Identity and Modality in OntoClean Massimiliano CARRARA∗ Pierdaniele GIARETTA †Vittorio MORATO †Marzia SOAVI Giuseppe SPOLAORE Department of Philosophy, University of Padua, P.zza Capitaniato, 3, Padua (Italy) †Department of Communication, University of Bologna, via A. Gardino 43, Bologna (Italy)
Abstract. The aim of this paper is to refine, integrate and apply the methodology of OntoClean. Three aspects are taken into account; two of them concern main ideas of OntoClean, the third one is a study of a particular important application. The first section deals with the topic of identity: formal constraints on identity criteria, compatibility and identity among identity criteria. The second section deals with rigidity, dependence and existence. The final section investigates how meta-property criteria can be applied to the notion of artifact.
Introduction OntoClean is an important contribution to a formal foundation for ontological analysis in knowledge representation. The adopted methodology appears to be quite useful to formulate taxonomic relationships in a consistent and informative way. In our paper we point out some problems concerning identity criteria, rigidity, dependence and existence, and we propose some solutions which could increase the adequacy of the methodology. Moreover, in the final section, we take into the account the case of artifacts - a case Guarino and Welty do not analyze - and we investigate how to qualify the notion of an artifact. 1 Identity Criteria 1.1 Formal Constraints on Identity Criteria As Guarino and Welty suggest in [1] an identity criterion is associated to a property K and has to answer the following question: If a and b are Ks, what are necessary and sufficient conditions for the object a to be identical with b? In Guarino and Welty’s opinion identity criteria are “the criteria we use to answer questions like, ‘is that my dog?”’ (see [1]: 4). That means identity criteria should be useful to justify identity judgments. Talking of identity conditions over time, Guarino and Welty present the following: How do we recognize people we know as the same person even though they may have changed? ∗
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as a question to be answered on the basis of an identity criterion for people. So identity criteria are understood in a logical-ontological sense, but are also taken to provide grounds to answer questions of the form: If a and b are Ks, how can we know that a is the same as b? We could read the Guarino and Welty’s approach as based on the idea that you cannot meaningfully talking about objects unless you know how, in general and in principle, to tell one from another and to say when you have the same once again. From such a point of view identity criteria have to satisfy a cognitive constraint which, however, is not explicitly stated by Guarino and Welty. What is it? It is difficult to specify such a constraint, but its presence is strongly suggested by the kind of formal characterization of identity criteria they look for and by their reactions to the difficulties they meet in this enterprise. One of them has been raised by two of us in [2]: because of the way in which “carrying an identity condition” is formally defined in [3], it follows that being-identical-with-a is a sortal. This consequence depends on the possibility of providing an identity condition which contains the very predicate being-identical-with-a. In [1], Guarino and Welty reply that “valid ICs must be informative”. This reply is somewhat odd, since it implies that the given definition of “carrying an identity condition” is inadequate and should be modified by adding this constraint. However, no hint is given about the way in which informativeness can be specified. They might mean that the identity conditions of ICs should be formulated in terms of predicates at least one of which is not identity. Let us observe that informativeness is not warranted by the formal constraint: the formula providing the identity condition should contain some predicates different from identity. In fact, such predicates could occur without having any substantial role as, for example, when they occur in tautological conjuncts, as in: x = y ∧ (R(x, y) ∨ ¬R(x, y)) where R is not the identity predicate. Yet, to exclude identity at all from the identity condition seems to be too strong. In general we doubt that there is any formal constraint enough to warrant that a formula satisfying such a constraint is an IC. We grant that a formal characterization is useful as a necessary condition, but it needs to be integrated with specific and not generalizable constraints depending on the nature of the entities at issue in order to approximate conditions which are both necessary and sufficient. Even if there were a precise sense in which the sameness formula expressing the identity condition must be informative, this requirement might be satisfied, and the definition of sortal might still be inadequate. Consider the following example of identity condition taken from Lombard in [4]: ∀x∀y(x is a physical object or a set ∧ y is a physical object or a set → (x = y ↔ F (x, y) ∨ F 0 (x, y))) where F (x, y) and F 0 (x, y) are supposed to give informative identity conditions for physical objects and sets. On the basis of the definition given by Guarino and Welty in [3] the property being a physical object or a set would be a sortal. To exclude that the sameness formula is a disjunction would not be enough, as shown by Lombard, by means of the following example of criterion of identity: ∀x∀y(x is a physical object or a set ∧ y is a physical object or a set → (x = y ↔ x and y have the same members and the same spatio-temporal history)).
