Much ado about ontological nihilism

ABSTRACT

According to ontological nihilism nothing exists. A recent argument purports to show that this view is indefensible, since its most plausible formulations are tacitly committed to quantificational claims that are inconsistent with the nihilist's view that there aren't any existents. I show that this objection begs the question against the nihilist. The objector's argument relies on an equivalence principle implying that claims which nihilists regard as non-quantificational should nonetheless be interpreted as equivalent to quantified claims, given that both kinds of assertion are assertible in the same contexts. This style of reasoning is supported by considerations of charity, which suggest that similarities in inter-personal patterns of language use provide evidence of similarity in the semantic content of speakers' utterances. However, related considerations also suggest that intra-personal patterns of language use constitute significant semantic evidence of the same kind. When we appreciate this and further recognize that nihilists are disposed to assert the negation of any positive, quantified claim, we see that it is too much to expect principles of semantic interpretation based on considerations of charity to decisively refute nihilism. This result has interesting metametaphysical implications concerning the role and scope of analogous arguments based on principles of interpretive charity.

KEYWORDS:

• Metaphysics
• ontology
• ontological nihilism
• principle of charity

Acknowledgments

I would like to thank Eliya Cohen, Boris Kment, Harvey Lederman, Gideon Rosen, Eyal Tal, and Hannah Tierney for all their help. Thank you also to an audience at the Australasian Association of Philosophy Conference (Wollongong, 2019) who gave valuable feedback on an earlier version of the paper. Most of all, I owe a deep debt of gratitude to Jason Turner for his help and support in the writing of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The most developed form of this argument is defended by Turner (2011). Related objections can be found in Quine (1980 [1953], 104), Burgess and Rosen (1997, 187) and Schaffer (2009, 369). Turner's argument is described as ‘probably the most urgent problem’ for fundamental nihilists in Bacon (2019, 278).

2 There are other desiderata for such responses: the relevant reconstrual should also preserve certain inferential connections for example. For simplicity we can set these aside; they serve mainly to exclude solutions that – unlike the proposal on which I will focus – avoid quantification by burying structure into syntactically simple expressions, or rely on artificial syntactic devices to engineer the right kind of inferential connections, see Turner (2011, 22–32).

3 See Strawson (2005 [1959], 202–3).

4 In generative grammar, these expletives are required in languages that do not permit pronoun omission (for instance, English and French), by the so-called extended projection principle (Chomsky 1986, 115–16).

5 Such analyzes are a live theoretical possibility in contemporary linguistics – see e.g. Szekely (2015).

6 A limitation arises because standardly features are placed somewhere and somewhen – Szekely (2015) and Clark (2004). Presentists seem to be able to say things like ‘WAS $\left(\mathrm{\exists }x\right(\mathrm{D}\mathrm{i}\mathrm{n}\mathrm{o}\mathrm{s}\mathrm{a}\mathrm{u}\mathrm{r}\left(x\right))$’ without ipso facto committing themselves to the existence of times other than the present (Sider 2001, 15ff). Feature-placers can do likewise; this strategy could also be extended to places using locative operators: ‘HERE(_)’ and 'THERE(_)' (Burge 2010, 166). This seems to have been Strawson's own view, Strawson (2005 [1959], 216).

7 Here and throughout, I use ‘¬’ for sentential negation and ‘∼’ for predicate negation.

8 See Turner (2011, 13) n.14 and Gamut (1991, 102–15).

9 For English interpretations of predicate functor expressions see Burgess (2008, 100–1).

10 To establish the equivalence between fully functorial and first-order languages, we first regiment the first-order claims we wish to translate in prenex normal form, comprising a string of quantifiers – the prefix – and the remaining formula – the matrix. Using a result in propositional logic, we can convert the matrix into conjunctive normal form such that the only propositional connectives are negation and conjunction. If, ignoring momentarily the quantificational prefix, we regard the resulting matrix as an open formula, we can use our predicate functors to construct an n-ary predicate that is semantically equivalent to the matrix. (‘∼’ and ‘$\mathrm{\&}$’ handle the propositional connectives, and $<<\text{‘}\mathsf{P}\mathsf{a}\mathsf{d}\text{’},\text{‘}\mathsf{I}\mathsf{n}\mathsf{v}\text{’},>>$ and ‘$\mathbb{I}NV$’ allow us to manipulate the order of arguments in relations in any way we might need.) Finally, considering again the prefix, we replace universal quantifiers with their duals, and trade existential quantifiers and negation for ‘Δ’ and ‘∼’ respectively. This gives us a sentence containing neither quantifiers nor variables that nonetheless fully paraphrases all but the ontological content of its first-order analogue.

11 The material discussed in the two preceding pages summarizes the discussion in Turner (2011, 38–43).

12 Functorial languages are, of course, products of philosophical imagination. One worry is that we can only grasp them by means of their first-order translations. Quine himself seems to have thought something like this (Quine 1980 [1953], 104). But this conclusion is not forced on us; philosophers are increasingly accepting that it may be possible to learn higher-order languages by ‘the direct method’, without relying on first-order translations (Williamson 2003, 416–17, 459). Something similar may hold for feature-placing languages (cf. Burgess 2008, 97–101).

