Two Demarcation Problems In Ontology Pawel Garbacz Department of Philosophy John Paul II Catholic University of Lublin, Poland Abstract his or her research interests. Or if not, then everything goes into the scope. In this paper I will attempt to characterise the difference be- tween ontological and non-ontological categories for the sake This paper is then about the proper subject matter of ap- of a better understanding of the subject matter of ontology. plied ontology. I will attempt to draw a demarcation line My account of ontological categories defines them as equiva- between ontological and non-ontological categories. To this lence classes of a certain family of equivalence relations that end I will search for the proper level of generality of the lat- are determined by ontological relations. As a result, the de- ter by looking at how philosophical ontology defines its sub- marcation problem for ontological categories turns out to be ject matter. I will discuss a number of attempts to capture the dependent on the demarcation problem for ontological rela- specific nature of the ontological categories, as they are used tions. in philosophy, and on the basis of this survey I outline my own proposal. The main point of my contribution is the idea Introduction that ontological categories are the most general categories that cut the reality at its joints, where cutting is provided There are a lot of ontologies out there. (Ding et al., 2005) by ontological relations. In consequence it will turn out that claim to harvest from the Internet more than 300 000 Se- this account depends on how one can draw a demarcation mantic Web documents, of which 1.5% may be unique on- line between ontological and non-ontological relations. tologies. But wait! Are you really willing to consider the so- called ontology of Bibtex entries (http://zeitkunst. org/bibtex/0.2/bibtex.owl) or the so-called on- Ontological categories in philosophical tology of the Catholic Church administration (Garbacz et al., metaontology 2010) as genuine ontologies? Or when someone creates his So there is philosophy, one of which distinct features is the or her first, ’Hello, world’, OWL ontology in Protege with set of terms or categories it employs, e.g., “being”, “causal- three classes and one object property, will you call the result ity”, “emergence”, etc. Some of them originated outside phi- a (real) ontology? losophy and sometimes persist in parallel discourses, others Some of these so-called ontologies may be considered were invented by and for philosophers and rarely are used faulty on the basis of their immaturity: some categories or elsewhere. relations of theirs may be claimed to be underspecified - for And there is ontology, which from its very beginning was instance because of the expressivity constraints of the formal considered as (one of) the most abstract branch in philoso- framework adopted – like OWL. Another reason may be the phy. So it seems that such categories as “substance” or ”per- inappropriate level of generality. After all, applied ontology durant” are among the most promising candidates for on- cannot pretend to cover all categories or concepts, i.e., some tological investigations. Other categories, such as “obliga- of them are out of the scope. Since applied ontology seems tion”, while remaining within the scope of philosophy, are to inherit the pretence for maximal generality from its pre- too specific for ontology itself. There are also other terms decessor, philosophical ontology, there must exist a kind of like “location” or “function” that seem to borderline cases cut-off point, or a cut-off zone with possibly vague bound- of ontological notions. Obviously, much depends on a par- aries, that would demarcate the proper subject matter of ap- ticular system of or trend in philosophy, so one category be plied ontology from the subject matters of other disciplines. ontological for one system but not for the other. For example, given the (long) history of philosophical on- tology and the short timespan of applied ontology it seems Then the question arises whether there exists some kind of reasonable to expect from an applied ontologist to build a reason or rationale for distinguishing ontology among other formal theory of endurants or properties but not a formal philosophical disciplines. Obviously, the rationale may be theory of tree ferns. The latter are simply too specific to fit purely historical, i.e., we may report that such and such re- garded a given list of terms as ontological or not. If the Copyright c 2015, for this paper by its authors. Copying permitted philosopher in question happened to be an influential fig- for private and academic purposes. ure in history of philosophy, his or her list of terms may be shared by other fellow philosophers. Although this kind of egories in their modal status. For example, using the Onto- research is indispensable, a purely historical account is not, Clean terminology ontological categories may be identified in my opinion, fully satisfactory. with rigid properties, i.e., if a property is essential for its in- There seems to be four main types of philosophical ac- stances, it is (or corresponds to) an ontological category. counts of ontological categories that provides such rationale Are these accounts satisfactory? Obviously, even a cur- – cf. (Westerhoff, 2005, p. 22-64): 1. universalist 2. substi- sory evaluation of the most prominent of them is beyond the tutional 3. identity-based 4. modal.Each account attempts to scope of this paper, but this question reveals that in order specify sufficient and/or necessary conditions for a