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There is a wide-spread conservative view on objects, which says that any object is an actual object. In other words, the adjective ‘actual’ is redundant, for it excludes no object. From this it follows that non-actual possible objects are not objects, that is, they are nothing. Thus on this view, the adjective ‘possible’ is equivalent to ‘actual’ when applied to objects and (ii) is false. This makes the notion of a possible object, or equivalently the notion of an actual object, uninteresting. The notion of an object is the basic notion and does all the work. There is another conservative view on objects, which does not deal in actuality or possibility directly. It deals in existence instead. It is the view that any object is an existing object. On this view, the following analog of (ii) is false: Not every object is an existing object, that is, some object is a non-existing object. This view makes the notion of an existing object equivalent to that of an object; existence adds nothing to objecthood. If we combine talk of actuality and talk of existence, we obtain four alternative conservative views with varying degrees of conservatism:
(1) Any object is an actual existing object;(2) Any object is an actual object, that is, it is either an actual existing object or an actual non-existing object;
(3) Any object is an existing object, that is, it is either an actual existing object or a non-actual existing object;
(4) Any object that is actual is an existing object;
(5) Any object that exists is an actual object.
(1) is a stronger claim than the other four. (2) and (3) are stronger than (4) and (5). (1)-(3) give characterizations of all objects, whereas (4) and (5) are more limited in scope. When the verb ‘exists’ is understood with the most comprehensive domain of discourse, (5) is known as actualism. If the domain of discourse for ‘exists’ is stipulated to consist only of actual objects, (5) is trivial and compatible with possibilism, the position which says that some object is outside the domain consisting of all actual objects; cf. (ii). Most of those who advertise their positions as actualist hold not only (5) with the most comprehensive domain of discourse in mind but also (1), and therefore (2)-(4) as well. There are some theorists who hold (5), or at least do not deny (5), but deny (1). They do so by denying (3), that is, by maintaining that some object is a non-existing object. Such a view is one version of Meinongianism. But let us start with actualism and possibilism.
We shall first examine possibilism. It is superficially the most commonsensical view. It is superficially commonsensical to hold that some objects are not actual: e.g., Santa Claus, the Fountain of Youth. If we understand this claim in terms of existence, that is, as the claim that there are — that is, there exist — some objects that are not actual, we have possibilism. As we have noted, ‘exist’ here should not mean “actually exist” but should be understood with a larger domain of discourse in mind. Such a domain is the domain containing not only actual objects but also non-actual possible objects as genuine objects. To flesh out the idea of such a domain as proposed by the best-known version of possibilism, it is necessary to start with the idea of a possible world. After we articulate and examine possibilism as couched in the possible-worlds framework, we shall discuss versions of actualism also couched in the possible-worlds framework. We shall then examine other theories outside the possible-worlds framework.
Independently of his counterpart theory, Lewis's definition of a possible object has some peculiar consequences, given that existence in general is understood as bearing of the part-of relation to the whole that constitutes the domain of discourse. Take any two possible worlds w1 and w2. Lewis wants to assert that both w1 and w2 exist in some sense. So for the assertion to be true, it must be true relative to a domain of discourse which contains as a sub-domain some whole of which both w1 and w2 are part. Not both are part of a single possible world or its part. The smallest whole of which they are part is the (mereological) sum of w1 and w2. So, some domain D containing such a sum as a sub-domain must count as an acceptable domain of discourse for evaluation of an existential claim. Consider a proper part p1 of w1 and a proper part p2 of w2. Let Gerry be the sum of p1 and p2. Then it is true to say that Gerry exists when the domain of discourse is D. So, there is a sense in which Gerry exists. In fact it is the same sense in which w1 and w2 exist. But Gerry is not a possible object, according to Lewis's conception, for Gerry does not have all of its parts in a single possible world. This is peculiar. Gerry is an object which exists in the same sense in which possible worlds exist but Gerry is not a possible object. Since — as sanctioned by the universality of mereological summation, which Lewis accepts — Gerry is an object, Gerry is an impossible object. But there is nothing impossible about Gerry any more than there is about the sum of w1 and w2. Perhaps the sum of w1 and w2 is an impossible object, too. But this idea flouts the initially plausible principle of recombination for possibility of objects, which says that if x is a possible object and y is a possible object independent of x, then the totality consisting exactly of x and y is a possible object. Defenders of Lewis's theory may take this to mean that the principle of recombination, despite its initial plausibility, is to be rejected. There is another unexpected consequence of Lewis's theory. If the sum of w1 and w2 is an impossible object, then the sum of all possible worlds is an impossible object, for the former is part of the latter and no impossible object is part of a possible object. But this makes the domain in which all possible worlds reside, or “logical space”, an impossible object. This appears unwelcome. Lewis does consider an alternative conception of a possible object, which says that a possible object is an object every part of which exists at some possible world or other (Lewis 1986: 211). This allows a possible object to have parts at different possible worlds. Lewis, who accepts the universality of mereological summation, does not deny that possible objects in this sense are as real as possible objects in his preferred sense. He however dismisses them as unimportant on the ground that we do not normally name them, speak of them, or quantify over them. But given that sets of possible worlds and sets of possible objects figure in important philosophical discussions concerning the identity of propositions and properties, these sets seem important. If the sum of the members of an important set is important, then Lewis's dismissal appears hasty. Again, defenders of Lewis may stand this line of reasoning on its head and conclude that the sum of the members of an important set is not always important.
