Proceedings of the Aristotelian Society Hosting and Publishing Talks in Philosophy Since 1880

PROCEEDINGS OF THE ARISTOTELIAN SOCIETY HOSTING AND PUBLISHING TALKS IN PHILOSOPHY SINCE 1880

The Linguistic Approach to Ontology LEE WALTERS

2020–2021 141ST SESSION CHAIRED BY BILL BREWER SENATE HOUSE VOLUME CXXI EDITED BY GUY LONGWORTH UNIVERSITY OF LONDON proceedings of the aristotelian society 141st session

issue no. 2 volume cxxi 2020–2021

the linguistic approach to ontology

lee walters university of southampton

monday, 18 january 2021

17.30–19.15

online via zoom Please visit our website for further details

contact [email protected] www.aristoteliansociety.org.uk

Lee Walters is an Associate Professor in Philosophy at the University of Southampton. Prior to joining Southampton, Lee studied philosophy at UCL and taught at Oxford. Lee’s main interests are in metaphysics, the philosophy of language, and philosophical Logic, with a particular emphasis on the philosophy of fiction. Lee has been an Associate Editor of Analysis; a trustee of the British Society of Aesthetics; has held a British Academy Mid-Career Fellowship; and has been a junior fellow at the Institute for Advanced Study, CEU, Budapest.

editorial note

The following paper is a draft version that can only be cited or quoted with the author’s permission. The final paper will be published in Proceedings of the Aristotelian Society, Issue No. 2, Volume CXXI (2021). Please visit the Society’s website for subscription information: aristoteliansociety.org.uk. The Linguistic Approach to Ontology

1. Introduction

Following Quine (1948), and more recently Hofweber (2016), I take the central ontological

question to be what is there? in a sense to be precisified in §3. This contrasts with some recent

approaches to ontology that take the central question to be what is fundamental? It is, of course,

interesting to explore relations of dependence and supervenience between different sorts of

entity, but this endeavour of explaining what depends on what, is an investigation of relations

within our ontology. And in order to fully explore these relations we need to determine what

our ontology consists of, namely what there is. In any case, there is room for both projects.1

What I want to do here is explore the prospects for the

Linguistic Approach to (Meta)Ontology: we determine what there is by examining

how natural languages work.

In §§2-3, I outline two linguistic approaches to ontology due to Frege and Hofweber, respectively. I reject such approaches (§4) for the familiar reason that empty names can figure in true sentences. Still there is a kernel of truth in both approaches. The truth that these approaches encapsulate is often thought to be the claim that true subject-predicate sentences are ontologically committing. This thought is appealing, but it is ultimately untenable. There is, however, a truth in the area namely that true property ascriptions are ontologically

committing. In §§5-6 I pull these two claims apart, defending the latter and rejecting the former.

1 Why not take the ontological question to be what exists? Well on the intended readings, I think this is equivalent to the question of what is there? The English word exist suffers from the drawback that we talk of events occurring or happening rather than existing (Williamson), but events are part of ontology – there are events, after all. We also say that Socrates no longer exists, but eternalists will want to include him in our ontology. Here, however, exists seems to be on all fours with there is since we do not say that Socrates is, but only that he used to be.

The package of these views faces two related challenges: what are predicates doing in subject-

predicate sentences, and what accounts for the semantic profile of empty names in the absence of a referent. In §6 I make a start on answering this. §7 briefly mirrors the previous debates concerning first-order ontology in the second-order case. The picture we are left with is one on which we need to determine which sentences ascribe properties to objects, and there does not appear to be any formal criterion for this.

Before commencing with the substance of the paper, let me say something about what I am doing here and the paper’s ambitions. This paper is wide-ranging and rests on controversial claims at many points, claims that cannot in the space available be defended in detail (I may have lost some readers already, simply by claiming that there are true sentences containing empty names). I make no apology for this. The issues that I want to address are wide-ranging and touch on many areas of philosophy, and no one paper could deal with all of them adequately. There are arguments in this paper, but I think reader will find it most fruitful if they take me to be sketching what I take the best approach to these issues to be, one that is intuitive, but nevertheless seeks to address the hard questions that face such a view. Even if you ultimately reject the view advocated here, I think there is still something to be learned by engaging with it and the debate it seeks to illuminate.

2. Fregeanism

A particularly influential approach to ontology is that inspired by Frege (1953). Fregeanism can be characterised for our purposes as the conjunction of the following two claims (cf.

MacBride, 2003: 108).

Syntactic Decisiveness: if an expression exhibits the characteristic syntactic features

of a singular term, then that fact decisively determines that the expression in question

has the semantic function of a singular term, i.e. the function of referring to a single

object.