category to answer it we should provide some kind of the adequacy to be an ontological category. criteria for theories of ontological categories. (Westerhoff, In a universalist account an ontological category is any 2005, p. 22-64) is the only known to me attempt to list such most general category of things there are. For instance, (Nor- constraints. His account amounts to the claim that a concep- ton, 1976) propounds that an ontological category is any nat- tion of ontological categories is adequate only if it defines a ural category that is directly subsumed by the universal cat- non-empty, but finite, set of ontological categories such that egory. A more recent attempt along these lines can be found 1. it allows for the fact that some categories are not onto- in (van Inwagen, 2012). logical; The substitutional approach defines ontological cate- 2. some ontological categories may subsume others; gories as equivalence classes by means of a specific type of substitution, where the latter may operate either within the 3. no ontological category (properly) overlaps any other. linguistic or the ontic structures. As for the former suppose On top of this formal criteria J. Westerhoff seems to assume that entities x and y are represented by two expressions (e.g., that an adequate account will not propound categories that nouns, nominal phrases, sentences, etc.) α and β. Consider are much more specific than the categories we know from a set of linguistic structures, usually sentences, in which, α the history of philosophy. occurs. The set in question is assumed to contain all and How do the above accounts score against such require- only those structures that exhibit some salient linguistic fea- ments? (Westerhoff, 2005, p. 22-64) raises the following ture, e.g., they are grammatical or meaningful. If for each concerns: (or some) element φ of this set, when you can swap α with 1. universalist accounts are unable to define a non-arbitrary β, you will get a linguistic structure with the same feature, cut-off point: then x is claimed to belong to the same category as y. F. (a) either they stop at the very first level, i.e., they provide Sommers showed in a series of papers how this idea may be a flat list of ontological categories such that neither of fleshed out - see (Sommers, 1959), (Sommers, 1963), (Som- them subsumes or is subsumed by others - as it is the mers, 1971). The other type of substitutional approach is case with (Norton, 1976), quite unique in philosophy – I am aware only of (Wester- hoff, 2005), who employed the notion of substitution over (b) or they do not set the cut-off point at all - this may be the ontic structures: instead of replacing words and phrases the problem with (van Inwagen, 2012), in sentences, (Westerhoff, 2005) shows that we can replace (c) or they could set up an, ontologically arbitrary, cut-off components of states of affairs in order to get the equiva- point, e.g., at the level of the most general scientific cat- lence classes playing the role of ontological categories. egories; see, for instance, (Schwarz and Smith, 2008, p. An identity-based account defines ontological categories 224). in terms of the identity criteria. For instance, (Dummett, 2. substitutional accounts tend to generate too specific or 1973, p. 73-76) defines ontological categories as the most ontologically odd categories, e.g., the category of build- general categories whose instances have the same criterion ings because of the predicate “has the green back doors” of identity. That is to say, he considers classes of proper – this is a consequence of their dependence on the nitty- nouns such that each noun in a class has the same criterion gritty details of the lexicon and grammar of ethnic lan- of identity - the example of such class contains ’man’, ’tai- guages;1 lor’, ’coward’, etc. Then he holds that in each such class 3. identity-based account, or to be more specific, the ac- there is the most general noun, e.g., ’person’ or ’animal’ in count from (Dummett, 1973, p. 73-76) provides only a flat the case of the class in question, and this noun is claimed to list of ontological categories; moreover it should be noted express an ontological category. One can argue that this type that they are vulnerable to the various controversies perti- is also exemplified in the formal theory of properties devel- nent to the notion of identity criteria – see, e.g., (Carrara oped by N. Guarino, Ch. Welty and others under the label of and Giaretta, 2004); OntoClean - see, for example, (Guarino and Welty, 2000), (Guarino and Welty, 2002), (Guarino, 2009). Although it is 4. modal accounts are too “generous”: such categories as not focused on the notion of ontological category per se, this mammals, vertebrates or chordates are rigid, but they do approach illustrates that besides criteria of identity also other not look very ontological (in the sense of philosophical ontological aspects may be taken into account when charac- ontology at least) – the cut-off point is set too far down terising the ontological research, mainly modalities and the the subsumption hierarchy. relation of ontological dependence. In this sense it can be an 1 Westerhoff, or course, believes that this issues does not con- instance of the fourth type as well. cern his own theory, but the lack of space prevents me from ex- A modal account finds the specificity of ontological cat- plaining the intricacies of his approach. The mixed accounts may fare better, but a general eval- instance, suppose that you want to characterise the way in uation of them is clearly impossible. As for OntoClean, it which colours, or