Sortals have played an instrumental role in resolving varioustheoretical challenges. They have helped tackle significant problemsin multiple areas of philosophy, including metaphysics, philosophy oflanguage, and philosophy of mind. Beyond philosophy, sortal conceptshave proven relevant in psychological fields, especially in theoriesrelated to infant cognitive development and human perception.Moreover, they have been applied in computer science, notably inartificial intelligence and knowledge representation.

Despite its importance, the notion of a sortal remains vague andambiguous. There are conflicting interpretations of this notion, andauthors write at cross-purposes. As a result, readers of any textabout sortals should approach the subject with caution. This confusionpartly stems from its origin as a technical term introduced by JohnLocke in 1690, who focused on concepts that define the essence ofthings. Later philosophers have reinterpreted the term to align withtheir philosophical goals, leading to a situation where the criteriafor what constitutes a sortal predicate can vary. For instance, PeterStrawson, who revived the term in 1959, emphasized sortals asproviding criteria for counting. For their part, Wiggins (1967, 2001)looked at sortals as telling us what a thing is, Dummett (1973) asproviding persistence criteria, Quine (1964) as a predicate thatdivides its reference, and Geach (1980) as conveying identitycriteria. In general, most of the authors working with the notion of asortal have proposed one or more of the following interpretations:

1. A sortal defines the essence of a thing or, at the very least,provides an answer to the question “What is it?”
2. A sortal offers a principle of individuation, enabling us tosingle out an entity
3. A sortal establishes criteria for identity and differentiation,specifying when something is the same as or different from a givenobject
4. A sortal provides a persistence criterion, determining whensomething continues or ceases to exist

These different characterizing features of sortals are not necessarilyindependent. For example, counting criteria presupposes identity anddifferentiation criteria, and the same applies to persistencecriteria. It is also claimed that a principle of individuation entailsidentity and differentiation criteria.

In addition to the above, grammatical criteria have also been adopted.It has been claimed that sortal predicates admit the definite article,the plural ending, the pronouns “same”,“other”, and “another”, and quantity wordssuch as “all”, “many”, and “one”,“two”, “three”, etc. These features havesuggested the idea of developing specific formal logics forsortals.

The longstanding debate on the so-called problem of universals hasalso complicated the discussions surrounding sortals. Variouspositions-nominalism, realism, and conceptualism- have been proposedas potential solutions to the problem, each supported by differentarguments for and against them. Different approaches to sortals can becontextualized within this spectrum of solutions. From a realistperspective, sortals are seen as properties; from a conceptualistview, they are regarded as concepts. Nominalist, on the other hand,consider sortals merely as predicates. For instance, from thenominalist perspective, words like “dog”,“house”, and “animal” would be consideredsortals. From the conceptualist perspective, the concept of a dog,house or animal would be viewed as sortals. From the realistperspective, the property of being a dog, a house, or animal wouldcount as sortals. Works on sortals can be generally classified underone of the three perspectives.

Despite the above complexities, we find common ground for thedifferent philosophical approaches in the various prototypes of whatcounts as a sortal or non-sortal predicate. These prototypes havecontributed to grounding the defining criteria and guided discussionson this subject. In general, it is widely accepted that most or manycommon count nouns are sortals, while most adjectives and intransitiveverbs are generally not. For example, expressions like“book”, “horse”, and “car” aretypically considered sortals, and those like “red”,“aromatic”, “stiff”, “deafening”,“cold”, “bitter”, “cry”, and“borrow” are not.

Most nouns that are not sortals can form sortals in contexts where aunit is implicated, often without the supplementary unit beingexplicit. Coffee and gold are not sortals by most accounts, but we canintelligibly ask how many coffees Harry drank or how many golds theski team won. It is understood from context that we are asking aboutcups of coffee andgold medals. These unitizedsortals can be in any of the forms discussed above.

• 1. Three main issues on sortals
• 2. The nature of a sortal
• 3. Pre-1959 views on sortals
• 4. Late 50s and subsequent years
• 5. The content provided by sortals
  • 5.1 Counting
  • 5.2 Individuation, essential sortals, and the “What is it?” question
  • 5.3 Identity, criterion of identity, and sortals
  • 5.4 Identity, indiscernibility, and the criterion of identity
  • 5.5 Is identity strongly sortal relative?
  • 5.6 Is identity weakly sortal relative?
• 6. Sortals and the mass-count distinction
• 7. The persistence criterion and substance sortals
• 8. Sortals for abstract objects
• 9. Sortals as terms that divide their references
• 10. Sortals and their role in cognition
  • 10.1 The concept of physical object
  • 10.2 Essentialist cognition, basic level categorization, and sortals
  • 10.3 Sortalism
• 11. Sortals and logic
  • 11.1 Sortals and standard logic
  • 11.2 Logics of sortals
• 12. Sortals and artificial intelligence
• 13. Conclusion
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. Three main issues on sortals

The above points to three clear issues regarding sortals. The firstconcerns the very notion of a sortal. As we have noted, this notionhas always been technical in nature, historically determined, andsomewhat theory-laden. Thus, it is crucial to clarify its underlyingelements separately and within a historical context to grasp what itscontent involves. We will focus our attention on these points insections 2–9.

The second issue addresses the logic of sortals. This arises fromexamining the grammatical criteria associated with sortals, such astheir use in constructions involving relative quantifiers andidentity. These features suggest the need to develop a logicincorporating these characteristics. Additionally, differentinterpretations of sortals-particularly from the theory ofuniversals-could result in varying reasoning principles. In section11, we will present the different logical theories of sortals thathave been developed thus far.

Finally, the third issue addresses the potential applications ofsortals across various fields. As noted earlier, sortals have played arole in resolving specific philosophical issues, as well as inpsychological research and advancements in artificial intelligence. Insections10 and12, we will explore these applications in psychology and artificialintelligence, respectively. Philosophical issues will be discussedthroughout the article.

2. The nature of a sortal

As mentioned above, the nature of a sortal has been historicallyshaped by its historical introduction and subsequent evolution underthe influence of various philosophical perspectives. The followingexposition intends to capture this development. We will start bytracing the history of the concept of a sortal, exploring how variousphilosophers have interpreted and developed the idea over time. Insome instances, we will highlight how the concept has been influencedby philosophical theories that address specific philosophical issues.In this exposition, we will distinguish between two key times: thepre-1959 period and the late 1950’s and subsequent yearsperiod.

On the other hand, the defining features of sortals, in line withvarious philosophical contexts, have been interpreted differently.These variations have led to diverse understandings of the notion of asortal. These interpretations will be examined in relation to thevarious criteria proposed as constitutive of the content purportedlyconveyed by sortals.

3. Pre-1959 views on sortals

Many philosophers (e.g., Wallace 1965) have claimed that the notion ofa sortal is the same notion as developed by Aristotle under the label“secondary substance” in several of his writings. However,this concept is complex and controversial (see Furth 1988 and theentry on Aristotle metaphysicsAristotle’s metaphysics). For this reason, the present discussion will not pursue theconnection further.

The first use of the term “sortal” is in Locke’sEssay Concerning Human Understanding (1975 [1690]).

