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Abstract Universals in Metaphysics and Semantics:

A Critical Evaluation

Dr Markku Keinänen (Turku), Dr Antti Keskinen (Tampere) and Dr Jani Hakkarainen

(Tampere)

Draft, please do not quote without permission.

Abstract

Joseph LaPorte, Genoveva Martí and Nathan Salmon have argued that general terms,

natural kind terms in particular, are semantically akin to proper names. They have singular

reference, they designate individuals. The most plausible candidates for these designata are

abstract universals. So the “designation theory” of general terms favours the doctrine of

abstract universals. However, in this paper we argue that this preference involves serious

metaphysical problems. Both the Russellian and Neo-Aristotelian doctrine of abstract

universals suffer from the problem that they cannot give a theoretically satisfactory account of

instantiation of universals by particulars. Hence we conclude that notwithstanding its

theoretical appeal, the designation theory of general terms ought to be reconsidered.

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Introduction

Realism, the view that there are universals, has had a shifting history in philosophy since

Descartes. Most early modern philosophers rejected Aristotelian Scholasticism outright, which

seemed to be, for the time being, a fatal blow to realism. Yet realism was not quite dead. In the

early 20th century, Peirce and Russell, among others, rehabilitated it, but it suffered another

serious drawback in the choking hands of Quine. However, recently realism, in the form of

assuming the existence of abstract universals, has gained again more popularity from two

different but connected directions.1

On the one hand, there are philosophers of language who are inspired by Saul Kripke’s

remark in Naming and Necessity that natural kind terms as semantically akin to proper names,

as “species-names” or rigid designators of kinds. Kripke’s discussion inspired a designation

theory of general terms, of natural kind terms in particular. This theory is, in one form or

another, advocated in the works of many contemporary semanticists, for instance Joseph

LaPorte and Genoveva Martí. According to this view, which we will call “the designation

theory”, some general terms, most notably natural kind terms, designate. As designation is a

form of singular reference, the referents of such general terms should be individuals. And the

most plausible view of kinds as individuals is that they are abstract universals. So designation

theorists tend to assume that there are abstract universals.

On the other hand, contemporary analytic metaphysicians do not reject Aristotelian

realism outright anymore. Two distinguished metaphysicians, Jonathan Lowe and Brian Ellis

have defended category systems that are explicitly Neo-Aristotelian in nature. The core of the

system is the Aristotelian ontological square where particular objects and properties are

instances of substantial and property universals. In addition to Neo-Aristotelianism, there is

Russellian realism, in which universals are abstract property universals that are directly

instantiated by particular objects. This view is exemplified by Gustav Bergmann’s and his

followers’, such as Herbert Hochberg’s, factualism.

It is therefore safe to conclude that the belief in the existence of abstract universals is

again a philosophical position that has to be taken seriously. In it, “abstract” means non-spatio-

temporal, the opposite of “concrete”. We will follow Lowe’s coinage (2006, 99) and call the

doctrine of abstract universals “weak immanent realism” (“WIR”, for short). Its proponents

1 For the sake of the argument, in this paper we follow the contemporary realist’s way of drawing the distinction

between universals and particulars. Universals can be instantiated, whereas particulars cannot have instances. See

e.g. Lowe 2006, 89.

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claim that it has significant theoretical virtues. Ellis and Lowe think that abstract universals

account for the fact that objects share properties, act as the truthmakers of natural law

statements, bind the necessary attributes of natural kinds together, provide the sortal

persistence-conditions of objects and are the referents of natural kind terms. In the last point,

designation theorists in semantics join with the Neo-Aristotelian metaphysicians. They believe

that their theory has the virtue that it extends the applicability of the notion of rigidity to natural

kind terms, and possibly certain other general terms, just as Kripke proposed in Naming and

Necessity. This extension of rigidity then easily yields the desired a posteriori necessity for

certain theoretical identification sentences. Combined with a suitable account of the different

kinds of uses of such rigid general terms—singular and predicative—the designation theory

has undeniable theoretical appeal, not least because of its elegant simplicity.

In this paper, our intention is to argue that notwithstanding its putative theoretical

merits, both metaphysical and semantic, WIR is not eventually a satisfactory philosophical

theory. Both of its forms that are considered relevant in metaphysics today, the Russellian and

Neo-Aristotelian, involve different but serious metaphysical problems about instantiation of

universals by particulars. For the Russellian realist, it is hard, if not impossible, to account for

the category distinction between facts and the mereological sums (or collections of) of the

constituents of the facts; so far Russellians have not been able to tell what the ontological costs

for this distinction are. But most Russellian realists postulate facts in order to avoid Bradley’s

regress with their account of direct instantiation. Moreover, the Russellian WIR suffers from

the problem that in it, abstract universals are causal difference makers or parts of concrete

particulars.

The problem for the Neo-Aristotelian is one of her basic formal ontological relations:

instantiation. If she commits herself to metaphysically contingent kind instantiation by objects

in order to allow of kind change, she does not have resources to explain contingent

instantiation, in which she has good reasons to believe. If she thinks, as she ought to as a Neo-

Aristotelian, that instantiation is always metaphysically necessary, she must rule out the

metaphysical possibility of kind change. So the Neo-Aristotelian is forced to grant in this

second horn of the dilemma that there are only very few natural kinds, which objects cannot

change. This betrays the Neo-Aristotelian promise to provide a comprehensive account of

natural kinds. The theoretical appeal of Neo-Aristotelian realism is seriously weakened, which

undermines the motivation to endorse it.

Hence, if our argument is solid, the doctrine of abstract universals ought to be

reconsidered. This conclusion is not only metaphysically relevant, since the position of

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designation theorists is only as strong as WIR. Their view in philosophical semantics comes as

a package with WIR. So our argument and conclusion have a fairly direct impact on a

contemporary semantic theory for general terms, most notably the theory of natural kind terms.

This should motivate philosophers of language to look for a semantic theory that does not

favour abstract universals. Even if our main conclusion is negative, we believe that there is an

important, novel lesson to be learned from it both in metaphysics and in philosophy of

language.

The structure of the paper is as follows. First, we argue that the designation theory tends

to assume the existence of abstract universals. After that, we will proceed to the critical

discussion of Russellian WIR, which leads us to argue against Neo-Aristotelian WIR. In the

conclusion, we return to the designation theory. We will draw consequences for it from the

difficult problems involved in the doctrine of abstract universals.

1. The Designation Theorist’s Assumption of Abstract Universals

In the semantic tradition following Kripke’s (1980) and Putnam’s (1975) work (the “KP-

tradition” for short), the view according to which the referents of natural kind terms are kinds,

hence universals, has gained wide popularity. Kripke apparently embraced this view in Naming

and Necessity: he considered natural kind terms as semantically akin to proper names, as

“species-names” or rigid designators of kinds (1980, 116-140).2 As is well known, Kripke was

not very explicit about the details of his view - it is unclear how exactly he intended to extend

the idea of rigid designation, originally introduced for singular terms, to general terms

(Haukioja 2012, Soames 2002, 245, 262-3). As of date no consensus has emerged on how this

is to be done, and some writers have argued that there is no fruitful way to extend the rigidity

distinction to general terms (Schwartz 2002; Soames 2002). However, Kripke’s “simple

proposal” about the extension of the notion of rigidity seems to have intuitive appeal since it is

so straightforward (López de Sa 2008, 264).