qualities in general, exist. If you claimed seems that none of the 12 types of properties classified in that two colours exists in the same way only if they depend (Guarino, 2009) may be identified with ontological cate- on entities from the same categories, then the colour of this gories. Consider the two top-most types: sortals and non- rose and the colour of that telephone box will exist in differ- sortals. Some ontological categories, like the top-most cate- ent ways provided that colours depend in their existence on gory of being, are non-sortals, while others, like persons are their bearers (e.g., on roses and telephone boxes). sortals. On the other hand, due to their generality, most of the Putting these two claims together we get: examples of ontological categories we know from history of ontology are rigid. x belongs to the same existential ontological category as y iff x depends on the same existential ontological categories as y. Towards a new perspective on ontological categories Of course, this characterisation is circular, so it cannot be considered as a simple definition of ontological categories. Reflecting on the four types of accounts discussed in the pre- However, it is not viciously circular, so it may serve to sep- vious section you may notice that each account groups en- arate ontological categories from non-ontological ones. In tities with respect to a particular ontological aspect of these what follows I will try to flesh out this idea in more rigorous entities and builds the definition of category around this as- way. pect: generality, identity, and modality. If we consider the Suppose that there is given a discourse or a body of actual history of ontology, one aspect that is clearly miss- knowledge that employs a certain set C of categories: ing here is existence or rather mode of existence. As one C1 , C2 , . . . : ontological and/or non-ontological. As far as can stipulate that a single ontological category collects enti- C1 , C2 , . . . are concerned, it is assumed that each entity from ties with the same criterion (or criteria) of identity, one can the domain, say some x, either falls under some category C also stipulate that ontological categories should be defined (written as: Inst(C, x)) or not - without any temporal or with respect to the mode of existence: two entities belong to modal qualifications.3 I will make no assumptions on the one ontological category if they exist in the same way. Ob- formal properties of this relation. In particular, I do not as- viously, when properly developed, this characteristics can sume that it is extensional, so there might be two different be seen as, at best, only a partial account of what ontologi- categories with the same extension. Therefore, it is useful to cal categories are because it focuses on their existential di- introduce the auxiliary notion of category extension: mension, so to speak, ignoring other relevant features, e.g., the modal status. In other words, this characteristics may be ext(C) , {x : Inst(C, x)}. (1) taken as a definition of existential ontological categories. x belongs to the same existential ontological category as y Suppose that there is given a binary predicate “dep” to re- iff x exists in the same way as y. fer to the relation of ontological dependence between the en- tities from its domain. Again I make no specific assumptions Then, existential ontological categories may be defined as about the formal properties of this relation except for the fol- the equivalence classes of the relation ’exists in the same lowing: if dep(x, y), then it is necessary that dep(x, y). way as’. For the sake of simplicity, “existential ontological Let me start with the auxiliary definition of dependence category” will be sometimes abbreviated to “ontological cat- between objects and ontological categories: egory” later on within this section. Now the question arises when two entities share the same deP(x, C) , ∃y[dep(x, y) ∧ Inst(C, y)]. (2) mode of existence. In what follows I will examine one pos- sible answer to this question: two entities exist in the same We can now define the equivalence relation that sorts out the way if they depend on entities from the same ontological entities with respect to the categories on which they depend: categories.2 x =dep y , ∀C[deP(x, C) ≡ deP(y, C)]. (3) x exists in the same way as y iff x depends on the same existential ontological categories as y. Intuitively, [x]dep , i.e., the equivalence class of x with respect Note that we cannot claim that two entities exist in the same to =dep , may be seen as a formal representation of the way way only if they depend on entities from the same categories (mode) of x’s existence. In other words, any two entities simpliciter because the latter may be too specific to charac- from [x]dep are claimed to exist in the same way. terise the relatively abstract notion of mode of existence. For 3 Although I find the modal accounts of ontological categories 2 The idea that the relation of dependence can be employed as inadequate, it seems unlikely that an entity may change its onto- a means to define ontological categories is by no means new. For logical category over time (or “over” possible worlds). The reason instance, (Thomasson, 1999, p. 115-136) sketches a landscape of is the historical fact that ontological categories are highly abstract. ontological categories defined in terms of her six kinds of onto- So perhaps x can stop being a dog without ceasing to exist (which logical dependence. The main difference between her definitions I find problematic). But if x is a substance, process, or boundary at and the