But it being evident, that things are ranked under Names into sorts orSpecies…theEssence of eachGenus,or Sort, comes to be nothing but that abstractIdea, whichthe General, orSortal (if I may have leave so to call it,fromSort, as I doGeneral fromGenus) Namestands for. And this we shall find to be that, which the wordEssence imports, in its most familiar use. (Bk.III, Ch.III,15)

Locke goes on to distinguish between real essences, which are mostlyhidden from us and determined by nature, and nominal essences, whichwe (somewhat) arbitrarily construct, but doesn’t say which hemeans to pick out by the expression “sortal”. It is ironicthat in discussion of the history of the term Locke and Aristotle arecited as the two historical sources, when a main point ofLocke’sEssay was to argue against Aristotelianessentialism (see the entry onLocke).

Roughly contemporaneously with Locke’s introduction of the term,Spinoza noted the importance of a sortal like term for counting thoughhe did not use the term “sortal” or a Latinequivalent.

He who holds in his hand a penny and a dollar will not think of thenumber two, unless he can call both the penny and the dollar piece byone and the same name, to wit, a piece of money or a coin. (Spinoza1674: 259)

The other pre-twentieth century author who is frequently cited as anantecedent of contemporary discussions is Frege. In Frege (1884) hemakes the point that in counting things, we need to know what kind ofthing we are counting. For example, something can be counted as onething, a deck of cards, or as fifty-two cards. Frege was perhaps thefirst to use the phrase (which is translated as) “criterion ofidentity”. There is disagreement about whether Frege intendedhis remarks to apply to all kinds of identity, as Dummett (1973)argues, or only to numbers, as Lowe (1989) argues, but Dummett’sis the more common interpretation.

Wright (1983) argues that one of Frege’s most importantcontributions was emphasizing that numbers are objects and that thisis intimately connected to Frege’s claim that “naturalnumber” is a sortal. Wright is aware of the difficulties incharacterizing sortals but remarks that “…whether or notit is ultimately rigorously explicable, the intuitive notion of asortal concept is clear enough for our immediate purpose” (1983:4). For further discussion see the entry onFrege.

4. Late 50s and subsequent years

The expression “sortal” reappeared on the philosophicalstage in the 1950s and 1960s in lectures and in the written work ofStrawson (1959), Quine (1960), Geach (1962), and Wiggins (1967) andvariations on the concept entered the mainstream philosophicalvocabulary. Because philosophers lecture and circulate manuscriptswith their ideas for years—sometimes decades—beforepublication, the dates of the main publications of the protagonistsconcerning sortals do not necessarily reflect the historicalpriorities and influences. The most accurate simple summary is thatthe ideas of Geach, Strawson and Quine co-evolved and thatWiggins’ writings built on a foundation laid by thosepredecessors.

The widespread use of the term “sortal” definitely derivesfrom Strawson, but readers should note that there are importantdifferences among these authors. For a start, Strawson applies“sortal” to universals, Quine to predicates, and Wigginsto concepts. In this way, these authors illustrate the realist,nominalist, and conceptualist interpretations of sortals’ naturethat we presented earlier.

For his part, Geach did not use the word “sortal” but mostcommentators identify his notion of a “substantivalexpression” with “sortal” in the other writers.While Geach appears to align more closely to Quine, given that“expression” seems to be a linguistic concept, Geachextends his conclusions across languages in ways that Quine wouldlikely dispute. These variations in terminology among the four authorswould not be important, if there were straightforward, universallyagreed upon connections between concepts, universals, and expressions.But there aren’t.

Strawson made no mention of Locke, Aristotle, Spinoza or Frege in thecontext of introducing the expression “sortal universal”inIndividuals in 1959.

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

Strawson had two main projects inIndividuals. The first wasto show that material bodies and persons occupy a central positionamong particulars and that items in these two categories are basic toour conceptual scheme. The second was to

establish and explain the connection between the idea of a particularin general and that of an object of reference or logical subject.(1959: 11–12)

Sortal universals are central to this second task because, accordingto Strawson, reference to particulars occurs by using expressions thatare 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 thatkind.

It is not difficult to see why someone would identify theserequirements. In order to know that there are exactly twoGs ina regionS, it is necessary and sufficient to know that

There is anx which is inS and hasG, aywhich is inS and hasG and is not identical tox, and for anyz, ifz is aG which is inS thenz is identical with eitherx ory.

The phrase “criterion of identity” seems to mean acriterion which gives a necessary and sufficient condition foridentity. In many cases, however, a weaker condition suffices forcounting. To conclude that there are exactly twoGs in regionS, all that is required is a sufficient condition forxandy to be distinct, and a sufficient condition forzto be identical withx ory. In the case of physicalobjects, it may be that being at the same location at the same time issufficient for identity, and being in entirely separate locations atthe same time is sufficient for distinctness. In most circumstances,these will suffice to countGs, but it is far short ofproviding answers about partially overlappingGs, and providesno guidance about identity across time. So often we may be able tocountGs without having a criterion of identity in the strongsense.

One of the unclarities of the phrase “criterion ofidentity” is that it is never spelled out what the criterion isto be applied to. For example, is it a criterion to be applied tonames of objects or to perceptual representations of objects or to theobjects themselves? It is also unclear how strictly we are tounderstand “criterion”. In “Entity andidentity” (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 anexplicitly statable necessary and sufficient condition that does notuse the identity relation, or one where the identity relation is onlyapplied to constituent parts of the objects. This can be done fornumbers and sets, but probably not for any kind of concrete objects.In 1997, he retracted that proposal in favor of the looser (and stillundefined) general philosophical use of the term (1997a: 2–3).In contrast, Wiggins understands the counting criterion very strictlyso one instance where there is not a determinate answer to a questionleads him to reject the counting criterion (2001: 75).

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

A term “A” is a sortal iff there can be cases inwhich “A” provides, without further conceptualdecision, and without borrowing other principles of individuation,principles adequate for countingAs. (1997: 43)

Since most philosophers who invoke the distinction want to reject“thing”, “object” and “entity” asnon-sortals, Griffin’s suggestion is inadequate or, at least, isa shift to a different concept with the same label. The question“How many things/objects/entity are in the spaceS?”, whereS is an empty space has the determinateanswer “zero”, so all of these terms pass the Griffinstandard. One could attempt to amend the criterion by requiring thatthere can be cases which satisfy the above criteria and where there isat least oneA. However, this fails to delineate the rightcases, because there are sortals such as “unicorn” and“square circle” which have no instances. These points, andthe observation that some of the various notions of sortal diverge,were first made in Feldman (1973) but have not been widely noted (seethe entry onrelative identity). We will revisit some of these issues in§10.1 on the concept of physical object.

5. The content provided by sortals

As illustrated above, the history of the sortal concept shows thatthere is no singular, universally accepted interpretation of itsmeaning. Moreover, as it will be discussed next, the criteria thatsortals are believed to convey can be understood in various ways,further contributing to the uncertainty surrounding its content.

5.1 Counting

As we have observed, sortals are widely regarded as a conceptualfoundation for counting. Therefore, one key criterion for determiningwhether a given predicate is a sortal is whether is makes sense to aska meaningful “how-many” question about it. The requirementfor the question to be meaningful should be understood not justgrammatically, but also in a subjunctively operative sense. That is,meaningfully asking such a question means that counting the entitiesto which the predicate applies is, subjunctively speaking, a feasibletask: a task that one could complete if there were no material or timeconstraints. This does not mean that carrying out the task should bepresumed to be computationally effective. Thus, the counting criterionconveyed by a sortal is not necessarily an algorithm. (For variousinterpretations of the counting criterion, see Wallace 1965 andGriffin 1977.)