Following Hofweber (2016), let us call expressions that exhibit the syntactic features of a

singular term, syntactic singular terms, and expressions that have the function of referring to a

single object, whether or not they carry out that function, semantically singular terms. Syntactic

Decisiveness claims that all syntactically singular terms are semantically singular terms.

Referential Minimalism: the mere fact that a semantically singular term features in a

true sentence (of a certain sort) determines that this expression refers to a single object.2

Together these two claims entail that true sentences (of a certain sort)3 containing syntactically

singular terms are ontologically committing, since they commit us to the objects referred to by

the syntactically singular terms in these sentences.

If we conceive of existential quantification into (syntactically) singular term position (nominal

quantification) as quantification over a domain of objects, then true sentences that contain such

quantification will also be ontologically committing, since such sentences can only be true if

there is an object that is a witness of the quantificational claim.

2 I am using reference and its cognates, as is standard in analytic philosophy, to pick out a relation between a singular term and an object. We should distinguish reference from aboutness. On the assumption that ‘Pegasus’ is an empty name, ‘Pegasus’ does not refer to anything and I cannot refer to Pegasus. Nevertheless, there are myths about Pegasus and I can think about Pegasus, or so it very much seems. Here I follow Crane (2013: 8-10). 3 I shall leave this qualification implicit until I return to it in §5.

So, a central ontological question for the Fregean is to determine the true sentences containing syntactically singular terms or an existential nominal quantifier. Once we have done this, our

(first-order) ontological commitments follow.

3. Hofweber’s Rejection of Fregeanism

Hofweber (2016) has recently outlined an interesting alternative linguistic approach to the

Fregeanism sketched above. Hofweber argues that there are two sorts of syntactically singular terms, since some but not all syntactically singular terms are semantically singular terms. That is, some but not all syntactically singular terms have the function of referring. Hofweber thus departs from the Fregean by rejecting Syntactic Decisiveness. For example, Hofweber argues that there are certain puzzling features of our number talk that are best explained by taking neither ‘the number of moons of Jupiter’ nor ‘four’ as used in (1) to be have the function of referring.

1. The number of moons of Jupiter is four.

Furthermore, just as Hofweber distinguishes between two sorts of syntactically singular term, he also distinguishes between two readings of nominal quantifiers

External quantification: nominal quantifiers range over a domain of objects as

assumed in §2.

Internal quantification: nominal quantifiers generalize into syntactic position and so

have an inferential role or substitutional reading.

External quantification is governed by a free logic. That is, we can only move from Fa to ∃x

Fx on the assumption that ‘a’ refers (similarly from ∀x Fx to Fa). This is because, some

syntactically singular terms are not semantically singular, they do not refer. Internal quantifiers, on the other hand, behave classically. That is, we can conclude that there is something

(internally) that is F (Σx Fx) from Fa and similarly from the claim that everything internally is

F (Π Fx) to Fa.

If Hofweber is right about number words, then generalizations about numbers – (there are) some numbers (that) are prime/perfect/larger than 10 – cannot be accounted for in terms of external quantification because none of the objects that the external quantifiers range over are identical to four, for example, because four is not a referring term. And a result, on Hofweber’s picture we need an internal reading of the quantifier. But couldn’t we make do with only internal quantifiers? No, unreferred to objects mean we need an external nominal quantifier, since there are no true sentences from which to reach

2. There are some objects that will never be referred to

which would be required if ‘some objects’ in (2) were an internally quantified noun phrase -

Σx Fx is true iff there is some (externally) substitution instance of x ‘a’ such that Fa. As a result, Hofweber concludes we need both external and internal nominal quantification.

If Hofweber is correct that there are merely syntactically singular terms and that some nominal quantifiers are internal quantifiers, then the Fregean approach to ontology is flawed.

Determining which sentences containing syntactically singular terms and nominal quantifiers are true, do not settle which objects we are committed to, since such sentences can be true in

the absence of the relevant objects. Rather, Hofweber argues that we should examine the

function of the relevant singular terms and quantifiers and to establish which of the following

is true of a subject area

Externalism: All nominal quantifiers have an external reading and all syntactically

singular terms are semantically singular.

Internalism: All nominal quantifiers have an internal reading and no syntactically

singular terms are semantically singular

Externalist domains of discourse are those which are ontologically committing, internalist domains are those which are committed to the absence of the relevant objects. Hofweber, then, thinks that Fregeanism is an overgeneralization: the Fregean approach assumes externalism across the board, but by carefully examining the function of linguistic expressions, we can determine that internalism is true of some domains and so the Fregean overpopulates our ontology. The central ontological question, for Hofweber, is then to establish what there is, in the externalist sense.