Physical objects vacuously have the same members and sets vacuously have the same spatio-temporal history1 . So, it seems that availability of adequate identity criteria is not enough for sortality. As for identity criteria, a reasonable conclusion could be that also for being a sortal only necessary conditions can be given. At most such conditions might be ranked according to some adequacy measure. A cognitive relevant aspect of identity criterion which does not appear to be adequately formalizable is the following one. A function which is sometimes assigned to identity criteria is to reduce issues of identity of a given kind to relations between objects of a more basic kind. This function is better expressed by the following schema of an identity criterion: ∀x∀y(f (x) = f (y) ↔ R(x, y)) where f (x) and f (y) are meant to be entities of the kind K suitably connected with x and y. A classical example is given by: the direction of x is identical with the direction of y iff x is a parallel to y. From this point of view identity criteria could be connected with a reductivistic conception in ontology. However, the basic idea of this ontological perspective could be rethought in cognitive terms without any reductivistic implication. The value of x and y could be thought as entities which are cognitively more accessible than f (x) and f (y). With respect to the above example: lines are easier to understand than directions. 1.2
Compatibility and Identity among Identity Criteria
While for the notions of identity criterion and sortal only formal necessary conditions can be specified, compatibility among identity criteria can be formally defined. The formal definition is not stated by Guarino and Welty, but it can be useful to state it, since compatibility among identity criteria may not be a completely clear notion and, on the other hand, it is used by Guarino and Welty in their specification (and application) of the subsumption relation. In [1] a property Φ is, by definition, +O iff it supplies an IC which is not inherited by a subsuming property Ψ different from Φ. The definition allows that a +O property Φ subsumes another +O property Ψ. This implies that Ψ does not carry the same IC carried by Φ. In [3], Guarino and Welty specify that properties with incompatible ICs are disjoint. So, in a subsumption chain, different ICs supplied by different properties of the chain should be compatible, i.e. the IC carried by the subsumed property must totally agree with the IC of the subsuming property within the extension of the subsumed property. In other words being the same Ψ should imply being the same Φ. Formally, if the identity conditions for Φs and Ψs are respectively represented by S and 0 S , consistency requires: ∀x∀y((Φ(x) ∧ Φ(y) ∧ Ψ(x) ∧ Ψ(y)) → (S(x, y) ↔ S 0 (x, y))). Of course, if S and S 0 are also identity conditions for objects which are not Φ or not Ψ the satisfaction of this condition is not enough to avoid, in general, the derivation of contradictory identity statements. A sufficient condition is coextensionality of S and S 0 , i.e.: 1
Of course, from some (not all) ontological points of view, it is possible to object that having (set-theoretic) members is a condition which is not defined over physical objects and, similarly, spatio-temporal properties are not defined over sets. However, at least to avoid the logical complications of such views, let us suppose that for every physical object x and every object y it is false that y is a member of x and that for every set x and every basic spatio-temporal property it is false that x has it.
∀x∀y(S(x, y) ↔ S 0 (x, y)). A stronger condition is necessary coextensionality of S and S 0 , i.e.: 2∀x∀y(S(x, y) ↔ S 0 (x, y)).