If counting were the only criterion for defining sortals, many of theso-called counting nouns would have to be classified as sortals.However, as noted earlier, nouns like “object” and“thing” would not meet this criterion unless we acceptthat the answers to the “how-many” question in these casescould be either an infinite or, as noted earlier, zero number ofobjects (things). Even with this possibility in mind, scholars, suchas Ayers(1977) and Wiggins (1977), continue to argue againstclassifying these and similar concepts as sortals. Therefore, thecounting criterion is not universally accepted as the definitivecharacteristic of sortals, and additional criteria are needed.

On the other hand, as mentioned earlier, while the counting criterionis one of the most commonly recognized features of sortals, it relieson other criteria that have been suggested as potential definingfactors for a predicate to be considered a sortal, such as those ofindividuation and identity. Therefore, we must consider additionalcriteria.

5.2 Individuation, essential sortals, and the “What is it?” question

An important idea in several philosophical theories is that sortalsprovide a criterion of individuation. The nature of the criterion isnot always clear, though, because the concept of individuation can beinterpreted differently. Sometimes it refers to the process by whichsomething becomes or is made into an individual, while at other times,it designates the characteristic of being an individual. In the lattersense, individuation is known as individuality (see Gracia 1988).

In light of the above, we can distinguish between a cognitive and ametaphysical sense of individuation (see Lowe 2003 and 2007). Thecognitive sense refers to the process of singling out an entity as anindividual in thought, perception, or linguistic reference. In themetaphysical sense, individuation is a relationship of ontologicaldetermination between entities. In this case, entities are assumed tometaphysically explain the individual character of other entities andcondition their individuality. For example, in the case of sets, theirmembers determine their individuality—that is, their individualcharacter.

It is important to note that there is no one-to-one correspondencebetween the cognitive and metaphysical senses of individuation. Forinstance, sortals like “architect”,“blacksmith”, and “teacher” provide cognitivecriteria of individuation but not necessarily for individuality.However, some sortals, such as those for natural kinds, may serve bothpurposes.

Individuation in the cognitive sense is involved in the counting andidentity criteria. For example, to ask how many horses there are inthe barn, one must be able to single out the horses in thought,perception, or language. Similarly, asking whether John is the sameperson as Peter presupposes a cognitive act of singling out.

Whether individuation suffices for counting is controversial. Forinstance, Wiggins in his later writings gives examples to show thatcriteria of individuation are insufficient to count objects under asortal:

…the concept crown gives a satisfactory way of answeringidentity-questions for crowns. But there is no universally applicabledefinite way of counting crowns. The Pope’s crown is made ofcrowns. There is no definite answer, when the Pope is wearing hiscrown, to the question “how many crowns does he have on hishead” (1980: 73; 2001: 75)

In a footnote to the same pages, Wiggins gives a list of otherexamples 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, onhis view, his account does not disagree with Strawson’s butcorrects and enlarges it (2001: 75). We find it puzzling that Wigginsdismisses “animal” as a sortal but is willing to include“machine” which seems at least as problematic. Accordingto Wiggins, only those concepts that possess clear criteria ofindividuation count as sortals, and he maintains that“animal” lack such a definite criteria. In his view,although the term “animal” can readily acquireindividuative force from contextual factors or the presence ofanother, more specific sortal predicate, it does not, in and ofitself, establish a single principle of individuation.

We should point out that, corresponding to the two senses ofindividuation discussed above, there are two philosophical theories inwhich sortals play a crucial role: perception sortalism andmetaphysical sortalism. The first theory, perception sortalism, holdsthat sortals are essential for perception, as they are thought to bethe means by which objects are identified (see Campbell 2002 andClarke 2006). In contrast, metaphysical sortalism asserts thatindividuals are individuated by their essences or as being of aparticular kind. These essences or kinds are considered real entities,which are expressed or captured by sortal predicates (see Lowe 2009for natural kinds, and Heil 2003 for artifacts). Subsequently, in§10.3, both philosophical theories will be revisited and examined oncemore.

Sortals that convey essences are referred to as essential sortals.Some argue that, in general, sortal specify the essences of the thingsthey categorize. However, this is a controversial position. There issignificant debate about whether the entire concept of essence iscoherent, which leads to disagreements about the existence ofessential sortals. For instance, Brody (1980) and Wiggins (2001)defend the idea of essential sortals, while Mackie (2006) arguesagainst it. Moreover, even among those who accept the existence ofessential sortals, there is disagreement about whether they operate ata general level, such as “animal” or, at a more specificlevel, such as “dog”.

Even assuming that there are essences, no consensus exists on whetherkinds have essences. For instance, Quine would argue that they do not.Additionally, among those who assert the existence of essences, thereis no agreement on what those essences are. Contemporary versions ofsortal essentialism attempt to address those issues, particularly thetheories put forward by Brody (1980) and Wiggins (1967, 1980, and2001) mentioned earlier. Another influential approach is offered bythe essentialism of origin, proposed by authors like Forbes (1985) andSalmon (1981) (for a discussion of these theories, see Robertson(1998, 2000)). Minimalist essentialism (Mackie 2006) is an alternativeto those two forms of essentialism.

In addition to the idea that sortals stand for essences, there is thebroader view that they answer the “What is it?”question.Unless the question is given a more specific technical sense, it seemsthat sortals in the broad Strawsonian sense— such as a “Akitten” or “A red table”— answer the questionadequately. The kitten does not go out of existence when it becomesadult, but it is no longer a kitten. This approach could encompass theessentialist perspective as well.

5.3 Identity, criterion of identity, and sortals

As we have indicated, the idea of a sortal has been closely linked tothe notion of identity and its related notion of a criterion ofidentity. Over time, different perspectives on such notions haveemerged, adding another layer of variation to understanding what thenature of a sortal entails. To clarify this aspect, we will now focusspecifically on the notions in question in their connection tosortals.

5.4 Identity, indiscernibility, and the criterion of identity

It is a law in many logical systems that things that are identicalshare all of their properties. This is known as the law of theIndiscernibility of Identicals. The controversial converse,known asthe Identity of Indiscernibles, says that thingsthat share all of their properties are identical. If“property” is understood sufficiently liberally, then thelatter principle is certainly true—any object \(b\) has theproperty of “being identical to \(b\)”, and if \(c\) alsohas that property, then \(b = c\). The question is whether theprinciple holds with any more restricted sense of property. Ladyman etal.(2012) discuss and relate different interpretations ofindiscernibility associated with various senses of properties. Many ofthese interpretations would ground different versions of the identityof indiscernibles principle. (See the entry onthis principle for philosophical perspectives other than those considered by Ladymanet al. (2012).)

One might closely link indiscernibility to the notion of a criterionof 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 thatif \(b\) and \(c\) both are \(F\), then if \(b\) and \(c\) instantiateexactly the same properties in \(\phi\) then \(b = c\).

