Towards Being

richard woodward

University of Barcelona

Noneists hold that Meinong was half right: right to distinguish existent

objects from non-existent ones, but wrong to distinguish those non-

existents that have being (the ‘subsistent’) from those that do not.1 For

the noneist holds that there is but one way of being: to be, she says, is

to exist, so that no non-existent object has any kind of being whatso-

ever. And her realm of non-being is really quite something: from num-

bers to fictional characters to possibilia and beyond, all manner of

things can be found there. Indeed, for any arbitrary characterization of

an object, there is object that satisfies that characterization.2

Allism is noneism with a twist. For whereas the noneist holds that

some objects have no kind of being at all, the allist holds that every

object has being: to be, she says, is to be self-identical. So the allist will

not embrace non-existent objects; indeed, she regards the idea of non-

existent objects as a contradiction in terms. And her realm of being is

extensive: from numbers to fictional characters to mere possibilia and

beyond, all manner of things can be found there. In particular, any

object that the noneist embraces is a denzien of the allist’s ontology.

And since the allist accepts a version of the noneist’s characterization

principle, her ontology is very bloated indeed.

Though most philosophers regard allism as being crazy, they at least

find it intelligible. For whilst the allist has crazy views about what

1 See Routley (1980) and Priest (2005).2 The question of exactly how the characterization principle should be understood is

vexed. Here I follow the proposal of Priest (2005) whereby the principle is unre-

stricted (it really is any characterization) but interpreted so that the relevant objects

do not have to satisfy the characterizations at the actual world but just at some

world or other. This contrasts with the proposal of Routley (1980) whereby the

principle is restricted.

TOWARDS BEING 1

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exists, she has standard ideas about existence itself, endorsing the

standard view about the relationship between existence and quantifica-

tion, and agreeing with the Quinean slogan that to be the value of a

variable. Her craziness, then, is just her willingness to quantify over

anything you care to mention. The noneist, by contrast, rejects the Qui-

nean conception of ontological commitment out of hand and maintains

that one can perfectly well quantify over objects that have no kind of

being at all.3 And that, the thought goes, is exactly the problem. In

rejecting the Quinean slogan and trying to quantify over things which

don’t exist, the noneist tries to do the impossible, and her attempts to

do so result in nothing but hot air. Thus Bill Lycan (1979, p.290)

describes noneist quantification as ‘‘literal gibberish or mere noise’’ and

Peter van Inwagen (1998, p.16) considers the thesis that there are no

things that don’t exist to be ‘‘so obvious that [he has] difficulty in see-

ing how to argue for it.’’

David Lewis (1990), however, suggests that we Quineans should be a

little more charitable to the noneist. What’s true, Lewis concedes, is

that noneism will be unintelligible to us if we take the noneist at her

word. But when we try to understand rival theorists, Lewis suggests,

we should try to make those theorists maximally intelligible to us. So

since taking the noneist at her word leads to trouble, we should try to

find a different interpretation. And the most attractive alternative,

according to Lewis, implies that noneism is not deserving of its name,

since the interpretation takes the noneist to be an allist in disguise.

Once noneism is made intelligible to us, then, its bloated ontology is

unmasked. Or so Lewis argues.

Graham Priest (2005, 2011) argues that Lewis’s attempt to reconcile

noneism with Quinean orthodoxy fails, contending that the reconcilia-

tory interpretation Lewis offers is inadequate and that his methodol-

ogy is badly flawed. My goal in this paper is to move the debate on

further. For whilst I think that Lewis’s reconciliatory interpretation

can be patched up to avoid Priest’s objections to it, I’m sympathetic

to the questions Priest raises about Lewis’s methodology. But as we

shall see, the interpretative worry about the noneism doesn’t so much

concern the question of whether the noneist is an allist in disguise so

much as it concerns the question of whether the noneist and the allist

are taking past each other. And as we shall see, whatever the merits

of Priest’s responses to Lewis, they do very little to counter this

worry.

3 Routley (1982, p.169) tells us that Quine’s slogan is ‘‘as false as it is simple’’ and

Priest (2005, p.110) tells us that it’s a mistake Quine wouldn’t have made ‘‘had he

known a little about medieval logic.’’