A useful overview of various issues concerning Lewis's possibilist realism, as well as actualist representationism, is found in Divers 2002, which is the first systematic attempt to defend Lewis's theory since Lewis 1986. Loux 1979 is the standard anthology of important writings in modal metaphysics up to that point.
Modal dimensionalism differs from Lewis's theory in a number of important respects but the most striking is the lack of counterpart theory, which is a cornerstone of Lewis's theory. Modal dimensionalism eschews counterparts and proposes that to say that you are the leader of a religious cult at a possible world is to say that you yourself exist at that world and are the leader of a religious cult at that world. Another difference between modal dimensionalism and Lewis's theory is that unlike the latter, the former eschews the merelogical conception of the existence of a possible object at a possible world. According to modal dimensionalism, just as a temporally or spatially persisting object is (arguably) not part of the temporal or spatial points at which it exists, a modally persisting object is not part of the possible worlds at which it exists. Modal dimensionalism also differs from Lewis's theory in not being a reductionist theory. It does not analyze the notion of a possible world in mereological terms but leaves it as largely primitive (Yagisawa 2002). This enables modal dimensionalists to allow the possibility of there being no concrete object, whereas on Lewis' theory, if there is no concrete object, there is no possible world. For a different attempt to reconcile possibilist realism with the possibility of the non-existence of anything concrete, see Rodriguez-Pereyra 2004.
Though free from some difficulties inherent in Lewis's theoretical machinery, modal dimensionalism has its own obstacles to overcome, not the least of which is to make substantive sense of the idea of an object's persisting not just in physical space and time but in modal space. One idea is to mimic the “endurantist” approach to temporal persistence and say that a possible object persists through many possible worlds by having all of its parts existing at each of those worlds. Another idea is to mimic the “perdurantist” approach to temporal persistence and say that a possible object persists through many possible worlds by having different parts (world stages) at different possible worlds and being the modal-dimensional “worm” consisting of those world stages. Note that this does not make the object mereological part of a possible world at which it exists. It only makes each of the object's world stages part of the object. Lewis, in contrast, has it that a possible object has all of its parts at a single possible world (where they are merelogical part of that world) and therefore does not persist through different worlds at all. Despite these differences, Lewis, speaking of the “perdurantist” version of modal dimensionalism, says that it is but a notational variant of his own theory. He then proceeds to criticize it (Lewis 1968: 40-2). Lewis formulates his opposition to modal dimensionalism more carefully in Lewis 1986: 213-20. Achille Varzi derives Lewis's theory from a theory similar to modal dimensionalism (Varzi 2001). Unlike modal dimensionalism, the theory he uses follows Lewis and defines the existence of a possible object at a possible world in terms of the object being mereological part of the world. Varzi notes some differences between this theory and Lewis's.
Lewis's possibilist realism faces the problem of specifying non-actual possible objects. Take Vulcan, the innermost planet between Sun and Mercury erroneously believed to exist by some astronomers in the nineteenth century, when the universe was assumed to be Newtonian. Vulcan is not actually between Sun and Mercury or actually anywhere at all. Vulcan also does not actually have any mass, shape, or chemical composition. Still it is possible that Vulcan be a unique planet between Sun and Mercury and have a particular mass m, a particular shape s, and a particular chemical composition c. It is also possible that Vulcan be a unique planet between Sun and Mercury and have a slightly different particular mass m′, a slightly different particular shape s′, or a slightly different particular chemical composition c′, where the slight difference in question lies within the range of deviations the original astronomers would have tolerated. So there is a possible world w at which Vulcan is a unique planet between Sun and Mercury and has m, s, and c, and there is a possible world w′ at which Vulcan is a unique planet between Sun and Mercury and has m′, s′, and c′. Clearly w and w′ are different worlds. On Lewis's theory, every possible object exists at only one world. So either the planet in question at w is not Vulcan or the planet at w′ is not Vulcan. Whichever planet that is not Vulcan is Vulcan's counterpart at best. Is either planet Vulcan? If so, which one? If neither is, where is Vulcan? What possible world hosts Vulcan? There seems to be no non-arbitrary way to answer these questions within Lewis's theory.