Hofweber’s discussion is fascinating, but I don’t want to commit to internalism about arithmetic. The arguments for and against Hofweber’s treatment of ‘the number of moons of

Jupiter’ and ‘four’ are nuanced and consideration of them would take us too far afield from the course I wish to explore. We should note in passing, however, that even if Hofweber is correct that such expressions are not semantically singular, this would not establish that Syntactic

Decisiveness is false. This is because Hofweber relies on an intuitive notion of syntactically

singular termhood, rather than providing a criterion.4 As a result, it would be open to the

Fregean to accept that ‘the number of moons of Jupiter’ is not a semantically singular term, but

also to deny that the term in question is syntactically singular. Indeed, the Fregean could take

the data that Hofweber adduces in favour of taking ‘the number of moons of Jupiter’ not to

function like a definite description, to argue that it is not thereby a syntactically singular term

at all.5 Still, noting this does nothing to diminish Hofweber’s case for an internal reading of

nominal quantifiers.

Whatever the merits of Hofweber’s arguments concerning talk about arithmetic, Syntactic

Decisiveness certainly is obvious, rather it is instead a substantive empirical claim. Moreover, we can cast doubt on Syntactic Decisiveness, by noting that syntactically plural terms may have the semantic function of referring to a single object, e.g., ‘the scissors’, or the gender neutral

‘they’, and so there can be a mismatch between syntax and semantics.6 So, I agree with

Hofweber that we need to investigate the semantic function of expressions of the same syntactic

type in order to determine our ontological commitments. But here I want to leave open the

question of merely syntactically singular terms and explore what follows when we focus

instead on semantically singular terms and, as we shall see, on predicates. So, let us leave to

one side the question of whether there are merely syntactically singular terms and whether any

discourses are internal, in Hofweber’s sense.

4 See Schwarzkopf for a recent discussion of criteria for singular termhood. My focus below will be on proper names which all sides take to be syntactically singular. 5 Cf. Kennedy and Stanley on ‘the average family’. 6 This observation does not falsify Syntactic Decisiveness, since that principle concerns syntactically singular terms. What appears to be falsified is: if an expression exhibits the characteristic syntactic features of a plural term, then that fact decisively determines that the expression in question has the semantic function of a plural term, i.e. the function of referring to multiple objects.

4. The Incompleteness of the External/Internal Distinction

Focusing on semantically singular terms, we can see that Hofweber’s approach to ontology is

incorrect, because it is incomplete. Independently of his case for merely syntactically singular

terms, Hofweber argues that we need an internal reading of the nominal quantifier. Hofweber

thinks this because he takes reference to be an achievement, and as a result there are

semantically singular terms that fail to refer (only a Meinongian would deny this). But this

argument for the internal reading is invalid – the mere existence of empty names implies nothing about quantifiers. What is needed to plug the gap are the following two claims

Non-Referring Truth: there are true sentences containing empty names.

Non-Referring Truth Nominal Generalization: we existentially generalize into

nominal position of some truths containing empty names.

But both these claims appear to be true, since sentences like (3) and (4) could be true

3. Dom thinks that Pegasus is a unicorn

4. There is something that Dom thinks is unicorn, namely Pegasus

Of course, there are philosophers who claim that empty names cannot be used in true sentences.

But such a position seems counterintuitive in the extreme and I’m not aware of any good

argument for the claim; it certainly does not follow from the rejection of descriptivism or

Fregean senses, or from the acceptance of object-dependent thought (Sainsbury 2005). Just as

there can be a picture of a dogs, even when there is no dog it is a picture of, there can be

thoughts about horses, even when there is no horse it is a thought of. And what is to stop us

characterising this thought about a horse as a thought about Pegasus, if the thought has the

requisite causal/intentional connection to the myth? In what follows, I will assume that empty

names can figure in true sentences, as seems to be the case. I note that this is a philosophically

controversial claim, but then again, which claim is not?

So, even without committing to merely syntactically singular terms (or more weekly that ‘the number of Jupiter’s planets’ is not a referring term, whether or not it counts as a syntactically singular term), we can see that we need both an external and an internal reading of nominal quantifiers.7 But that we need an internal reading of the nominal quantifier for discourses

containing empty names, shows that Hofweber’s Externalism/Internalism distinction is not

exhaustive, for there are domains that use semantically singular terms and an internal reading

of the quantifier. That is, in (4), the quantifier is to be read internally, whereas ‘Pegasus’ is a

semantically singular term, albeit one that fails to refer. Moreover, given that some of these

discourses talk about unnamed objects, we have discourses that use semantically singular terms

and both internal and external readings of the nominal quantifier. For example, whereas (5)

requires the quantifier be read internally, (6) requires that it be read externally.

5. Leverrier thought that Vulcan lay between Mercury and the Sun, so there is something

Leverrier thought lay between Mercury and the Sun, namely Vulcan.

