## 1. Overview



The notion of a sortal overlaps with significant and long unresolved
philosophical controversies in philosophy of language, metaphysics and
philosophy of mind. Philosophers disagree about whether there are
essences and those who agree that there are disagree about whether
essences exist at a very general level--*animal*--or
a specific level--*tiger*. And philosophers disagree about
criteria of identity. Some believe that criteria of identity are
relative to a sortal in ways that can conflict, two things might be
the same ship but not the same wood. Others believe that identity
conditions vary by sortal but do not conflict--that the criteria
for the identity of ships is different from that for people but since
people are not ships, the answers could not conflict. Others believe
there is only one general identity criterion regardless of sortal, and
others argue that there are no identity criteria. On one extreme view
(Sider 1996), nothing exists at more than an instant. We, like most of
the literature on sortals, will not take that view into account in
what follows.



Most, though not all (Geach, Lowe) agree that sortal words apply to
things that we can count rather than things we measure. Sortals go
with numbers and plurals. "Dog" is a sortal,
"water" is not, so we say that we need *two*
dog*s* but that we need *more* water. One confusing
aspect of the distinction is that although "water" is not
a sortal, there is often a tacitly understood qualifier in the context
that combines to provide a sortal. At the grocery store, we might say
we need two waters meaning two *bottles* of water; or in a
restaurant we might ask for two waters, meaning two more
*glasses* of water. So although "water" is not a
sortal, the phrase "bottle of water" is, at least in one
sense of the term. There are also quirks of language, English speakers
decide *how many* vegetables to buy, but Germans consider
*how much* *Gemuse* to buy, in spite of the fact that
"*Gemuse*" means vegetable.



The counting characterization of what a sortal is includes many varied
forms; we can count dogs, brown dogs, old brown dogs, old brown
dachshunds, breeds of dog. But at most one of these characterizes the
essence of the things we are counting. When being careful,
philosophers call this subset *essential* sortals. But not everyone is always careful. Also, there is a deep disagreement over whether the entire concept of an essence makes sense 
and so there are debates over whether there are a special subcategory
of essential sortals. For example, both Brody(1980) and Wiggins(2001) argue for there being essential sortals, while Mackie(2006) against it. And among those who hold that there are essential sortals, there is disagreement over whether these are at a
general level such as "animal" or a specific level such as
"dog"



One point of agreement is that we must have a sortal in mind for
counting to make sense. If we are looking at a barnyard and asked to
count how many, we need to know what sort of thing we are counting. We
could count animals or chickens or goats or tables or legs. Sortals
specify the "kind of thing we are counting" and thus are
associated with counting and a number. They contrast with other terms
that involve measuring and an amount. Linguists distinguish count
nouns, nouns that go with "How many?" and take plurals,
from mass nouns that go with "How much?" and do not take plurals,
Confusingly, many nouns have both a count and a mass meaning, so we
can ask both *how many* chicken*s* the farmer owns and
*how much* chicken you would like on your plate.?



Often in order to count we also need to know when we have the same
thing and when we have another, so sortals are also involved with
identity. Identity questions are usually easy to answer when we are
discussing currently existing things, though for very large objects
the question can be tricky: Is the river that flows through Peoria
Illinois the same one that flows through New Orleans? 



Questions of identity through time are more often difficult, because
they involve issues of persistence. If a kitten grows up it ceases to
be a kitten but it is the same cat and the same animal. But if we tear
down our garage and build a tree house out of the lumber it is not the
same building. When does something survive change and when not? Which
kinds of changes? Sortals providing criteria for continued existence through time (or so-called "persistence criteria") are often referred as "substance sortals". By their features, essential sortals will clearly qualify as substance sortals but not necessarily vice-versa. Similarly to the case of essential sortals, there are systematic disagreements among philosophers whether the substance sortals are to be located at a
relatively specific level, e.g., "dog",
"river" or at the level of a more general category, e.g., "animal", "geographic feature".



In considering sortals, counting, and identity, it is important to
bear in mind that the superficial forms of language use can hide
complexity. For example, if we say that Sam and Maria own the same
car, we probably do not mean that they are co-owners, but that they
each own a car and that those cars are instances of the same model.
What appears to be a question of identity between objects is actually
a question of identity between *kinds* of cars.



But there are real, famous historical issues about identity that lead
to disagreements about the relation between essential sortals and
identity. Some philosophers believe that there is a unique universal
identity relation which holds, or doesn't, independently of any
sortals. Others argue that identity is always relative to a sortal
because we may have a statue of Lincoln which is a different statue
than one of Caesar even though the lump of bronze from which the first
was made is the same lump of bronze that constitutes the second. So in
this case, the sortals "statue" and "lump of
bronze" give different answers to the identity question.



While there is considerable agreement that sortals "provide a
criterion of identity" there is disagreement on what is required
for a criterion of identity. Some philosophers have more stringent
expectations than others requiring that the statement of the criterion
not use terms involving the sortals in question or similar terms.
Also, as noted above some philosophers believe there is only one
universal identity relation independent of sortals, and while others
argue that there are no criteria of identity.



As a final preliminary to our more detailed history and analysis, we
note that there is important variation between authors in whether
"sortal" is applied to linguistic items, e.g.,
*words* like "cat" or "lake" or
"cloud"; abstract entities such as the *property* of
being a cat or of being a lake or a cloud; or to psychological entities
such as the *idea* or *concept* of a cat or lake or
cloud. The first interpretation views sortals as being linguistically determined.The second sees sortal categories as part
of the world's furniture independent of how we describe it, and
the last is associated with a range of positions in between. These three different interpretations of the nature of sortals have been labeled as nominalist, realist, and conceptualist, respectively. Work on sortals may, in general, be classified under one of these three categories.


## 2. Sortals and the mass-count distinction



Linguists have long distinguished between mass and count nouns on
grammatical grounds and that distinction is close to the sortal vs
non-sortal distinction philosophers deploy. Count nouns form plurals
and occur in constructions involving "How many ..."
Mass nouns do not pluralize and occur in constructions involving
"How much ...?" We ask how many cats our friend owns
and how much cat food. Some words, especially those involving food,
have both a mass and a count sense. We can ask both how many chickens
our friend owns and how much chicken you want for dinner. (See Pelletier (1979, 2010), as well as the entries on the logic and the metaphysics of mass expressions, for detailed discussions on the mass-count distinction, from philosophical, linguistic, and cognitive perspectives.)



