In Defence of Transcendentism 1. Introduction What is for an object to persist through time? An answer to this question is both the main aim of a theory of persistence and a fundamental step towards a suitable theory about the truth conditions of sentences involving temporal characterizations of persisting objects. However, since for an object to persist is for it to exist at different times, another question that conceals itself behind the aforementioned one is: what is for an object to exist at a time? In other words, how should we construe the relation between objects and times? Contemporary metaphysicians often overlook this question, and usually assume that for an object to exist at a time is for it to be located at that time. In light of this implicit assumption, different theories of persistence are in turn construed in terms of the way in which objects are located at extended regions of time, e.g. by being uniquely located at those extended regions or by being multiply located at each instant that makes up those extended regions (Gilmore 2006, Sattig 2006, Parsons 2007, Calosi 2011, Donnelly 2011, Costa and Giordani 2013). Let us call immanentism the view that objects are located at times. In their (2013), Giordani and Costa make this assumption explicit, criticize it, and put forward an alternative view, which they call transcendentism. Just like immanentism, transcendentism is a view concerning the way in which objects exist at times. While immanentism claims that existence at a time is location, transcendentism denies that objects are located at times, and claims that for an object to exist at a time is for it to participate in events that are located at that time. More generally, transcendentism and immanentism are views about the relation of some kinds of entities to regions of a dimension. In this sense, transcendentism and immanentism about existence at a time echo other views about the relation of other entities to regions of other dimensions. A clear example is constituted by the dispute between immanentist and transcendentist views as regards the spatial profile of universals1. In that other context, immanentism is the view that universals are located at regions of space, while transcendentism is the view that universals are not located at regions of space, and that universals are related to space in an indirect way only, by being instantiated by objects which are in turn located in space (Armstrong 1989, Lowe 1998, Lowe 2006, Gilmore 2003). Going back to transcendentism about existence at a time, its fundamental tenet is then that objects are not located at times, but exist at times only in virtue of their participating in events which are, in turn, located at those times. On the one hand, transcendentism is supposed to capture the idea that the relation between events and time seems to be intuitively more intimate than the one between objects and time (Wiggins 1980, Simons 1987). On the other hand, it is also supposed to constitute a version of endurantism which offers several advantages over its rivals, in that it is not committed to controversial claims to which other views are committed, such as the claims that multilocation or extended simples are possible (Giordani and Costa 2013). It would be helpful to say something more about what precisely do the immanentist and the transcendentist about existence at a time disagree about. We have characterized their dispute as a dispute on whether objects are located at times. But what is for something to be located at a region, and what is to 1 It is worth noting that in the philosophical literature two senses of transcendence are distinguished: an existential one, according to which universals are transcendent iff they do not ontologically depend on their instances, and a locative one, according to which universals are transcendent iff they are not located in space (Lowe 2006, 98-100). The relevant sense here is of course the locative one. deny such a claim2? Here we take location or, to be more precise, exact location, to be a binary relation connecting an entity to a region of a dimension. When, and only when, x is located at region r, x and r have the same shape and size, and bear the same distance relation in the relevant dimension (Gilmore 2006). So for example I am located at a region of space that has my same shape and size, and stands at my same spatial distance to other objects. In the case of temporal location, this means that a located entity is earlier and later than others and has a temporal shape and size – i.e. it is either temporally extended or punctual. This characterization of the relation of location allows us to highlight some claims that the transcendentist denies and the immanentist is committed to: transcendentism denies that objects have a temporal size (be it extended or punctual) and that they bear temporal distance relations to other objects. Strictly speaking, only events have a temporal extension and bear temporal distance relations to other entities located in time. Another substantial claim that is affirmed by the transcendentist and denied by the immanentist is that the relation between objects and times is composed by two further relations: participation and events' location at those times. On the other hand, we take location to be not composed by further relations. In her (2013), Kristie Miller has offered a thorough analysis of transcendentism about existence at a time. She begins by distinguishing two possible questions about the location of an object at a region of a dimension: Metaphysical question If an object occupies a region that is extended along some dimension D, then in what manner does that object occupy that region? Semantic question 2 We thank an anonymous referee for raising this question. If an assertion states that an object is characterized in a certain manner at a certain time, then what are the truth conditions for that assertion? After having distinguished these questions, she argues that transcendentism fails at answering the metaphysical one, and is problematic with respect to the answer it gives to the semantic one. In her own words, What we can say is that transcendentism does not offer us a new account of the metaphysics of occupation. Moreover, the semantics it offers for talk about objects across times and worlds is consistent with the view that objects do exactly occupy regions and that they do so in one of the three standard ways (Miller 2013, 227). In what follows, we aim at answering Miller's objections. Let us begin with the metaphysical ones. 2. Miller's metaphysical worries We take Miller to be raising two metaphysical worries against transcendentism, the first worry being explicitly stated while the second one being unstated and lurking. The first metaphysical worry concerns the question of whether or not transcendentism constitutes a new metaphysics of persistence. Extant theories of persistence differ because they offer different ways in which an object is located at an extended region of time, whereas transcendentism does not offer a new way in which an object can be located