13 To get the conclusion that nihilism is untenable, we need to show not just that ‘Δ’ is equivalent to ‘∃’, but further that we should interpret both expressions as existential quantifiers – cf. Alston (1958). I will assume henceforth that this further step is in good standing.

14 Other metasemantical objections to the equivalence argument exist – see e.g. Donaldson (2015, 1062–3). The most developed response is Diehl (2018). Like Diehl, I will challenge the equivalence principle on which the argument relies. Her argument, however, differs from mine: she suggests that this principle commits its proponent to an implausible dispositionalist semantics. Diehl's proposal is intriguing. A steadfast defender of the equivalence argument might try to resist her conclusion by rejecting the counter-examples to the dispositionalist semantics, which involve more fine-grained distinctions between meanings than the cases that motivate the equivalence principle. I am agnostic about the merits of such a response, but in any case it would not succeed against the present objection.

15 Babic and Cocco (2020) suggest that – given a (somewhat Carnapian) conception of fundamentality on which the fundamental facts should form a ‘metaphysical semantics’ from which everything else can be derived (2059) – claims that are not formulated using the syntax of a functorial language cannot be fundamental in a theory like functorial nihilism. It does not follow, though, that the denial of existents cannot be a core part of the nihilist's view. On the proposed conception of fundamentality, any theory will comprise a non-fundamental totality claim to the effect that nothing else exists or obtains, beyond what is implied by the fundamental facts. Such totality claims are a vital part of any theory, regardless of whether or not they count as fundamental. Moreover, this conception of fundamentality is not forced upon us. We might prefer to allow our metaphysics to dictate what is fundamental, rather than deferring to what can be articulated in a particular representational idiom, as in the Carnapian picture.

16 This analogy would not be acceptable to all self-styled nihilists. O'Leary-Hawthorne and Cortens (1995, (157)) for instance reject it. On their view, nihilists need not be understood as denying that there are objects but simply as providing a deflationary interpretation of our object-talk. The idea that quantification over objects is dispensable is an interesting view, as is the view that quantification over numbers is dispensable. But the latter view is not nominalism, since it does not say there are no numbers, and analogously the former is not nihilism as I understand it, since nihilists should reject the claim that there are objects (cf. Burgess 2008, 90–2).

17 Sortal adjectives characteristically imply criteria of identity or persistence for the entities of which they hold, where characterizing adjectives do not, see Strawson (2005 [1959], 168).

18 E.g. Russell's theory of knowledge by acquaintance Russell (1905, 492–3) or Williams' tropological theory of reality Williams (1953a) and Williams (1953b). For general discussion see Szekely (2015, 15–24).

19 See Clark (2004). For an opposing perspective see Burge (2010, 170).

20 This much is conceded even by the opponents of these analyzes, see Burge (2010, 164–6).

21 This principle states an absolute (that is, decisive) condition for interpreting speakers, where it might be more accurate to claim only that if the antecedent holds then there is some evidence that favors not giving a and b the same interpretation. This is to preserve the analogy with the equivalence principle, which is similarly absolutist. If both principles are weakened to merely evidential claims then the original objection does not get going, but since both principles formalize the same intuition that meaning is shaped by patterns of use, if one deserves to be stated in absolutist terms then so does the other.

22 It is also open to the nihilist's opponent to claim that restricted converse equivalence does not apply here because the hypothetical multilingual nihilists would be uninformed about the relevant fact that there are cats. But this is dialectically inappropriate as the basis for an objection to nihilism since it begs the question against the nihilist.

23 Turner (2010, 14); drawing on Lewis (2004, 11).

24 I assume here that the existential elimination rule applies only if there is a constant available in our language.

25 Adopting a neutral free logic does require that we give up a number of classical theorems. For instance, ‘$Fa\vee \mathrm{\neg }Fa$’ is no longer valid. The introduction of non-classicality does not, however, give rise to an objection to the nihilist. For as we have seen, classical logic contains an ontological assumption that is unacceptable from their perspective. Moreover, it is possible to define a ‘strong negation’ operator that holds of a formula whenever that formula is not true (i.e. is either false or truth valueless) (see Smiley 1960). We can construe ‘¬’ as it appears in ‘$\mathrm{\neg }\mathrm{\exists }x(x=x)$’ as strong negation. This ensures that adopting a neutral free logic does not require the nihilist to abandon her claim to grasp the quantifier semantically speaking.

26 The ‘typical’ witch seems to have been female, unmarried, over 50 years of age, living in a rural setting, and from the lower-strata of society (Levack 2016, 128–45). Such generalizations are clearly not exceptionless.

27 ‘Witch’ is sometimes used in hyperbole or metaphor. Someone might want to argue that this shows that there is no real difference between the case of ‘solid’ and of ‘witch’; such an argument would be mistaken. Statements in which we affirm that there are witches are clearly non-literal; if someone sincerely maintained that there are witches, we would judge them to be seriously misguided.

28 Turner (2011, 51–2).