Perhaps the first well-developed formulation of the view of kinds as designata of natural

kind terms is found in Nathan Salmon’s development of Putnam’s semantic theory (2005, 123,

148).3 Salmon’s theory involves an analysis of the relation of cross-world conspecificity of

2 There are some passages, though, in which Kripke seems to consider some (rigid) natural kind terms as

predicates, thus adding to the confusion about his view.

3 The aim of Salmon’s discussion, originally published in 1982, was to show that kind essentialism, in the form

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individuals that assumes kinds (such as the water-kind and the species tiger) as “intermediate

entities” to which individuals are intra-worldly related by the relation of instantiation (which

Salmon signifies by the symbol “∈ ”). Other semantic theorists who have adopted the

theoretical option of taking universals as designata of general terms (especially kind terms)

include Joseph LaPorte (2000; 2004, 2006), Bernard Linsky (2006), Dan López de Sa (2008),

Ilhan Inan (2008), Genoveva Martí and José Martínez-Fernández (2010). Among

metaphysicians, this kind of semantic view has been endorsed by E.J. Lowe (2009).

It has not been common for semanticists in the KP-tradition to discuss the exact

metaphysical nature of kinds as referents of kind terms. For example, it is not always made

explicit whether a semanticist conceives of kind universals as abstract (non-spatio-temporal)

or as concrete (spatio-temporal) entities - in metaphysics both options have their proponents

(see below). At least, it is perhaps safe to assume that all agree that kinds are universals, not

particulars.4 Salmon, as well as LaPorte, is unusually explicit, stating that kinds are abstract

universals (Salmon 2005, 46; LaPorte 2004, 38; cf. LaPorte 2013, 12), and the abstract

character of kinds is acknowledged more or less in passing by others, too (Inan 2008, §5; Martí

2004, 142). Since we are not aware of any semantic theory of kind terms that would involve

the view that kinds are concrete, we shall assume in the present paper that kinds as abstract

universals is the default option among semanticists. A further question is what, if anything, is

made of the distinction between kinds and properties as abstract universals designated by rigid

general terms; our present discussion will apply to both options.5

One of the central challenges for the theory of general term designation is the so-called

trivialization of rigidity problem. To take up LaPorte’s much discussed example, it seems

natural to think that “soda” designates the soda kind in all possible worlds (hence is rigid), and

that “the beverage my uncle requests at Super Bowl parties” designates this kind in the actual

world but not in every world (hence is non-rigid). However, it can be replied that also the latter

of necessity of theoretical identity statements like “Water = H2O”, is not a consequence of Putnam’s semantic

theory per se.

4 In principle, one could hold that kinds, whether kinds of objects or properties, are sets of objects and sets are

abstract particulars and individuals. But this view has the implausible consequence that the number of the members

of a kind is fixed, because of the identity-conditions of sets. Its more plausible version is to say that kinds are sets

of possible objects, but it leads to modal realism, which is a high price to pay. So we can set this nominalist

position aside. Regarding properties, another nominalist possibility is that they are identified with functions in

possible world semantics, where functions are taken to be sets. We shall show in the conclusion that at the moment

this reductive account of properties is too much underdeveloped as a metaphysical view to be an option for

designation theorists. Neither is it, as far as we know, endorsed by any designation theorist.

5 As we argue elsewhere [SELF-REFERENCE OMITTED], a convincing case against concrete universals has

been made on metaphysical grounds by Lowe (1998, 156) and Douglas Ehring (2002).

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general term rigidly designates a kind, namely the kind that is instantiated by beverage samples

in a world w if and only if my uncle requests that kind of beverage in w; we may call this kind

universal “BMURASP” (Devitt 2005, 141; Schwartz 2002, 267-9). Devitt argues that

LaPorte’s view that “the beverage my uncle requests at super bowl parties” is not rigid while

“soda” is, is based on a “selective realism” about universals. Devitt concludes that a rigid/non-

rigid distinction for general terms that assumes selective realism to avoid trivialization leaves

the whole semantic issue hanging on “a controversial metaphysical issue in the theory of

universals” (Devitt, op. cit.). In contrast, Martí (2004, 141-2) argues that such a metaphysical

issue is beside the point; regardless of how abundant one’s stock of universals happens to be,

the semantically important question is whether a term designates a universal or only expresses

it.

As Devitt sees it, the trivialization problem concerns a genuine ontological issue - an

issue of what there is. The other well-known problems facing the designation theory6 do not as

directly concern the ontology of universals. While the general term designation theorists have

taken time to respond to the worries about the assumption of “unusual kinds” like BMURASP,

the very assumption of universals in the first place is rarely taken up as an issue in itself. Devitt,

who advocates a different account of general term rigidity7, argues that a semantic distinction

like rigid/non-rigid should not rule out nominalism; the semantic theory of the designation

theorists is useless for one who denies the existence of universals (2005, 143). To adopt that

semantic theory, one would have to side with the realist.

Contrary to Devitt, Ilhan Inan (2008) argues that although the view that there are rigid

general terms may well involve a commitment to kind universals as designata8, the semantic

distinction between rigid/non-rigid general terms is itself independent of the metaphysical issue

of realism about kinds. However, it seems that the very distinction between rigid and non-rigid

general terms, as Inan and other general-term designation theorists construe it, does require

6 See e.g. Marti and Martinez-Fernandez 2010, Haukioja 2012, 403-405.

7 Devitt’s own account is based on the notion of predicates as rigid appliers (2005; Devitt and Sterelny 1999).

8 Inan suggests that it may well be the case that a general term such as “tiger” can be rigid only in singular

occurrence, as opposed to an occurrence within a predicate (2008, 228). If this were indeed the case, the rigidity

of a general term would be sensitive to its logical position. According to Inan, a general term has a singular

occurrence within a sentence if that term could occupy one of the argument places of a predicate within that

sentence. Inan’s distinction between singular occurrence and occurrence within a predicate is analogous to Martí

and Fernandez’s (2010) distinction between having a kind semantics and having an exemplifier semantics; in both

cases, it is a matter of the role of the general term in the logical structure of the sentence under consideration.

LaPorte, too, argues for a somewhat similar distinction (2000; 2006). According to LaPorte, descriptions like “the

insect kind most commonly farmed for honey” have two different kind of uses, as rigid and as non-rigid.

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commitment to the existence of kind universals. This can be seen by considering a case where

a nominalist applies the Kripkean test of rigidity (Inan 2008, 218-19) to general term F: she

asks after the truth of the sentence “F might not have been F”, where F is given a singular-

occurrence reading and the modal operator has narrow scope. The nominalist will inevitably

get the result that the sentence is not true or without any truth value. And she will get this result

not because “F”, as a designator of a kind universal, is rigid and the kind F could not be

anything other than itself, but because any singular occurrence of a general term amounts to a

token of an empty term. It is then up to one’s preferred account of the truth value or lack thereof

of sentences containing empty terms whether one treats the sentence as false or as truth

valueless. If a nominalist opts for the former, then she will treat all sentences of this form as

false and hence all general terms in singular occurrence as rigid, which would trivialize rigidity

for general terms; if she opts for the latter, the Kripkean test will not yield the rigidity

distinction for general terms at all.

Contrary to what Inan claims, it seems not to be the case that the ontological dispute

over the existence of universals would have “no bearing on the notion rigidity which is

basically a semantic one” (2008, 228). Certainly, a nominalist would be an unlike supporter of

a semantic theory according to which general terms in singular occurrence resemble singular

terms in that their semantic function is to refer to individuals; for she would also have to

maintain that unlike proper names, general terms in singular occurrence invariably fail to refer

since the metaphysical category of their purported referents is empty. Even if one could

formulate a consistent theory of this sort, it is hard to see what its point would be. A more

serious consequence of a nominalist orientation is that the rigid/non-rigid distinction for

general terms which the realist gains from the semantic theory would be lost on the nominalist.