(1)
We do not need it since S or S 0 may be identity conditions holding only in some worlds and not in others, but if ICs are to warrant identity through all worlds, identity conditions should be equivalent to identity in all worlds and this implies that identity conditions be necessarily coextensional. (1) can be used to define identity among ICs in the following way, the identity criteria for the Ks: (x = y ↔ F (x, y)) and (x = y ↔ G(x, y)) are the same IC if and only if: 2∀x∀y(F (x, y) ↔ G(x, y)). This notion of identity among identity criteria may not be the most adequate and, perhaps, there is no adequate identity criterion for identity criteria. What we want to stress here is just that all the above discussions presuppose that identity criteria have their own identity. Guarino and Welty themselves explicitly speak of same or different ICs in many passages, for example in the definition 6 of [3]. What do they mean? They might accept the proposed definition as a first good candidate to characterize the identity of identity criteria as they are intended to be. Surely the alternative of referring to formulas representing identity criteria in a suitable formalization does not work. For, slightly different formulas can be equivalent and intuitively express the same identity criterion. Necessary coextensionality among identity conditions allows to neglect some irrelevant differences in formulation, but it does neglect some other, relevant, differences. For example, as concerns triangles the conceptual difference between having the same three edges and having three edges, two of them and there internal angle in common. There is another feature that is worth accounting for the identity among identity criteria. It would be quite informative and useful to understand how identity criteria can be different one from another. For example, it is very likely that when an identity criterion for a subsumed property differs from the identity criterion for a subsuming property, the former is based on predicates which specifically apply to the entities belonging to the extension of the subsumed property. For example, the IC for men that is based on having the same mind, is clearly not generalizable to all living beings. 2 2.1
Rigidity, Dependence, and Existence A Problem with Rigidity
The modal logic underlying OntoClean is quantified S5 with a fixed domain and an actual existence predicate E whose extension varies across worlds. This choice is qualified by a possibilist metaphysics, where in the domain of every world there are both actual and possible objects. With respect to a world wi , a possible object is simply an object that is not in the extension of E with respect to wi . In OntoClean, rigidity is defined as follows (where Φ is a property):
Definition 1. Φ is rigid =def. 2∀x∀t(Φ(x, t) → 2∀t0 Φ(x, t0 )). From this definition, it immediately follows that 1. to have a rigid property at some t is sufficient to eternally have it (hence, we shall omit the temporal parameter when dealing with rigid properties). 2. to possibly have a rigid property is indeed sufficient to necessarily have it2 . Theses 1 and 2 make the attribution of rigidity to have some counterintuitive consequences. Let us assume, as it is usual, that being concrete is a rigid property. Traditionally, it is believed that, necessarily, every concrete object has spatio-temporal location and causal efficacy. Consider now something that Guarino and Welty consider as a typical merely possible object: Pegasus. If we (plausibly) assume that it is possible that Pegasus is concrete, we must conclude that Pegasus is actually concrete, and thus spatio-temporally located and causally efficacious. But, in this case, nothing could be said to exclude Pegasus from the realm of existence. In general, if we adopt the traditional characterization of concreteness, then every concrete object actually exists. Thus, it seems that one cannot claim, simultaneously, that being concrete is rigid while actually existing is not, contrary to what Guarino and Welty seem to maintain. The above argument does not rely on some specific features of possibilia, in fact it could be easily reproduced for past objects. If we assume (reasonably) that Socrates ceased to exist after his death, say after time t and he remains nevertheless a concrete object, we should conclude that Socrates after t has both location and causal efficacy. But, again, if this is true, in which sense can we say that Socrates does not exist after t? Perhaps more implausibly, this goes for future objects too: Socrates, before his conception, was already located and efficacious. One could react to this argument claiming that the traditional characterization of concreteness has to be dismissed. But this has to be done carefully. In fact, if we simply claimed that e.g., Pegasus is concrete but it has neither spatio-temporal location nor causal efficacy, nothing could be said to exclude Pegasus from the realm of abstract objects such as numbers. Indeed, it seems that, if we completely reject the traditional characterization of concreteness, we are left with no intelligible way to distinguish concrete entities from abstract ones. 2.2
Possible Solutions
The simplest solution would be to relativise rigidity to actual existents, namely: Definition 2. Φ is rigid =def. 2∀x∀t(E(x, t) ∧ Φ(x, t) → 2∀t0 (E(x, t0 ) → Φ(x, t0 ))). Now we can simultaneously maintain that being concrete is a rigid property and that it is possible for a concrete object not to be concrete (of course, just in the case it does not actually exist); our problem then vanishes. But consider the following case: a is an actually existing koala; nothing prevents the existence of a possible world wi where a is not in the extension of E but in the extension of, say being a carburettor. This looks (and, indeed, is) quite absurd. The problem is that we did not put any constraints on what properties non-actually-existing objects have. A possible way 2
This claim can be formally proved.
