranging over a subdomain of spatiotemporally existing beings, a sentence like:

is true. For, insofar as it is a non-spatiotemporal being, the fictum Santa Claus does not figure in that subdomain. Yet if the quantifier contextually occurs nonrestrictedly, i.e., as ranging over the overall domain containing any being whatsoever, then (1) is false. For Santa does figure in that domain. In other terms, (1) works just as:

(2) is true when the quantifier contextually ranges restrictedly just over the things that are in my fridge (supposing that my fridge is beerless, of course), yet false otherwise.^[2] Likewise, in the case of SNE, a sentence like:

is true iff the first-order existence predicate is contextually interpreted restrictedly, as meaning a nonuniversal first-order property of existence, spatiotemporal existence, and thereby as applying just to the subdomain of the spatiotemporally existing beings. Yet it is false otherwise; namely, iff the first-order existence predicate is contextually interpreted nonrestrictedly, as meaning a universal first-order property of existence, which holds of all the members of the overall domain of beings (in the best interpretation, the property of being identical with something), and thereby applying to all beings that domain.^[3] As Amie Thomasson has even recently summed up: “handling nonexistence claims involving fictional names is tricky: in some cases […], they are clearly true; in other cases […], they may be false” (2010: 112–3).^[4]

3 Walton’s criticism to the contextualist treatment

Kendall Walton, however, has objected that this treatment does not suitably account for SNE in particular. For if one utters:

where “Charlie” is the name of a cheetah, this utterance can hardly be used in order to say that Charlie does not figure in Taronga Zoo, while being somewhere else. If it is true, it is then true in any context. Mutatis mutandis, the same holds of (3).

Curiously enough, Walton immediately adds that the above utterance of (4) “would more likely serve as an announcement of Charlie’s death” (2003: 241). Let me skip the issue that, in its involving temporal matters, Walton’s proposal could be at most taken as a plausible paraphrase not of (4), but of:

For, by elaborating a bit a suggestion of Gareth Evans’ (1982: 372), one may more plausibly interpret what Walton has in mind by taking (4) as instead announcing something along the following lines:

given that Charlie’s alleged parents, or gametes for that matter, never met (in such and such circumstances). Clearly enough, however, (3) could not be plausibly paraphrased either along the lines of (4′) or along the lines of (4′′). Since Santa metaphysically is a non-spatiotemporal being, it cannot be true either that it has passed away, or that it had no spatiotemporal career, for no concrete generation put it into being.^[5] Thus, Walton must engage himself at least in holding that different SNE must have altogether different semantic interpretations: one when they involve spatiotemporal beings, another one when they involve (at least apparently) non-spatiotemporal beings such as ficta.^[6]

4 The contextualist reply

In this respect, let me immediately remark that if the above is the case, then the contextualist treatment of SNE is semantically more economical than Walton’s. For it does not claim that the first-order existence predicate has different meanings tout court, as Walton seems to suggest. Instead, it claims that the predicate has the same meaning when it is interpreted in the same restricted context, i.e., as meaning the first-order nonuniversal property of spatiotemporal existence. This makes (3) true and (4) false. Further, it adds that the predicate changes meaning only once it is interpreted in the same nonrestricted context, i.e., as meaning existence as a universal property, the property of being identical with something. This makes both (3) and (4) false.

But maybe semantic richness is a virtue rather than a vice in this situation, Walton might reply. Yet, a defender of the contextualist treatment of SNE may first of all retort that it is neither arbitrary nor ad hoc, as Walton seems to see it. For, as Predelli (2002) has shown, it applies to SNE just as it applies to any sentence involving any first-order predicate whatsoever. In Predelli’s (2002: 74) (adapted) example:

is true in a context where by “student” one means “student of the (local) philosophy department”. For, even though Smith is a student of the (local) art research program, is not a member of the set of the students of the (local) philosophy department. Yet it is false in a context where by “student” one means “student of the (local) philosophy department or student of the (local) art research program”. For Smith, by being a student of that program, is a member of the set of students belonging either to that department or to that program.

Moreover, it cannot be the case that the contextualist treatment may work for GNE but not for SNE, as Walton apparently suggests: “[a]lthough domain restrictions on quantified ‘there is no’ and ‘there are no’ constructions are perfectly common and ordinary, predicative statements concerning existence do not admit of correspondingly restricted readings” (2003: 240–1). For the quantifier restriction is justified precisely by narrowing down its relevant domain to beings that have the first-order nonuniversal property of existence meant by the corresponding contextual use of the first-order existence predicate. For example, (1) is true when the quantifier ranges over beings that spatiotemporally exist, where, as I said before, spatiotemporal existence is the first-order nonuniversal property of existence that is meant by the corresponding contextual use of the first-order existence predicate. This justification is quite standard. For it concerns any contextual restriction of the quantifier. Indeed, (2) is true when the quantifier ranges over things that are located in the fridge, where being located in the fridge is the first-order nonuniversal property that is meant by the corresponding contextual use of the first-order predicate “is located”.