Hence, in contrast to what some contemporary semanticists claim, the metaphysics of

universals cannot be kept separate from the discussion concerning the semantics of general

terms. It is far from established that the theorist of general term designation could simply

suspend all judgment concerning the metaphysical dispute between nominalists and realists.

Surely, most if not all theorists of general term designation are perfectly happy to

embrace some form of realism about universals, whether selective or not. Indeed, the

fruitfulness of realism in semantic theory may be seen as indirect support for realism itself. It

must be kept in mind, however, that the position of the general term designation theorist is only

as strong as the case for realism, and so the failure of realism as a metaphysical position would

have a fairly direct impact on a contemporary semantic theory for general terms, most notably

the theory of natural kind terms.

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2. Weak Immanent Realism

Let us therefore consider how realism fares in the metaphysical literature nowadays.

Following tradition, it is standard to distinguish two mutually exclusive forms of realism that

takes universals to be abstract (e.g. Lowe 2006, 25 and 98-99). The first form is the “Platonist”

view, on which universals are transcendent: capable of existing without particular instances.

The second, opposite realist position is the “Aristotelian” immanentist view on which

universals depend for their existence upon their particular instances. So the Aristotelians

believe that there cannot be uninstantiated universals, whereas the Platonists allow for this

metaphysical possibility. In this paper, we shall focus on Aristotelian realism for two reasons.

First, Platonic realism is not a commonly held metaphysical position on universals at the

moment.9 Secondly, as will be observed in the conclusion, it is very hard, if not impossible, for

the Platonist to avoid the force of our arguments against Aristotelian abstract universals.

Lowe divides Aristotelian realism into two types, “strong” and “weak”, depending on

how we understand the immanence of universals “in” their particular instances (2006, 98-99).

According to strong immanent realism (1998, 156, cf. 2006, 98-99), universals are literally in

their concrete instances, hence themselves concrete (Armstrong 1989, 98-9 and 1997; Smith

1997; Hawley and Bird 2011). This is a view that is not be discussed in the present paper. Our

focus will be on weak immanent realism (henceforth “WIR”), according to which universals

are abstract, that is, non-spatio-temporal (Bergmann 1967, 49; Ellis 2001, 73-76; Lowe 2006,

99).

In the contemporary metaphysical literature, one can find two forms of WIR. They may

be labelled Russellian and Neo-Aristotelian. Russellians consider property universals as

directly instantiated by objects or bare particulars, whereas Neo-Aristotelians believe that

property universals are instantiated by tropes or modes (that is, particular properties) which in

turn characterize objects.10 In what follows, we shall first take up the case of Russellian

universals and then turn to the Neo-Aristotelian option.

9 Cf. Berman (2008) and Tugby (2013) for recent but rare defenses of Platonic realism.

10 Lowe prefers “mode” to “trope” as he thinks that particular properties are objects’ ways of being (1998, 78;

2006, 14-15). Nevertheless, henceforth we will use only “trope” for the sake of brevity.

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Russellian Realism

Russellian realism is a “two-category” or “three-category” ontology that introduces

objects or bare particulars and property universals, and possibly “ties” or “nexus”, but rejects

tropes. In it, property universals are directly instantiated or exemplified by objects or bare

particulars. Russellians take the relation of instantiation or exemplification as either primitive

or grounded. Depending on how instantiation is grounded, one may distinguish two forms of

Russellian WIR, Armstrongian and Bergmannian. The Armstrongian version explains

instantiation by reference to the existence of an entity over and above objects and universals: a

fact (or, a state of affairs). Both facts and objects are concrete, but universals are abstract.

Suffice it here to focus on atomic facts that are considered as complex entities, each of which

has object a and property universal P as its constituents. An atomic fact exists if a instantiates

P.11

Bergmann (1967, 11, 14, 22-23, 44-45), Hochberg (1978; 339) and J.P. Moreland

(2001, ch.5) add another universal, the fundamental tie or nexus of exemplification to this.12

Its theoretical role is to connect a bare particular and a property in a fact. For them, the entity

instantiating the property is thus a bare particular, a bare individuator, not an ordinary object.

They think that ordinary objects are complex facts constituted by the instantiations of monadic

properties by a bare particular. Bare particulars instantiating monadic properties are atomic

facts. On this view, both ordinary objects and their constituent atomic facts are particulars.

The Russellian WIR is partly motivated by solving a version of the problem generally

known as Bradley’s regress. Assume that object a has a property P contingently, which means

that a and P can exist without being connected to each other (a could be not-P). From this, it

seems to follow that there has to be an ontological ground for a instantiating P; the mere

existence of a and P is not sufficient for a instantiating P. This ground is that a and P are

connected by an entity over and above them: the relation of first-order instantiation. But now

we face another call for explanation: what is the ontological ground for the fact that are a and

P connected by the relation of first-order instantiation? In order to account for that, we must

introduce a three-place instantiation relation to connect instantiation and the entities it relates,

namely, a and P, and so on. Thus, in order to give an ontological ground for one instantiation,

11 Armstrong himself (1989, 1997) is a factualist and realist believing in concrete universals.

12 Hochberg (2009, 103) changes his earlier view and replaces the nexus with compresence

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we must postulate an infinite number of instantiation relations.

Facts are entities designed to block Bradley’s regress (cf., e.g., Bergmann 1967, 6-12;

Armstrong 1997, sec. 8.12; Hochberg 1978, 336-340). The main idea is that the existence of a

fact suffices to stop the regress before it gets started. The instantiation of P by a amounts to the

existence of the fact that Pa, which is a complex, third entity having these two constituents. P

is instantiated by a because the fact Pa exists. In Bergmann’s and Hochberg’s earlier view, the

tie of exemplification is a connector that can connect without itself being connected. Tie E

connects a and P without launching Bradley’s regress because its connecting a and P amounts

to the existence of the fact that E ties a and P. Both views avoid Bradley’s regress, since there

is no need for an additional entity (e.g., the relations of instantiation) that would ground

instantiation. So factualism seems to be a promising way to avoid Bradley’s regress.

However, at the end of the day, factualism betrays this promise; the problem just moves

to another place. In order to see that, let us consider the categorial nature of facts. As we pointed

out, facts are complex entities. Their existence is contingent relative to the existence of their

constituents (P and a, and possibly the tie of exemplification). So the fact that Pa cannot be

identified with the mereological sum of its constituents, P + a (+ the tie of exemplification); a

and P (and the tie of exemplification) might exist without constituting the fact that Pa

(Hochberg 2009, 107). For example, if a ball and redness (and the tie of exemplification) exist,

it does not follow that the ball is red.

According to Vallicella (2002, 20), “[t]he difficulty with this is that it seems to be a

contradiction to say of a whole [fact, our addition] that it is an entity in addition to its parts

when it is composed of them.” The factualist might claim that there is no contradiction and

insist that the existence of the fact does not reduce to the existence of its constituents; the

constituents and their formal features determine only the possibility of the fact but not its

existence. The world is constituted by facts, which are instantiations of the property universals

by objects and form an additional irreducible category of entities. Thus, there is no

contradiction in distinguishing between facts and sums of their constituents.