to solve this difficulty is to adopt serious actualism3 , the thesis that exemplification implies actual existence; formally, in a second- order formulation: ∀Π∀x(Πx → Ex)
(2)
(2) puts exactly the constraint needed: for every world wi , the non-actually-existing objects in wi do not have any property. The problem is that if Π is, e.g., ¬E, then (2) entails: ∀xEx4
(3)
but (3) is a formulation of actualism, the thesis that everything (actually) exists, which is incompatible with the OntoClean’s possibilist metaphysics. This incompatibility could, of course, be solved, but at the price of heavy ad hoc restrictions on (2)5 . Reasonably, such a revolutionary solution would not be welcome by Guarino and Welty. They are, in fact, committed to the thesis that possible objects have genuine non-modal properties (e.g., being a man) even in those possible worlds where they do not exist: this clearly follows from their original definition of rigidity (see definition 1). Furthermore, in [3] they explicitly consider a non-modal property like being a unicorn as rigid and actually exemplified even if not by actual existents6 . As philosophers, we have, of course, many perplexities about this modal metaphysics, but we think that, as far as Guarino and Welty’s project is concerned (i.e. evaluating the greatest number of ontologies), such qualms could be set aside. Our main goal in this article is not to convert Guarino and Welty to our favorite philosophical views but rather to try correct and reform some parts of the system leaving the general framework as untouched as possible. A less revolutionary approach consists in sticking with the original definition of rigidity (definition 1) while having an alternative characterization of concreteness. The idea is to qualify the relations among being concrete, having a location and being causally efficacious in such a way that being concrete at t does not imply actually having location/causal efficacy at t. This thesis could be expressed by the following conditional: 2(∀x(concrete(x) → 3∃t∃s(occupy(x, s, t) ∧ causally efficacious(x, t)))).
(4)
Arguably, to be causally efficacious is a tricky notion. An alternative characterization could be: 2(∀x(concrete(x) → 3∃t∃s(occupy(x, s, t)))). (5) With (5), our problem disappears: we can now allow possible and past objects to be concrete in a world, without simultaneously having a location in that world. The adoption of (4) or (5) is not arbitrary: it rightly excludes from the realm of concreteness those objects, such as numbers, that cannot (even conceptually) have a location. Similar difficulties arise in relation to other notions. Consider the property being a living being. If it is rigid, it follows that, e.g., Socrates is a living being even when he is dead. So, being a living being cannot imply being alive. A way out along the same lines seen for concreteness could be adopted by claiming that being a living being implies that it is possible to be alive. Other properties might raise similar difficulties and it is natural to ask whether there is an a priori way to determine the form of each specific solution for each problem. The most plausible answer is “no!”, but something general and useful can be said, which suggests itself 3
See [5] and [6]. We would obtain ∀x(¬Ex → Ex) from which (3) follows by consequentia mirabilis. 5 E.g., the modification of Leibniz’s Law and the exclusion of negative properties and of self-identity. 6 See [3, page 56]. 4
as a possible alternative (but compatible) solution. In general the difficulty seems to be this: a rigid property Φ is such that it does not necessarily imply the actual existence of its instances; Φ prima facie implies Ψ, and Ψ is such that, necessarily, it implies the actual existence of its instances. Perhaps, the simplest and most coherent way to solve this problem within the general methodology of OntoClean is to distinguish between two kinds of properties: those that are actual-existence-entailing (say P +E , Q+E , . . .) and those that are not (say, R−E , S −E , . . .) and to maintain that only existing instances of rigid properties have +E properties. For example: 2(∀x∀t(concrete(x) ∧ E(x, t) → ∃s(occupy(x, s, t)))) (6) and 2(∀x∀t(living being(x) ∧ E(x, t) → alive(x, t))).