The grammatical distinction is robust. Almost all speakers of a
language agree on which sentences are grammatical and which are not.
But philosophers disagree about the extent to which count nouns match
up with sortals. The sentences "There are three red things on
the shelf" and "Two objects collided" are definitely
grammatical, so "red thing" and "object" are
count nouns, but most philosophers argue that they are not sortals.
For example, Hirsch and Wiggins think not because they claim that you
cannot count red things or objects, even though the request to do so
is grammatical. Others think that we can count red things but that the
only two possibly correct answers are "infinitely many"
and "none". If nothing red is present there are no red
objects. But if some red thing is present then so are the top half of
it, and also the bottom half, each of which are counted as a red
thing, And the three thirds giving us three more red things, and so on
*ad infinitum*. Whether this is the best understanding of
"thing" is disputed. We won't linger over that
debate just now, but the issue recurs later when we discuss sortals
and concept acquisition in children.



The count-mass distinction tracks closely in most instances with the
intuitive difference between stuff and things we appealed to at the
beginning, but not always. There are some differences in English that
don't seem systematic For example, "vehicle" and
"vegetable" are count nouns, which makes sense because car
and carrot are. But fruit and furniture are mass nouns although the
things they refer to, apples and chairs, are referred to by more
specific count nouns. And languages differ--as mentioned before,
English speakers count their vegetables, but German speakers ask how
much *Gemuse* you want, even though
"*Gemuse*" refers to the same things as
"vegetable". And in Italian both
"*frutta*" and "*verdura*" are
mass nouns.



A related distinction is the one between counting and measuring. But
while the differences between typical cases of counting--how many
oranges do we have--as opposed to measuring--how much rice
do we have--are clear, other cases are perplexing. Salmon (1997)
offers multiple possible analyses of sentences such as "There
are two and a half oranges on the table", but he finds all of
them wanting. 


## 3. History of sortal from 1690-1959



Many philosophers (e.g., Wallace 1965) have claimed that the notion of
a sortal is the same notion as developed by Aristotle under the label
"secondary substance" in several of his writings. However,
that concept is both complex and controversial (see Furth 1988 and the entry on Aristotle's metaphysics) and we will not pursue the connection.



The first use of the term "sortal" is in Locke's
*Essay Concerning Human Understanding* (1975 [1690]).



> 
> 
> But it being evident, that things are ranked under Names into sorts or
> *Species*...the *Essence* of each *Genus*,
> or Sort, comes to be nothing but that abstract *Idea*, which
> the General, or *Sortal* (if I may have leave so to call it,
> from *Sort*, as I do *General* from *Genus*) Name
> stands for. And this we shall find to be that, which the word *Essence*
> imports, in its most familiar use. (Bk.III, Ch.III, 15)
> 
> 
> 



Locke goes on to distinguish between real essences, which are mostly
hidden from us and determined by nature, and nominal essences, which
we (somewhat) arbitrarily construct, but doesn't say which he
means to pick out by the expression "sortal" It is ironic
that in discussion of the history of the term Locke and Aristotle are
cited as the two historical sources, when a main point of
Locke's *Essay* was to argue against Aristotelian
essentialism (see the entry on Locke).



Roughly contemporaneously with Locke's introduction of the term,
Spinoza noted the importance of a sortal like term for counting though
he did not use the term "sortal" or a Latin
equivalent.



> 
> 
> He who holds in his hand a penny and a dollar will not think of the
> number two, unless he can call both the penny and the dollar piece by
> one and the same name, to wit, a piece of money or a coin. (Spinoza
> 1674: 259)
> 
> 
> 



The other pre-twentieth century author who is frequently cited as an
antecedent of contemporary discussions is Frege. In Frege (1884) he
makes the point that in counting things, we need to know what kind of
thing we are counting. For example, something can be counted as one
thing, a deck of cards, or as fifty-two cards. Frege was perhaps the
first to use the phrase (which is translated as) "criterion of
identity". There is disagreement about whether Frege intended
his remarks to apply to all kinds of identity, as Dummett (1973)
argues, or only to numbers, as Lowe (1989) argues, but Dummett's
is the more common interpretation.



Wright (1983) argues that one of Frege's most important
contributions was emphasizing that numbers are objects and that this
is intimately connected to Frege's claim that "natural
number" is a sortal. Wright is aware of the difficulties in
characterizing sortals, which we will explore below, but remarks that
"...whether or not it is ultimately rigorously explicable,
the intuitive notion of a sortal concept is clear enough for our
immediate purpose" (1983: 4). For further discussion see the entry on Frege.


### 3.1 Strawson on sortals



The expression "sortal" reappeared on the philosophical
stage in the 1950s and 1960s in lectures and in the written work of
Strawson (1959), Quine (1960), Geach (1962), and Wiggins (1967) and
variations on the concept entered the mainstream philosophical
vocabulary. Because philosophers lecture and circulate manuscripts
with their ideas for years--sometimes decades--before
publication, the dates of the main publications of the protagonists
concerning sortals do not necessarily reflect the historical
priorities and influences. The most accurate simple summary is that
the ideas of Geach, Strawson and Quine co-evolved and that
Wiggins' writings built on a foundation laid by those
predecessors.



The widespread use of the term "sortal" definitely derives
from Strawson, but readers should note that there are important
differences among these authors. For a start, Strawson applies
"sortal" to universals, Quine to predicates, and Wiggins to
concepts. Thus, these authors illustrate the realist, nominalist, and conceptualist interpretations of sortals' nature. Geach did not use the word "sortal" but most commentators identify his notion of a "substantival
expression" with "sortal" in the other writers. Although Geach seems closest to Quine, since "expression"
seems to be a linguistic notion, Geach generalizes his results across
languages in ways that Quine would not find agreeable. These
differences in usage among the four authors would not be important, if
there were simple direct agreed upon relations among concepts,
universals, and expressions. But there aren't.



Strawson made no mention of Locke, Aristotle, Spinoza or Frege in the
context of introducing the expression "sortal universal"
in *Individuals* in 1959.



> 
> 
> A sortal universal supplies a principle for distinguishing and
> counting individual particulars which it collects. (1959: 168) 
> 
> 
> 



Strawson had two main projects in *Individuals*. The first was
to show that material bodies and persons occupy a central position
among particulars and that items in these two categories are basic to
our conceptual scheme. The second was to



> 
> 
> establish and explain the connexion between the idea of a particular
> in general and that of an object of reference or logical subject.
> (1959: 11-12)
> 
> 
> 



Sortal universals are central to this second task because, according
to Strawson, reference to particulars occurs by using expressions that
are associated with sortal universals.