The problem with the factualist answer is that it merely assumes that the distinction

between the fact that Pa and the sum P + a (+ the tie of exemplification) is a primitive

distinction between two categories of entities: facts and mereological sums. So factualists just

stipulate that instantiation amounts to the existence of a new kind of entity, a fact (Dodd 1999,

155). They merely assert that when a ball does instantiate redness, or redness is, indeed,

connected to a bare particular by the tie of exemplification, there is the fact over and above

these constituents that the ball is red.

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The factualists assume that the category distinction between facts and the sums of their

constituents is both primitive and further inexplicable (e.g. Hochberg 1978, 338). But it seems

to be unacceptable to leave it without further explication. All category distinctions are in a need

for an ontological ground; there must be some features of entities owing to which they belong

to the category at issue. In some category systems, entities themselves can be considered as

such a ground by standing in certain formal relations to other entities.13 Nevertheless, facts and

the aggregates of their constituents (possible facts) are indistinguishable with respect to the

formal features of their constituents. We cannot distinguish between them on the basis of

formal relations either. The only way to distinguish between facts and the non-existent possible

facts is by recourse to instantiation. Since instantiation is explained in terms of fact existence,

any attempt to account for the latter in terms of the former is also excluded. Therefore, we need

to postulate other entities to ground this category distinction. As a consequence, the original

Bradley’s regress problem transforms to a problem about the ontological ground of the alleged

category distinction between facts and the corresponding mereological sums of the constituents

of a fact.14 Hence, we do not know the actual ontological costs of factualism: what categories

of entities factualists have to assume eventually to make their view work.15

Factualism is not the only way the Russellian realist might try to avoid Bradley’s

regress. She might reject facts and consider instantiation relations as primitive: if object a and

property universal P exist, it is a further primitive fact about a and P that a instantiates P. But

this falls into the trap of Bradley’s regress in the manner explained just above. In the Russellian

context, instantiation is not an internal relation that would not be an entity over and above a

and P (or a formal relation, cf. the discussion of Neo-Aristotelianism below). Consequently,

after having introduced the first-order instantiation relation, we must introduce a further, three

place instantiation to ground the first instantiation. The obtaining of the first instantiation

ontologically depends on the obtaining of the multi-place instantiations and the regress seems

13 Cf., e.g., Lowe (2006, 114 ff.) for such a suggestion with respect to the categories introduced in his four-category

ontology. Formal ontological relations are discussed more below.

14 Bergmann (1967: 9) does not accept the existence of mereological sums; according to him, “[a] collection of

entities is as such itself not an entity”. All complex entities are facts, which are built from simples by means of

the tie(s) of exemplification. Nevertheless, we can ask Bergmann what is the ontological ground of an entity of

being a fact, i.e., a collection of entities, which includes a suitable tie of exemplification, being a complex entity.

This is a question similar to the present problem: the latter is just transformed to a question of what makes a

plurality of entities a fact.

15 Cf. Dodd (1999); Vallicella (2002); Wieland & Betti (2008) and Betti (2014) for a similar unity problem, which

is to account for the unity of the fact in contradistinction to the non-unity of the mereological sum of its

constituents.

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vicious (cf. Maurin 2012, 800-1).

Another serious problem in factualism concerns the status of Russellian universals as

abstract entities. In contrast to the Neo-Aristotelian property universals, Russellian universals

are directly instantiated by objects or bare particulars. According to the Armstrongian version

of this theory at least, universals are themselves assumed to take part in their concrete

instantiations. Facts are concrete entities having abstract universals as their parts. This violates

the prima facie plausible principle that all parts of concrete (spatial or spatio-temporal) entities

are themselves concrete (spatial or spatio-temporal). The fact that Pa is constituted by concrete

particular a and abstract universal P. Unlike the mereological sum P + a, which does not seem

to have any determinate location, Pa is stipulated to have the same location as a. However, the

factualist does not spell out of how an abstract universal can be localized as a part of its

instantiations (atomic facts). Calling facts “ordinary objects”, “particulars” or “property

instances” does not add to our understanding of this matter.16

Hochberg steers away from this problem by holding that facts are abstract (2009, 108).17

Nevertheless, this move is a counsel of despair. It seems that the best a posteriori candidates

of property universals are basic physical properties (such as determinate masses and electric

charges), which contribute to the causal powers of the objects having these properties. If

properties bestow causal powers on objects, these powers always act in some spatial locations.

Furthermore, it is the locations of the instantiations of these properties by objects, on

factualism, the locations of atomic facts, that determine the locations of the corresponding

causal powers. For instance, the location of the instantiation of electric charge e by object a at

time T determines the location of the corresponding causal power in an electric field at T. The

claim that atomic facts are abstract would make the essentially local character of causal powers

that the property instantiations determine a mystery.

Armstrongian upholders of abstract universals do not suffer from this problem as they

do not think that facts are abstract. Still they face a closely similar problem owing to their view

that universals are abstract. Armstrong himself (1997, sec. 3.82) argues against abstract

16 If the factualist goes on to maintain, as Armstrong does, that universals are concrete, then she falls into the trap

of Lowe’s (1998, 156; 2006, 99) and Ehring’s (2002) incoherence argument against concrete universals, as we

have argued elsewhere [SELF-REFERENCE OMITTED].

17 Bergmann’s view is unclear. He maintains that ordinary objects, which complex facts are, are concrete (1967,

48). This supports the reading that also atomic facts are concrete on his view. However, Guido Bonini (2009) has

argued that Bergmann eventually believes that atomic facts are abstract. They have only a concrete constituent, a

bare particular. If Bergman opts for the former view, his position suffers from the problem of a concrete entity

having an abstract part. If he believes that facts are abstract, he has to answer to the next problem.

13

universals on the basis that universals bestow causal powers on objects. He adopts the so-called

Eleatic Principle and claims that every property universal must make a difference in the causal

powers of objects that instantiate it. For instance, if an object instantiates the rest mass universal

m, m has to be a causal difference-maker (in terms of gravity). Armstrong uses this demand to

justify the claim that every universal is a part of the space-time system and his rejection of

abstract universals. By the above argument, the instantiations of abstract universals making

difference in the causal powers of their instantiations are concrete. Hence, if an Armstrongian

subscribes to the Eleatic Principle, there is a high intellectual pressure for her to defend the

abstractness of universals.

To sum up, then: our first critical point is that the factualist attempt to avoid Bradley’s

regress just moves the problem to another place. According to it, facts, considered as single

entities, are instantiations of universals by objects or bare particulars. It remains completely

unclear what extra entities we have to postulate in order to make the category of facts a

functioning part of a category system - in contradistinction to the mereological sums (or

collections) of objects (or bare particulars) and properties (and possibly the tie of

exemplification), in particular. Secondly, the abstractness of a property universal, on the one

hand, and the concreteness of its instantiations, on the other, introduces further unanswered

questions such as how an abstract universal entity can be a part of a concrete particular, or

causally efficacious. Hence, Russellian WIR is theoretically a very unattractive position.

Our conclusion at this point is that the supporters of abstract immanent universals, both

metaphysicians and designation theorists, should consider the Neo-Aristotelian alternative of

the view. Accordingly, we will next discuss Neo-Aristotelian realism. We shall conclude,

nonetheless, that even if it is a more sophisticated position than Russellian WIR, it suffers from

a different serious problem.