(7)
This leaves open the question of the (non-rigid and non-actual-existence- entailing) properties which non-actually-existing instances of a rigid property have, but, perhaps, it is a problem we can live with. 2.3
A Problem with Dependence
The notion of rigidity given in definition 1 seems to have bad interactions also with other notions in OntoClean. Take the relation of external dependence. In OntoClean, external dependence between two properties Φ and Ψ is defined as: Definition 3. Φ externally depends on Ψ =def. 2∀x(Φx → ∃y(Ψy ∧ ¬P (y, x) ∧ ¬C(y, x)))7 . Definition 3 defines the external dependence between Φ and Ψ in terms of an ontological dependence among the Φs and the Ψs. Using definition 3, it is possible to capture the distinction between intrinsic and extrinsic properties: Φ is extrinsic iff there is a property Ψ such that Φ externally depends on Ψ; otherwise, Φ is intrinsic. (8) An informal characterization of an intrinsic property is: “a property that a thing has (or lacks) regardless of what may be going on outside of itself”8 . Intuitively, being an uncle or being a widow are extrinsic properties while being square or being human are intrinsic. Such a distinction is quite problematic9 as it is the notion of ontological dependence10 . Nevertheless, definition 3 and (8) present specific difficulties. It is easy to show that, for every rigid properties Φ and Ψ (excluding some extremely improbable cases), Φ externally depends on Ψ and vice versa. Consider the rigid properties being a kangaroo and being a snake. The relevant instance of the definiens of definition 3 is: 2∀x(being a kangaroo(x) → ∃y being a snake(y) ∧ ¬P (y, x) ∧ ¬C(y, x)).
(9)
Given that, by definition 1, every kangaroo (or snake) is necessarily so11 and given that snakes are neither parts nor constituents of kangaroos (and vice versa), it follows that the consequent 7
Where P and C stand, respectively, for parthood and constitution. See [7]. 9 See, for example, the related entry ‘extrinsic-intrinsic’ in the Stanford Encyclopedia of Philosophy: . 10 See [8]. 11 An anonymous referee has suggested the idea that by adopting definition 2 as a definition of rigidity instead of definition 1 the “kangaroo problem” would not arise. We have chosen not to adopt definition 2 in this context for the same reasons mentioned in section 2.2. 8
of (9) is necessarily true (in those models where there is at least one snake) and that, therefore, (9) is true too; thus, implausibly, being a kangaroo and being a snake result to be mutually externally dependent. We shall call this difficulty the “kangaroo problem”. 2.4
Possible - but partial - solutions
The weakness of the constraints put by definition 3 on rigid properties seems to be the source of the “kangaroo problem”: the only condition that a given couple of rigid properties < Φ, Ψ > must satisfy to make the definiens of definition 3 true is that instances of the second member be neither parts nor constituents of relevant instances of the first. A simple fix would be to relativise the definiens of definition 3 to actually-existing objects12 : Definition 4. Φ externally depends on Ψ =def. 2∀x∀t(E(x, t) ∧ Φx → ∃y∃t0 (E(y, t0 ) ∧ Ψy ∧ ¬P (y, x) ∧ ¬C(y, x))). Now the “kangaroo problem” does not arise anymore because there are obviously worlds where no snake (the Ψs) actually exists while kangaroos (the Φs) do. Another quite general solution would be to modify definition 3 by requiring its definiens to be true in every world in every intended model (which is not equivalent to requiring validity). In the case of the “kangaroo problem”, given that there are surely intended models in which to being a snake, but not to being a kangaroo, is assigned the null extension with respect to every world, in those models the definiens of definition 3 is false. Yet, even if both solutions seems to do the right job for the “kangaroo problem”, it is not clear if they warrant that being a kangaroo does not depend on any other relevant property (think to, e.g., being a physical object), and so that being a kangaroo be intrinsic. Thus, adopting definition 4 or requiring the definiens of definition 3 to be true in every intended model are far from being convincing general solutions to the problem of adequately defining the intrinsic/extrinsic distinction. Such difficulties met in connection with this distinction could even reinforce the idea that it lies at a different level from other distinctions drawn in OntoClean. 3 Being an artifact 3.1 Problems with the classical notion A case in which the solution just proposed seems to be particularly suitable for solving some crucial problem of the taxonomy is that of artifacts. Let us start our analysis from the following classical definition of artifact: An artifact is a concrete object intentionally produced by human being. We do not include among artifacts abstract objects, for they need a particular analysis of condition of production. We impose that the author have to be a human being, for beside the fact that this choice agrees with the classical notion, we regard it as an innocuous restriction. Obviously, if we want to include among artifacts all the intentionally produced objects, the realm of artifacts can be expanded in relation to the adopted notion of intentional action and 12
We do not follow the simplicity-preserving practice of Guarino and Welty of omitting explicit quantification over time; we prefer to restore it while managing with an admittedly non-rigid property such as existence.