2 RICHARD WOODWARD

1. Noneism or Allism?

Noneists distinguish two kinds of quantification: neutral quantification

on the one hand, and loaded quantification on the other. Neutral quan-

tification is achieved by a pair of quantifiers: the ‘general’ quantifier

‘A’ (for all) and the ‘particular’ quantifier ‘S’ (for some). The domain

of unrestricted neutral quantification is the universal domain, which the

noneist identifies with the set of all existent and non-existent objects.

So ‘Ax(Fx � Gx)’ should be read as saying that all objects that are Fs

are Gs and ‘Sx(Fx ^ Gx)’ should be read as saying that some object is

both an F and a G.

Loaded quantification is then introduced and defined as a restricted

form of neutral quantification. Where ‘"L’ and ‘$L’ are the loaded

quantifiers and ‘E!’ is an existence predicate, we have:

"LxFx ¼def Ax(E!x � Fx) $LxFx ¼def Sx(E!x ^ Fx)

In this setting, ‘"LxFx’ says that all existent objects are F and

‘$LxGx’ says that some existent object is G. The semantic distinction

between neutral and loaded quantification thus allows the noneist to

accommodate the truth of the claim that some things don’t exist

(i.e., Sx�E!x).

The distinction between neutral and loaded quantification lies at the

heart of noneism. But since we members of the Quinean establishment

admit only one form of quantification, the noneist sees a semantic dis-

tinction where we see none. And so a question emerges: how do the

noneist’s two forms of quantification relate to our solitary one? Well,

Priest (2005, p.13) tells us that we must not read SxFx as saying that

there exists something, x, such that Fx, the implication being that our

orthodox quantifiers do not match up to Priest’s neutral quantifiers but

to his loaded quantifiers. And this sits very well with the noneist’s own

self-conception as a radical heretic who opposes the orthodox concep-

tion of quantification and existence.

The trouble is that if we assume that the noneist’s loaded quantifiers

are our orthodox ones, it’s very difficult to see how to make sense of

what the noneist is up to when she uses her neutral quantifiers. The

very best we can say, as Lewis (1990, p.158) puts it, is that the noneist

is trying to ‘‘quantify without quantifying.’’ But since we’ve got no

good way to make sense of this idea, there is no wonder that many

Quinean’s have thought that the notion of nonbeing is nonsense.4

4 Even though it fits the rhetoric of Routley and Priest, there is something a little odd

about the Lewisian thought that that the distinction between loaded and neutral

quantification is at the heart of noneism. For loaded quantification is defined in

terms of neutral quantification. What’s at the heart of noneism is the idea that

existence is not to be analyzed in terms of identity.

TOWARDS BEING 3

If this were the end of the matter, the debate between the noneist and

the Quinean would quickly reach stalemate, with the noneist accusing

the Quinean of being stubbornly dogmatic and the Quinean accusing the

noneist of trying to do the impossible. But note that what got us into

trouble was our initial hypothesis that our ordinary quantifiers matched

up to the noneist’s loaded quantifiers. And whilst this hypothesis was

natural—remember that the noneist kept insisting that we interpret her

this way—it’s not the only option: we could instead take our ordinary

quantifiers to match up with the noneist’s neutral quantifiers.

If we went with this interpretative hypothesis, noneism would no

longer be unintelligible to the establishment, because we wouldn’t have

any problem understanding what the noneist is up to when she neu-

trally quantifies. We would also be able to understand loaded quantifi-

cation, for that is just a restricted form of neutral quantification.5

Indeed, one might think that this interpretative hypothesis makes the

real disagreement apparent: the noneist holds that only the objects in a

certain restricted domain deserve to be called ‘existent’ whereas the

Quinean thinks otherwise. From the point of view of the orthodoxy,

then, the noneist is mistaken in thinking that the restricted domain of

loaded quantification marks a genuine difference between those objects

that exist and those that do not. And though we find it puzzling that

the noneist sees a distinction that is not there, ‘‘a disagreement over

whether some alleged distinction is genuine is at least a familiar and

intelligible sort of disagreement’’ (1990, p.162).