Neo-Aristotelian Realism

The self-proclaimed Neo-Aristotelians, Lowe (2006, 99) and Ellis (2001, 73-4), are

perhaps the two most prominent contemporary representatives of WIR in metaphysics. In

contrast to Russellian Realism, the Neo-Aristotelian accommodates two categories of

universals at least, substantial kind and property universals. Kind universals are instantiated by

objects and property universals by tropes. According to the Neo-Aristotelian, instantiation is a

basic formal ontological relation. As a formal ontological relation, instantiation contributes to

14

spelling out the categorial nature of particulars and universals. Moreover, universals are

immanent because they necessarily have some particulars as their instances.18

It is the relation of instantiation that causes the severe problem for Neo-Aristotelian

Realism. This problem has the form of a dilemma. Tentatively formulated, the dilemma goes

as follows.

1st horn: if the Neo-Aristotelian holds that there is metaphysically contingent

instantiation between objects and kinds, then it is difficult, if not impossible, to make sense of

this contingent instantiation in the Neo-Aristotelian framework.19 It seems that instantiation

must be, if there is to be instantiation in the first place, a metaphysically necessary relation. In

the Neo-Aristotelian category systems, instantiation is supposed to be a formal ontological

relation. Formal ontological relations hold because the related entities exist. In other words,

they do not require anything else to hold than the existence of their relata. As a consequence,

formal ontological relations hold necessarily given that the relata exist. Hence, they are

ungrounded internal relations: they are metaphysically necessary relations (assuming the

existence of the relata), and their holding is grounded by the very existence of their relata. A

good example of a formal ontological or ungrounded internal relation is numerical distinctness.

If two entities are numerical distinct, their existence is sufficient for their numerical

distinctness.

The metaphysical contingency of some cases of instantiation would mean that there is

a sense in which a particular object is an instance of some kind K and another sense in which

it is not an instance of K. For example, let us assume, for the sake of illustration, that Dobbin

would be contingently an instance of the kind horse. Consequently, Dobbin would not be not

be an instance of this kind universal in a strict formal ontological sense: the existence of Dobbin

would not be sufficient for its being a horse. Still, there would be a sense in which Dobbin is

an instance of the kind horse. Since natural kinds are identified with kind universals in Neo-

Aristotelianism, there would be a sense in which Dobbin is a horse and some other sense in

which he is not. This seems unintelligible.

18 In other words, universals are generically dependent for their existence on their instances (particulars).

According to Lowe (2006, 37), this generic dependence (in his terms, non-rigid existential dependence) is

constituted by the formal relation of instantiation between universals and its instances.

19 The view that instantiation between a property universal and a trope would be contingent has no known

advocates.

15

2nd horn: if instantiation is taken to be a metaphysically necessary relation, then kind

change from one natural kind to another is impossible. Because of the necessity of instantiation,

given that an object instantiates a natural kind as a universal, it cannot fail to instantiate this

universal. For example, if Dobbin instantiates, of metaphysical necessity, the kind horse, then

it is not metaphysically possible for Dobbin not to be a horse. This is a problematic implication

as there are plausible empirical examples of natural kind change and good general ontological

grounds to allow of the metaphysical possibility of kind change. The Neo-Aristotelian can deal

with this problem only by denying the existence of many specific prima facie natural kinds.

This at odds with Ellis’ and Lowe’s attempt to provide a comprehensive account of natural

kinds from elementary particles to chemical kinds (Ellis 2001, ch. 2.3; Lowe 1998, ch. 8; 2006,

ch. 9).

Next, we will argue for the dilemma in detail and show that Ellis’s and Lowe’s views

are, indeed, subject to it. For that purpose, first we have to provide a few basic details of Ellis’

and Lowe’s Neo-Aristotelian realism more, which are necessary for our argument.

Ellis (2001, 74) maintains that there are three different categories of particulars, namely,

objects, tropes and processes, whilst Lowe (2006, 23) is confined to introducing two: objects

and tropes. Different kinds of particulars instantiate different kinds of universals. In Lowe’s

four-category ontology, objects instantiate kinds and tropes instantiate attributes. To this

picture, Ellis, in his six-category system, adds particular processes instantiating process kinds.

However, the different kinds of particulars are connected to the different kinds of universals

by the same formal ontological relation of instantiation.20

As we pointed out above, instantiation is a formal ontological relation in the Neo-

Aristotelian framework. This entails that it is an ungrounded internal relation (as distinctness

is): the existence of the entities connected by it is sufficient for instantiation obtaining. This

nature of instantiation has two consequences that are relevant for the present purposes.

The first consequence is a principle that may be called “NFR” (necessity of formal

ontological relations). NFR states that it is metaphysically necessary that if the relata of a

formal ontological relation exist, the formal ontological relation obtains. So instantiation is, as

a formal ontological relation, a metaphysically necessary relation for the Neo-Aristotelian.21

20 Lowe (2006, 2009), unlike Ellis (2001), restricts the use of the term “kind” to substantial kind universals, i.e.,

kinds of objects. He calls property kind universals (kinds of tropes) “attributes” (cf. LaPorte 2013, 17-18, n.8).

21 The principle that the existence of a truthmaker necessitates the truths it makes true is fairly widely accepted,

cf. e.g., Lowe 2011. NFR (as applied to formal ontological predications) has independent motivation, although it

would also be a consequence of this more general principle.

16

Second, instantiation is not itself any kind of relational entity (a member of some of

Lowe’s four or Ellis’ six categories). The formal ontological relation of instantiation holds

because there are the two entities and a formal ontological relational predication made true by

these entities.22 Thus, according to Neo-Aristotelian, tropes instantiate attributes (property

universals). Given that a -e trope exists, it is an instance of the corresponding attribute, the

property universal of -e charge. This trope is by its very nature (or, “essence”) -e trope and

instantiates the corresponding property universal; there is no need to postulate any other entities

(cf. Lowe 2011, 242). The same result can be generalized to substances and the kind universals

they instantiate.

According to the Neo-Aristotelian, every object is necessarily an instance of some kind

universal. By NFR, every object is necessarily an instance of the substantial kind it actually

instantiates. As a consequence, any object is necessarily an instance of some definite kind K,

that is, any object is connected to a definite natural kind by the formal ontological relation of

instantiation. The best explanation Neo-Aristotelians can give to this is that all objects have a

specific nature (or, essence), i.e., that they are not “bare particulars” and that they are instances

of some specific kind K because of their specific nature. For instance, helium-4 isotopes or

water molecules belong to the respective natural kinds (helium-4 atom, water molecule)

because of their being the objects they are. Hence, the formal ontological relation of

instantiation holds between particulars (substances or tropes) and their kinds because the

instances of kinds are the entities they in themselves are.23

It is a central feature of Neo-Aristotelianism that particular substances or objects do not

instantiate kinds in virtue of bearing certain tropes. Dobbin is a horse because Dobbin is what

it is, rather than having some particular properties that would ground the fact that Dobbin is a

horse.

After outlining some basic features of the Neo-Aristotelian category system, we are in

a position to discuss the above mentioned dilemma in more detail. The key point is that the

nature of instantiation as a formal ontological relation and Neo-Aristotelian essentialism jointly

rule out the metaphysical possibility of kind change. Kind change would mean that object a

first belongs to some natural kind K and then ceases to be its member of by becoming a member

of a distinct kind K’. Kinds K and K’ are contingent to object a, since a could have existed for

22 Cf. Lowe (2006, 44-47, 59). For a further discussion of formal ontological relations, see Smith & Mulligan

(1983), Correia & Keller (2004) and the other articles in the same issue of Dialectica.