account developed here is that I attempt to build a formal time t, then for each other time at which x exists, x is still a sub- account to distinguish ontological categories from other categories stance, process, or boundary. Therefore, I did not find it necessary within a certain body of knowledge. to relativise the notion of instantiation to times or possible worlds. Now if ways of existence provide the necessary and suf- 1. objects (Obj), properties (Pro), and states of affairs (Soa) ficient conditions for ontological categories, the following are ontological categories; condition needs to be introduced: 2. endurants (End) and perdurants (Per) are not (existen- ∀C∃x ext(C) = [x]dep . (4) tial!) ontological categories because they are too specific, i.e., they both exist in the same way; So the extension of each category is a set of entities with 3. entities (Ent) are not ontological categories because it is the same mode of existence if we construe the former along too general, i.e., its instances exhibit two different ways the lines of definition 3. In order to account for the usual of existence. assumption that ontology covers the whole realm of being, we also need to guarantee that the collection of ontological Note however that when we slightly modify the follow- categories covers the whole domain: ing theory by removing Obj from its signature, the universal category of entities becomes the only ontological category. ∀x∃C Inst(C, x). (5) Suppose that the theory in question includes now the follow- Note that this condition is equivalent to 6 provided that 4 is ing theses: taken for granted: ∀xEnt(x) (15) ∀x∃C ext(C) = [x]dep . (6) ∀x[Ent(x)≡End(x)YPer(x)YPro(x)YSa(x)] (16) ∀x[End(x)→¬∃ydep(x,y)] (17) A finite, non-empty set C of categories is a set of (exis- tential) ontological categories if it satisfies conditions 4 and ∀x[Per(x)→¬∃ydep(x,y)] (18) 5. ∀x[Pro(x)→∃y[(End(y)∨Per(y))∧dep(x,y))] (19) To illustrate ho such framework may function consider a ∀x,y[Pro(x)∧dep(x,y)→End(y)∨Per(y)] (20) first-order formal theory with a signature that contains the ∀x{Sa(x)→∃y,z[(End(y)∨Per(y)∧dep(x,y)∧Pro(z)∧dep(x,z)]}(21) following predicates: ∀x,y{Sa(x)∧dep(x,y)→[End(y)∨Per(y)∨Pro(y)]} (22) 1. Ent as a unary predicate, which is intended to represent the universal category; Now endurants and perdurants do not qualify as ontologi- cal categories for the same reason as before. The category of 2. Obj, Per, End, Pro, Soa as unary predicates, which are in- properties is not an ontological category. Assume it were. tended to represent, respectively, the categories of objects, Then its mode of existence would be represented by the perdurants, endurants, properties, and states of affairs; same categories as the the mode of existence of states of af- 3. dep. fairs and this would violate condition 4. For the same reason Suppose that the theory in question includes the following the category of states of affairs is not an ontological cate- theses:4 gory. On the other hand, the category of entities (Ent) qual- ifies for this status: it represents its own mode of existence ∀xEnt(x). (7) since there are no other, more specific, categories. ∀x[Ent(x)≡Obj(s)YPro(x)YSoa(x)] (8) Of course, not every body of knowledge or a formal the- ∀x[Obj(x)≡End(x)YPer(x)] (9) ory is doomed to have its set of ontological categories. For example, if we strip our toy example even further by taking ∀x[Obj(x)→¬∃ydep(x,y)] (10) out predicate Ent, then we will get a theory without ontolog- ∀x[Pro(x)→∃y(Obj(y)∧dep(x,y))] (11) ical categories. ∀x,y[Pro(x)∧dep(x,y)→Obj(y)] (12) It can be shown that for each set of categories conditions 4 and 5 (together with the auxiliary definitions) allow for at ∀x{Sa(x)→∃y,z[(Obj(y)∧dep(x,y))∧(Pro(z)∧dep(x,z)]} (13) most one set of ontological categories – up to the extensional ∀x,y{Sa(x)∧dep(x,y)→[(Obj(y)∨Pro(y)]} (14) equivalence of categories: Informally, there are objects, properties, and states of affairs. Fact 1. If {D1 , D2 , . . . } and {E1 , E2 , . . . } are sets of onto- An object may be either an endurant or a perdurant. Proper- logical categories, then ties depend on objects (and only on objects) and objects do 1. for each category Di there exists category Ej such that not depend on anything. States of affairs depend both on ob- ext(Di ) = ext(Ej ), jects and on properties (and only on them). 2. for each category Ei there exists category Dj such that By the above account ext(Ei ) = ext(Dj ). 1. the empty set represents the way in which objects exist, Proof. Assume otherwise. Let Di and Ej be two extension- 2. the set of objects represents the way in which properties ally different categories, i.e., ext(Di ) 6= ext(Ej ). Due to 5 exist, there must exist at least one such pair of extensionally differ- 3. the set of objects and the set of properties represent the ent categories that ext(Di ) ∩ ext(Ej ) 6= ∅. So let x belong way in which states of affairs exist. to both extensions. Now because Di and Ej are ontological As a result, in this theory: categories condition 4 implies that there are y and z such that ext(Di ) = [y]dep and ext(Ej ) = [z]dep . Then by defi- 4 ’Y’ stands for exclusive disjunction. nition 2, ∀C[deP(x, C) ≡ deP(y, C)] and ∀C[deP(x, C) ≡ deP(z, C)]. Thus ∀C[deP(y, C) ≡ deP(z, C)], so [y]dep = In the previous section “x =dep y” was claimed to char- [z]dep and ext(Di ) = ext(Ej ). acterise the mode of existence (of x and y). Now “x =r y”, its generalisation, may be claimed to characterise this onto- Finally, let me note that the account defined in this sec- logically salient aspect that is determined by relation r. tion (schema 4 and condition 