of intentional agents. So, for example, we could include stick used by monkeys for catching ants, or paintings made by elephants, etc. We will try to apply the eight meta-properties presented in OntoClean and their attribution to the property being an artifact, in order to individuate the ontological constraints on the subsumption relationships among the property of being an artifacts and sortal properties. The eight meta-properties are: +I The property carries a common identity criterion for all its instances. −I The property does not carry a common identity criterion for all its instances. +U The property carries a common unity criterion for all its instances. −U The property does not carry a common unity criterion for all its instances. ∼ U No instance of the property satisfy a unity criterion. +R The property is essential to all its instances: an instance of a rigid property cannot stop satisfying that property. −R The property is not essential to all its instances: some instances of a non rigid property can stop satisfying that property. ∼ R No instance of the property has it essentially: all instances of the property can stop satisfying it. Let us start with identity. Given the notion of artifact just described it is not possible to single out a common synchronic and diachronic identity criterion for all artifacts. An object is an artifact iff it is the result of an intentional human production. With “intentional human production” we refer to a sequence of human actions that, from the design phases to the material execution, are aimed at the creation of a particular object. Clearly, we do not want to exclude cases of partial automation of the production procedure. So, any object that has started to exist at the right conditions is an artifact. Objects of different kinds can be artifacts; the only restrictions are due to our technical and technological limits. If we consider being an artifact as an essential property, having being intentionally produced is a necessary property common to all artifacts. Can we add something to this condition for obtaining necessary and sufficient conditions for their identity? Given the definition adopted, it seems natural to look for conditions that concern the origin of the objects. The most plausible elements of the origin that could be considered are the following: the matter that constitutes the object at its origin, and the identity of the author. That is to say that an artifact would not be the same object if it would have been produced by a different author or if it would have been constituted of a different amount of matter at its origin. But even this principle cannot be accepted as general necessary and sufficient condition for individuation of artifacts. First because the identity of the author seems to be of great importance for the works of art but totally irrelevant for other kinds of artifacts13 , and second because it is easy to imagine circumstances in which two artifacts could be constituted of the same amount of matter at their origin: think to a chair built up with exactly the same wood of which a table were built. So, a first proposal for the property of being an artifact seems to be “−I”. That is to say that would not be possible to consider the kind of artifacts, strictly speaking, a sortal kind. 13 It is worth noticing that it would be possible to consider many other elements of the origin like space and time location or the specific intention of the author or the instruments used for the production, etc. But the proposal just given seems to us more plausible and in agreement with current discussion in literature.
Obviously, this does not commit us to the idea that it would not be even possible to find common necessary and sufficient criteria for specific kinds of artifacts, like the kind of cars, of forks, of hammers, etc. In this case a good attempt would be that of specifying criteria based on function and structure of the objects. We can observe, on the other hand, that Guarino and Welty propose as sortal kind or kinds of the backbone taxonomy, also properties that does not carry criterion for diachronic identity common to all their instances. Artifacts being concrete objects, it is possible to consider the following simple criterion of synchronic identity: two artifacts are the same objects iff they are composed of the same matter. And this would be sufficient for considering the kind of artifacts as a kind of the backbone taxonomy, and labelled it “+I”. But this choice does not agrees with the classical notion of sortal kind and criterion of identity. So we will not consider this option, and we propose “−I” for artifacts kind. Now we can consider the principle of unity “−U ”. A principle of unity for an object O, is a principle that fixes a rule for establishing if a given object or a portion of matter is a part of O. Clearly there are some artifacts that have their own unity principle, presumably related in most cases with their function, but it would not be possible to single out a common criterion of unity for tables, statue, Ferrari and cakes etc. So, we can conclude that being an artifact is not “+U ”. On the other hand, we have artifacts that are similar to amount of water, for example wine, industrials perfumes etc. that according to Guarino and Welty don’t carry any unity principle. Finally, given that for some artifacts it is possible to individuate some criterion of unity we cannot even label being an artifact with“ U ”. So the right choice seems to be to label it with “−U ”. As concerns rigidity we propose to consider being an artifact as rigid property, because artifactual objects seem to be treated differently from non artifactual objects. We commonly think of them as intended to have a certain function, as if it makes sense to take into account what could be the intention at their origin, and this kind of information seems to be presupposed by our practical reasoning. So, it seems of great importance, at least for an ontology aiming to deal with problems of our common categorization of objects, to treat the category of artifacts as a singular and specific kind like other kinds of natural objects. Moreover, an object that is an artifact cannot exist without the property of having been intentionally originated by a human being, nor ceasing to satisfy it during its existence, which means that it is a rigid property for all its instances: we can label it with “+R”. As concerns meta-properties we propose the followings: −I, +R, −U . 3.2
A possible collocation for artifacts
In [1] some properties that are not sortals are considered. They are classified into two types: roles and attributes. These properties, as being an artifact does, include objects of different kinds. Nevertheless, if we accept the classical notion of artifact, given at the beginning, is not possible to consider being an artifact as an attribute for it is quite obvious that attributes cannot be rigid properties +R while being an artifact is a rigid property. The same goes for roles. Being an artifact cannot be a sortal, not a role, not an attribute, it can be introduced as a category as for example social entities (−I, +R, +U ). For better capture the nature of artifacts we propose to introduce a new kind of property. Following an idea clearly stated by R. Dipert and R. Hilpinen we can call it historical property. As Dipert claims in [9, page 15]: Artifactuality does not consist in any present physical qualities of a thing . . . I suggest that a correct characterization of artifactuality requires a historical definition.