Strawson thus emphasizes two characteristics. Sortals



(1)
 give a criterion for counting the items of that kind
(2)
 give a criterion of identity and non-identity among items of that kind


It is not difficult to see why someone would identify these
requirements. In order to know that there are exactly two *G*s in
a region *S*, it is necessary and sufficient to know that



There is an *x* which is in *S* and has *G*, a *y*
which is in *S* and has *G* and is not identical to
*x*, and for any *z*, if *z* is a *G* which is in
*S* then *z* is identical with either *x* or
*y*.



The phrase "criterion of identity" seems to mean a
criterion which gives a necessary and sufficient condition for
identity. In many cases, however, a weaker condition suffices for
counting. To conclude that there are exactly two *G*s in region
*S*, all that is required is a sufficient condition for *x*
and *y* to be distinct, and a sufficient condition for *z*
to be identical with *x* or *y*. In the case of physical
objects, it may be that being at the same location at the same time is
sufficient for identity, and being in entirely separate locations at
the same time is sufficient for distinctness. In most circumstances,
these will suffice to count *G*s, but it is far short of
providing answers about partially overlapping *G*s, and provides
no guidance about identity across time. So often we may be able to
count *G*s without having a criterion of identity in the strong
sense.



One of the unclarities of the phrase "criterion of
identity" is that it is never spelled out what the criterion is
to be applied to. For example, is it a criterion to be applied to
names of objects or to perceptual representations of objects or to the
objects themselves? It is also unclear how strictly we are to
understand "criterion". In "Entity and
identity" (published in 1976 and reprinted in Strawson 1997b)
Strawson proposed being quite strict, limiting the phrase
"criterion of identity" to cases where there either is an
explicitly statable necessary and sufficient condition that does not
use the identity relation, or one where the identity relation is only
applied to constituent parts of the objects. This can be done for
numbers and sets, but probably not for any kind of concrete objects.
In 1997, he retracted that proposal in favor of the looser (and still
undefined) general philosophical use of the term (1997a: 2-3).
In contrast, Wiggins understands the counting criterion very strictly
so one instance where there is not a determinate answer to a question
leads him to reject the counting criterion (2001: 75).



At the other end of the spectrum, Griffin (1997) only requires
that



> 
> 
> A term "*A*" is a sortal iff there can be cases in
> which "*A*" provides, without further conceptual
> decision, and without borrowing other principles of individuation,
> principles adequate for counting *A*s. (1997: 43)
> 
> 
> 



Since most philosophers who invoke the distinction want to reject
"thing", "object" and "entity" as
non-sortals, Griffin's suggestion is inadequate, or at least is
a shift to a different concept with the same label. The question
"How many things/objects/entity are in the space
*S*?", where *S* is an empty space has the determinate
answer "zero", so all of these terms pass the Griffin
standard. One could attempt to amend the criterion by requiring that
there can be cases which satisfy the above criteria and where there is
at least one *A*. However, this fails to delineate the right cases,
because there are sortals such as "unicorn" and
"square circle" which have no instances. These points, and
the observation that some of the various notions of sortal diverge,
were first made in Feldman 1973 but have not been widely noted
(see the entry on relative identity). We will revisit some of these issues in
 Section 7.1
 on sortals and infant cognition.


### 3.2 Criteria of identity



It is a law in many logical systems, *The Indiscernibility of
Identicals*, that things that are identical share all of their properties. The controversial
converse, *The Identity of Indiscernibles*, says that things that share all of their properties are identical. If "property" is
understood sufficiently liberally, then the latter principle is certainly
true--any object *b* has the property of "being
identical to *b*", and if *c* also has that property
then \(b = c\). The question is whether the principle holds with any
more restricted sense of property. Ladyman et al.(2012) discuss and relate different interpretations of indiscernibility associated with various senses of properties. Many of these interpretations would ground different versions of the identity of indiscernibles principle. (See the entry on this principle for philosophical perspectives other than those considered by Ladyman et al.(2012).) 


 
One might closely link indiscernibility to the notion of a criterion of identity (together with its connection to sortals) when "criterion of identity" is understood as follows:



For any sortal *F* there is a set of properties \(\phi\) such that
if *b* and *c* both are *F*, then if *b* and *c*
instantiate exactly the same properties in \(\phi\) then \(b = c\).



Some attempts to give content to the phrase "criterion of
identity" can be understood in this framework. Black (1952)
argues that purely internal properties of objects do not suffice; his
example is a universe with two spheres which share all of their
internal properties, i.e., are the same color, weight, composition,
etc. There are a wide range of philosophical views about criteria of
identity. Brody (1980) takes the two identity and indiscernibility
principles as jointly *definitive* of identity and consequently
argues that no further criteria of identity are required. Baker (1997)
argues that there are no criteria of identity across time, while
Jubien (1996), Merricks (1998) and Zimmerman (1998) articulate reasons
to doubt that there are any criteria of identity. Lowe (1989,1997, and 2009) are
more recent attempts to clarify the concept


### 3.3 Is identity strongly sortal relative?



One of the novel claims in Geach's *Reference and
Generality* was that identity is relative in the strong sense that
for two sortal expressions *F* and *G*, *b* and
*c* might be the same *F*, but not the same *G*. Geach
used the expression "substantival" to characterize the
kinds of term *F* and *G* are. His
"substantival" coincides in many cases with sortals as
understood by others, but cannot be entirely the same since he cites
"gold" as an example of a substantival, in fact:



> 
> 
> we can speak of the same gold as being first a statue and then a great
> number of coins, but "How many golds?" does not make
> sense. Thus "gold" is a substantival term, though we
> cannot use it for counting. (1962: 64)
> 
> 
> 



One of the examples he gives is that *b* might be the same river
as *c*, but not the same water. Or, if some bronze is made into
first one statue, then a different one, then the two statues are not
the same statue but are the same bronze.



Quine (1964) and others were critical of Geach's solution to
these puzzles and defended the view that there is only one unqualified
sense of identity. In each of the problem cases, his strategy was to
try to show that one of the statements of the form "same *G*
as" is not a true identity statement. So in the river example,
Quine would deny that the water is identical to the river and thus the
two statements are about different objects. Almost all of
Geach's examples can with some plausibility be treated by
distinguishing more carefully between objects of reference or
distinguishing constitution from identity. Thus one might say that the
bronze at different times constitutes the two statues but is not
identical with them. Whether constitution really is or isn't
identity is a matter of continuing debate; for articulations of the
two sides see Johnston (1992), Noonan (1993), Baker (2007, chap.3), and the entry on material constitution. For
later stages in the debate between Quine and Geach, see the entry on identity .



Sometimes it appears that identity is relative, when in fact ambiguity
of reference is present. We might say that George and I took the same
bus, meaning that we both took a bus on route #56. Or you might say of
the same events that we took different buses, because I took the #56
at 10:25 and George took one at 12:30. But these are not conflicting
identity statements about the same things. The first concerns sameness
of bus routes, while the second concerns time specific instances of
the route. 