5) satisfies all aforementioned For instance, consider a relation of participation, part, formal constraints from (Westerhoff, 2005, p. 22-64) except such that part(x, y) means that x participates in (the whole for 2 - the (existential) ontological categories always form a of) y. Suppose again that End and Per are among categories flat list with no hierarchy. C1 , C2 , . . . and are such that To wrap up, although the above characteristic of ontolog- ical categories is circular, in certain cases it may produce ∀x,y[part(x,y)→End(x)∧Per(y)]. (27) unambiguous results, which are partially adequate to an in- ∀x[End(x)→∃y part(x,y)]. (28) tuitive understanding of ontology one might have. ∀x[Per(y)→∃y part(y,x)]. (29) The perspective generalised Then the quotient set of “=part ” has three equivalence classes: Needless to say, the account defined by conditions 4 and 5 is by no means satisfactory as an account of all ontologi- 1. {x : ∃y part(x, y)} cal categories, for instance, we saw that it may be incapable 2. {x : ∃y part(y, x)} to capture the ontologically important distinction between 3. {x : ¬∃y[part(x, y) ∨ part(y, x)]} endurants and perdurants. So let me explain how it can be generalised. The first two classes are extensions of End and Per and these Consider again the set C of categories: C1 , C2 , . . . . As- two may be claimed to characterise this ontologically salient sume that there is a finite set of binary ontological relations: aspect that is determined by ’part’. The third equivalence r1 , r2 , . . . , rn 5 – one of them may be the relation of existen- class is a kind of the recycle bin for the participation rela- tial dependence. This seems to me a crucial assumption in tion. Every entity that is not involved in this relation ends up my account and I will get back to it in the next section – for there, so the ontological significance of any category whose now suppose that we can somehow know which relations are extension is equal to this class seems to be minor. ontological and which are not. Each ontological relation gives rise to a quotient set Auxiliary definition 2 will be now replaced with two def- whose members will be taken as the extensions of our on- initions tological categories. As a result, we get a faceted classifica- tion, where each facet is a set of ontological categories de- dom(r, 1, x, C) , ∃y[r(x, y) ∧ Inst(C, y)]. (23) termined by, via 26, an ontological relation – for the notion of faceted classification see, for instance, (Mills, 2004). dom(r, 2, x, C) , ∃y[r(y, x) ∧ Inst(C, y)]. (24) One may now consider any relation ri and its correspond- ’dom(r, 1, x, C)’ is to mean that x as a member of the do- ing constraint on ontological categories: main of relation r is related by this relation to some member ∀C∃x ext(C) = [x]ri . (30) y of category C. Definition 23 amounts to 2 when r is dep: deP(x, C) ≡ dom(dep, 1, x, C). ’dom(r, 2, x, C)’ is to be Since the proof of Fact 1 did not make any assumptions understood in the analogous way. about the properties of dep we can generalise it to estab- For each relation we can now define two equivalence rela- lish Fact 2: tions, both of which to be captured by the same definitional Fact 2. If {D1 , D2 , . . . } and {E1 , E2 , . . . } are sets of onto- schema: logical categories, then x = y , ∀C[dom(r, m, x, C) ≡ dom(r, m, y, C)], 1. for each category Di there exists category Ej such that (25) ext(Di ) = ext(Ej ), where m ranges over all natural numbers from 1 up to the 2. for each category Ei there exists category Dj such that arity of relation r. ext(Ei ) = ext(Dj ). Now if x = y, this is to mean that x and y happen to be related by relation r to entities from the same categories. Combining such sets of ontological categories, i.e., tak- x = y is to be understood in the analogous way. Inci- ing products of equivalence classes from different quotient dentally, when r is symmetric, x = y ≡ x = y. sets, we could get the extensions of more specific ontologi- Finally, ’=r ’ is to denote the product of all such equiva- cal categories. Probably the simplest way to account for that lence relations - in our case the product of and possibility is to replace previous condition 4 with the “con- dition schema”: : x =r y , ∀m x = y. (26) k Y ∀C∃r1 , r2 , . . . , rk ∃x ext(C) = [x]ri , (31) 5 For the sake of simplicity, I restrict the scope of my account to i=1 binary relations. As far as I can see it does not affect its generality. Qk I hope that extending this account for the relations with arbitrary where 1 ≤ k ≤ n and “ i=1 ” stands for the k-ary intersec- arities should be straightforward. tion of sets. As before, in order to account for the universality of the each relation r, there exists y and z such that x belongs to collection of ontological categories, I assume condition 32: [y]r and [z]r . Then, following the Qnproof Fact 1Qwe can show n that [y]r = [z]r . Consequently, i=1 [y]ri = i=1 [z]ri and ∀r∀x∃C ext(C) = [x]r . (32) ext(Di ) = ext(Ej ). A finite, non-empty set C of categories is a set of ontolog- Finally, let me note that the account defined in this section ical categories (with respect to a set of ontological relations: (schema 31 and condition 32) satisfies all aforementioned r1 , r2 , . . . , rn ) if both sets satisfy condition 32 and one or formal constraints from (Westerhoff, 2005, p. 22-64). more conditions that fall under schema 31. To illustrate how such framework may function I will sup- Ontological relations plement the first example discussed in the previous section Both the general framework and the specific examples with the example from this section. In other words, let me clearly