6. There are planets that have not been named/some planets have not been named.

7 Cf. Crane and Sainsbury. Are the external and internal readings of the nominal quantifier exhaustive? Perhaps not, since neither can prima facie account for the truth of ‘some things are unnamed whereas others do not exist’.

Hofweber is correct that if externalism is true about a domain, then the truth of (some) claims

in that domain are ontologically committing. But, in order to determine whether a domain is

ontologically committing, it is not sufficient to determine whether its singular terms are

semantically singular, since some domains are neither internal nor external. As a result, we

must also determine whether these semantically singular terms successfully refer (and/or which quantifiers in that domain are to be read externally). That is, Referential Minimalism, as an unrestricted claim, appears to be false regardless of whether Syntactic Decisiveness is true.

And because of this we should reject that either Fregeanism or Hofweber provide fully general answers. Nevertheless, we can agree with the Fregean and Hofweber that what is there?, when this is read externally, remains a central ontological question. It is just that not all domains are external, even leaving to one side any internal domains.

5. Property Ascriptions

How then should we determine whether a semantically singular term does in fact refer? Is there a purely linguistic test for whether such a term refers? The Fregean says there is, since she endorses Referential Minimalism. But as we have just seen, Referential Minimalism, as an unrestricted claim, appears to be false. A popular Fregean approach limits the scope of

Referential Minimalism to subject-predicate sentences only, which would thus yield, given

Syntactic Decisiveness,

The First-Order Existence Principle (1EP): Fa → ∃x x=a

where ‘Fa’ is a sentence formed by combining a name with a verb phrase (e.g. ‘is tall’, ‘runs’).8

8 1EP and related principles below are formulated in terms of monadic predicates. We could generalise the discussion to the case of n-place predicates, but for ease of presentation I usually consider only the monadic case. Nothing of substance here turns on the restriction to the monadic case.

But why should we accept 1EP and Referential Minimalism even so circumscribed? 1EP is a

theorem of classical logic. However, as we have just seen, the external quantifier (∃x) is not

classical, but free. We can discern two arguments in favour of 1EP in Williamson (2013). First,

Williamson argues that 1EP follows from the following

Being Constraint: ∀x (Fx → ∃y x=y).

B: P →◊P

7. ◊∃x x=a

That is, given Being Constraint and B, it is inconsistent to deny that a exists but to accept that

a could have existed. I agree with Williamson that Being Constraint is an overwhelmingly

principle that can be accepted both by those who embrace the necessary existence of

everything, such as Williamson himself, and those who deny it, such as Stalnaker (REF) (see

Williamson (2013: §4.1)). Williamson himself accepts B since it follows from the simplest,

strongest modal logic, S5. I do not find such considerations compelling and I am not myself

committed to S5, but I have no wish to dispute B here.9 The most promising way to resist

Williamson’s argument is to reject (7). As Williamson himself says of a related claim, “[a]fter

Kripke’s work, however, the envisaged view of … names rests on a discredited descriptivism

about names (2013: 152). That is, although there could have been something with all or most

of the properties associated with a, why should we think that means that a could have existed,

especially given the fact that there could have been multiple things with these properties.

9 Dummett (1993) argues against B. I show (Walters, 2014), however, that even if we accept Dummett’s premises what he has is an argument against S5 not B. Moreover, I suggest that the natural culprit, if S5 is to be rejected, is the S4 axiom rather than B.

The problem with rejecting (7), as Williamson sees it, for those who reject 1EP is to explain

how an empty name can have a meaning such that not all empty names are intersubstitutable.

As such, that leaves those who deny 1EP with the challenge of accounting for the non-defective

semantic profile of empty names. I shall return to this in the next section.10 The important point to note is that rejecting 1EP does not require rejecting Being Constraint since we can instead reject (7) when ‘a’ does not refer. Similarly, rejecting 1EP does not require rejecting

Non-Modal Being Constraint: ∀x (Fx ⊃ ∃y y=x).

Non-Modal Being Constraint is not at issue between the classical logician and his free logical

opponent, since it is a theorem of both free and classical logic. The simple reason being that

Pegasus and the other nonexistents that the free logician countenances are not within the range

of the external quantifiers.

A second line of argument to be found in Williamson for 1EP is more interesting. Williamson

asks ‘[h]ow could a thing be propertied were there no such thing to be propertied?’ (2013:

148).11 But note that what Williamson’s rhetorical question supports in the first instance is not

1EP, but rather

Property Ascription 1EP: if ‘Fa’ is a property ascription, then Fa → ∃x a=x.