Some attempts to give content to the phrase “criterion ofidentity” can be understood in this framework. Black (1952)argues that purely internal properties of objects do not suffice; hisexample is a universe with two spheres which share all of theirinternal properties, i.e., are the same color, weight, composition,etc.

There are a wide range of philosophical views about criteria ofidentity. Brody (1980) takes the two identity and indiscernibilityprinciples as jointlydefinitive of identity and consequentlyargues that no further criteria of identity are required. Baker (1997)argues that there are no criteria of identity across time, whileJubien (1996), Merricks (1998) and Zimmerman (1998) articulate reasonsto doubt that there are any criteria of identity. Lowe (1989,1997, and2009) are more recent attempts to clarify the concept

Finally, there are well-known historical debates about identity thatlead to disagreements regarding the relationship between essentialsortals and identity. Some philosophers argue that there is a unique,universal identity relation that holds (or does not) independently ofany sortals. In contrast, others maintain that identity is alwaysrelative to a sortal. For example, we may have a statue of Lincoln anda statue of Caesar, which are considered distinct statues, even thoughthey are both made of the same lump of bronze. In this case, thesortals “statue” and “lump of bronze” providedifferent answers to the identity question. These examples underscorethe necessity of now considering notions of identity assortal-relative.

5.5 Is identity strongly sortal relative?

One of the novel claims in Geach’sReference andGenerality was that identity is relative in the strong sense thatfor two sortal expressionsF andG,b andc might be the sameF, but not the sameG. Geachused the expression “substantival” to characterize thekinds of termF andG are. His“substantival” coincides in many cases with sortals asunderstood 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 greatnumber of coins, but “How many golds?” does not makesense. Thus “gold” is a substantival term, though wecannot use it for counting. (1962: 64)

One of the examples he gives is thatb might be the same riverasc, but not the same water. Or, if some bronze is made intofirst one statue, then a different one, then the two statues are notthe same statue but are the same bronze.

Quine (1964) and others were critical of Geach’s solution tothese puzzles and defended the view that there is only one unqualifiedsense of identity. In each of the problem cases, his strategy was totry to show that one of the statements of the form “sameG as” is not a true identity statement. So in the riverexample, Quine would deny that the water is identical to the river andthus the two statements are about different objects. Almost all ofGeach’s examples can with some plausibility be treated bydistinguishing more carefully between objects of reference ordistinguishing constitution from identity. Thus, one might say thatthe bronze at different times constitutes the two statues but is notidentical with them. Whether constitution really is or isn’tidentity is a matter of continuing debate; for articulations of thetwo sides see Johnston (1992), Noonan (1993), Baker (2007, chap.3),and the entry onmaterial constitution. For later stages in the debate between Quine and Geach, see the entryonidentity .

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

One example that does not readily lend itself to these approaches isthe problem of the Christian Trinity. According to this doctrine, Godthe Father, Jesus, and the Holy Spirit are three persons but one Godor one substance. Thus, they provide an alleged example wherebandc are distinct persons but the same substance. We will notenter the debate, which is been conducted for over a millennium, as towhether this doctrine is coherent, but refer the reader to a moderndiscussion in Cartwright 1987. It is certainly accurate to say thatall of Geach’s examples are contested. For details on how theproblematic character of such examples can be systematicallydispelled, see, for instance, Wiggins (2001, chap. 2).

5.6 Is identity weakly sortal relative?

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

The weak sortal relativity claim consists of saying that the identityrelation for sets is different from those for numbers, which isdifferent from those for people and artifacts like cars, and numbers.For sets it involves members of whatever kind, for numbers relationsto numbers and for persons and artifacts continuity of life and offunction. For abstract non-mathematical things, the relation is evenless clear—the question when two ideas are the same idea isoften only settled in a court case about copyright or patentinfringement.

In other words, there are two conceptions of identity: On one thegeneral identity relation is pieced together from the differentidentity relations for different categories of things. Foraandb to be identical is for them to be the same person or thesame number or the same artifact or …. On the other conception,there is a general notion of identity, perhaps given by the identitylaws discussed in Section 5.4 , and the specific ones are ways of instantiating that relation. Thebest argument for the first view is that the pieces seem too diverseto be parts of the same general relation. The best argument for thesecond is that as we move from domain to domain, and even invent newones, the general identity scheme guides our development of anunderstanding of the more local notion. (For a detailed analysis ofWiggins’ claims see Snowdon 2009.)

6. Sortals and the mass-count distinction

Linguists have long distinguished between mass and count nouns basedon grammatical factors. Mass nouns include terms for materials likewater, gold, iron, and meat. However, like sortals, mass terms conveyidentity criteria and can appear in relative identity statements. Forinstance, one might say c is the same gold as b, referring to a goldbucket (c) that was melted to form a gold bracelet (b).

The fact that mass terms can convey identity criteria has led somephilosophers to group them with sortals (e.g. Lowe 2009). Others arguethat mass terms should be treated within the sortal vs. non-sortaldistinction. A key reason for this is grammatical. Count nouns formplurals and appear in constructions like “How many…”. Mass nouns, on the other hand, do not pluralize andtypically occur in constructions such as “How much…?”. For example, we ask how many cats someone owns, buthow much cat food they have. Some words have both a mass and a countsense, such as “chicken”. We can ask both how manychickens someone owns and how much chicken they want for dinner. (Formore in-depth discussions on the mass-count distinction, fromphilosophical, linguistic, and cognitive perspectives, see Pelletier(1979, 2010), as well as the entries onthe logic andthe metaphysics of mass expressions, .)

The grammatical distinction is robust; nearly all speakers of alanguage agree on which sentences are grammatical and which are not.However, philosophers continue to debate how closely count nouns alignwith sortals. For example, while the sentences “There are threered things on the shelf” and “Two objects collided”are grammatical correct and so “red thing” and“object” are count nouns, many philosophers contend thatthey are not sortals, as previously noted. Hirsch (1977) and Wiggins(1977), for instance, claim that you cannot count red things orobjects, even though the request to do so is grammatical. Others thinkthat we can count red things, but the only correct answers are“infinitely many” and “none”- if there are nored objects, there are none, but if some red thing is present, its tophalf, bottom half, and various of its parts can be counted as separatered things, such as the three thirds or eight eights of the object,leading to an infinite number of red things. This view is contested,and the debate resurfaces later when we discuss, in Section 10, the role of sortals in cognition.

The philosophical distinction between “stuff” and“things” might also be instrumental in the above debate.Some stuff composes things—such as wood constituting a ship. Thecount-mass distinction often aligns with this difference but notalways. For example, while “vehicle” and“vegetable” are count nouns, “fruit” and“furniture” are mass nouns, even though the specific itemsthey refer to-for instance, apples and chairs-are countable.Additionally, different languages treat these concepts differently—In English, vegetables are counted, while in German, speakersask how muchGemuse you want, even though“Gemuse” refers to the same things as“vegetable”. In Italian both “frutta”and “verdura” are mass nouns.

Finally, there is the distinction between counting and measuring.While the differences between counting—how many oranges do wehave—and measuring—how much rice do we have—areclear, other cases are perplexing. Salmon (1997) offers multiplepossible analyses of sentences such as “There are two and a halforanges on the table”, but he finds all of them wanting.