indicate that the above account of ontological cate- considered the formal theory composed of axioms 7-14 and gories is heavily dependent on ontological relations. It seems 27-29. Two available relations determine two quotient sets: that if we are not able to solve the demarcation problem for 1. relation dep determines the quotient set with 3 equiv- the latter, the demarcation problem for the former will re- alence classes, which are extensions of categories: main open as well. So, what is an ontological relation, i.e., Obj, Pro, Soa; what is it about ontological relations that separate them from 2. relation part determines the quotient set with 3 equiva- the non-ontological ones? lence classes, two of which are extensions of categories: Before I attempt to elaborate on this issue, let me note End and Per, and the third is the complement of the union that ontological relations are formally less demanding than of the other two. ontological categories in the sense that the former do not to require all formal constraints specified in (Westerhoff, If you take all products of equivalence classes from 2005, p. 22-64). First, the evidence why a set of ontologi- these sets, you will get 5 sets, which are extensions of cal relations must be hierarchical is much more scarce. In Obj, Pro, Soa, End, and Per. philosophy the ontologist usually employs a certain number Since the above definition of ontological categories is of relations (e.g., causation, identity, constitution, parthood, based on a schema, a set of ontological categories can- dependence, truth-making, etc.) without worrying whether not be unique in the sense of Fact 1 or 2. There is, how- they can be arranged in a hierarchy or not. In particular he ever, a different sense of uniqueness that they exhibit. Let or she is not after the most general relation, similar to the set {D1 , D2 , . . . } of ontological categories be called more OWL object property owl:topProperty. Secondly, the fine-grained than set {E1 , E2 , . . . } of ontological categories evidence why any two ontological relations must not (prop- if for each category Di there exists category Ej such that erly) overlap is also missing. ext(Di ) ⊆ ext(Ej ). Set {D1 , D2 , . . . } of categories will be Philosophical metaontology seems to neglect the demar- called most fine-grained if no set of ontological categories is cation problem for ontological relations. So a survey of the- more fine-grained. ories of ontological relations, similar to the survey from Fact 3. If {D1 , D2 , . . . } and {E1 , E2 , . . . } are most fine- (Westerhoff, 2005, p. 22-64), still awaits its surveyor. In grained sets of ontological categories (with respect to a set what follows I will discuss the merits of three recent ac- of ontological relations), then counts of relations that, although do not explicitly define 1. for each category Di there exists category Ej such that ontological relations, prima facie are applicable for such a ext(Di ) = ext(Ej ), task. The first account is an exemplification of the modal ac- 2. for each category Ei there exists category Dj such that count of ontological relations. The results from the previous ext(Ei ) = ext(Dj ). section of this paper, it seems to me, develop the idea of fac- Proof. Given the above definition of sets of ontological cat- tored ontology put forward by (Simons, 2012, p. 130): “An egories, all most fine-grained sets of ontological categories ontology which explicitly mentions and gives an account of (with respect to a given set of ontological relations) satisfy the factors distinguishing the [ontological - PG] categories the following condition: I call a factored ontology.” Although P. Simons is sceptical about the prospects of demarcating ontological from non- n Y ontological categories, he lists several relations that can play ∀C∃x ext(C) = [x]ri , (33) the role of “the factors distinguishing the categories”: depen- i=1 dence, parthood, instantiation, causation, identity. Moreover, where n is, as before, equal to the number of ontolog- probably not being satisfied with a simple list, he points to ical relations. Suppose then that sets {D1 , D2 , . . . } and “their interesting common feature” due to which he names {E1 , E2 , . . . } satisfy conditions 33 (and, obviously, 32). Let them internal relations: Di and Ej be two extensionally different categories, i.e., A relation R is internal to A and B iff it is essential to ext(Di ) 6= ext(Ej ) such that ext(Di ) ∩ ext(Ej ) 6= ∅ (see A and B jointly that ARB, so that necessarily, if A and the proof of Fact 1). So let x belong to both Q extensions. By B both exist, then ARB. (Simons, 2012, p. 138) n condition 33 Qn this implies that ext(D i ) = i=1 [y]ri and Is such concept suitable for my account of ontological cate- ext(Di ) = i=1 [z]ri overlap on (at least) x. As a result, for gories? I think not. By this definition all relations between math- other hand, there may exist a kind of ontological dependence ematical or logical entities will be internal relations, includ- that picks up most of the usual ontological relations. Finally, ing mathematical functions and the like. There are also in- Guarino uses a particular ontological relation, which is, by ternal relations outside the domain of abstracta that do not the way, an ontological relation par excellance, to define his look like anything ontological. Think about the relation of internal relations. This may be acceptable in a classification having the same spin (value), being a conjugated acid of, or of relations, but is problematic as component of a defini- about the phylogenetic relation. So the concept of internal tion of