10 To be more precise, Williamson thinks the best prospect for giving empty names meaning either commit us to (7) or else to an alternative advocated by Bacon (2013) namely that although a could not have existed, there could have been something ‘a’ actually refers to i.e. ◊∃x@Refers(‘Pegasus’, x). It is Bacon’s treatment that Williamson objects to with the Kripkean rejection of descriptivism cited above, but this line of thought applies both to (7) and Bacon’s view. 11 Williamson actually asks this question in a discussion of Being Constraint, but it is illuminating o ask it here.

We only get from Property Ascription 1EP to 1EP, if we assume, that true subject-predicate

sentences ascribe properties to objects. Do we have reason to accept this?

As well as the Fregean picture of singular terms sketched above, there is a related picture of

predicates which endorses

Syntactic Decisiveness*: if an expression exhibits the characteristic syntactic features

of a predicate,12 then that fact decisively determines that the expression in question has

the semantic function of a predicate, i.e. to ascribe a property (when it combines with a

singular term).13

Syntactic Decisiveness* bridges the gap between Property Ascription 1EP and 1EP and so we have our linguistic test for reference and with it a Fregean approach to ontology. The question

then becomes, should we accept Syntactic Decisiveness. I think this is a key question in helping

us determine our first-order ontology, and this can be brought out by noting the following

inconsistent triad that I think helps structure the debate:

8. Subject-predicate sentences express property ascriptions (Syntactic Decisiveness*).

9. There are true subject-predicate sentences containing empty names (denial of 1EP).

12 I haven’t provided a criterion of predicatehood, but implicitly verb phrases are predicates. This is consistent with accepting or rejecting Dummett’s (1973: 37-38) criterion which says that a predicate is what results when we remove one or more referring expressions from a sentence. I think, like Williamson (1989:98), that Dummett’s criterion confuses the physical act of substituting a name for a variable with the syntactic operation of predication. This can be brought out when we start to consider the different ways of parsing complex sentences. See Williamson (2013: §4.1). 13 The parenthetical qualification is crucial, since predicates also form sentences when combined with quantified noun phrases, but in such cases they are not ascribing a property to anything, even if they are in some sense picking one out.

10. A property ascription cannot be true, if there is no object ascribed the property (Property

Ascription 1EP).

Only someone in the grip of a philosophical theory would deny (10), maintaining 1EP, given the truth of singular negative existentials such as

11. Pegasus does not exist.

As one of our most respected philosophers puts it

If any verb phrase can be substituted for Fs in (1EP) then ‘does not exist’

can. But then we get the inference from a does not exist to a exists, so ‘a

does not exist’ is self-contradictory and so by classical logic a exists is a

logical truth and necessarily a exists will be a logical truth by standard

modal logic. But “This is an absurd result” (Williamson, 1989: 97).

I agree, although Williamson no longer does, so 1EP is to be rejected, meaning that either

Property Ascription 1EP or 1EP has to go.

Positive free logicians typically say that property ascriptions can be true even when there is no thing to be propertied. But I share Williamson’s puzzlement as to how this could be the case.

Very plausibly a property ascription is true iff there is a referent of the singular term and this has the property ascribed by the predicate, otherwise what is it to truly ascribed a property to

an object?14 Positive free logicians have rejected this, I think, because they assume that true predications are property ascriptions. But they can and should accept Property Ascription 1EP.

Instead, we should say that true subject-predicate sentences containing empty singular terms

are not property ascriptions and so reject Syntactic Decisiveness*. (Similarly, we should that

true sentences containing transitive verbs and empty names are not relation ascriptions). This

allows us to answer Williamson’s question satisfactorily; a property ascription can’t be true if

there is no thing to be propertied, but counterexamples to 1EP are not property ascriptions.

Moreover, pulling apart subject-predicate sentences from property ascriptions allows us to give

an illuminating gloss of the positive free logician’s distinction between existence-entailing and

predicates that are not existence-entailing; existence-entailing predicates have as their function the ascription of properties, whereas predicates that do not entail existence do not have this function. This, then, raises the question of what do predicates that are not existence-entailing do, if they do not ascribe properties?

Those who reject 1EP therefore face two challenges. First, there is Williamson’s challenge to specify a non-defective semantic profile for empty names, such as ‘Pegasus’, that does not rely either on the claim that Pegasus could have existed or on the claim that there could have been something ‘Pegasus’ actually refers to. Second, to specify what role predicates that do not ascribe properties play. As we shall see, these two challenges are interrelated.

14 Cf. Braun (1993: 463) “If P is a proposition having a single subject position and a one-place property position, then P is true iff the subject position is filled by one, and only one, object, and it exemplifies the property filling the property position. If P is not true, then it is false”.