7. The persistence criterion and substance sortals

Questions of identity over time are difficult because they involveissues of persistence. For example, when a kitten grows up, it ceasesto be a kitten but is still the same cat and the same animal. Incontrast, if we tear down a garage and build a treehouse from the samematerials, it is no longer the same building. If a car is crushed intoa metal cube, it no longer exists as a car, but if the car istransformed into a boat, does one thing exist as a car and then as aboat? Some views suggest that when a person dies, they cease to exist,while others propose that the same person may be reincarnated in a newform. Similarly, is a werewolf sometimes a person and sometimes awolf, or are they always a werewolf, neither a person nor a wolf?

In general, when does something survive change, and when it does not?Which kinds of change allows for continued existence? Sortals, whichprovide criteria for persistence through time are often referred assubstance sortals. By their characteristics, essential sortals willqualify as substance sortals, but the reverse is not necessarily true.Similarly to the case of essential sortals, there are systematicdisagreements among philosophers whether the substance sortals are tobe located at a relatively specific level, e.g., “dog” and“river”, or at the level of a more general category, e.g.,“animal”and “geographic feature”.

The sortals that Wiggins regards as crucial, the substance sortals,are a proper subset of the ones Strawson is concerned with.Substance sortals contrast withphase sortals; thelatter typically only apply to some temporal segment of an object.Kitten is a phase sortal because when a cat matures it ceases to be akitten but it does not go out of existence. Substance sortals are alsocontrasted 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 isa restriction of the other or both are restrictions of some othersortal.

This seems problematic because it is plausible that plant and animalare both substance sortals. While they do not overlap, anothercandidate for being a substance sortalcarnivore overlapsboth. This would probably not disturb Wiggins, since he already deniesthat “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 ordinarycontexts of what things are. But this is because “animal”so easily takes on an individuative force from a context and/or someother sortal predicate that is ready to hand. But the designation“this animal” is complemented in all sorts ofdifferent ways. In itself it determines no single principleof individuation. (2001: 129)

We said earlier that in contrast with Strawson, Wiggins is concernedprimarily with the narrower class of substance sortals. Yet if we readhis account carefully, it emerges that in the end individuation restswith an even smaller class which he calls“ultimate” sortals:

By an ultimate sortal I mean a sortal which either itself restricts noother sortal or else has a sense which both yields necessary andsufficient conditions of persistence for the kind it defines and issuch that this sense can be clearly fixed and fully explained withoutreference to any other sortal which restricts it. (1967: 32)

…I shall callx’s ultimate sortal concept… the sortal concept which is individuative ofx andrestricts no other sortal concept. (1980: 65)

The idea is that “cat” and “dog” may both beindividuated by the same criterion, so the fundamental criterion isnot only associated with them but with other substance sortals thatfall under the same ultimate sortal. We know from Wiggins’sremarks that “animal” is not a sortal, so the ultimatesortal for “cat” and “dog” is somewhere in thehierarchy above those concepts but below “animal”.Surprisingly, given the centrality of this notion, Wiggins nowheregives an example of what he regards as an ultimate sortal. (At 1980:123 he does speculate inconclusively that “man” might bethe ultimate sortal for Julius Caesar.)

Without more specificity about when principles of individuation arethe same and different, the foundation of Wiggins’s account ismurky. For example, we don’t have enough information todetermine whether some middle level term such as “mammal”is an ultimate sortal or not.

There are also other problems. Wiggins recognizes that his account ofindividuation of biological kinds in terms of “characteristicforms of activity” does not transfer well to prototypicalartifacts. He tries to meet this concern by giving an analysis interms of function for artifacts such as clocks. However, he seems toassume that there are not problematic intermediate cases betweennatural kinds and pure artifacts. Many kinds of things, e.g., riversand lakes, can be either natural or artificial. They can also bepartly 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), forcritical discussions on Wiggins’ view on artifacts; see also theentry onartifacts for more general discussions of this notion in diverse areas ofphilosophy.)

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

Almost everything that has been said so far has been mainly directedat words standing for the various species of natural substances. Theaccount could be extended and adapted without overwhelming difficultyto predicates of genera, wherever these were still determinate enoughto be autonomously individuative. (2001: 86)

Unfortunately, his own favorite examples, “elm” borrowedfrom 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 mostcommonly used biological terms are expressions for some classificationabove the level of species. Since Wiggins is cautious about extendinghis account to genera, he may have very few substance sortals by hisaccount.

Another issue with using species as the model of sortals is thatcontemporary philosophers of biology generally agree that speciesdon’t have essences, though there is disagreement among themabout the best way to characterize species (for details, see the entryonspecies). However, Wiggins defends a different version ofessentialism—namely, individual essentialism. This is the viewthat an individual is essentially a member of the species it belongsto (Wiggins 2001, chap. 4), and it is logically independent of speciesessentialism. For example, a given whale, is essentially a member ofthe species whales, even if the species itself possesses no essentialproperty. Therefore, rejecting species essentialism does notnecessarily entail rejecting individual essentialism. Moreover, thereare attempts by Wiggins to argue that species don’t haveessences. He states, for example, thatspecies is an:

…insecure concept in plant-taxonomy, and threatened even inzoology by such phenomena as ring-species and the imperfecttransitivity of the relation interbreeds in the wild with—theoperational test of identity of species. (1967: 62)

There is no incoherence here on Wiggins’ part because, aspointed out above, species essentialism is logically independent ofindividual essentialism. Nevertheless, Wiggins’ essentialism is,like species essentialism, also subject to criticism based oncontemporary results from the philosophy of biology (Laporte 1997 andOkasha 2000). But see Ferner (2016) for a sympathetic discussion ofWiggins’ doctrines from the perspective of biology, and Devitt(2018) for a recent defense of individual essentialism, whichconsiders the views and criticism in question.

8. Sortals for abstract objects

Most discussions of sortals focus on kinds of physical objects, but bythe definitions given many sortals also apply to abstract objects. Andin some of these cases the question what a criterion of identity isbecomes even more difficult. We can ask how many new ideas a politicalcandidate has, how many governments Italy has had since 1950 and howmany books David Wiggins has written. Ideas, governments and books (inthe sense of type of book, not specific copies) are all abstractobjects. We comment on changes in corporations over time—Applehas grown—which implies identifying Apple over time in spite ofchanges. But we are far short of having criteria to make decisions inharder cases: Did Rice Institute cease to exist in 1960 or was it justtransformed with a new name and some changes in charter to RiceUniversity. The buildings, faculty and students all persisted, but didthe educational institution?

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

Mathematics also presents issues about what counts as a criterion,even when the definition is quite precise. Two irrational numbersx andy are identical if they have exactly the samerelations to each of the rational numbers. Pi is identical with3.14… because Pi is greater than 3, 3.1, 3.14, etc. and lessthan 4, 3.2, 3.15, etc. But does this count as a criterion? It appealsto the less than relation, which is a close cousin to identity itselfand it involves relations to similar entities.

Yet another issue involves possible identification between differentkinds 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 samenumber? Different understandings of number and different philosophiesof mathematics offer differing answers. But these controversies seeminsufficient reason to deny “number” the status of asortal.