One example that does not readily lend itself to these approaches is
the problem of the Christian Trinity. According to this doctrine, God
the Father, Jesus, and the Holy Spirit are three persons but one God or
one substance. Thus they provide an alleged example where *b* and *c* are
distinct persons but the same substance. We will not enter the debate,
which is been conducted for over a millennium, as to whether this
doctrine is coherent, but refer the reader to a modern discussion in
Cartwright 1987. It is certainly accurate to say that all of
Geach's examples are contested. For details on how the problematic character of such examples can be systematically dispelled, see, for instance, Wiggins (2001, chap. 2).


### 3.4 Is identity weakly sortal relative?



Wiggins and others argue that identity is dependent on a sortal in a
weaker sense. The criterion for the identity of sets is perhaps the
one clear and uncontroversial case: Two sets are identical, the same
set, if and only if they have the same members. (Notice that while the
criterion is clear, the appeal to identity reappears with reference to
the members.) While it is perhaps less uncontroversial, my car is the
same as the car I owned five years ago even though the oil, tires,
battery and have been replaced; the car can remain the same even
though some parts change. My friend is the same person as he was five
years ago in spite of many natural changes in the molecules composing
his body, some dental fillings, an artificial hip and a new cornea
lens. Two natural numbers are the same if they gave the same
successor, and two real numbers are identical iff they bear all of the
same order relations to the other numbers, =3.14.... Notice that
in all of these cases appeal to identity recurs with reference to
parts (whether body or automotive) or relations to other objects of
the same category. 



The weak sortal relativity claim consists of saying that the identity
relation for sets is different from those for numbers, which is
different from those for people and artifacts like cars, and numbers.
For sets it involves members of whatever kind, for numbers relations
to numbers and for persons and artifacts continuity of life and of
function. For abstract non-mathematical things the relation is even
less clear--the question when two ideas are the same idea is
often only settled in a court case about copyright or patent
infringement. 



In other words, there are two conceptions of identity: On one the
general identity relation is pieced together from the different
identity relations for different categories of things. For *a*
and *b* to be identical is for them to be the same person or the
same number or the same artifact or .... On the other conception,
there is a general notion of identity, perhaps given by the identity
laws discussed in
 Section 3.2,
 and the specific ones are ways of instantiating that relation. The
best argument for the first view is that the pieces seem too diverse
to be parts of the same general relation. The best argument for the
second is that as we move from domain to domain, and even invent new
ones, the general identity scheme guides our development of an
understanding of the more local notion. For a detailed analysis of
Wiggins' claims see Snowdon 2009.


## 4. Substance sortals



The sortals that Wiggins regards as crucial, the substance sortals,
are a proper subset of the ones Strawson is concerned with.
*Substance* sortals contrast with *phase* sortals; the
latter typically only apply to some temporal segment of an object.
Kitten is a phase sortal because when a cat matures it ceases to be a
kitten but it does not go out of existence. Substance sortals are also
contrasted with restricted sortals, e.g., "red table".
Wiggins has a detailed theory of the structure of substance sortals,
arguing that if any two substance sortals overlap, then either one is
a restriction of the other or both are restrictions of some other
sortal.



This seems problematic because it is plausible that plant and animal
are both substance sortals. While they do not overlap, another
candidate for being a substance sortal *carnivore* overlaps
both. This would probably not disturb Wiggins, since he already denies
that "animal" is a substance sortal.



> 
> 
> It is not to be denied that the words "this animal"
> suffice to express a rough and ready identification in ordinary
> contexts of what things are. But this is because "animal"
> so easily takes on an individuative force from a context and/or some
> other sortal predicate that is ready to hand. But the designation
> "this animal" is complemented in all sorts of
> *different* ways. In itself it determines no single principle
> of individuation. (2001: 129)
> 
> 
> 



We said earlier that in contrast with Strawson, Wiggins is concerned
primarily with the narrower class of substance sortals. Yet if we read
his account carefully, it emerges that in the end individuation rests
with an even smaller class which he calls
"*ultimate*" sortals:



> 
> 
> By an ultimate sortal I mean a sortal which either itself restricts no
> other sortal or else has a sense which both yields necessary and
> sufficient conditions of persistence for the kind it defines and is
> such that this sense can be clearly fixed and fully explained without
> reference to any other sortal which restricts it. (1967: 32)
> 
> 
> 
> ...I shall call *x'*s ultimate sortal concept
> ... the sortal concept which is individuative of *x* and
> restricts no other sortal concept. (1980: 65)
> 
> 
> 



The idea is that "cat" and "dog" may both be
individuated by the same criterion, so the fundamental criterion is
not only associated with them but with other substance sortals that
fall under the same ultimate sortal. We know from Wiggins's
remarks that "animal" is not a sortal, so the ultimate
sortal for "cat" and "dog" is somewhere in the
hierarchy above those concepts but below "animal".
Surprisingly, given the centrality of this notion, Wiggins nowhere
gives an example of what he regards as an ultimate sortal. (At 1980:
123 he does speculate inconclusively that "man" might be
the ultimate sortal for Julius Caesar.)



Without more specificity about when principles of individuation are
the same and different, the foundation of Wiggins's account is
murky. For example, we don't have enough information to
determine whether some middle level term such as "mammal"
is an ultimate sortal or not.



There are also other problems. Wiggins recognizes that his account of
individuation of biological kinds in terms of "characteristic
forms of activity" does not transfer well to prototypical
artifacts. He tries to meet this concern by giving an analysis in
terms of function for artifacts such as clocks. However, he seems to
assume that there are not problematic intermediate cases between
natural kinds and pure artifacts. Many kinds of things, e.g., rivers
and lakes, can be either natural or artificial. They can also be
partly artificial, as when a river is dredged or a lake enlarged. Nevertheless, Wiggins (2016, chap. 16, sec. 16-17, and chap. 12) might provide criteria for deciding upon these cases. (See Carrara & Vermass (2009), Baker (2004, 2008), and Losonsky (1990), for critical discussions on Wiggins' view on artifacts; see also the entry on artifacts for more general discussions of this notion in diverse areas of philosophy.)



Moreover, in his own favorite cases of biology, he remarks:



> 
> 
> Almost everything that has been said so far has been mainly directed
> at words standing for the various species of natural substances. The
> account could be extended and adapted without overwhelming difficulty
> to predicates of genera, wherever these were still determinate enough
> to be autonomously individuative. (2001: 86)
> 
> 
> 



Unfortunately, his own favorite examples, "elm" borrowed
from Putnam (1975) and "frog" are not terms for species.
"Elm" is a genus and "frog" an order. In fact,
a quick consultation with a good dictionary will reveal that most
commonly used biological terms are expressions for some classification
above the level of species. Since Wiggins is cautious about extending
his account to genera, he may have very few substance sortals by his
account.