Finally, the contextualist treatment can nicely account for a kind of sentences that are a species both of GNE and SNE, i.e., comparative negative existentials (CNE). In CNE of both kinds, different kinds of items are compared with respect to their existential status. Now, if we keep fixed one the terms of the comparison, then the truthvalue of a CNE depends on the different comparison group the sentence respectively mobilizes. For example, both:

and:

are indisputably true. Yet both:

and:

appear to be false. With respect to (6)–(7), in (8)–(9) one term of the comparison – Santa – remains fixed while the comparison group changes. The ‘Max’-case originally comes from Fred Kroon (2003:156). In it, one supposes that a student of Kroon himself, by mistakenly assuming that “Max” is a proper name in overhearing Kroon’s saying to his students “When giving a job talk, go to the max!” replies by saying “Who is Max and why shout at him?”.^[7] The ‘Snazzo’-case originally comes from Kripke (2013: 81), where “Snazzo” is just a name made-up by Kripke himself that not only does not even allegedly refer to a fictional entity, but it also fails to refer to any entity whatsoever of any other kind. In order to explain why both (8)–(9) are false, it would be important remark to reply that, unlike Santa, Max and Snazzo have no being whatsoever. Indeed, people would reject the opposite comparisons, which are false as well:

Now, the contextualist treatment can nicely deal with such cases.^[8] For it may say, on the one hand, that both (6) and (7) are true, since both the quantifier and the first-order existence predicate are contextually restricted to a subdomain of spatiotemporal existing beings that fall under the first-order nonuniversal property of spatiotemporal existence, and that domain includes both Obama and Trump but not Santa. On the other hand, the contextualist may go on saying, (8)–(9) are both false, just as (10)–(11) for that matter, since both the quantifier and the first-order existence predicate are used contextually nonrestrictedly as respectively ranging over and applying to the overall domain of beings that fall under the first-order universal property of being identical with something. With respect to those comparisons, that domain merely includes Santa.^[9]

Interestingly enough, the contextualist treatment has further applications. For there are, possibly unexpected, interesting commonalities between beings of different kinds that all are however all identical with something. Now, such commonalities explain the truth-values that more complicated CNE possess. First of all, even if (6) and (7) are true, insofar as Santa is not a spatiotemporal existing being like Obama and Trump, the following couple of sentences:

are as false as (8)–(9). For in (12) and (13) both the quantifier and the first-order predicate respectively are contextually used nonrestrictedly, i.e., as respectively ranging over and applying to the overall domain of beings all sharing the universal property of existence, being identical with something (exist, in the first-order universal sense). Yet, it is false that unlike Max and Snazzo, both Obama and Santa do not figure in the overall domain of beings. For it is the other way around. Again, people would reject the opposite comparisons, which are false as well:

Moreover, even beings different from ficta can be terms of CNE. Consider possibilia, i.e., entities that do not actually spatiotemporally exist yet they might have so existed. Elip, the merely possible son of Elisabeth I of England and Philip II of Spain, is a case in point. Now, from a contextualist point of view, even possibilia allow one to see commonalities between entities of different kind, such as non-spatiotemporal and spatiotemporal existing beings. For on the one hand, the following couple of sentences are true:

insofar as both the quantifier and the first-order predicate of existence are contextually taken, respectively, as restrictedly ranging over and applying to a subdomain of beings sharing a wider yet again nonuniversal property of existence, i.e., either spatiotemporal or nonspatiotemporal existence, what Meinong (1960) labeled Sein. Indeed, unlike Obama and Santa, Elip does not belong to that subdomain. Yet again, the following couple of sentences are false:

insofar as both the quantifier and the first-order predicate of existence are contextually taken, respectively, as nonrestrictedly ranging over and applying to the overall domain of beings that all share the universal property of existence. Indeed, it is false that unlike Max and Snazzo, Elip does not figure in the overall domain of beings. For it is the other way around. People would reject the opposite comparisons, which are false as well:

Finally, not even this contextualist treatment of CNE is ad hoc. For a similar account may be put forward in order to explain the truth-value shift of other comparative sentences. To see just an example, consider a couple of sentences inspired to Charles Travis’ (1997) Pia’s example. Suppose that Pia paints in green some of the russet leaves of her plants while also painting in another color, say blue, some of her russet pears. In this ‘artefactual’ context, the comparative sentence:

is true. For in that context, the predicate “green” means roughly the same as “artefactually green”. And only Pia’s leaves, not her pears, are artefactually green. Yet the different comparative sentence, which confronts Pia’s leaves with some market’s russet pears:

sounds false in a ‘biological’ context, where the predicate “green” means roughly the same as “biologically green”. For both the market’s pears and Pia’s leaves are biologically russet.

5 Conclusion

In this paper, I have tried to show that, pace Walton, the contextualist treatment of negative existentials in general, that is, both GNE and SNE, can be vindicated. For (1) it is neither arbitrary nor ad hoc; (2) it simultaneously accounts both for GNE and SNE; (3) it accounts for new linguistic data, i.e., CNE, again in a non ad hoc way.^[10]