9. Sortals as terms that divide their references

W.V. Quine (1960) introduced the characterization of sortals as termsthat divide their references. Clearly, this characterization differsfrom that of Strawson, Wiggins and Geach, although in footnote 1 ofQuine 1960: 90 he says that his expression is equivalent toStrawson’s “sortal”. Unfortunately, that cannot beexactly true since 1960: 91 Quine says that “object”divides its reference, though we have seen “object” is nota sortal by the criteria of Strawson or Wiggins because it does notenable counting. We should note that in other of his writings (1969,1981) he also used the expression “individuative word” asan alternative to the expression “term that divide”.

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

G divides its reference iff it is never the case that ifa isG,a can be divided into two parts which areG

While this characterizes “cat” as a sortal and“object” as a non-sortal, it also excludes some terms thatare sortals by the counting criteria, e.g., garden hoses, rocks, pilesof snow, sand dunes, amoeba and ice cubes. He also discusses theconverse:G divides its reference just in case whenevera andb areG, the result of puttinga andb together is neverG.

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

The closest Quine comes to an explicit formulation of acharacterization is in contrasting individuative terms with massterms:

So-calledmass terms like “water”,“footwear” and “red” have the semanticalproperty of referring cumulatively: any sum of parts which are wateris water. (1960: 91)

By “sum” here he almost certainly means the mereologicalsum, not the result of physical juxtaposition. This would mean that“object” and “space time region” would not besortals, but “spatio-temporally continuous object” and“space-time region with volume less thanx” aresortals. These results may be consistent with Quine’s viewsgiven that he has indicated that he accepts “object”, butthey diverge from the Strawson-Wiggins intent. Note that the threeterms 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 stuffand things. (See Laycock 2011 and the entry onobject for further discussion.)

In any event, Quine’s view of the distinction is much morepragmatic 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 theirreference differently and the third not at all. (1960: 91)

Even this characterization of a contrast is dubious if we note that bythe last criterion “object with mass more than 2 kg” isnot an individuative term since the sum of any two such objects isanother such object, whereas “object with mass less than 2kg” fails the test since the sum of two such objects sometimeshas mass over 2 kg. It is difficult to see any important respect inwhich the two expressions divide their reference differently. Objectmore than 2 kg and object less than 2 kg seem to divide theirreference.

Another example, given by Feldman (1973), can be used to illustratethe somewhat capricious nature of the distinction and its languagedependence. He claims that “five-foot garden hose” is anindividuative term since no part of it is a five-foot garden hose, but“garden hose” is not individuative. The latter claimrequires some qualification. If being a garden hose requires acoupling on one end and a nozzle on the other, then the halves of agarden hose are not garden hoses. If being a garden hose requiresneither a nozzle nor coupling, then each half (indeed eachn^th, up to somen) of a garden hose is agarden hose. If being a garden hose requires a coupling but not anozzle, then one half of a garden hose is a garden hose but the otheris not. Although the differences may be important to the gardener, itis difficult to see anything metaphysically deep here.

10. Sortals and their role in cognition

The concept of a sortal has made its way into the philosophy ofcognition and psychology, particularly cognitive developmentalpsychology. Among others, sortal-related issues in these fieldsinclude how sortals contribute to cognitive development, specificallyin humans (though also in non-human primates), their role inperception, and their connection to language, object-based attention,and the elements and structure of the (human) mind in its cognitivefunction.

10.1 The concept of physical object

A central issue in development psychology involves understanding whenand how individuals develop the ability to recognize, identify anddetermine the persistence of objects over time and space. Some arguethat the concept of a physical object plays a crucial role in thisability, serving as foundation for forming sortal concepts.

Ayers (1974), for instance, argued that the concept of a physicalobject is crucial for human cognition and its construction, as itprovides criteria for counting and persistence. According to him, aphysical object is a discrete entity, a natural unit or structure thatexists, continues to exist, and ceases to exist independently of ourconceptualization. Its unity is defined by causality. Moreover, aphysically object is not simply matter filling a continuous space-timeregion; it exists as a maximal entity. This means that we typically donot regard any proper part of a physical object as an object on itsown. This characteristic allows us to identify, count, and track thepersistence of object over time and space.

Despite the above, Ayers does not regard the concept of a physicalobject as a sortal concept. He argues that a sortal concept mustprovide the essential features that define an object. While theconcept of a physical object enables individuation and identification,it does not explain the unity and continuity of objects based on theiressential features. In this regard, Ayers aligns with the view ofsortals as concepts that provide the essence of the objects they applyto.

In contrast to Ayers, Xu (1997) views the concept of a physical objectas a sortal, emphasizing that it includes counting and persistencecriteria. This differentiates her perspective from Ayer’s. Sheunderstands the concept of a physical object as a bounded, coherent,three-dimensional entity that moves as a whole. Because the nature ofsuch entities, Xu suggests that physical objects can persist throughsubstantial transformations, citing the Biblical example ofLot’s wife turning into a pillar of salt (Xu 1997), a view thatAyers would reject. But, in an line similar to Ayers, she thinks thatthe concept of physical object persists in adults’ and can beapplied to unfamiliar objects.

She also argues that the concept of physical object is integral tocognitive development and appears in infants at an early stage. Basedon her research and that of others (Xu & Carey 1996,1999 Spelke1996), she suggested that acquiring the concept of a physical objectrepresents a key milestone in cognitive growth, paving the way formore sophisticated sortal concepts associated with languagedevelopment. Sarnecki (2008) concurs, proposing that a general sortalconcept is a necessary step toward acquiring language-basedsortals.

In addition to the concept of physical object, Xu (2002) has suggestedthat linguistic labels may influence the acquisition of sortalconcepts in infants as young as 9-months. Quine (1960) had alreadyhighlighted this crucial role of language in developing sortal-likepredicates, proposing that the ability to distinguish the world intoobjects only develops with language and the conceptual framework ofidentity and quantification. However, experimental evidence from Sojaet al. (1991) challenges Quine’s perspective. Moreover, researchresults in primates, such as those presented in Phillips and Santos(2007), and Mendes et al.(2008), provide additional empirical supportagainst Quine’s claim. Nonetheless, a nuanced version ofQuine’s view, particularly regarding quantitative distinctions,has found empirical backing in research by Imai and Genter (1997) andYoshida and Smith (2003).

Xu’s interpretation of the concept of physical objected as asortal has faced significant criticism. Critics argue, for example,that it excludes stationary objects, does not adequately express thenature of objects, and it is not maximal as she intends a physicalobject to be. Additionally, the experiments supporting Xu’sclaims have been challenged. Critics have suggested that thesefindings may instead reflect infants’ perceptual ability toattend to and track objects using spatiotemporal information, evenbefore fully developed system of concepts is in place. For furtherdetails on these critiques, see Ayers (1977), Casati (2004), Hirsch(1977), Rips and Leonard (2019), and Wiggins (1977). It is importantto note that these different papers reveal the discrepancy thatpervades the several interpretations of the nature of a sortal.

Finally, given the importance of object knowledge in navigating theenvironment, it is plausible that other species share some aspects ofthe concept of physical object. There is some preliminary evidence ofthis in primates, and recent findings suggest that young chickens mayalso possess such a concept (Fontanari et al.2014).