Lewis’s point is that the Quinean has two ways to interpret the

noneist. The first takes the noneist’s loaded quantifiers to be the

Quinean’s quantifiers; the second takes the neutral quantifiers to be

the Quinean’s quantifiers. The former interpretation has the benefit of

taking the noneist at her word, but the price the Quinean pays is that

the noneist’s attempts to quantify neutrally are rendered utterly unintel-

ligible. The latter interpretation, Lewis contends, is thus superior since

it maximizes mutual intelligibility. Of course, it also implies that the

Quinean should reckon the noneist to be an allist in disguise. But better

a crazy allist than a nonsensical noneist!

2. Interpreting ‘‘Exists’’

Lewis’s interpretation makes noneism intelligible to Quineans by taking

the noneist’s neutral quantifiers to be the Quinean’s quantifiers. But in

order for this interpretation to be viable, we also need to know how to

understand the noneist’s loaded quantifiers too. All we’ve been told so

5 Or to be precise: we would be able to understand loaded quantification if we can

make sense of the noneist’s existence predicate. See §2 below.

4 RICHARD WOODWARD

far is that loaded quantification is a restricted form of neutral quantifi-

cation, where the relevant restriction is to those objects that exist. But

whilst the noneist takes the predicate ‘exists’ as a primitive, the Qui-

nean notion of existence is defined in terms of identity. And so the

question that emerges is this: how should the Quinean interpret ‘exists’

as noneist’s use that term?

To develop to answer to this question, it’s worth remembering that

whilst the Quinean doesn’t distinguish between the existent and the

non-existent, she does distinguish different kinds of existent objects.

And so a natural interpretative tactic is to find a Quinean distinction

between two kinds and then interpret the noneist’s distinction between

the existent and the non-existent in terms of it. And we don’t need to

look too hard to find a decent first candidate: the distinction between

abstract objects and concrete ones. This interpretation delivers the right

results in a host of cases. For instance, suppose that Priest claimed that

numbers are non-existent objects, by means of the following claim:

�Sx(Nx ^ E!x)

Then the present interpretation tells us that the Quinean should under-

stand Priest as claiming that numbers are non-concrete objects, i.e., as:

�$x(Nx ^ C!x)

Where ‘C!’ is a (perhaps primitive) concreteness predicate and ‘$’ is thefamiliar existential quantifier upon which we have come to rely. And

whether or not the Quinean accepts this claim, it at least makes Priest’s

notion of existence intelligible to the establishment.

Priest (2005, p.154) argues that this interpretation is inadequate

because it breaks down in modal contexts:

Consider the claim that Holmes does not exist, but could have done

so. This is a claim to which the noneist will assent. The [interpreta-tion] is that Holmes is not concrete, but could have been. This hardlyseems to be true. If Holmes is not a concrete object, what is he? He is

not a set, number, property or other sort of abstract object. And if heis, since abstract objects have their modal status necessarily, it is notpossible for him to be concrete object.

The trouble is plain to see. For instance, Priest thinks that merely pos-

sible objects don’t exist but might have done so. On the present inter-

pretation, the Quinean will understand Priest as holding that mere

possibilia are abstract objects that might have been concrete. But that

cannot be, if abstract objects are necessarily abstract. Similarly, Priest

thinks that he exists contingently. On the present interpretation, the

Quinean will understand Priest as holding that he is a concrete object

TOWARDS BEING 5

and the he might have been an abstract object. But that cannot be, if

concrete objects are necessarily concrete.

Of course, not everyone accepts that whether an object is concrete is

a non-contingent matter.6 But I won’t press that point, since Priest’s

worries can be resolved in a more elegant manner by modifying our

interpretation of Priest’s existence predicate. Rather than interpreting

‘exists’ in terms of ‘is concrete’, we can instead interpret Priest as using

‘exists’ to pick out those objects that are concrete and actual. Priest’s

claim that Holmes doesn’t exist but might have done so will now be

interpreted by the Quinean as saying that Holmes isn’t concrete and

actual but might have been so. And even if agree with Priest that

Holmes is necessarily concrete, this interpretation will work if Holmes

isn’t necessarily non-actual.