ontological relations. One may ask why distinguish relations is too broad for my purposes. In addition I have existential dependence over other paradigmatic cases of on- doubts whether certain relations in Simons’ list are really tological relations, e.g., identity. internal relations. Consider the relation of parthood. Even if Nonetheless, one may argue that it is possible to inflate this horn is part of that bike (at a certain time), then it does the meaning of existential dependence in such a way so that not seem to be necessary that when they both exist (at a cer- all, or at least most of, paradigmatic cases of ontological tain time), then the horn is part of the bike. It would be if relations involve existential dependence. In particular, the mereological essentialism were true, but a metaontological inflation in question should make room for parthood, iden- view, i.e., a theory of ontological relations, shouldn’t pre- tity, and difference as the genuine cases of existential depen- suppose a controversial ontological view. dence. As a matter of fact P. Simons provides another description The third account of ontological relations can be based on of internal relations. When the sentence ’A stands in R to B’ (Smith and Grenon, 2004). This paper develops an account is true and R is an internal relation, then ’[. . . ] we do not of formal ontological relations, but the examples of we find need a third thing alongside A and B to act as truthmaker there cover most, if not all, of these relations that the ontol- for it, for by the nature of internal relatedness, A and B be- ogists were always interested in. The final version of their tween them suffice to make it true that ARB’ (Simons, 2012, definition reads: p. 138). Simons clothes this claim in the form of paradox: Formal relations are those relations which hold (some- “Internal relations are actually badly named in my view, be- times inter alia) between entities which are constituents cause there are no such things (as particulars or universals) of ontologies of different types and which are such that, as internal relations.” (Simons, 2012, p. 138). Still, I do not if they hold between entities of given types, then neces- see how to employ such a view for the demarcation problem sarily all entities of those types enter mutatis mutandis at stake. into those relations. (Smith and Grenon, 2004, p. 295) A similar view on relations can be found in (Guarino, B. Smith and P. Grenon mainly consider two types of on- 2009, p. 64-65) – although the terminology is different. N. tologies: SPAN and SNAP, i.e., ontologies of endurants and Guarino defines first the notion of formal relations, which ontologies of perdurants, so for instance the relation of par- appear to be equivalent to Simons’s internal relations, and ticipation that links the former with the latter is a formal then refines it with the help of his notion of internal rela- ontological relation by the above criterion. tions: This proposal suffers, in my view, from some minor tech- Within formal relations, I distinguish between the inter- nical issues with the lack of clarity and certain sloppiness. nal and the external ones, depending whether there is an But even if these problems were overcome, it cannot feed existential dependence relationship between the relata. my definitions of ontological categories with the required The basic kinds of internal relationships I have in mind list of ontological relations. Namely, it seems that the for- (all formalized in DOLCE) are parthood, constitution, mer presupposes the latter, i.e., in order to know which re- quality inherence, and participation, [. . . ]. (Guarino, lations are (formal) ontological, you need to which portions 2009, p. 64) of reality are represented by which categories, and this as- sumes that beforehand you somehow separated the ontolog- Are internal relations, in Guarino’s sense, suitable for be- ical categories from the rest. In short, (Smith and Grenon, ing ontological relations? Again I think that the answer is 2004) assume that in order to solve the demarcation prob- negative. One of the reasons is the same as in the case of Si- lem for ontological relations you need to solve the demar- mons’s account: there are ontological relations that are not cation problem for ontological categories while my analysis formal relations in Guarino’s sense, e.g., parthood. There implies the inverse dependence. are parts that are not existentially dependent on the wholes Taking the failure of the above attempts for granted I to which they (accidentially) belong and there are wholes would like to go back to the initial idea of ontology as the that are not existentially dependent on their parts, e.g., bikes most general field of study. Namely, I will demarcate onto- and horns. The other reason may be the same as in the case logical relations as the most general relations within a set of Simons’s account: there may be internal relations outside of relations. Suppose that that a body of knowledge at stake ontology. I annotate this claim with the modal qualification contains a set of binary relations: r1 , r2 , . . . , rn . There are because its validity depend on a particular type of existen- two meanings one can attach to the “more/most general” tial dependence in question. For instance, if it is the historic qualification: rigid dependence, then the relation of parenthood is an inter- 1. r is more general1 than r0 iff the latter is included in the nal relation. If it is the constant rigid dependence, then the former, i.e., relation of causation is not internal despite the fact that it may be taken as a paradigmatic