10.2 Essentialist cognition, basic level categorization, and sortals

Gelman (2003,2013) and others have provided evidence suggesting a modeof cognition of an essentialist character already operative inchildren. According to this view, specific categories of object andsubstances — such as natural and social kinds, artifacts andthose represented by mass terms and sortals—are assumed topossess an underlying, unobservable reality. This assumption explainsand grounds children’s inductive inferences based on thecategories in question. It also accounts for children’s tendencyto assign causal, non-obvious properties, and fixed, immutableboundaries to these categories. Children view some of these propertiesas innate. Research results (Caccione et al. 2016; Mendes et al.2018,2011; and Santos et al.2002) suggest that essentialist thinking mayemerge in humans at a pre-linguistic stage, particularly through theprocess of sortal object individuation. This phenomenon may also beevident in certain primates (Phillips et al.2010).

A related line of research, initiated by Rosch (1973) and Rosch et al.(1976), suggests that there is a category of basic level objects.While the specificity of classification can vary with context, thereis a tendency to prefer a particular in most situations. For example,while we might generally describe something as a mammal or a poodle,the most common and natural noun would be “dog”. Roschfound considerable cross-cultural agreement on what constitutes asbasic-level objects, although some variation exists. Basic-levelcategories are characterized by being the most informative, withfeatures such such as shape, color, form of movement providing keyinformation about other properties of the object. For example, aself-moving and dog-shaped it is likely to bark, eat meat, chase cats,etcetera.

Although Rosch’s basic-level categories offer useful answers tothe question “What is it?” they do not provide thetraditional essences philosophers and psychologist often discuss.Traditional essences are typically viewed as necessary and sufficientconditions for being a member of that kind. From this perspective,learning a new sortal requires knowing the defining features and howthey combine to create the kind. However, according to Rosch’sconception, sortal words are learned through exposure to families ofprototypes, with the primary learning experience involvingfamiliarization with prototypical examples of the kind. Prototypes arethe most representative examples, elicit the fastest responses whenqueried, and are the most frequently cited when asked for examples ofa category. For example, in the category of birds, robins are one ofthe most prototypical, swans are intermediate, and penguins are veryunprototypical. Evidence supporting Rosch’s theory, includingthe failure to produce adequate necessary and sufficient conditionsfor many common sortals, as well as the positive experimentalevidence, suggest that categories function more fluidly thattraditional essence-based account. This view aligns withWittgenstein’s conception of categories.

In relation to the idea of essence, Markman (1989) and Markman et al.(2003) have argued that children’s early language learning isguided by several principles, one of which is the mutual exclusivityconstraint. This principle suggests that when learning words, aguiding assumption is that distinct words refer to distinct things.While this assumption is not always true, Markman and others provideevidence that this constraint is operative, and that in the languagelearning environment of young children it is a very helpful, ifimperfect constraint. If Rosch is correct about the existence of apreferred basic level of objects, it may be that speakers generallyuse words at that level of objects and thus the exclusivity constraintmay be supported by the basic level object hypothesis. However,experimental data on these issues appear to be conflicting (Mervis etal. 1994). Scholl (2008) offers a useful discussion of whether and howphilosophy and psychology can interact to deepen our understandingthese issues.

10.3 Sortalism

The idea that entities require sortals for their individuation andidentity is a broad position known as sortalism. Various forms ofsortalism have been developed from either a metaphysical orpsychological perspective, as mentioned in section5.2. When the focus is metaphysical, the view is referred asmetaphysical sortalism. In this case, sortals are themetaphysical conditions for the identity, individuation, and essenceof entities. (For instance, see Wiggins 2001 and Loew 2009). Ifsortalism is addressed from a psychological perspective, it isreferred aspsychosortalism orsortalism ofthought.

Psychosortalism starts with the clear idea that human perceptionnecessitates the individuation and differentiation of the perceivedentities. In other words, when one encounters an object in theperceptual space—whether through sight, hearing, touch, smell,taste or any other sense—one must identify it as an individualand distinguish it from others in the same context in order toperceive it. Several philosophers and psychologists claim that thisprocess of individuation and differentiation relies on sortal concepts(see Mcnamara 1986; Carey and Xu 1996 and 1999; Clark 2006; and Quine1950 and 1960). Based on this claim, a second claim is upheld: sortalsconstitute the necessary elements to determine the persistence ofobjects and allow us to track them across space. Both of these twoclaims summarize the main tenets of psychosortalism or sortalism ofthought.

While possessing sortal concepts enables effective perception (and soare sufficient for this task), their role as necessary conditions iscontentious. Several arguments suggest that individuation anddifferentiation can occur without sortal concepts, relying instead onmechanisms that delineate and direct conscious attention to objectsbased on spatiotemporal and property information. This form ofindividuation is shared by animals, such as cats and dogs. (SeeCampbell 2002 and 2006, Raftopolous and Muller 2006).

Other arguments have challenged the evidence or pointed to linguisticphenomena that would be inexplicable if sortalism were correct. Forexample, the ability to refer to an object with a demonstrativewithout invoking a sortal concepts poses an important challenge(Goodman 2012). Experimental findings also indicate thatpsychosortalism fails to accurately predict how people judgeindividual artifacts and natural kinds. These results suggest thatrelying on sortal concepts alone cannot fully account for our abilityto individuate and identify objects (Leonard and Rips 2015) or thatsuch concepts may not be necessary for individuation (Tiago 2009).

Finally, it is important to distinguish perception and metaphysicalsortalism from predication sortalism. The latter posits thatpredication is a cognitive act in which an entity (the subject of thepredication) is classified and cognitively singled out. Predicationsortalism claims that this act originates from the application ofsortal concepts. This view is compatible with anti-psychosortalism,which holds that perception does not require sortal concepts. (Forpredication sortalism, see Freund 2021).

11. Sortals and logic

11.1 Sortals and standard logic

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

Sometimes in applications of first order logic, i.e., when we aredealing at length with a specific class of interpretations the domaindivides into intuitively disparate kinds of objects, e.g., people andnumbers. In the usual formulation, one has predicates, e.g., \(Px\)and \(Nx\) which are true of those kinds of things respectively, andso one translates the English sentence “All numbers areodd” as \((\forall x)(Nx \rightarrow Ox)\) and “Someperson is tall” as \((\exists x)(Px \mathbin{\&} Tx)\). In amany-sorted logic distinct variables are used for the different kindsof objects, perhaps \(m\), \(n\),… for numbers and \(p\),\(q\),… for people. In this language combinations of variableswith predicates are sometimes restricted so that \(Nm\) and \(Tp\) arewell-formed but \(Np\) and \(Tn\) are not. If one does not make thisrestriction, then the notation is exactly equivalent to standardfirst-order logic. A many-sorted language is expressively equivalentto a single sorted one which has additional predicates for the varioussorts of things (cf. Quine 1966).

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

A related use of many-sorted logic is to provide a kind of translationfrom second-order logic into a first-order logic. In this case insteadof having second-order quantification over sets (or properties), onestays with a first-order language which is supplemented with apredicate true of all and only sets (or properties), a distinct styleof variables for those entities, and with a two-place relation ofeither membership or instantiation.