6. The Varieties of Predication

We know from Property Ascription 1EP that there cannot be true property ascriptions involving empty names. But there are, or at least appear to be, true subject-predicate sentences containing empty names. So, it follows, that true subject-predicate sentences containing empty names are not property ascriptions. This, then, raises the question of what is the function of these sentences and, in particular, what are the predicates in such sentences doing if not ascribing properties?

We should note at the outset that there is no reason to expect a uniform answer to this question.

If some predicates ascribe properties and others do not, there may well be further divisions among the predicates that do not as ascribe properties. Indeed, that is what I shall argue is the case.

We can, I have suggested, divide predicates into those that entail existence, that is those for which 1EP is true, and those that do not entail existence, those for which 1EP is not true. I think we can make a further subdivision in each case. There are at least two sorts of existence entailing predicate. First, there are predicates that ascribe properties, such as is red, is very large, and runs. Second, there are predicates that have the semantic function of ascribing properties, but which fail to do so, because there is no property in question that the predicate picks out. Such predicates are akin to empty names, and plausible examples include is a unicorn, and is a Hobbit.15 Of course, there are no unicorns or Hobbits, and so 1EP is vacuously

true.

15 I am not here subscribing to an Aristotelian view of properties, since properties can be tethered to the concrete world in ways other than by being instantiated. See (Stalnaker 2012: 133 n3) and Walters 2013: 476-477 for discussion.

In some cases, it may not be clear whether an existence entailing predicate ascribes property or fails to ascribes one. For instance, does is round and square ascribe a property no object could

have or fail to ascribe a property at all? Stalnaker (2012), for example, thinks there are no

properties that cannot be instantiated. On such a view, we would classify is round and square as failing to ascribe a property. On more permissive views, there are such impossible properties, and so is round and square does ascribe a property, albeit one that no object could have. We need not settle the issue here.

The more interesting case is that of predicates that do not entail existence. On the view I am

interested in defending there are two sorts of subject-predicate truths containing empty names:

singular negative existentials and representation-dependent truths. Let us take these in turn.

What role does does not exist play, if not to ascribe the property of nonexistence to an object?

Negative free logicians, such as Sainsbury (2005), have long maintained that rather than ascribing a property of nonexistence does not exist denies the ascription of the property of existence. So far, so familiar.

Accepting this, then, opens up the possibility that in general complex predicates may do something other than ascribe properties, they might, instead, say something about property ascriptions. Perhaps this approach can be applied to representation truths, truth such as

12. Holmes is a fictional character

13. Vulcan was postulated by Leverrier.

For example, one might think that is a fictional character, rather than ascribing a property of

being a fictional character, says that the ascription of being a character is fictional, i.e. made

within a fiction. So, Holmes is a fictional character is equivalent to fictionally, Holmes is a

character (Sainsbury 2005: Chapter 6). A problem with this view is that it overgenerates

fictional characters, since real people can appear in fiction. In whatever sense it is true that

fictionally, Prince Andrei is a character, it is also true that fictionally, Napoleon is a character.

So, Prince Andrei and Napoleon are both fictional characters according to this view. But since

Napoleon is not a fictional character, this view is false.

So, if ‘is a fictional character’ isn’t ascribing a property to its subject or being used to say

something about a property ascription to its subject, what is it doing? I propose that is a fictional character is instead used to characterise a representation. We know that the truth of ‘Holmes is a fictional character’ has something to do with representation, this is what I mean when I classified it as a representation-dependent truth. It is because Conan Doyle wrote A Study in

Scarlet, using the name ‘Holmes’, that (12) is true.

Following Tiedke (2011), I assume that names are associated with not only a referent (or are empty), but also a tag which marks how they were introduced.16 This allows us to provide the

following truth conditions:

14. N is a fictional F iff fictionally, N is F, and ‘N’ has the FIC tag.

Holmes is thus a fictional character since ‘Holmes’ has the FIC tag and fictionally, Holmes is

a character i.e. a person. Napoleon is not a fictional character since, ‘Napoleon’ does not have the FIC tag.

16 Tiedke puts her FIC tag to uses that I do not, for she wants to say it is true that Holmes is a detective. I am quite happy to say that it false that Holmes is a detective, although it is fictionally true and we sometimes make believe that it is true.

The above allows us to distinguish between Holmes and Napoleon, even though they both

appear in fiction, but consider the following case. An author writes about a real person, Kit, in

a fiction but refers to him with the name 'Oliver'. Oliver is not a fictional character, but a real

person, although he is not really called Oliver. What this case shows is either that a name being

introduced in a fictional context is not sufficient for it having the FIC tag since emptiness is

also required, or else that (14) needs to be amended so that N is fictional F only if ‘N’ is empty

as well as having the FIC tag.