The modal-dimensionalist version of possibilist realism offers the ready answer, “The planet at w and the planet at w′ are both (world stages of) Vulcan”, but faces an only slightly different challenge of its own. It seems intuitive to say that there is a possible world at which Vulcan exists between Sun and Mercury and some remote heavenly body distinct from Vulcan but qualitatively identical with it in relevant respects (such as mass, shape, chemical composition, etc.) also exists. Let w1 be such a world and call Vulcan's double at w1 ‘Nacluv’. Thus at w1, Vulcan and Nacluv exist, Vulcan is between Sun and Mercury, and Nacluv is somewhere far away. It is possible for Vulcan and Nacluv to switch positions. So there is a possible world, w2, which is exactly like w1 except that at w2 Nacluv is between Sun and Mercury and Vulcan is far away. Since Vulcan and Nacluv are two distinct objects, w1 and w2 are two distinct worlds. But this difference seems empty. Given that w1 and w2 are exact qualitative duplicates of each other, on what ground can we say that the object between Sun and Mercury at w1 and far away at w2 is Vulcan and the object far away at w1 and between Sun and Mercury at w2 is Nacluv, rather than the other way around? It is unhelpful to say that Vulcan and Nacluv are distinguished by the fact that Vulcan possesses Vulcan's haecceity and Nacluv does not. An object's haecceity is the property of being that very object (Kaplan 1975, Adams 1979, Lewis 1986: 220-48). Since what is at issue is the question of which object is Vulcan, it does not help to be told that Vulcan is the object possessing the property of being that very object, unless the property of being that very object is clarified independently. To say that it is the property of being that very object which is Vulcan is clearly uninformative. It is not obvious that there is any way to clarify it independently.
Alternatively, one might choose to insist that if anything at any possible world is Vulcan, it has to possess at that world the properties relevant to the introduction of the name ‘Vulcan’, such as being the heavenly body with such-and-such mass and orbit and other astrophysical characteristics and being between Sun and Mercury in a Newtonian universe. This is supported by descriptionism concerning the semantics of proper names, according to which ‘Vulcan’ is a proper name which is semantically equivalent to a definite description (‘the heavenly body with such-and-such mass and ...’). But forceful criticisms of descriptionism for proper names were launched in the early 1970s (Donnellan 1972, Kripke 1972). Kripke's criticism has been especially influential. The kernel of Kripke's criticism rests on the intuitive idea that a sentence containing a referring proper name expresses a singular proposition about the referent independently of any qualitative characterization of the referent but that a corresponding sentence containing a description does not so express a singular proposition. If Kripke's criticism applies to ‘Vulcan’, it is difficult to defend descriptionism for ‘Vulcan’. But ‘Vulcan’ and other apparent proper names of non-actual possible objects may not be as readily amenable to the Kripkean considerations as proper names of actual objects. The so-called “problem of empty names” is the problem of providing a semantic theory for “empty names” like ‘Vulcan’ as non-descriptional designators. For some recent contributions to the project of solving this problem, see Everett & Hofweber 2000.
It is important to note that according to most versions of actualist representationism, the universe, as it (actually) is, is not the actual world. Since the actual world is a possible world and every possibly world is a representation, the actual world is a representation. The universe, as it (actually) is, is not a representation but includes all representations, along with everything else. But it does not include non-actual possible objects. The universe includes all and only those objects which exist.
In actualist representationism, existence is conceptually prior to actual existence. This is in concert with the priority of the truth of any proposition P over the actual truth of P. P is actually true if and only if P is true at the actual world, which in turn is so if and only if the actual world represents P as true. But by definition, the actual world is the possible world which represents P as true if and only if P is true. Likewise, for an object to exist at the actual world is for the actual world to represent it as existing; the actual world represents an object as existing if and only if the object exists. Actual existence is thus reducible to existence simpliciter.