ontological relation. On the ∀x, y[r0 (x, y) → r(x, y)]. (34) 2. r is more general2 than r0 iff the field of the latter is in- Acknowledgments cluded in field of the former, i.e., This research has been supported by the DEC- 0 2012/07/B/HS1/01938 grant funded by National Science ∀x, y[r (x, y) → ∃z[r(x, z) ∨ r(z, x) ∨ r(y, z) ∨ r(z, y)]]. Centre (Poland). (35) The former meaning is stronger than the latter, i.e., if one References relation is more general1 than the other, then it is also more Carrara, M. and Giaretta, P. (2004). The many facets of iden- general2 . Still neither the most general2 relation needs to be tity criteria. Dialectica, 58(2):221–232. most general1 nor vice versa.6 As for the former consider a Ding, L., Pan, R., Finin, T., Joshi, A., Peng, Y., and Kolari, set containing the relation of identity and the relation of im- P. (2005). Finding and ranking knowledge on the semantic proper parthood. The relation of identity is obviously most web. In Proceedings of the 4th International Semantic Web general2 (in any set) and in the set in question it is not most Conference, pages 156–170. Springer. general1 because of the improper parthood. As for the lat- Dummett, M. (1973). Frege. Philosophy of Language. New ter observation consider the relation of participation, which York: Harper & Row, Publishers. links, say, substances and processes. If you consider a set of relations in which it is the most general1 relation, then if Garbacz, P., Trypuz, R., Szady, B., Kulicki, P., Gradzki, P., this set contains the identity relation, then participation will and Lechniak, M. (2010). Towards a formal ontology for not be most general2 provided that there are other kinds of history of church administration. In FOIS, pages 345–358. entities than just substances and processes. Guarino, N. (2009). The ontological level: Revisiting 30 I take these two kinds of generality as characteristic to the years of knowledge representation. In Conceptual Mod- aforementioned understanding of ontology. So an ontologi- elling: Foundations and Applications. Essays in Honor of cal relation in a set of relations: r1 , r2 , . . . , rn is any mem- John Mylopoulos, pages 52–67. Springer Verlag. ber of this set that is either the most general1 or the most Guarino, N. and Welty, C. (2000). A formal ontology general2 relation. of properties. In Knowledge Engineering and Knowledge This characteristic is not to be taken as a fully-fledged Management: Methods, Models and Tools, pages 97–112. definition of ontological categories – it is to separate onto- Springer Verlag. logical relations from non-ontological in a set of relations. Guarino, N. and Welty, C. (2002). Identity and subsumption. As a result, its epistemic quality depends on the set in ques- In Green, R., Bean, C., and Myaeng, S., editors, The Seman- tion – for instance, if the set includes a gerrymandered re- tics of Relationships: an Interdisciplinary Perspective, pages lation like the union of the relation of participation, the re- 111–126. Kluwer. lation of constitution, and the geometric relation of paral- Mills, J. (2004). Faceted classification and logical division lelhood, then this relation may be classified as an ontolog- in information retrieval. Library trends, 52(3):541–570. ical relation. Another issue with this characteristic is that it may yield counter-intuitive consequences for some onto- Norton, B. (1976). On defining ’ontology’. Metaphilosophy, logical systems. Consider an ontology where the relation of 7(2):102–115. (proper) parthood is not general2 , i.e., where there are enti- Schwarz, U. and Smith, B. (2008). Ontological relations. ties that neither have or are parts, e.g., God. Then in any set In Munn, K. and Smith, B., editors, Applied Ontology. An of relations that contains both the relation of parthood and Introduction, chapter 10, pages 219–234. ontos Verlag. the relation of improper parthood the former relation is not Simons, P. (2012). Four categories and more. In Tahko, ontological in the sense above. T. E., editor, Contemporary Aristotelian Metaphysics, pages 126–139. Cam. Conclusions Smith, B. and Grenon, P. (2004). The cornucopia of formal- ontological relations. Dialectica, 58(3):279–296. Even if the above attempt at demarcating ontological cate- Sommers, F. (1959). The ordinary language tree. Mind, gories (and the subordinate attempt at demarcating ontologi- 68:160–185. cal relations) is another failure, I hope that it at least justifies the need for a more insightful understanding of the speci- Sommers, F. (1963). Types and ontology. The Philosophical ficity of ontological research. This need may be less acute Review, 72:327–363. in philosophy than in applied ontology, where the prolifera- Sommers, F. (1971). Structural ontology. Philosophia, 1(1- tion of ontological artefacts appears to have endangered the 2):21–42. consistency of this field. To separate it conceptually from Thomasson, A. L. (1999). Fiction and Metaphysics. Cam- other fields we need to make certain distinctions among its bridge University Press. basic components: categories and relations. Ontologiae est van Inwagen, P. (2012). What is an ontological category? In distinguere. Novak, L., amd Prokop Sousedik, D. D. N., and Svoboda, 6 D., editors, Metaphysics: Aristotelian, Scholastic, Analytic, The term “most” refers to the maximal elements with respect pages 11–24. Ontos Verlag. to a given relationship, so a relation is most general1,2 in a set of relations if there is no more general1,2 relation in this set. Conse- Westerhoff, J. (2005). Ontological Categories. Clarendon quently, most general relations need not to be unique. Press.