23 Cf. Lowe 2011, 241-242; however, Lowe (2006, 116) maintains that objects are rigidly existentially dependent

(only) on the “highest kinds” they instantiate.

17

a shorter period and been a member either of these kinds.

In the first horn of the dilemma, the Neo-Aristotelian meets the challenge that there is

contingent kind instantiation by objects. Recall that she identifies natural kinds with substantial

kind universals. Therefore, the contingency of some natural kinds would entail that there would

be an object (e.g., a particular atom of the atomic isotope carbon-14) instantiating a kind

universal (being a carbon-14 atom) contingently. This contingent instantiation ought not to be

confused with the formal ontological relation of instantiation connecting objects and their

necessary natural kinds. Consequently, the Neo-Aristotelian would have to make a distinction

between instantiation in strict formal ontological sense (in which carbon-14 atom a perhaps

instantiates the kind universal of being an atom and -e trope instantiates the attribute of -e

charge), and instantiation in some other loose sense (in which a instantiates the kind universal

of being a carbon-14 atom).

However, it seems very difficult, if not impossible, for the Neo-Aristotelian to make

sense of these two different kinds of instantiation: how can a given object fail to instantiate

kind K in the strict formal ontological sense but still instantiate K in some other loose sense?

Allowing of contingent instantiation seems to be therefore a non-starter for the Neo-

Aristotelian.24

The leading Neo-Aristotelians have clearly recognized the general need to allow of the

metaphysical possibility of kind change. Both Ellis (2001, 238-239) and earlier Lowe (1998,

ch. 8) maintain that there are purely metaphysical reasons to allow for the contingency of

natural kinds. Lowe makes a distinction between the sortal persistence-conditions of objects

and their diachronic identity-conditions (1998, 183-4). To understand this significant

distinction, let us illustrate it with a tiger. As a tiger and a living organism, she instantiates the

natural kind tiger and belongs to the most specific category of living organisms. The natural

kind tiger provides the sortal persistence-conditions for her: under which conditions she

persists as a tiger (as an instance of this natural kind). Instead, the diachronic identity-

conditions for her being one and the same entity (object) over time are shared by all living

organisms. The natural kind tiger therefore shares diachronic identity-conditions with other

natural kinds in the category of living organisms but it has distinctive sortal persistence-

conditions. So this distinction leaves room for the metaphysical possibility that the tiger would

persist as the same entity even if she did not persist as a tiger. It is metaphysically (if not

24 Although Ellis or Lowe do not deal with this difficulty, we shall discuss some possible solutions critically

below.

18

biologically) possible that she turns into a lion, for example. In general, as objects belonging

to the same most specific ontological category but different natural kinds in the category have

the same identity-conditions, Lowe should allow of the metaphysical possibility that an object

is a member of a natural kind different from its actual kind (Lowe 1998, ch. 8; 2006, 116; 2009,

17). Ellis (2001, 238-239) suspects that the identity of an object depends on its temporal and

causal history rather than the natural kinds to which it belongs. Therefore, it seems that an

object is not necessarily an instance of the specific kind it instantiates.

There are also actual empirical cases that may be plausibly interpreted as examples of

kind change. Consider β-- decays, in which the total charge of an atomic nucleus increases by

the emission of an electron and an electron neutrino. An instance of this is the decaying of a

carbon-14 atom into a nitrogen-14 atom. Prima facie, one and the same atom persists through

this process because the total number of its nucleons remains the same, but the atom changes

its natural kind from a carbon-14 atom into a nitrogen-14 atom. The atom changes its nuclear

charge and natural kind because one of the nucleons changes from a neutron into a proton.

According to Ellis (2001, 238), “there is a powerful continuity argument to suggest that as an

individual, the former atom still exists, but now as an atom of another kind.” One might also

claim, although this is more contestable, that elementary microparticles25 as well as molecules

offer other examples of objects changing their natural kind while remaining in existence.26

So, in the first horn of the dilemma, the Neo-Aristotelian is forced to grant that the idea

of contingent kind instantiation and kind change is a non-starter. Still there is empirical

evidence interpreted in a certain plausible way which supports contingent kind instantiation

and the purely metaphysical reasons to allow of kind change. In the Neo-Aristotelian

framework, kinds form a hierarchy and the identity-conditions of objects seem to come only

with the most general kinds (or, as in Lowe’s system, with categories). Hence, the Neo-

Aristotelian cannot escape the first horn merely by insisting that kind change is not

metaphysically possible. This would only mean that she falls into the second horn of the

dilemma, where she meets the same challenge from another direction.

In the second horn, it is assumed that instantiation is a metaphysically necessary

relation. Sticking to this assumption has the main benefit of preserving the conception of

instantiation as one and the same formal ontological relation between particulars (objects or

25 For example, d-quarks turning into u-quarks in β-- decays.

26 If considered as single entities, these quarks drastically change their central properties (such as mass and electric

charge) in β-- decays. However, as in the atomic case, there is a one-to-one replacement of a particle belonging to

a general kind (quark) with a particle of the same general kind (another kind of quark).

19

tropes) and their kinds (and as in tropes instantiating attributes). Moreover, bare particulars,

objects without metaphysically necessary properties, are avoided because, according to the

Neo-Aristotelian, every object has metaphysically necessary properties that characterize the

natural kind(s) it instantiates (Lowe 2006, 62).

The cost of sticking to the metaphysically necessity of instantiation is that it rules out

the metaphysical possibility of kind change. Since we have shown that there are good reasons

for the Neo-Aristotelian not to rule out kind change, the costs of adopting this view are very

high. To be more specific, the second horn of the dilemma has an unwanted consequence for

the Neo-Aristotelian realist: there are very few natural kinds, kinds which objects cannot

change. That is the result for which we argue next.

It seems that as a reply to the problem of the possibility of kind change, the Neo-

Aristotelian may adopt the following strategy, which we call “the sub-sort strategy”. It consists

of two steps. The first step is to deny that certain alleged natural kinds (e.g., being a carbon-

14 atom) are genuine natural kinds. According to Lowe’s philosophy of language (2009), all

terms designating genuine natural kinds are semantically simple kind terms. Semantic

simplicity does not always go hand in hand with syntactic simplicity: Lowe’s example is, on

one hand, “ice”, which he regards as semantically complex and not a designator of a distinct

kind and, on the other hand, “heavy water” which is semantically simple (its semantics is not

determined compositionally by the semantics of “heavy” and “water”) and designates a distinct

kind of chemical substance, namely D2O (2009, 31). The semantically complex “kind terms”

do not refer to kind universals. They are, as Lowe (2009, 30,188) puts it, complex sortal terms,

which can be analysed into a natural kind term, which refers to a kind universal, and predicative

expressions attributing certain further features to the object.

All “kind terms” allegedly denoting to contingent natural kinds are now taken as

complex sortal terms. Using our example above, “a carbon-14 atom” is taken to be shorthand

for something of the form “an atom which has the nuclear mass m and nuclear charge n”.

Hence, the specific mass m and nuclear charge n would not characterize the natural kind to

which carbon-14 atom a belongs (i.e., atom) but rather just the atom a itself. In terms of Lowe’s

(2006, 2009) four-category ontology, atom a would possess these properties occurrently (by

possessing the respective tropes) rather than dispositionally (by being an instance of a kind

characterized by these property universals).27 But a would not instantiate the substantial kind

27 Lowe (2009, 188ff.) presents similar examples of complex sortal terms picking up sub-sorts of kinds, e.g.,

ravens having some abnormal genetic condition. However, he does not deploy them for the purposes considered

20

universal carbon-14 atom.