Non-actual possible existence is defined as existence at some possible world other than the actual world, which in turn is defined in terms of existence simpliciter as follows: x exists at a possible world w not identical to the actual world if and only if x would exist if w were actual, that is, if the universe were as w represents it to be. According to this picture, non-actual possible existence is not a special mode of existence completely separate from actual existence, hence existence simpliciter, but instead a “would-be” existence simpliciter on a counterfactual supposition. There is no room for non-actual possible objects in this picture. Many representations which are possible worlds other than the actual world include representations of the existence of non-actual possible objects, but non-actual possible objects are not mereological part of those possible worlds. Neither are they set-theoretic members, or constituents in any other sense, of those possible worlds. For them to exist at those possible worlds is for the worlds to say (represent) that they exist; nothing more, nothing less. This is a non-realist picture of the existence of the non-actual. Non-actual possible objects are thus nothing at all. This is the conservative view (1).
Let us examine how actualist representationists handle apparent modal truths asserting the possibility of non-actual objects. There are two types of such truth and the first type is easy to handle. It is possible that Julius Caesar (congenitally) had a sixth finger on his right hand (whereas, we assume, he actually had only five fingers). This possibility only calls for a possible world to represent Julius Caesar as having had a sixth finger on his right hand, which may easily be done by means of, say, the (interpreted English) sentence, ‘Julius Caesar had a sixth finger on his right hand’.
One way to handle this without postulating a non-actual possible object is to say that there was an actual finger belonging to someone else but it could have belonged to Julius Caesar's right hand as his extra finger (congenitally). If this sounds biologically too bizarre, an actualist representationist may say instead that there are actual elementary particles none of which was part of Julius Caesar's body but which collectively could have constituted his sixth right finger. This is along the lines of David Kaplan's possible automobile (Kaplan 1973: 517, note 19) and Nathan Salmon's Noman (Salmon 1981: 39, footnote 41). Kaplan imagines a complete set of automobile parts laid out on a factory floor ready for assembly. If the parts are assembled, a particular automobile will be created; if not, not. Suppose that the parts are destroyed before they are assembled. Then the particular automobile which would be created if the parts were assembled is in fact not created. It is a non-actual possible automobile. Salmon, taking a cue from Kripke's suggestion of the necessity of origin (Kripke 1972), imagines a particular human egg and a particular human sperm which could merge into a particular human zygote and develop into a particular human being. Suppose that the egg and the sperm in fact fail to merge, hence fail to develop into a human being. The particular human being, Noman, who would be created if the egg and the sperm merged and developed normally is in fact not created. Noman is a non-actual possible human being. This line of thought escapes the bizarreness of the previous account and affords actualist representationists a powerful means to accommodate many apparently recalcitrant modal truths about non-actual possible objects, provided that these non-actual possible objects can be individuated uniquely by means of actually existing potential parts. In fact, it goes even further and affords actualist representationists a way to maintain that Kaplan's automobile is not only possible but is an actual object after all. This can be done by not only individuating Kaplan's automobile uniquely by means of the collection of the automobile parts but identifying the automobile with the collection. If the automobile is identical with the collection, then there exists an actual object which actually is not an automobile but is a collection of automobile parts and which is possibly an automobile, that is, represented as an automobile by some possible world. Similarly, actualist representationists may identify Noman with the collection of the egg and the sperm. Noman is an actual object which actually is not a human being but is a collection of an egg and a sperm and which is possibly a human being. The case of Julius Caesar's sixth finger can be handled likewise. There exists an actual object which actually is not a finger but is a (widely scattered) collection of particles and which is possibly Julius Caesar's sixth right finger.
But now consider the planet Vulcan. There is no collection of actual particles which were supposed to constitute Vulcan. So, if Vulcan is a non-actual possible object, which it apparently is, it seems possible for Vulcan to exist and not be constituted by any actual particles differently located and arranged. Likewise, it seems perfectly possible that Julius Caesar had an entirely new sixth finger satisfying the conditions (a) and (b), that is, a finger which was not constituted by any actually existing particles and satisfied (a) and (b). Despite initial plausibility, an actualist representationist may choose to deny such a possibility. To do so is, in effect, to commit oneself to the position that the universe, as it actually is, already contains maximally possible constituents of any possible universe, that is, it is impossible for any universe to contain even a single constituent object not already in the universe as it actually is. To make this plausible is not an easy task. If, on the other hand, an actualist representationist chooses not to deny the possibility in question, s/he appears to have to say that Julius Caesar's entirely new sixth finger is not an object but is possibly an object. But then the problem is to make sense of the finger's being nothing yet possibly something. How can there be a true predication of any kind, including “is possibly an object”, of nothing?