Yet another problem for species as the model of sortals is that most
philosophers of biology now agree that species don't have
essences, though there is disagreement among them about the best way
to characterize species (for details, see the entry on species). A rejection of species essentialism doesn't necessarily carry a rejection of the essentialism Wiggins has advocated. His is individual essentialism, i.e., the view that an individual is essentially a member of the species it belongs to (Wiggins 2001, chap. 4). Thus, a given whale, for example, is essentially a member of the species whales; this even in the case where there is no essential property such a species possesses. Moreover, there are attempts by Wiggins to argue that species don't have essences. He states, for example, that *species* is an:



> 
> 
> ...insecure concept in plant-taxonomy, and threatened even in
> zoology by such phenomena as ring-species and the imperfect
> transitivity of the relation interbreeds in the wild with--the
> operational test of identity of species. (1967: 62)
> 
> 
> 



There is no incoherence here on Wiggins' part because species essentialism is logically independent of individual essentialism. Nevertheless, Wiggins' essentialism is, like species essentialism, also subject to criticism based on contemporary results from the philosophy of biology (Laporte 1997 and Okasha 2000). But see Ferner (2016) for a sympathetic discussion of Wiggins' doctrines from the perspective of biology, and Devitt (2018) for a recent defense of individual essentialism, which considers the views and criticism in question.


## 5. Definitions of "sortal"


### 5.1 Sortals, essences and existence



Returning to our distinctions of ways of characterizing sortals, we
can begin by repeating the observation that the counting criteria
include many more things as sortals than do 3-5, which are also
given as the definition of a sortal:



(3)
 gives a criterion for the continued existence of an item of that kind
(4)
 answers the question "What is it?" for things of that kind
(5)
 specifies the essence of things of that kind


Unless the question is given a more specific technical sense, it would
seem that "What is it?" is quite satisfactorily answered
by sortals in the broad Strawsonian sense. "A kitten" or
"A red table" both seem reasonable, so (4) can diverge
from (3). The kitten does not go out of existence when it becomes
adult, but it is no longer a kitten. Evaluating (5) is very difficult
since there is no consensus on whether kinds have essences (Quine
would say "none") and there is no consensus among those
who assert the existence of essences as to what they are. Contemporary versions of sortal essentialism provide a possible solution to these problems, particularly the theories of Brody (1980) and Wiggins (1967, 1980, and 2001). Another possible influential solution is offered by the essentialism of origin, such as the one proposed in Forbes (1985) or Salmon (1981) (for a discussion of these theories, see Robertson (1998, 2000)). Minimalist essentialism (Mackie 2006) is an alternative to those two forms of essentialism.



In a different direction, Wiggins in his later writings gives examples
to show that criteria of individuation and persistence are
insufficient to count objects under a sortal, and thus some
expressions meet conditions 3-5 but
not 1-2.



> 
> 
> ...the concept crown gives a satisfactory way of answering
> identity-questions for crowns. But there is no universally applicable
> definite way of counting crowns. The Pope's crown is made of
> crowns. There is no definite answer, when the Pope is wearing his
> crown, to the question "how many crowns does he have on his head"
> (1980: 73; 2001: 75)
> 
> 
> 



In a footnote to the same pages, Wiggins gives a list of other
examples of terms which permit individuation but not counting:
"wave, volume of fluid, worm, garden, crystal, piece of string,
word-token, machine". Wiggins continues by explaining that, on
his view, his account does not disagree with Strawson's but
corrects and enlarges it (2001: 75). We find it puzzling that Wiggins
dismisses "animal" as a sortal but is willing to include
"machine" which seems at least as problematic


### 5.2 Sortals and individuative terms



Quine's terminology in this area differs from that of Strawson,
Wiggins and Geach. In 1960 he uses the expression "term that
divides its reference", but in other writings (1969, 1981) he
uses the expression "individuative word". In footnote 1 of
Quine 1960: 90 he says that his expression is equivalent to
Strawson's "sortal". Unfortunately, that cannot be
exactly true since 1960: 91 Quine says that "object"
divides its reference, though we have seen "object" is not
a sortal by the criteria of Strawson or Wiggins because it does not
enable counting.



Quine does not give an explicit criteria for determining when a term
"divides its reference", but some have been proposed on
his behalf. Wallace (1965) discusses two understandings of the term.
The first is



*G* divides its reference iff it is never the case that if
*a* is *G*, *a* can be divided into two parts which are
*G*



While this characterizes "cat" as a sortal and
"object" as a non-sortal, it also excludes some terms that
are sortals by the counting criteria, e.g., garden hoses, rocks, piles
of snow, sand dunes, amoeba and ice cubes. He also discusses the
converse: *G* divides its reference just in case whenever
*a* and *b* are *G*, the result of putting *a* and
*b* together is never *G*.



This will get the easy cases right, as above, but also fails on the
same problematic list. (Most of these points were made in Feldman
1973 where he also explores various other ways of modifying these
principles.)



The closest Quine comes to an explicit formulation of a
characterization is in contrasting individuative terms with mass
terms:



> 
> 
> So-called *mass* terms like "water",
> "footwear" and "red" have the semantical
> property of referring cumulatively: any sum of parts which are water
> is water. (1960: 91)
> 
> 
> 



By "sum" here he almost certainly means the mereological
sum, not the result of physical juxtaposition. This would mean that
"object" and "space time region" would not be
sortals, but "spatio-temporally continuous object" and
"space-time region with volume less than *x*" are
sortals. These results may be consistent with Quine's views
given that he has indicated that he accepts "object", but
they diverge from the Strawson-Wiggins intent. Note that the three
terms listed above have some significant differences;
"water" refers to a kind of stuff, "footwear"
to a kind of thing, and "red" is a property of both stuff
and things. (See Laycock 2011 and the entry on
 object
 for further discussion.)



In any event, Quine's view of the distinction is much more
pragmatic than most. In explaining the distinction he says:



> 
> 
> The contrast lies in the terms and not in the stuff they name.
> ...consider "shoe", "pair of shoes", and
> "footwear": all three range over exactly the same stuff,
> and differ from one another solely in that two of them divide their
> reference differently and the third not at all. (1960: 91)
> 
> 
> 



Even this characterization of a contrast is dubious if we note that by
the last criterion "object with mass more than 2 kg" is
not an individuative term since the sum of any two such objects is
another such object, whereas "object with mass less than 2
kg" fails the test since the sum of two such objects sometimes
has mass over 2 kg. It is difficult to see any important respect in
which the two expressions divide their reference differently. Object
more than 2 kg and object less than 2 kg seem to divide their
reference.