Other examples of historical properties can be the followings: being born in 1924, having been in India for holiday last summer, etc. They seem to amount simply to descriptions of past events, that can be totally contingent with respect to the object considered. But in the case of artifacts some events in the history of an object assume a great relevance for we are inclined, mainly for practical reasons, to pay attention to them. We seem to give great importance to the idea embodied in an artifact, that is to say to the intentions of the author of the object. And this is true of works of art as well as of other every-day artifacts. In Dipert’s words: A culture obviously seeks, for reasons of overall efficiency, to provide objects that “recommend themselves” for a function. These are objects intentionally modified to be recognized as having been intentionally modified to serve a function; they are artifacts14 . Even if commonly historical properties are not considered necessary properties, as can be evident form the above examples there seems to be no contradiction in the idea of an historical and necessary property, consider for example the debate on the essentialism of the origin. Having proposed to consider being an artifact as an essential property, what we have is an historical property essential to its instances. Using the classification of properties offered by Guarino and Welty we have the possibility for introducing the category of historical properties, some of them will be simply attribute others can be considered essential properties, among this we can find being an artifact. A final important observation is that given the adoption of S5 and the definition of rigidity (definition 1)15 , as we have already observed, an artifact would be an artifact in every possible world even before its production and after its ceasing to exist! Following the results of the previous sections we can change the initial definition of artifacts and introduce the notion of artifact through the following conditions: 2(∀x(artifact(x) → 3∃a∃t(produce(a, x, t)))) 2(∀x∀t(artifact(x) ∧ E(x, t) → ∃a∃t0 (t0 ≤ t) ∧ produce(a, x, t0 ))). With these restrictions we can still qualify the property of being an artifact as an historical property at least as concerns existent artifacts, with the same meta-properties just stated on the basis of the previous definition: −I, −U , +R. These restrictions gives us a notion defined both on non existent and existent artifacts and still sufficiently near to the intuitive notion given at the beginning. References [1] Nicola Guarino and Christopher Welty. An overview of ontoclean. In Handbook on Ontologies. Springer Verlag, 2004. [2] Massimiliano Carrara and Pierdaniele Giaretta. Identity criteria and sortal concepts. In Christopher Welty and Barry Smith, editors, Formal Ontology in Information System, pages 234–243. ACM Press, 2001. [3] Nicola Guarino and Christopher Welty. Supporting ontological analysis of taxonomic relations. Data and Knowledge Engineering, 39(1):51–74, 2001. 14 15
See [9, page 93]. See above footnote 11.
[4] Lawrence B. Lombard. Events. A Metaphysical Study. Routledge & Kegan Paul, 1986. [5] Christopher Menzel. Actualism, ontological commitment and possible world semantics. Synthese, 85:355– 389, 1990. [6] Alvin Plantinga. The Nature of Necessity. Oxford University Press, Oxford, 1974. [7] Stephen Yablo. Intrisicness. Philosophical Topics, 26:479–504, 1999. [8] Kit Fine. Ontological dependence. Proceedings of Aristotelian Society, 95:269–290, 1995. [9] Randall R. Dipert. Artifacts, Art Works and Agency. Temple University Press, 1993.