One difficulty with this view is the failure to produce a single plausible example of such an essence. We saw that possibilist realism faces the problem of specifying non-actual possible objects. Plantinga's version of actualist representationism faces its own version of the Quinean challenge, namely, the problem of specifying the individual essences which are supposed to replace non-actual possible objects. What individual essence did Julius Caesar have? What readily comes to mind is the property of being Julius Caesar. As Barcan, Marcus, and Kripke have forcefully argued (Barcan 1947, Marcus 1961,Kripke 1972), identity is necessary; that is, if an object x is identical with an object y, it is necessarily the case that x is identical with y. Given this, it is easy to see that Julius Caesar necessarily had the property of being Julilus Caesar and everything other than Julius Caesar necessarily lacks it. However, it is implausible to suggest that this property is independent of Julius Caesar. Our canonical specification of it by means of the noun phrase ‘the property of being Julius Caesar’ certainly is not independent of our canonical specification of Julius Caesar by means of the name ‘Julius Caesar’, and this does not seem to be an accidental fact merely indicative of the paucity of our language without deep metaphysical underpinnings. Kaplan's automobile and Salmon's Noman merely push the dependence of the individual essence to the level of the constituent parts of the object of which it is an individual essence. This difficulty is magnified when we ask for a specification of an individual essence of Vulcan or Julius Caesar's entirely new finger. For more on individual essence, see Lycan 1994 and Plantinga 2003.
Meinong distinguishes two ontological notions: subsistence and existence. Subsistence is a broad ontological category, encompassing both concrete objects and abstract objects. Concrete objects are said to exist and subsist. Abstract objects are said not to exist but to subsist. The talk of abstract objects may be vaguely reminiscent of actualist representationism, which employs representations, which are actual abstract objects. At the same time, for Meinong, the nature of an object does not depend on its being actual. This seems to give objects reality that is independent from actuality. Another interesting feature of Meinong's theory is that it sanctions the postulation not only of non-actual possible objects but of impossible objects as well, for it says that ‘The round square is round’ is a true sentence and therefore its subject term stands for an object. This aspect of Meinong's theory has been widely pointed out, but non-trivial treatment of impossibility is not confined to Meinongianism (Lycan and Shapiro 1986). For more on Meinong's theory, see Chisholm 1960, Findlay 1963, Grossmann 1974, Lambert 1983, Zalta 1988: sec.8. For some pioneering work in contemporary Meinongiasim, see Castañeda 1974, Rapaport 1978, Routley 1980. We shall examine the theories of two leading Meinongians: Terence Parsons and Edward Zalta. We shall take note of some other Meinongians later in the section on fictional objects, as their focus is primarily on fiction. Parsons and Zalta not only propose accounts of fictional objects but offer comprehensive Meinongian theories of objects in general.
Parsons' theory is based on the Meinongian distinction between nuclear and extra-nuclear properties. Nuclear properties include all ordinary properties, such as being blue, being tall, being kicked by Socrates, being a mountain, and so on. Extra-nuclear properties include ontological properties such as existence and being fictional, modal properties such as being possible, intentional properties such as being thought of by Socrates, and technical properties such as being complete. See Parsons 1980: 24-27, 166-74 for more on nuclear and extra-nuclear properties and a test for distinguishing between them. Parsons' theory can be encapsulated in the following two principles:
(P1) No two objects have exactly the same nuclear properties;(P2) For any set of nuclear properties, some object has all the nuclear properties in the set and no other nuclear properties.
Take the set of nuclear properties, {being golden, being a mountain}. By (P1) and (P2), some unique object has exactly the two nuclear properties in the set. That object is the golden mountain. Take another set of nuclear properties, {being square, being round}, and the two principles give us the round square. Both of these objects are radically incomplete; they have no particular weight, height, or size, among many other properties. The need for distinguishing nuclear properties from extra-nuclear properties is readily seen by considering the set, {being golden, being a mountain, being existent}. If (P2) is to apply to such a set, it should yield an object having the three properties in the set. Such an object is golden, a mountain, and existent, that is, a golden mountain that exists. But then it should be true that a golden mountain exists, which is in fact not true. Parsons defines a possible object as an object such that it is possible that there exist an object having all of its nuclear properties. On this conception, all existing objects are possible objects, some golden mountains are possible objects, and the round square is not a possible object. It is worth noting that in Parsons' theory, negation needs to be handled delicately (Parsons 1980: 19-20, 105-06, Zalta 1988: 131-34) . Take the set, {being round, being non-round}. By (P2), we have an object, x, which is round and non-round. So, x is non-round. If we can infer from this that it is not the case that x is round, then we should be entitled to say that x is round and it is not the case that x is round, which is a contradiction. Thus, we should not be allowed to infer ‘It is not the case that x is round’ from ‘x is non-round’.