Another, example, given by Feldman (1973), can be used to illustrate
the somewhat capricious nature of the distinction and its language
dependence. He claims that "five-foot garden hose" is an
individuative term since no part of it is a five-foot garden hose, but
"garden hose" is not individuative. The latter claim
requires some qualification. If being a garden hose requires a
coupling on one end and a nozzle on the other, then the halves of a
garden hose are not garden hoses. If being a garden hose requires
neither a nozzle nor coupling, then each half (indeed each
*n*th, up to some *n*) of a garden hose is a
garden hose. If being a garden hose requires a coupling but not a
nozzle, then one half of a garden hose is a garden hose but the other
is not. Although the differences may be important to the gardener, it
is difficult to see anything metaphysically deep here.


## 6. Sortals for abstract objects



Most discussions of sortals focus on kinds of physical objects, but by
the definitions given many sortals also apply to abstract objects. And
in some of these cases the question what is a criterion of identity
becomes even more difficult. We can ask how many new ideas a political
candidate has, how many governments Italy has had since 1950 and how
many books David Wiggins has written. Ideas, governments and books (in
the sense of type of book, not specific copies) are all abstract
objects. We comment on changes in corporations over time--Apple
has grown--which implies identifying Apple over time in spite of
changes. But we are far short of having criteria to make decisions in
harder cases: Did Rice Institute cease to exist in 1960 or was it just
transformed with a new name and some changes in charter to Rice
University. The buildings, faculty and students all persisted, but did
the educational institution?



The question can perhaps be made more pointed if we consider sortals
for collections that do not imply complex structure. Corporations are
complex, as are educational institutions. In contrast, a flock of
birds does not entail a great deal of complexity, just enough birds in
one location. We can sometimes definitively say that two flocks are
the same: if exactly the same birds flew over the lake this morning as
did yesterday then the two flocks are in fact one. And if none of the
birds that flew over the lake yesterday were in today's flock,
then they are definitively different. But suppose most but not all
were the same birds?



Mathematics also presents issues about what counts as a criterion,
even when the definition is quite precise. Two irrational numbers
*x* and *y* are identical if they have exactly the same
relations to each of the rational numbers. Pi is identical with
3.14... because Pi is greater than 3, 3.1, 3.14, etc and less
than 4, 3.2, 3.15, etc. But does this count as a criterion? It appeals
to the less than relation, which is a close cousin to identity itself
and it involves relations to similar entities. 



Yet another issue involves possible identification between different
kinds of numbers. There is a natural number 2, a positive integer +2,
a rational number 2/1, a real number 2.0000... Are these the same
number? Different understandings of number and different philosophies
of mathematics offer differing answers. But these controversies seem
insufficient reason to deny "number" the status of a
sortal.


## 7. Sortals and cognition


### 7.1.Sortals for infants



Is "physical object" a sortal? The general opinion among
philosophers is that physical object is not a sortal. One reason for
this conclusion is that to say something is a physical object does not
give its essence, it doesn't determine what kind of thing it
is--this depends on the essence notion of sortal. A second
argument is that it does not provide criteria for counting--the
two halves of a physical object are also physical objects--this
depends on the counting notion of sortal. A third is that it gives the
wrong persistence conditions--the physical object which is a car
for a period of time and then becomes a cube of crushed metal is not
the same thing. This combines the essence and counting criteria for
sortals.



Ayers (1974) argued that the concept of a physical object is
fundamental to human cognitive processing and that it does provide
criteria for counting and persistence even though it is not a sortal
since it does not specify an essence. One important part of his
argument is the clarification that a physical object is not simply the
stuff of spatio-temporally continuous space time region but is a the
stuff of a maximal region. That is, we do not generally regard any
proper part of a physical object as a physical object.



The psychologist Xu (1997) has argued that the concept of a physical
object is an essential part of cognitive development and is present in
infants at a quite early stage. And she argued that physical object is
a sortal because there are counting and persistence conditions (Spelke
1990). In contrast to Ayers, she argued that the physical object
persists through even fairly dramatic changes, including her Biblical
example of Lot's wife becoming a pillar of salt (Xu 1997). Her
position based on her own work and that of others (Xu & Carey
1996, Spelke 1996) is that the acquisition of the physical object
concept is a crucial stage in cognitive development and is a step
toward the development of the more refined sortal concepts that come
with language acquisition. And she agrees with Ayers that the
primitive concept remains in the cognitive repertoire of adults and
can be deployed in cases where someone is confronted with a physical
object whose further characteristics are as yet unknown. A similar
argument is presented in Sarnecki (2008) for the necessity of a
general sortal for objects as an intermediate step toward the
acquisition of the sortals of language.



Quine (1960) articulated the claim that differentiation of the world
into objects occurs only with the acquisition of language and with the
conceptual apparatus of identity and quantification. Soja et al.(1991) have provided experimental evidence that might empirically refute Quine's view. Moreover, research results in primates, such as those presented in Phillips and Santos (2007), and Mendes et al.(2008), provide additional empirical support against Quine's claim. Nonetheless, a weaker version of Quine's view has found empirical backing in Imai and Genter (1997) and Yoshida and Smith (2003), as far as quantitative differences are concerned. Also, Xu (2002) has argued that linguistic labels may play a role (in 9-months-old infants) in the acquisition of sortal concepts in infancy.



In any case, given the basic importance of object information for navigating the
surrounding world, it would be surprising if at least some aspects of
the concept of physical object was not shared by other species. There has been some
uncertain evidence of this in primates, and recently appears to be
strong evidence of such a concept in very young chickens (Fontanari
et al.2014).


### 7.2 Sortals, essences and basic level objects



Gelman (2003,2013) and others have provided evidence suggesting a mode of cognition of an essentialist character already operative in children. Specific categories of object and stuff (such as those represented by mass terms and sortals for natural and social kinds, as well as for artifacts) are here assumed to possess an underlying reality that cannot be observed directly. This assumption explains and grounds children's inductive inferences based on the categories in question. It also explains children's implicit assignment of causal and other non-obvious properties, as well as sharp and immutable boundaries to such categories. Children view some of these properties as innate. Research results (Caccione et al. 2016; Mendes et al.2018, 2011; and Santos et al.2002) highlight the possibility that essentialist cognition might develop in humans at a pre-linguistic stage, in the form of sortal object individuation. This might apply to certain primates as well (Phillips et al.2010). 