Now, there is one reading of ‘is actual’ on which (non)-actual objects

are necessarily (non)-actual. This is the rigid reading of actuality,

according to which an object o is actual at a world w just in case o

inhabits our world, a. But this isn’t the notion of actuality that is rele-

vant to my interpretation of Priest’s existence predicate. I require a

shifty reading of actuality, according to which an object o is actual at

w just in case is an inhabitant of w. Assuming that the inhabitants of

the worlds vary, we immediately get the result that Holmes is contin-

gently non-actual and Priest is contingently actual.7 For though

Holmes does inhabit our world, there are worlds that realize the

Holmes stories and so Holmes is actual at those worlds. Similarly,

though Priest inhabits our world, he does not inhabit every world and

so he is not necessarily actual. This new interpretative hypothesis, then,

does not break down in modal contexts.

In correspondence, Priest has objected to my interpretation because it

implies that his notion of existence is indexical in character, which

cannot be right since he holds that the facts about what exists are abso-

lute. I’m not sure exactly what problematic notion of indexicality Priest

has in mind, since all sides of the debate agree that whether an existen-

6 See, e.g., Linsky and Zalta (1996) and Williamson (1998). There is also a delicate

issue about whether ‘Billy is concrete’ can be true at worlds where Billy doesn’t

exist, but since Priest seems to want to allow for such things—remember, ‘Holmes

exists’ is false at a despite it being true at a that Holmes is concrete—I won’t dwell

on this point here.7 This need not involve a variable domain semantics: everyone, be they friends of fixed

domains or flexible domains, thinks that something shifts from world to world. For

Priest, what shifts from the world to world is the answer to the question: what

exists? For Linsky and Zalta (n. 6 above), it’s the the answer to the question: what’s

concrete? On the present view, it’s the answer to the question: what’s actual? My

use the term ‘inhabits’ is an effort at maintaining neutrality in the formulation of

the issue.

6 RICHARD WOODWARD

tial statement is true depends on which world we are evaluating it from.

Of course, Priest is at liberty to introduce a new notion of existence—

call it existence simpliciter—where an object o exists simpliciter in the

sense at a world just in case o is a part of a. But then we can just inter-

pret this new predicate in terms of the rigid notion of actuality I intro-

duced above. I find it difficult to believe that this is what Priest has in

mind, however, since our definition entails that what exists necessarily

exists. But in any case, if Priest wants to allow that existence facts are

contingent, then it better turn out that the extension of ‘exists’ varies

from world to world. The index-relativity involved in my interpretation

of Priest’s existence predicate is, in this way, pretty mundane.

To take stock, Priest objected to Lewis’s attempt to reconcile none-

ism with Quineanism by arguing that the Quinean cannot provide an

adequate interpretation of the noneist’s existence predicate. But even if

this objection are decisive against the interpretation of existence in

terms of concreteness, it does not threaten the interpretation sketched

above. On this interpretation, the Quinean interprets the noneist as

using the term ‘exists’ to pick out those objects that are actually con-

crete, where ‘actually’ is read in a shifty sense. This interpretation does

not break down in modal contexts, and thereby dodges the objections

Priest lodged against its predecessor.

3. To Be or Not to Be? (What Was the Question?)

Though Priest questioned the adequacy of Lewis’s interpretation of

noneism in Towards Non-Being, his most recent response to Lewis reflects

a change of defensive strategy. Rather than questioning the adequacy of

the reconciliatory interpretation, Priest (2011) questions its significance:

There is absolutely no reason why, in a dispute between noneists andQuineans, everything said by one side must be translated into terms intel-ligible to the other. No one ever suggested that the notions of the SpecialTheory of Relativity need to be translated into categories that make sense

in Newtonian Dynamics (or vice versa) . . . though there may be partialoverlap, each side may just have to learn a new language game.