11.2 Logics of sortals

Standard logic treats all predicate expressions alike—thepredicates can be interpreted as any subset of the domain ofquantification. If any of the claims discussed above about sortals arecorrect, then the sortal predicates have distinctive properties, and amore sophisticated logical treatment might provide philosophicalillumination. One obvious and agreed on principle is that in generalthe negation of a sortal predicate is not a sortal. This contrastswith 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), but you also cannot count thenon-cats since they include dogs, table, molecules,etcetera. However, for two of the other logical operators,disjunction and conjunction, the situation seems more complex. Theexpressions “dog or cat”, “apple or orange”and “fork or spoon” all seem to be well-behaved withrespect to counting and identifying; we can easily imagine a cityordinance forbidding homeowners to have more than four dogs or cats.On the other hand, “dog or natural number” and “cator clock” seem to provide methods of counting but seem unnaturalas sortals.

The first “sortal logic” was developed in Stevenson(1975). Stevenson develops an account in which he says “We useideas of Geach, Wallace and Wiggins, although we depart from each incertain respects” (1975: 186). Although the formalism followsWallace in some respects, the main ideas seem to be those of Wigginsrather than Geach. Specifically, his theorem 3.4.5 affirms that forany sortalsF,G, ifb andc are the sameF, andb is aG, thenb andc arethe sameG, which is a denial of Geach’s relativeidentity thesis.

Two principles that Stevenson adopts following Wiggins are:

(i)

For every sortalF, eitherF is an ultimate sortal,or there is an ultimate sortalG such thatF is arestriction ofG.

(ii)

If two sortalsF andG intersect, i.e., they areboth true of at least one object, then there is a common sortalH of which bothF andG are restrictions.

Stevenson proves the formal consistency and completeness of his set ofaxioms. It should be noted that completeness here is with respect tothe language used. Since this is a minor adaptation of standard logic,there is no treatment of tense or modality, some essential elements ofWiggins’s notion of sortal cannot be expressed, e.g., if asortalF applies tob at one time, then it applies tob at all times at whichb exists, and if a sortalF applies tob, thenF necessarily applies tob.

Stevenson does not permit combinations of sortal expressions,presumably because there is no easy way to deal with disjunctions andconjunctions of sortals in his formulation. However, a slightcomplication of his language would suffice to handle the problem. Heuses “\(uS\)” for the ultimate sortal which governs sortal“\(S\)”. If instead he introduced a set of letters \(U'\),\(U''\) … for ultimate sortals, he could then superscriptsortal 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 thedisjunction of \(S^{U'}\) and \(T^{U''}\) since they are governed bydifferent ultimate sortals.

Cocchiarella (1977) presents a formal language, though no axioms orrules, for a logic of sortals which includes both tense and modaloperators. His approach, like Wiggins, considers sortals to beconcepts. Unlike Wiggins he gives a definition of “sortalconcept”: as a socio-genetically developed cognitive ability orcapacity 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 ofwhich various artifact sortals are restrictions, nor that everyintersection of sortals must fall under an ultimate sortal.Cocchiarella’s approach also goes beyond Stevenson’s inthat it involves second-order logic, i.e., it includes quantificationover sortal concepts.

Cocchiarella’s ideas have been presented in more rigorous formaldetail with axioms and consistency and completeness results forsecond-order logic in Freund (2000), tense logic (2001) and modalities(2004). More recently, Freund (2019) has formulated severalbidimensional logics for sortals that consider modal, tense, andepistemic modalities, as well as complex sortals (i.e., sortals thatinvolve logical combinations of other sortals). These systemspresuppose a conceptualist philosophical background closely related toCocchiarella’s but somewhat more general.

Belnap and Müller develop an alternative account of sortalswithin a non-standard formal logic for tense and modality. Unlike theusual background of possible worlds for modality, they use ideas fromBressan (1972) and adoptcases as the fundamental backgroundnotion They define a sortal as a predicate which is modally constantand provides separability. A predicate is modally constant iff itapplies necessarily to something whenever it possibly applies. Theidea is that while someone might possibly be a student withoutnecessarily being a student, if they are human, they are necessarilyhuman. Thus “student” is not a sortal but“human” is. A predicate is modally separated just in caseit is necessarily true that if any two things having the property arepossibly identical, then they are in fact necessarily identical. Usingtheir technical terminology of cases, if two things which have amodally separated property coincide in any case, then they coincide inevery case. Belnap and Müller are explicit that they areproviding a formal framework for classifying predicates, but thatapplications will require other kinds of thought:

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

12. Sortals and artificial intelligence

Guarino, Carrara, and Giaretta (1994) develop an account of sortalswithin knowledge representation, a subfield of artificial intelligenceintended to bridge the gap between abstract formal logics and naturallanguages. Their definition of a sortal is that it is a predicate thatprovides countability and is temporally stable. A predicate providescountability if it does not apply to any proper part of what itapplies to. As they explain this, “student” providescountability because no proper part of a student is a student; but“red” does not provide countability because parts of redthings are also red. Temporal stability means that if the predicateapplies to something at one time, then it must at some other times aswell. This is approximately the concept Strawson had in mind. They goon to distinguish a subset of these, the substantial sortals. Asubstantial sortal is one that, if it applies at all, necessarilyapplies all times. This is in close agreement with Wiggins’ useof the term. So while “student” provides countability andis temporally stable, it is not ontologically rigid, so it is a sortalbut not a substantial sortal. On the other hand, a cat is alwaysnecessarily a cat.

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

We should also note that there is a shared core of concerns in theselast two approaches, it is clear that in addition to the superficialdifference that Belnap and Müller restrict “sortal”to approximately the substantial sortals as defined in Guarino et al.(1994), there are differences even in the area of overlap. Modalrigidity and modal constancy are very similar. (Some caution isnecessary here since the modal logic frameworks differ.) But Belnapand Müller emphasize modal separability and do not mention acounting requirement, Guarino et al. (1994) require countability butare not concerned with modal identities.

In addition to Guarino et al. (1994), computational applications ofthe notion of sortal can be found recently inupper ontology, arelatively new field in computer sciences. For example, Guizzardi andWagner (2010) make central use of the notion of sortal in a conceptualframework they call Unified Foundational Ontology (UFO). Thisframework can be used in the design and evaluation of conceptualmodeling languages. In UFO, the focus on sortals is on the identitycriteria 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 andanti-rigid sortals. An instance of a rigid sortal S will be aninstance of S in every possible world in which it exists. Anti-rigidsortals will not comply with this feature. From the authors’examples and further claims, it is clear that rigid sortals correspondto substance sortals and anti-rigid to phase sortals. Because possibleworlds are involved, UFO’s framework seems to be committed toindividual essentialism. One will then ask whether UFO’s generalgoal is achievable, given the critique of such essentialism byphilosophers of biology. We should finally note that one can alsoappeal to a tense logic framework to illuminate the distinctionbetween substance and phase sortals, in contrast with UFO’smodal approach. (See Rybola and Pergl (2016a, 2016b), and Miletic andSariyar (2022), for further examples of recent applications of thenotion of sortal in computational ontology.)

13. Conclusion

A large number of thoughtful philosophers have believed that thecategory ofsortal was philosophically significant and thisis a strong indication that there is something important they areattempting to delineate and analyze. In the last two decades cognitivepsychologists and formal ontologists have applied the term in theirresearch. However, our dissection of the definitions and discussionsshow that there are numerous distinctions in question and while thesedistinctions have significant overlap, they are not identical. Itremains to be seen whether the sortal/non-sortal distinction marks onevery important difference, or numerous less important distinctionsrelated in complex ways.

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