A related line of research initiated by Rosch (1973), Rosch et
al. (1976) suggests that there is a category of basic level
objects. Although context can lead to classifications at greater or
lesser levels of specificity, in most contexts there is a common level
of description that speakers prefer. For example, while we might
generally describe something as a mammal or a poodle, the most common
and natural noun would be "dog". Rosch found considerable
commonality in what are regarded as basic level objects across
cultures although there is some variation. Her characterization of the
basic level classifications is that those are the level at which
relatively accessible information (shape, color, form of movement)
provide the most information about other properties of the object. If
it is self-moving and dog-shaped it is likely to bark, eat meat, chase
cats, *et cetera*. 



Although Roschian basic level objects are good candidates for
informative answers to the question "What is it?" they do
not provide traditional essences. Traditional essences as
conceptualized by philosophers and most psychologists are necessary
and sufficient conditions for being a member of that kind. On that
conception, learning a new sortal requires knowing the elements and
how they combine to define the new kind. On Rosch's conception,
sortal words are learned in families and the primary learning
experience is becoming familiar with the prototypical members of the
kind. Prototypes are the best examples, produce the quickest responses
when subjects are queried about kinds, and are the most frequently
cited when subjects are asked to give examples. In the category of
birds, robins are one of the most prototypical, swans are intermediate
and penguins are very unprototypical. Evidence for Rosch's view
of categories, which has clear roots in the views of Wittgenstein,
consists of the failure to produce adequate necessary and sufficient
conditions for most common sortals, as well as the positive
experimental evidence just cited.



Related to the issues of essence, Markman (1989) and Markman et
al. (2003) have argued that children's early language learning
is guided by several principles, one of which is the mutual
exclusivity constraint. This constraint is that in learning words a
guiding assumption should be that distinct words refer to distinct
things. While this is not always true, Markman and others provide
evidence that this constraint is operative, and that in the language
learning environment of young children it is a very helpful, if
imperfect constraint. If Rosch is correct about the existence of a
preferred basic level of objects, it may be that speakers generally
use words at that level of objects and thus the exclusivity constraint
may be supported by the basic level object hypothesis. However, the
experimental data are apparently conflicting on these questions
(Mervis et al. 1994). Scholl (2008) provides a useful discussion of
whether and how philosophy and psychology can interact beneficially in
understanding these issues.


## 8. Sortals and Logic


### 8.1 Sortals and standard logic



Some philosophers, perhaps most notably Carnap (1950) have used a
concept closely akin to sortals in formulating many-sorted logics.
There is a technical point to be explained and a controversy to be
discussed in relation to these.



Sometimes in applications of first order logic, i.e., when we are
dealing at length with a specific class of interpretations the domain
divides into intuitively disparate kinds of objects, e.g., people and
numbers. In the usual formulation, one has predicates, e.g., *Px*
and *Nx* which are true of those kinds of things respectively,
and so one translates the English sentence "All numbers are
odd" as \((\forall x)(Nx \rightarrow Ox)\) and "Some
person is tall" as \((\exists x)(Px \mathbin{\&} Tx)\). In a
many-sorted logic distinct variables are used for the different kinds
of objects, perhaps *m*, *n*,... for numbers and
*p*, *q*,... for people. In this language combinations
of variables with predicates are sometimes restricted so that
*Nm* and *Tp* are well-formed but *Np* and *Tn*
are not. If one does not make this restriction then the notation is
exactly equivalent to standard first-order logic. A many-sorted
language is expressively equivalent to a single sorted one which has
additional predicates for the various sorts of things (cf. Quine
1966).



From a purely technical point of view, one can introduce different
kinds of variables to reflect any distinction one wants, e.g., there
could be distinctive styles of variables for even numbers as opposed
to odd ones, or for left-handed people as opposed to right-handed.
However, Carnap and others who advocated a many-sorted logic for
reasons that were more ontological than pragmatic introduced different
variables only for what they believed were metaphysically distinct
kinds of entities, e.g., numbers, physical objects, sense data. In
this respect, there is some parallel with ultimate sortals as
discussed above, although Carnap does not make an explicit connection
with earlier writers.



A related use of many-sorted logic is to provide a kind of translation
from second-order logic into a first-order logic. In this case instead
of having second-order quantification over sets (or properties), one
stays with a first-order language which is supplemented with a
predicate true of all and only sets (or properties), a distinct style
of variables for those entities, and with a two-place relation of
either membership or instantiation.


### 8.2 Logics of sortals



Standard logic treats all predicate expressions alike--the
predicates can be interpreted as any subset of the domain of
quantification. If any of the claims discussed above about sortals are
correct, then the sortal predicates have distinctive properties, and a
more sophisticated logical treatment might provide philosophical
illumination. One obvious and agreed on principle is that in general
the negation of a sortal predicate is not a sortal. This contrasts
with the predicates of standard logic where if *F* is a
predicate, so is \(\neg F\), (not-*F*).



This principle holds regardless of which interpretation of
"sortal" you take. Not only is "is not a cat"
not a substantive sortal (Wiggins), you cannot count the non-cats
since they include dogs, table, molecules, *et cetera*.
However, for two of the other logical operators, disjunction and
conjunction, the situation seems more complex. The expressions
"dog or cat", "apple or orange" and
"fork or spoon" all seem to be well-behaved with respect
to counting and identifying; we can easily imagine a city ordinance
forbidding homeowners to have more than four dogs or cats. On the
other hand, "dog or natural number" and "cat or
clock" seem to provide methods of counting but seem unnatural as
sortals.



The first "sortal logic" was developed in Stevenson
(1975). Stevenson develops an account in which he says "We use
ideas of Geach, Wallace and Wiggins, although we depart from each in
certain respects" (1975: 186). Although the formalism follows
Wallace in some respects, the main ideas seem to be those of Wiggins
rather than Geach. Specifically, his theorem 3.4.5 affirms that for
any sortals *F*, *G*, if *b* and *c* are the same
*F*, and *b* is a *G*, then *b* and *c* are
the same *G*, which is a denial of Geach's relative
identity thesis.



Two principles that Stevenson adopts following Wiggins are:



(i)
 For every sortal *F*, either *F* is an ultimate sortal, or there
is an ultimate sortal *G* such that *F* is a restriction
of *G*.
(ii)
 If
two sortals *F* and *G* intersect, i.e., they are both true
of at least one object, then there is a common sortal
*H* of which both *F* and *G* are restrictions.