The analogy is illustrative. Just as the Quinean is blind to the distinction

between neutral and loaded quantification, the Newtonian is blind to

the distinction between rest mass and relativistic mass. But the mere fact

that there are relativistic distinctions that cannot be understood in

Newtonian terms shouldn’t lead us to question the intelligibility of those

distinctions. And, by analogy, the mere fact that there are quantifica-

tional distinctions that cannot be understood in Quinean terms

shouldn’t lead us to question the intelligibility of those quantificational

TOWARDS BEING 7

distinctions. To Priest, Lewis looks like a Newtonian scrambling around

for some way of interpreting relativistic distinctions in outmoded terms.

Notice that Priest conceives of Lewis as demanding that everything

that the noneist says should be interpretable in Quinean terms.

Whether or not this is accurate as a reading of Lewis, there is a differ-

ent way to understand the significance of the reconciliatory interpreta-

tion, and one which casts doubt upon Priest’s analogy.

Suppose that two theorists, Billy and Alice, are in dispute: Billy

accepts theory T1, Alice accepts theory T2 and, on the face of things,

T1 and T2 cannot both be true. And suppose that their dispute has

reached deadlock. But, having studied both theories, we realize that

there is a systematic and recursively specifiable way to translate

between the two theories which has the following result: that for every

sentence which T1 says is true, there is a corresponding sentence which

T2 says is true and for every sentence which T2 says is true, there is a

corresponding sentence which T1 says is true. To be clear: the transla-

tion function only matches truths to truths and falsehoods to false-

hoods, and it does so in a systematic and compositional manner.8

Observing their dispute, we begin to question what Billy and Alice are

fighting about, and suspect that the dispute is merely verbal. T1 and T2

begin to look like notational variants.

Now, the dispute between proponents of Newtonian Mechanics and

proponents of the Special Theory of Relativity cannot be understood

in this way. There is no way of relating the sentences of the one theory

to sentences of the other which has the features detailed above.

Newton’s theory really is blind to the distinction between relativistic

mass and rest mass. And that, at least in part, is why Newtonian

Mechanics and Special Relativity disagree about the structure of physi-

cal reality and not only about which words we should use to describe

physical reality. As Priest might put it: when we moved from the New-

tonian picture of spacetime to the relativistic one, we had to learn a

new language game because there was only partial overlap between the

conceptual resources of the two theories.

What of the dispute between the noneist and the allist? Well, remem-

ber that the allist is a Quinean about existence, holding that to be is to

be a value of a variable. And recall that the allist is prepared to quan-

tify over (using her Quinean quantifiers) all and only those entities that

the noneist is prepared to quantify over (using her neutral quantifiers).

Moreover, we also know that whenever the noneist says that some

object exists, the allist will say that the very same object is concrete.

8 I’ll assume that the translations preserve logicality in the sense that every theorem

of T1 is mapped to a theorem of T2, and vice versa.

8 RICHARD WOODWARD

And when we put these two things together, we can set up a scheme

for translating between noneism and allism: we just swap the noneist’s

quantifiers for the allist’s and the former’s existence predicate for the

latter’s concreteness predicate. The striking result is that this transla-

tion scheme is guaranteed to always take us from truths to truths and

from falsehoods to falsehoods.

The upshot is that the dispute between noneists and allists seems to

be very different from the dispute between Newtonian Mechanics and

Special Relativity. We know that there is no way to understand relativis-

tic notions using only Newtonian resources. But the fact that it’s possi-

ble to systematically translate between the language of the noneist’s

theory and the language of the allist’s theory raises serious doubts about

whether the noneist and the allist really are disagreeing on anything over

than which words to use. ‘‘And this worry doesn’t demand that in any

case of a dispute between two theorists,’’ everything the one says needs

to be translatable into terms that are intelligible to the other. Rather, the

worry is that if there is a systematic translation scheme for mapping true

sentences of the one theory to true sentences of the other, then there is a

good case for thinking that the dispute is merely verbal in character. To

put that point otherwise, it’s far from clear that the noneist and the allist

have to learn a new language game because there is total overlap

between the conceptual resources of the two theories.