If Julius Caesar's entirely new right finger satisfying (a) and (b) is to be a Meinongian object of Parsons' theory, the best candidate appears to be a non-existent incomplete object corresponding to the set of properties, {being a finger, belonging to Julius Caesar's right hand, being never burnt}. This set includes neither the property of being constituted by particles which do not (actually) exist nor the property of being possibly burnt. Both of these properties are extra-nuclear properties, hence are ineligible to be included in a set to which (P2) applies. So (P2) does not confer them on the object corresponding to the set. How then does the object come to have the properties? It is not obvious how this question should be answered (Parsons 1980: 21, note 4, where Parsons says, “The present theory is very neutral about de re modalities”), but we should at least note that on Parsons's theory, objects are allowed to have properties not included in their corresponding sets of nuclear properties: e.g., the round square, whose corresponding set only includes roundness and squareness, has the property of being non-existent and the property of being incomplete. Also, Parsons allows nuclear properties which are “watered-down” versions of extra-nuclear properties. So the set may include the “watered-down” versions of the two extra-nuclear properties in question and that may be enough. For more on these and related issues in Parsons' theory, see Howell 1983, Fine 1984.
(Z1) Objects which could sometimes have a spatial location do not, and cannot, encode properties;(Z2) For any condition on properties, some object that could never have a spatial location encodes exactly those properties which satisfy the condition.
Some object is the round square, for, by (Z2), among objects which could never have a spatial location is an object which encodes roundness and squareness. The noun phrase, ‘the round square’, unambiguously denotes such a necessarily non-spatial object. Other noun phrases of the same kind include those denoting numbers, sets, Platonic forms, and so on. There are, however, many noun phrases which are ambiguous. They allow an interpretation under which they denote an object which is necessarily non-spatial, and also allow an interpretation under which they denote an object which is possibly spatial and possibly non-spatial. The phrase, ‘the golden mountain’, is an example. The golden mountain in one sense is an object which is necessarily non-spatial and which encodes goldenness and mountainhood. The golden mountain in the other sense is an object which actually is non-spatial but could be spatial. When we say that the golden mountain in the second sense is golden, it means that necessarily if the golden mountain is spatial, it is golden. Since, by (Z1), such an object cannot encode properties, all predications in the preceding sentence have to be understood as exemplification. Similarly with Julilus Caesar's entirely new finger satisfying (a) and (b).
Zalta endorses the claim that some objects are non-actual possible objects, so he appears to side with possibilists. But he defines a non-actual possible object as an object which could have a spatial location but does not (Zalta 1988: 67). So the claim means for Zalta that some objects could have a spatial location but do not. This is compatible with actualism, provided that all such objects are actual in the sense of actually existing (Linsky and Zalta 1994, also Williamson 1998). If we understand Zalta's theory this way, we have the following actualist picture: All objects are actual and existing, some objects are necessarily non-spatial, and other objects are possibly spatial and possibly non-spatial. (For an alternative interpretation of Zalta's formal theory, according to which some objects do not exist, see Zalta 1983: 50-52, 1988: 102-04, Linsky and Zalta 1986: note 8.) Among the last type of objects are those which are actually spatial but possibly not, like you and me, and those which are possibly spatial but actually not, like the golden mountain in the appropriate sense. The distinction between the golden mountain in this (exemplification) sense and the golden mountain in the other (encoding) sense is key to overcoming some objections (Linsky and Zalta 1996).
If we confine our attention to necessarily non-spatial objects, a definition of a possible object which corresponds to Parsons' definition is easily available to Zalta: A possible (necessarily non-spatial) object is a (necessarily non-spatial) object such that some object could exemplify exactly the properties it encodes. In this sense, the object which encodes goldenness and mountainhood is a possible object but the object which encodes squareness and roundness is not. Julilus Caesar's entirely new finger satisfying (a) and (b) can be treated in the same way as the golden mountain. Complications similar to those which arise for Parsons' theory do not arise for Zalta's theory, for all properties are equally subject to encoding, including those properties Parsons regards as extra-nuclear. For a comparison of the two-kinds-of-property approach and the two-kinds-of-predication approach, see Rapaport 1985.
The line of argument Kripke uses, if successful, is applicable to all non-actual natural kinds (except for natural-kind analogs of Kaplan's automobile or Noman). It is unclear that something like it is successfully applicable to individuals like Vulcan, but if it is, we must say that such individuals are impossible objects. Some theorists liken Vulcan to fictional objects, as we will see in the next section, and some theorists argue that fictional objects are impossible objects (Kaplan 1973, 1980 version of Kripke 1972: 157-58, Fine 1984: 126-28). If Vulcan is an impossible object, the problem of uniquely specifying Vulcan, as opposed to Nacluv, becomes less urgent, for it is not evident that we should be able to specify an impossible object uniquely and non-trivially.