The second step of the sub-sort strategy is to reject the claims of contingency of any

natural kind identified with a kind universal. Continuing the above example, the Neo-

Aristotelian would maintain that only the general kind (i.e., the kind atom) but not the specific

kind is a kind universal and necessary to its instances. The sub-sort strategy would be a

combination of these two steps: as every object is necessarily an instance of some natural kind,

the Neo-Aristotelian attempts to find out for every object a (a sufficiently general) natural kind

to which it necessarily belongs (which it cannot change). If some more specific “kinds” are

contingent to their instances, they would be derivative sub-sorts of kinds: only groups of objects

picked up by the complex sortal terms. However, such sub-sorts of kinds would not be any

constituents of reality (entities), substantial universals instantiated by the objects, that is,

natural kinds as Neo-Aristotelians consider them. Hence, Neo-Aristotelians cannot

accommodate them any of the basic functions assigned to natural kinds: being instantiated by

objects, collecting the essential properties of kinds, or acting as truthmakers of law

statements.28

If we restricted our discussion to elementary particles, atoms and molecules, it might

well be a plausible suggestion that at least some general kind is necessary to each of them.

Nevertheless, even if we make this restriction, the Neo-Aristotelian is driven to the view that

there are in fact very few natural kinds. Lowe (2013, sec.6) applies the four-category ontology

to elementary particles and considers the specific natural kinds of elementary particles (e.g.,

electron and down quark) as kind universals having the basic functions mentioned above.29 In

order to make this suggestion work, one must consider the specific natural kinds necessary to

their instances. One might defend this assumption, although it contradicts the above suggestion

about quarks changing their kind (cf. n.25). A far more serious problem with this view is that

such standard a posteriori examples of natural kinds as atomic isotopes (e.g., the kind of

carbon-14 atoms) would not meet the strict standards set to natural kinds. Nor is there any

reason to expect that the specific natural kinds of more complex objects (e.g. living organisms)

here.

28 For both Ellis (2001) and Lowe (2006, 2009, 2013), the last two functions are closely interconnected. It is kind

universals that are supposed to explain that the world contains certain kinds of objects with certain essential

properties and that certain laws are true of these objects (Ellis 2001, ch. 2; Lowe 2006, 134-136, 2013).

29 Earlier, Lowe maintains that elementary particles are quasi-objects as they do not have determinate identity-

conditions (1998, 62ff., 2006, 75). On this view, their kinds cannot be genuine natural kinds because genuine

natural kinds are substantial kinds of objects for Lowe.

21

would satisfy them either.30

Hence, the second horn of the dilemma forces the Neo-Aristotelian realist to a far too

restrictive conception of natural kinds: there are only some very general natural kinds (such as

atom, molecule, living organism) and only more specific natural kinds of micro-particles. Even

then, we have to make empirically contestable metaphysical assumptions about kind change

concerning elementary particles, even if it is obvious that there cannot be kind change from a

very general natural kind to another (e.g. an organism changing into an atom).31

This foils the Neo-Aristotelian attempt to provide a comprehensive theory of natural

kinds applicable to the kinds of objects at the different levels of complexity. The specific

chemical or biological kinds, for instance, even though appearing in the standard examples of

the prominent Neo-Aristotelians (and defenders of Kripke-Putnam semantics), do not qualify

as natural kinds. Consequently, contrary to Ellis’ (2001, 238) explicit suggestion, the Neo-

Aristotelian cannot keep individual essences separate from kind essences. Since instantiation

is a formal ontological relation, objects and tropes must already “select” the natural kinds to

which they belong. Both tropes and substances are connected to their kinds by exactly the same

formal ontological relation (i.e., instantiation), which must have the same modal properties and

the same grounding, namely, the nature (or, essence) of the particular.

3. Conclusion

We concluded above that Russellian WIR suffers from two main problems. (1) It either

leads to Bradley’s regress or does not give any satisfactory account of the category distinction

between facts and the mere mereological sums (or collections) of the constituents of facts

(objects and properties, or bare particulars, properties and the tie of exemplification). (2) It

does not give any explanation how an abstract universal can be a part of a concrete particular

or contribute to the causal powers of the concrete particular. These two problems are not only

unsolved at the moment but are also very difficult to resolve - indeed, it is difficult to see how

it is possible to solve them. Therefore, the Russellian WIR is theoretically a very unattractive

30 According to the best-developed essentialist theories of the identity-conditions of such complex objects as

organisms (cf., e.g., Wiggins 2001), only some very general kinds are necessary to them. No claims about the

necessity of the specific kinds (e.g., definite species - assuming that they can be considered as natural kinds) is

made.

31 There is an additional complication in Lowe. Earlier, Lowe (1998, 184) thinks that very general natural kinds

such the organism do not actually qualify as kinds, which are universal entities, since they are categories, which

are not beings.

22

metaphysical view. As a consequence, it is not a credible option to construct substantial natural

kinds by means of the aggregates of Russellian property universals either, as complex

Russellian universals, for instance (cf. Hawley & Bird 2011).

Neo-Aristotelian realism avoids the specific problems of Russellian realism. Since the

Neo-Aristotelians postulate tropes, there is no need for facts. This alone brings economy and

keeps us away from non-calculable ontological costs, as was shown above. Property universals

are instantiated by tropes, which, in turn, characterize objects (Lowe 2006, 2009). According

to the Neo-Aristotelian WIR, all universals are abstract. Since universals are not parts of their

instantiations or any other concrete entities, there is no further problem of explaining of how

they can be localized as parts of the spatio-temporal reality.

Still the Neo-Aristotelian faces a serious dilemma: she must either (i) allow of the

metaphysical contingency of the relation of instantiation between objects and substantial kinds,

or (ii) rule out the metaphysical contingency of natural kinds and the possibility of kind change.

Since instantiation is a formal ontological relation, alternative (i) is a non-starter -

notwithstanding the reasons for allowing of kind change. Thus, the Neo-Aristotelian must take

the second horn, i.e., assume that substantial natural kinds are necessary to their instances.

In view of the standard a posteriori examples, this leads to the conclusion that there are

only very general natural kinds such as atom, molecule and living organism. However, it is the

(alleged) specific natural kind universals (e.g., helium atom, water molecule and tiger) that are

supposed to do the much-acclaimed ontological work. They are supposed to bring together the

essential properties of kinds, act as truthmakers of laws of nature, or act as referents of the

interesting natural kind terms. If Neo-Aristotelians have only natural kind universals of the

general natural kinds as their disposal, the categorial scheme they advocate loses most of its

theoretical appeal. One of the main motivations for Neo-Aristotelianism is therefore seriously

threatened. The sub-sort strategy does not have these benefits: the sub-sorts are powerless to

do any ontological work as they are not any kind of entities themselves. Even if we consider

the specific natural kinds of elementary particles as kind universals (by making controversial

assumptions) in addition to these very general kinds, we have an insufficient basis for a fruitful,

comprehensive theory of natural kinds. So the cost of the second horn of the dilemma for the

Neo-Aristotelian, from her point of view, is high. Hence we conclude that there is no safe

escape for her from the dilemma.