Though I’ve presented things in terms of setting up a translation

scheme between noneism and allism, there is a different way to develop

the worry which lacks certain distracting connotations.9 Let’s spot for the

moment that noneism is true. Now imagine that we rewrite our noneism

theory: whereas previously we said that an object exists, we now say that

an object is actually concrete, and where we previously said that an object

is self-identical, we now say that an object exists. No one seriously thinks

that this relabelling exercise has changed anything: all we’ve done is

rewritten the theory in a different way. But our rewritten noneist theory

just is allism and our new quantifiers are defined in exactly the same way

as Quine’s! It now seems like we should start to feel a bit guilty about

some of the mud we threw at the orthodoxy. When Quine told us that to

be is to be the value of a variable, we should have said: ‘indeed, we just

wouldn’t have put it that way.’

So whilst Priest is correct that it is foolish to demand that everything

said by one side of a dispute must be translated into terms intelligible

to the other side, I submit that the significance of the reconciliatory

interpretation of noneism is independent of this demand. The real

9 So, e.g., I don’t think that trying to appeal to the relative naturalness of her theory

will be of any help to the noneist.

TOWARDS BEING 9

worry is that the noneist and the allist are not really disagreeing at all,

that the only difference between their respective theories resides in how

they respectively use the word ‘exists.’ Whether this worry is what

Lewis had in mind in ‘Noneism or Allism?’ is unclear, but I submit

that it is a genuine and serious worry to which the noneist is obliged to

answer. And it is also a worry that remains unanswered.

Conclusion

Noneists tend to present themselves as radical heretics who stand

opposed to the orthodox, Quinean conception of existence and quanti-

fication. Lewis recommends that we do not take the noneist at her

word, claiming that the noneist is in allist in disguise. I’ve tried to sure

up Lewis’s argument in light of Priest’s replies. If I’m right, there is a

systematic way to translate between noneism and allism. And the real

worry that emerges doesn’t so much concern the question of whether

the noneist is an allist in disguise as it concerns the question of whether

the debate between the noneist and allist is anything other than a

merely verbal dispute. I do not claim that this worry is fatal, but I do

claim that Priest’s extant responses to Lewis do not address it. At the

very least, I submit that the ball in back in Priest’s court.10

References

Lewis, David. 1990. Noneism or Allism? Mind 99:23–31.

Linsky, Bernard & Zalta, Edward. 1996. ‘‘In Defense of the Contin-

gently Nonconcrete’’, Philosophical Studies 84:283–94.

Lycan, William. 1979. ‘‘The Trouble with Possible Worlds’’, in

Michael J. Loux (ed.), The Possible and the Actual, Ithaca: Cornell

University Press, pp. 274–316.

Priest, Graham. 2005. Towards Non-Being. Oxford: Oxford University

Press.

10 Thanks to Elizabeth Barnes, Ross Cameron, John Divers, Dominic Gregory, Bob

Hale, Joseph Melia, Joseph Morrison, Daniel Nolan, Tatjana von Solodkoff, Jason

Turner, and Robbie Williams. Very special thanks to Graham Priest: this paper

wouldn’t be existent/concrete/actual were if not for his encouragement and advice.

A distant relative of this paper was presented at the CMM seminar in Leeds in

2007 and I thank my audience on that occasion for helpful discussion. My research

on this paper was partially supported by my involvement in the ‘‘The Nature of

Assertion: Consequences for Relativism and Fictionalism’’ project (FFI2010-

169049), the ‘‘Vagueness and Physics, Metaphysics, and Metametaphysics’’ project

(FFI2008-06153), and the ‘‘Philosophy of Perspectival Thoughts and Facts’’ project

(CSD2009-00056). Many thanks to the DGI, MICINN, and the Spanish Govern-

ment for supporting these projects.

10 RICHARD WOODWARD

——. 2011. ‘‘Against Against Non-Being’’, Review of Symbolic Logic

4:237–253.

Routley, Richard. 1980. Exploring Meinong’s Jungle. Canberra: Philos-

ophy Department Monographs, Research School of Social Sci-

ences, Australian National University.

——. 1982. ‘‘On What There Is Not’’, Philosophy and Phenomenological

Research 43:151–177.

van Inwagen, Peter. 1998. ‘‘Meta-Ontology’’, Erkenntnis 48:233–50.

Williamson, Timothy. 1998. ‘‘Bare Possibilia’’, Erkenntnis 48:257–73.

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