There are two main problems with the claim that fictional objects are possible objects. One is the problem of impossible fictional objects. Some fictional objects are ascribed incompatible properties in their home fiction by their original author (usually inadvertently). This seems to be sufficient for them to have those properties according to their home fiction, for what the author says in the fiction (inadvertently or not) holds the highest authority on truth in fiction. Suppose that a fictional object has a property if it has that property according to its home fiction. Then those fictional objects are impossible objects, for no possible object has incompatible properties. The other problem is the failure of uniqueness. It may be viewed as the problem of meeting the Quinean demand for clear identity conditions. Holmes is a particular fictional object. So if we are to identify Holmes with a possible object, we should identify Holmes with a particular possible object. But there are many particular possible objects that are equally suited for the identification with Holmes. One of them has n-many hairs, whereas another has (n+1)-many hairs. No fictional story about a particular fictional object written or told by a human being is detailed enough to excluded all possible objects but one to be identified with that fictional object, unless it is a fiction about an actual object or a non-actual possible object analogous to Kaplan's automobile or Noman.
Strangely enough, there is also a problem with the claim that fictional objects are non-actual objects. That is, there is some plausible consideration in support of the claim that fictional objects are actual objects. We make various assertions about fictional objects outside the stories in which they occur and some of them are true: for example, that Sherlock Holmes is admired by many readers of the Holmes stories. The simplest and most systematic explanation appears to be to postulate Holmes as an actual object possessing the properties such true assertions ascribe to him. Fictional objects may then be said to be theoretical objects of literary criticism as much as electrons are theoretical objects of physics. This type of view enjoys surprisingly wide acceptance. (Searle 1974, van Inwagen 1977, 1983, Fine 1982, Salmon 1998, Thomasson 1999). The theorists in this camp, except van Inwagen (van Inwagen 2003: 153-55), also think that fictional objects are brought into existence by their authors as actual objects. Even if this type of view is to be followed, it must still be denied that Holmes is actually a detective, for if we enumerate all individuals who are actually detectives, Holmes will not be among them. By the same token, Holmes is not actually a resident of Baker Street or even a human being. Though actual, Holmes is actually hardly any of those things Conan Doyle's stories describe him as being. Holmes must not be a concrete object at all but instead an abstract object which has the property of being a detective according to Doyle's stories, the property of being a resident of Baker Street according to Doyle's stories, and so on.
Meinongian theories overcome the problems of impossibility and non-uniqueness in a straightforward way. According to Parsons' theory, a fictional object x which originates in a certain story is the object that has exactly the nuclear properties F such that according to the story, Fx (Parsons 1980: 49-60, 228-23). A fictional object to which the story ascribes incompatible properties is simply an impossible object, but such an object is harmless because it does not exist. As for the problem of non-uniqueness, Sherlock Holmes is not identified as a complete object. Instead Holmes is said to be the object having just the nuclear properties Holmes has according to the stories. There is no number n such that Holmes has exactly n-many hairs according to the stories. So Parsons' Holmes does not have n-many hairs, for any n. It is an incomplete object. Zalta offers a similar picture of fictional objects which is subsumed under his general theory of encoding. According to him, a fictional object x which originates in a certain story is the object that encodes exactly the properties F such that according to the story, Fx (Zalta 1988: 123-29). Zalta's treatment of the problem of impossibility is similar to Parsons'. A fictional object to which the story ascribes incompatible properties is an object which encodes those properties, among others. Such an object is harmless because it does not exemplify the incompatible properties. Zalta's solution to the problem of non-uniqueness is equally similar to Parsons'. Sherlock Holmes, for Zalta, is simply an incomplete object which does not encode the property of having exactly n-many hairs, for any n. Though not meant to be a fictional object, Vulcan may be given the same treatment as explicitly fictional objects. According to Parsons, the word ‘Vulcan’ is ambiguous. In one sense, it is the name of a fictional object which originates in a false astronomical story. In the other sense, it does not refer to anything. Zalta does not recognize Parsons' second sense and simply regards ‘Vulcan’ as the name of a fictional object.