The Platonic realist faces the same challenge as the Aristotelian immanentist. She has

to give an account of how some abstract universals are instantiated (or, exemplified) by

particulars. If the instantiation by objects is direct as in Russellian realism, the Platonist will

23

have to explain why this does not lead to Bradley’s regress. For her, taking abstract universals

as parts of their concrete instances is not an option because universals are not “in” their

instances. If the Platonist opts for the Neo-Aristotelian account of instantiation with allowing

for the metaphysical possibility of uninstantiated universals, she will end up in the same

dilemma as the Neo-Aristotelian. It does not matter whether one is a Platonic or Neo-

Aristotelian realist; one faces the same problem with the modal status of instantiation (either

contingent, which is hard to understand, or necessary, which rules out kind change). It is

difficult to find any third, theoretically attractive alternative. So it seems that it is hard, if not

impossible, for the supporter of abstract universals to find a safe haven in “the Platonic

heaven”. The postulation of Platonic universals does not give her any advantage in solving of

the above problems of WIR. Therefore, it is not surprising that there are very few recent

supporters of Platonic Realism in metaphysics.

Chemical elements, chemical substances and biological kinds have figured centrally

also in the semantic literature, as examples of designata of general terms. Kripke (1980, 116-

140) discusses for instance gold, cat, and tiger in this connection. Putnam’s semantic theory,

with its examples of biological species, substances (most famously water), and chemical kinds

(H2O) is explicitly cast in terms of kinds as designata and the relation of instantiation between

kinds and their members by Salmon (2005). In the contemporary semantic literature, substance

and biological kind terms have retained their position as standard examples (e.g. LaPorte 2004,

cps. 3 and 4; 2013, 9-10). If it turns out, as it now seems, that many of the semanticists’

favourite examples of kinds as designata cannot be accommodated by the best metaphysical

theories available, the semantic theory must be reconsidered, too.

Some designation theorists do not seem to make much of an issue about whether to take

the abstract universal designated by a specific term as a kind or as a property. Thus, for example

LaPorte (2000, 294, n. 2; 2013, 17-8, n. 8) thinks his position does not require taking a stand

on such questions; he presents his way of speaking about kinds here as merely a matter of

simplicity of expression. However, others, for example López de Sa (2008), talk only of

properties in this connection. Hence, instead of speaking of, say, water as a kind, they speak of

the property of being water.32 In the absence of any indications about the involvement of trope

32 See also LaPorte 2006, 325-6. Other writers who do not seem to make any relevant distinction between kinds

and properties include Martí (2004, 141-2) and Inan (2008, 222). Schwartz, on the other hand, argues that

LaPorte’s talk of kinds in (2000) is “a dodge” to hide the metaphysical issue—the existence of “unusual” abstract

objects as designata—on which Schwartz takes LaPorte’s rigidity distinction for general terms to hang (Schwartz

2002, 268-70). LaPorte disagrees (2013, cf. 5).

24

theory, these theorists can perhaps be understood along the lines of the Russellian view about

the relation between properties and their instances. Consequently, these theorists must face,

and deal with, the hard metaphysical difficulties Russellian WIR involves.

LaPorte (2013, 107-8) notes that general terms as rigid designators are available also to

the nominalist, if she adopts the view that the designata are functions on models of possible

world semantics, hence sets, which are not universals but particulars (and individuals). For

instance Martí (2004) construes the relevant designata as functions, though not as the typical

ones from worlds to sets of objects but as functions from worlds to such typical functions. Rigid

general terms designate functions that yield the same function as value regardless of which

world is chosen as the argument.

The crucial question here is, as LaPorte notes, how the functions are understood. Are

they understood as formal models of the real designata, kind universals or property universals,

or are they understood rather as a reduction of the purported universals to set-theoretic

particulars. Martí clearly favours the former option, since she makes it explicit that on the view

she wishes to defend, the designata are universals such as kinds (Martí and Martinez 2010, 46).

On this option, the properties or kinds as universals are clearly thought to be somehow “more

than the relevant functions”; they are universals rather than function particulars (LaPorte 2013,

107).33 The latter, reductivist option would amount to the claim that the relevant functions in

possible worlds semantics perform all the theoretical work for which property or kind

universals were needed in the first place, and that hence these universals can be dispensed with

in favour of the relevant set-theoretic particulars.

Haukioja (2012, 404-5) points out that the reductivist option needs to be supplemented

with an account of how the truth of a theoretical identity such as “Brontosaurus = Apatosaurus”

might be discovered. Such an account is obviously needed since the reductivist view would

construe such identity statements as being about functions, which, as abstract entities, are

causally inert. Since we cannot observe the relevant functions, we must somehow reason to the

identity from observations of causally efficacious spatio-temporal particulars. Although

Haukioja takes a bleak view of the prospects of giving such an account that would do significant

theoretical work, perhaps this challenge could be met by the reductive theorist of kind and/or

property universals.

In addition to this, the reductivist would also owe us an accompanying reductive account

33 Accordingly, LaPorte acknowledges that the reductive account is hardly tenable, even if right after saying so

he astonishes the reader by saying that “it does not matter here” (2013, 107).

25

of instantiation. A particular cannot instantiate another particular; furthermore, it seems to

make no sense to say that a particular, say a horse, instantiates a function from possible worlds

to functions from possible world to objects. The particular horse may of course be a value of

the latter kind of function for some arguments. What is needed, then, is a metaphysical system

in which instantiation is explained away in terms of the relevant kind of functions in possible

worlds semantics. It is hard to see how this could be done without sneaking back in as

assumptions some of the features of the universals, especially if one wants to hold on to the

view that instantiation is a formal ontological relation.

We do not wish to argue here, however, that such a reductivist account could not be

given. If it could, then a theory on which general terms would designate abstract particulars

(functions) would be possible. Obviously such a theory would not be targeted by the present

discussion. Our criticism only concerns those general term designation theories—the majority

of them, it is safe to say—on which the designata are understood to be abstract universals,

which are perhaps modelled as functions in possible worlds semantics, but not reduced to or

identified with such functions.

Designation theorists’ view requires entities as designata of general terms, most notably

of natural kind terms. So it just will not do for them to be silent about these metaphysical issues.

As was seen above, designation theorists’ favourite candidates for the designata are abstract

universals. If designation theorists choose the Neo-Aristotelian doctrine of abstract universals,

instead of the Russellian account, their view is subject to the problems involved in kind

instantiation by objects. As instantiation is metaphysically necessary, true natural kinds must

be necessary to the objects instantiating them. Basically, natural kinds are kinds of highly

general nature, which objects cannot change. So there are not very many of them.

Consequently, there are not many designata for natural kind terms, which throws a deep

shadow on the possibility of the designation theory to have a comprehensive semantic account

of natural kind terms.

All in all, providing a theoretically satisfactory metaphysical account of universals is a

pressing issue for the designation theory. Otherwise, it is not clear at all whether the designation

theory is eventually able to provide a semantic explanation of the reference of general terms,

most notably natural kind terms. If it indeed were the case that there are no universals (their

category is empty), the designation theory might have the consequence that natural kind terms

(in singular occurrence) have no designata: they are empty terms. This seems to entail that the

designation theory trivializes or loses the rigidity/non-rigidity distinction in the case of natural

26

kind terms. Although we have not shown that there are no universals in this paper, we have

argued that there is no theoretically satisfactory account of abstract universals in the

metaphysical literature at the moment (recall that conceiving of universals as concrete is even

more problematic). As long as designation theorists cannot supply this deficiency, or come up

with a viable nominalist option, there are good reasons not to subscribe to their semantic theory

for general terms, notwithstanding its elegant simplicity. Since we have grave doubts that they

can come out with such a theory, we think that philosophers of language should look for a

semantic account of general terms that does not favour abstract universals, or, universals at any

rate.

27

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