Suppose, however, that I write a novel concerning Le Verrier and his hypothetical planet

Vulcan, but that I use the name 'Hephaestus' instead of 'Vulcan'. Should we say that Hephaestus

is a fictional character. My inclination is to say not. If that’s right, then our account of is a fictional character must be tweaked even further. I think this can be done in terms of name using practices, but I will not explore the issue further here.17

Such an approach allows us to start to answer both of the challenges at the end of §5 for those who reject 1EP. First, we have started to address Williamson’s challenge to provide a semantics for (necessarily) empty names that allows for failure of substitutivity of empty names, since some, but not all, empty names will be associated with the FIC tag (‘Vulcan’ is not, for example). In a compositional semantics, the semantic value of ‘Holmes’ might be the ordered pair <{}, FIC>, whereas the semantic value of Napoleon might be the ordered pair

<{Napoleon}, REF>. It is well known that for an intensional language, the semantic value of a name could be given by the singleton of its referent, if it has one, and the empty set

17 See Salis (2013) for an overview of the issues.

otherwise.18 Here we generalize the idea, somewhat, to a hyperintensional language, by appeal

to Tiedke’s FIC and REF tags.

Second, we have said what it is that is a fictional character does, it characterises a

representation or representations, since N is a fictional character iff there is a fiction that says

N is a person, and also that ‘N’ has the features required for it to have the FIC tag. In a

compositional semantics, is a fictional character could have the semantic value {<{}, FIC>}.

As a result, we have

15. Holmes is a fictional character iff <{}, FIC> ∈ {<{}, FIC>}

which given what else we’ve said, yields the correct truth-conditions.

A similar account can be given of other truths containing empty names, all of which will, in

some sense, be representation dependent (see Forbes 2006 for a discussion of how this might

work in the case of intensional transitives).

7. Second-Order Ontology

The above discussion has been focussed on first-order order ontology – what objects are there,

externally speaking? But there is a related question in second-order ontology, what properties

are there, again externally speaking (see below).19 As I noted above, just as there is a Fregean

picture of names, there is a related picture of predicates. Above, we focused on

18 Evans, Everett, Rami. 19 Some philosophers think that questions of second-order ontology just are questions in first-order ontology, since properties are objects. Others, inspired by Frege (REF), take objects and properties to be nonoverlapping ontological categories. I take no stand on the issue here, but because of the existence of debate, and the variety of syntactic positions quantifiers can bind, I treat the questions separately.

Syntactic Decisiveness*: if an expression exhibits the characteristic syntactic features

of a predicate, then that fact decisively determines that the expression in question has

the semantic function of a predicate, i.e. to ascribe a property (when it combines with a

singular term).

but the following claim is the other part of the package

Ascription Minimalism: the mere fact that an ascribing expression features in a true

sentence (of a certain sort) determines that the ascribing expression ascribes a property.

So, for the Fregean, second-order ontology, just like first-order ontology, consists in identifying which sentences are true.

But just as

16. Lee thinks that Pegasus is a unicorn

shows that unrestricted Referential Minimalism is false, it also shows that Ascription

Minimalism is false (at least given the claim that the function of ‘is a unicorn’ is to ascribe a

property), I think, since the predicate ‘is a unicorn’ does not succeed in ascribing a property. If this is right, then we need to admit an internal reading of the second-order quantifier to account for

17. There is something that Lee thinks Pegasus is, namely a unicorn.

Just as in the first-order case, this internal quantifier will be classical.

In order to decide whether a second-order domain of discourse is ontologically committing, we need to decide whether the predicates ascribe properties. Is there a purely linguistic test for this? As above, the Fregean might want to limit their minimalist claim to subject-predicate sentences. If we limit to Ascription Minimalism to subject-predicate sentences, we get

The Second-Order Existence Principle (2EP): Fa → ∃Y≈F

That unrestricted Ascription Minimalism is false does not show that 2EP is false, since there

are no true sentences of the form ‘a is a unicorn’, but that does not give us reason to endorse

2EP.

2EP is a theorem of classical second-order logic, but as we’ve just noted, the logic for the

second-order external quantifier is free. Just as with 1EP, we might motivate 2EP by appeal to

Williamson’s rhetorical question. Williamson asks, remember, ‘[h]ow could a thing be

propertied were there no such thing to be propertied?’ (2013: 148). And we might add, how

could a thing be propertied were there no such property for the thing to exemplify? But what

this question supports in the first instance is not 2EP, but rather

Property Ascription 2EP: if ‘Fa’ is a property ascription, then Fa → ∃Y≈F.

We only get from Property Ascription 2EP to 2EP, if we assume, that true subject-predicate sentences ascribe properties to objects. Now this is what Ascription Minimalism claims, but I have argued against this in the previous two sections.