For another Meinongian approach to fictional objects, see Castañeda 1979. Charles Crittenden offers a view in a Meinongian spirit but with a later-Wittgensteinian twist (Crittenden 1991). Like Parsons, Crittenden maintains that some objects do not exist and that fictional objects are such objects. Following later Wittgenstein, however, he sees no need to go beyond describing the “language game” we play in our fictional discourse and dismisses all metaphysical theorizing. Robert Howell criticizes Parsons' theory, among others, and recommends an approach which construes fictional objects as non-actual objects in fictional worlds, where fictional worlds include not just possible but impossible worlds (Howell 1979). Nicholas Wolterstorff argues for the view that fictional objects are kinds (Wolterstorff 1980). For criticism of this view, see Walton 1983. Van Inwagen 2003 contains useful compact discussions of some Meinongian and non-Meinongian theories of fictional objects.
Gregory Currie denies that fictional names like ‘Sherlock Holmes’ are proper names or even singular terms (Currie 1990). He claims that sentences of fiction in which ‘Sherlock Holmes’ occurs should be regarded as jointly forming a long conjunction in which every occurrence of ‘Sherlock Holmes’ is replaced with a variable bound by an initial existential quantifier in the way suggested by Frank Ramsey (Ramsey 1931). If he is right, theoretical need for fictional objects is diminished.
Kendall Walton urges that we should take seriously the element of make-believe, or pretense, inherent in the telling of a fictional story by the author and the listening to it by the audience (Walton 1990, also Evans 1982: 353-68). According to this pretense theory, the pretense involved in the language game of fictional discourse shields the whole language game from a separate language game aimed at non-fictional reality, and it is in the latter language game that we seek theories of objects of various kinds as real objets. If this is right, any search for the real ontological status of fictional objects appears to be misguided. For the view that the pretense theory is compatible with a theory of fictional objects as real objects, see Zalta 2000.
If it is possible that something is F, then something is such that it is possible that it is F.
The formal logical sentence with this meaning is known as the Barcan Formula, after Ruth C. Barcan, who published the first systematic treatment of quantified modal logic, in which she postulated the formula as an axiom (Barcan 1946), and who has published under the name ‘Ruth Barcan Marcus’ since 1950. If we read ‘F’ as meaning “non-identical with every actual object”, the Barcan Formual says that if it is possible that something is non-identical with every actual object, then something x is such that it is possible that x is non-identical with every actual object. The antecedent is plausibly true, for there could have been more objects than the actual ones. But if so, the consequent is true as well. But no actual object is non-identical with every actual object, for every actual object is identical with itself, an actual object. Assuming the necessity of identity, if an object y is identical with an object z, it is not possible that y is non-identical with z. So, no actual object is such that it is possible that it is non-identical with every actual object. Therefore, any object x such that it is possible that x is non-identical with every actual object must be a non-actual possible object.
The converse of the Barcan Formula is also a theorem along with the Barcan Formula in classical logic and is as interesting. The Converse Barcan Formula, as it is known, says the following:
If something is such that it is possible that it is F, then it is possible that something is F.
The ontology of non-actual possible objects does not have as direct relevance to the Converse Barcan Formula but is an integral part of the view that quantifiers in quantified modal logic range over all possible objects, non-actual as well as actual. This view validates the Converse Barcan Formula. If we read ‘F’ as meaning “does not exist”, the Converse Barcan Formula says that if something x is such that it is possible that x does not exist, then it is possible that something does not exist. The antecedent is plausibly true, for any one of us, actual people, could have failed to exist. But if so, the consequent is true as well. But on actualist representationism, no possible world contains a representation which says that something does not exist, for it is contradictory provided that ‘something’ means “some existing thing”. So if the consequent is to be true on actualist representationism, ‘something’ should not mean “some existing thing” but rather should mean “some thing, irrespective of whether it exists”. That is, the existential quantifier in the consequent needs to have a free range independently of the possibility operator in whose scope it occurs, and this is what the view in question allows. The consequent does not even appear to be threatened with contradiction if we assume this view and let the existential quantifier range over all possible objects, including non-actual ones.
In classical logic, the domain for quantification is assumed to be non-empty and every individual constant is assumed to refer to something in the domain. In free logic, neither of these assumptions is made. Thus free logic appears to be particularly suited to theorizing about non-existent objects (see Lambert 1991, Jacquette 1996). For a criticism of the free-logical approach to fictional discourse, see Woods 1974: 68-91. Interestingly, the Barcan Formula and the Converse Barcan Formula are not derivable in free logic.
Marcus herself proposes the substitutional reading of quantification to skirt the need for non-actual possible objects (Marcus 1976), and later suggests combining it with objectual quantification over actual objects (Marcus 1985/86).
This writing was partially supported by the Faculty Fellows Program of the College of Humanities at California State University, Northridge for Spring 2004.
| Takashi
Yagisawa takashi.yagisawa@csun.edu |
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