Stevenson proves the formal consistency and completeness of his set of
axioms. It should be noted that completeness here is with respect to
the language used. Since this is a minor adaptation of standard logic,
there is no treatment of tense or modality, some essential elements of
Wiggins's notion of sortal cannot be expressed, e.g., if a
sortal *F* applies to *b* at one time, then it applies to
*b* at all times at which *b* exists, and if a sortal
*F* applies to *b*, then *F* necessarily applies to
*b*.



Stevenson does not permit combinations of sortal expressions,
presumably because there is no easy way to deal with disjunctions and
conjunctions of sortals in his formulation. However, a slight
complication of his language would suffice to handle the problem. He
uses "*uS*" for the ultimate sortal which governs
sortal "*S*". If instead he introduced a set of
letters \(U'\), \(U''\) ... for ultimate sortals, he could then
superscript sortal expressions to indicate the ultimate sortal that
governs them. He could then permit the disjunction of \(S^{U'}\) and
\(T^{U'}\) since they are governed by the same ultimate sortal, but
forbid the disjunction of \(S^{U'}\) and \(T^{U''}\) since they are
governed by different ultimate sortals.



Cocchiarella (1977) presents a formal language, though no axioms or
rules, for a logic of sortals which includes both tense and modal
operators. His approach, like Wiggins, considers sortals to be
concepts. Unlike Wiggins he gives a definition of "sortal
concept": as a socio-genetically developed cognitive ability or
capacity to distinguish, count and collect or classify things (1977:
441). He disagrees with Wiggins on both principles
 (i) and (ii) above,
arguing that while they may be true for natural kind terms, there are
no reasons to believe that there are ultimate sortals of which various
artifact sortals are restrictions, nor that every intersection of
sortals must fall under an ultimate sortal. Cocchiarella's
approach also goes beyond Stevenson's in that it involves
second-order logic, i.e., it includes quantification over sortal
concepts.



Cocchiarella's ideas have been presented in more rigorous formal
detail with axioms and consistency and completeness results for
second-order logic in Freund (2000), tense logic (2001) and modalities
(2004). More recently, Freund (2019) has formulated several bidimensional logics for sortals that consider modal, tense, and epistemic modalities, as well as complex sortals (i.e., sortals that involve logical combinations of other sortals). These systems presuppose a conceptualist philosophical background closely related to Cocchiarella's but somewhat more general.



Guarina, Carrara, and Giaretta (1994) develop an account of sortals
within knowledge representation, a subfield of artificial intelligence
intended to bridge the gap between abstract formal logics and natural
languages. Their definition of a sortal is that it is a predicate that
provides countability and is temporally stable. A predicate provides
countability if it does not apply to any proper part of what it
applies to. As they explain this, "student" provides
countability because no proper part of a student is a student; but
"red" does not provide countability because parts of red
things are also red. Temporal stability means that if the predicate
applies to something at one time then it must at some other times as
well. This is approximately the concept Strawson had in mind. They go
on to distinguish a subset of these, the substantial sortals. A
substantial sortal is one that, if it applies at all, necessarily
applies all times. This is in close agreement with Wiggins' use
of the term. So while "student" provides countability and
is temporally stable, it is not ontologically rigid, so it is a sortal
but not a substantial sortal. On the other hand, a cat is always
necessarily a cat.



Although there are obvious affinities with Strawson and Wiggins, it
should be noted that Guarino et al. (1994) are primarily concerned
with the distinction between kinds and properties of kinds, while the
philosophers were more concerned with things and the stuff they are
made of.



Belnap and Muller develop an alternative account of sortals
within a non-standard formal logic for tense and modality. Unlike the
usual background of possible worlds for modality, they use ideas from
Bressan (1972) and adopt
*cases* as the fundamental background notion They define a
sortal as a predicate which is modally constant and provides
separability. A predicate is modally constant iff it applies
necessarily to something whenever it possibly applies. The idea is
that while someone might possibly be a student without necessarily
being a student, if they are human they are necessarily human. Thus
"student" is not a sortal but "human" is. A
predicate is modally separated just in case it is necessarily true
that if any two things having the property are possibly identical,
then they are in fact necessarily identical. Using their technical
terminology of cases, if two things which have a modally separated
property coincide in any case, then they coincide in every case.
Belnap and Muller are explicit that they are providing a formal
framework for classifying predicates, but that applications will
require other kinds of thought:



> 
> 
> whether a particular predicate is absolute is assumed to be not a
> matter of logic, but rather of science and metaphysics. (Belnap &
> Muller 2014: 397)
> 
> 
> 



While there is a shared core of concerns in these last two approaches,
it is clear that in addition to the superficial difference that Belnap
and Muller restrict "sortal" to approximately the
substantial sortals as defined in Guarino et al. 1994, there are
differences even in the area of overlap. Modal rigidity and modal
constancy are very similar. (Some caution is necessary here since the
modal logic frameworks differ.) But Belnap and Muller emphasize
modal separability and do not mention a counting requirement, Guarino
et al. (1994) require countability but are not concerned with modal
identities.



In addition to Guarino et al. (1994), computational applications of the notion of sortal can be found recently in *upper ontology*, a relatively new field in computer sciences. For example, Guizzardi and Wagner (2010) make central use of the notion of sortal in a conceptual framework they call Unified Foundational Ontology (UFO). This framework can be used in the design and evaluation of conceptual modeling languages. In UFO, the focus on sortals is on the identity criteria they provide, which contrasts with Guarino et al. (1994) where the emphasis is put instead on countability and persistence. Besides, UFO makes a distinction, among sortals, between rigid and anti-rigid sortals. An instance of a rigid sortal S will be an instance of S in every possible world in which it exists. Anti-rigid sortals will not comply with this feature. From the authors' examples and further claims, it is clear that rigid sortals correspond to substance sortals and anti-rigid to phase sortals. Because possible worlds are involved, UFO's framework seems to be committed to individual essentialism. One will then ask whether UFO's general goal is achievable, given the critique of such essentialism by philosophers of biology. We should finally note that one can also appeal to a tense logic framework to illuminate the distinction between substance and phase sortals, in contrast with UFO's modal approach.(See Rybola and Pergl (2016a, 2016b) for further examples of recent applications of the notion of sortal in computational ontology.) 


## 9. Conclusion



A large number of thoughtful philosophers have believed that the
category of *sortal* was philosophically significant and this
is a strong indication that there is something important they are
attempting to delineate and analyze. In the last two decades cognitive
psychologists and formal ontologists have applied the term in their
research. However, our dissection of the definitions and discussions
show that there are numerous distinctions in question and while these
distinctions have significant overlap, they are not identical. It
remains to be seen whether the sortal/non-sortal distinction marks one
very important difference, or numerous less important distinctions
related in complex ways.