So, as in the first-order case, in the second-order case we need to determine which property ascriptions are true, and this requires us to ascertain which predicates have the function of ascribing properties.

I assumed in the discussion of first-order ontology above that there are indeed true and false property-ascriptions. But we could put the points I made there in more neutral terms: some, but not all predicates have the semantic role of describing objects or of mapping objects to truth values. The job of the first-order ontologist is then to determine which predicates have this function, and which sentences containing these predicates are true.

The second-order case is different, however. Since on such a picture, talk of properties could be dispensed with altogether, Syntactic Decisiveness* being rejected in favour of

Syntactic Decisiveness**: if an expression exhibits the characteristic syntactic features

of a predicate, then that fact decisively determines that the expression in question has

the semantic function of a predicate, i.e. to describe an object (when it combines with

a singular term).

On such a picture there is no quick linguistic route to a second-order ontology of properties.

What would be needed would be to establish

Description-Property Link: If a predicate putatively describes an object, it has the role

of ascribing a property.

Perhaps there are good arguments for Description-Property Link. And perhaps some of these

are linguistic, at least in a broad sense – perhaps the best metasemantics for (some) predicates

involves the assignment of properties to them. But whereas it is relatively uncontroversial that

objects play at least some role in the semantics of names, it is much more controversial what role, if any, properties play in the semantics of predicates.

Of course, we have seen good reason to reject Syntactic Decisiveness** along with Syntactic

Decisiveness* in §6. If this is right, then predicates as a class cannot be characterized semantically in terms of (a) ascription of properties (Liebesman), (b) mapping referents to truth-values (Davidson), or (c) denoting non-objects (Frege).

8. Conclusion

Both the Fregean and Hofweber think we can settle ontological questions by examining language. I am sympathetic to this approach and indeed to the views they offer. But I have suggested here that neither can be embraced wholesale, even leaving to one side the possibility of syntactically singular terms that are not semantically singular, and even when we focus on subject-predicate sentences and generalizations from them.

The truth that both approaches approximate is that there cannot be a true ascription of a property being F to an object x, in the absence of the property being F or the absence of x. But it is doubtful whether which true sentences are property ascriptions can be read-off from syntax,

and that a sentence has subject-predicate form does not settle the issue. To decide whether a

sentence is a property ascription requires reflecting on whether the singular terms in that

sentence refer and what story we can tell about the role of the predicates in that sentence.

References

Braun, D. 1993: Empty names. Nôus 27: 449–469.

Crane, T. 2013: The Objects of Thought. Oxford: Oxford University Press.

Dummett, M. 1981. Frege Philosophy of Language. Second Edition. London: Duckworth.

Dummett, M. 1993: Could There Be Unicorns? In his The Seas of Language. Oxford: Oxford

University Press, pp. 328-348.

Evans, G. 1982: The Varieties of Reference. Oxford: Clarendon Press.

Frege, G. 1953: The Foundations of Arithmetic. Translated by J.L. Austin. Oxford: Blackwell.

Hofweber, T. 2016: Ontology and the Ambitions of Metaphysics. Oxford: Oxford University

Press.

Jones, N. 2018: Nominalist realism. Noûs 52: 808–835.

Kripke, S. 1980: Naming & Necessity. Oxford: Blackwell.

MacBride, F. 2003: Speaking with Shadows: A study of Neo-Logicism. British Journal for the

Philosophy of Science 54: 103-163.

McCarthy, A. and Phillips, I. 2006: No New Argument Against The Existence Requirement.

Analysis 66: 39-44.

Quine, W.V.O. 1948: On What There Is. Review of Metaphysics 2: 21-38. Reprinted in Quine

1980: From a Logical Point of View: Nine Logico-Philosophical Essays. Revised Second

Edition, Cambridge, MA: Harvard University Press.

Sainsbury, R.M. 2005: Reference without Referents. Oxford: Oxford University Press.

Salis, F. 2013: Fictional Names and the Problem of Intersubjective Identification. dialectica

67: 283-301.

Schiffer, S. 1996: Language-Created Language-Independent Entities. Philosophical Topics 24:

149–67.

Stalnaker, R. 2012: Mere Possibilities. Princeton: Princeton University Press.

Tiedke, H. 2011: Proper Names and their Fictional Uses. Australian Journal of Philosophy 89:

707-726.

Walters, L. 2013: Repeatable Artworks as Created Types. British Journal of Aesthetics 53:

461-477.

Walters, L. 2014: The Possibility of Unicorns and Modal Logic. Analytic Philosophy 55: 295-

305.

Williamson, T. 1989: Being and Being So. Acta Analytica 4: 93-114.

Williamson, T. 2013: Modal Logic as Metaphysics. Oxford: Oxford University Press.

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