at an extended region of time. Miller is certainly right in pointing out that extant theories of persistence put forward ways in which objects can be located at extended regions of time. For example, according to perdurantism, a persisting object is uniquely located at the extended region of time of its persistence. For another example, according to multilocationism, a persisting object is multiply located at each instantaneous region making up that extended region of time. Miller is also certainly right in pointing out that transcendentism does not offer a new way in which persisting objects can be located at extended regions of time. Yet, this fact can hardly be seen as a point against transcendentism, given that the aim of transcendentism is not offering a new way in which objects can be located at times, but rather that of offering a new way in which objects can exist at, and persist through, times. In so doing, transcendentism outright denies that objects are located at times. Hence, it should come as no surprise that the view does not offer a new way in which objects can be located at times. From this point of view, charging the transcendentist of not offering a new way of being located at times is a bit like charging an antirealist about universals of not having offered a new theory about the way in which particulars instantiate universals, or charging an atheist of not having offered a solution to the problem of evil. We see another worry that seems to be lurking behind Miller's paper and that is worth addressing for a better understanding of the transcendentist theory of persistence. The worry concerns the relation between objects and events. Given that transcendentism explains the presence of objects at times in terms of events, the view may be thought to imply that events are more fundamental than objects3. Moreover, this implication may be thought to be problematic, either per se, because one may have independent reasons to believe that events are not more fundamental than events, or in the context of transcendentism, insofar as if objects supervene on events, and events are located in time, also objects are going to be located in time, contra transcendentism4. We do not think that transcendentism implies that events are more fundamental than objects. As far as we can see, transcendentism is compatible 3 In Miller's words: „For, according to transcendentism, claims about objects, at, and across, time and modal space, are made true by the existence of certain events. One might, then, think it natural to say that an object is composed of, or grounded by, or supervenes on, the events that are the truthmakers for claims about that object at, and across, times and worlds". 4 We thank an anonymous referee for distinguishing these two ways in which the implication can be problematic. with any view concerning the fundamentality relation between objects and events. In particular, we do not see a valid inference path starting from the claim that (i) objects are present at times in virtue of participating in events, to the claim that (ii) objects are less fundamental than events. Let us try to make the argument underlying this conclusion more explicit. A principle of the following form seems to be at work in the inference from (i) to (ii): P1. if some facts about x hold in virtue of some facts about y, then x is less fundamental than y. As such, P1 does not seem to be convincing. Suppose that Sam is Mary's only child. There are some facts about Mary that hold in virtue of facts about Sam, for example the fact that Mary is a mother. Yet, Mary is not less fundamental than Sam. We think that P1 is false, yet this is not to say that there is no connection between 'in virtue of' relations and fundamentality relations (even though it is notoriously difficult to come up with a definition of one in terms of the other). Here are two possible plausible connections between 'in virtue of' and fundamentality: P2. if all facts about x hold in virtue of some facts about y, then x is less fundamental than y. P3. if the fact that x exists simpliciter holds in virtue of some facts about y, then x is less fundamental than y. Yet, it seems that neither P2 nor P3 can be employed to infer (ii) from (i). As regards P2, according to an intuitive interpretation of transcendentism, there are several claims about objects that do not hold in virtue of facts about events. For example, all essential facts about Socrates, or several identity facts about Socrates, such as the fact that Socrates is identical to Socrates or that Socrates is different from Plato, seem not to hold in virtue of any event in which Socrates participates. P3 does not seem to be of much help either. The facts about objects that according to the transcendentist hold in virtue of facts about events are not facts about the existence simpliciter of objects, but about their presence at some times5. A different way of spelling out Miller's worry (or perhaps another worry lurking behind her paper) goes as follows. Participation is the relation supposed to hold between objects and events. But how can we make sense of participation? Does participation imply that objects are less fundamental than events? Does it imply that if events are located entities, objects are located entities as well? In order to answer these questions, let us have a look back at the fundamental ontological kit on which transcendentism is built. Transcendentism assumes that both events and objects exist. Now, once one assumes the existence of both a body and its electric charge, of both the football players and the football match, of both Socrates and his life, one will not conceive of these pairs of entities as completely unrelated ones, but rather will think of introducing a way of relating them. This relation between an object and its events has been dubbed by metaphysicians in different ways. Kim talks of an object as 'being the constitutive object of' an event, while Lombard talks of an object as 'being the subject of' an event. We prefer to prefer to talk of an object 'participating in' an event, but we take our terminological choice of being of no impact on our metaphysics of that relation. If one believes that events exist simpliciter in virtue of facts about objects, or vice versa, one may think of making sense of participation in terms of the 'in virtue of' relation. Yet we do not think that talking of participation per se implies that events are more or less fundamental than objects. Under some construal of the participation relation, it may turn out that location transfers from the event to its participant, so that if events are located at a 5 In Sider's (2001, 59) words: „Existence-at must be distinguished from quantification. By 'there is', I intend atemporal quantification over all objects, not just those located at any particular time (...). 'Exists-at' is not the logician's '∃'." region, also their participants are located at that region. For example, if participation is construed as parthood, and if parts must be located at a subregion of their wholes, then the temporal location of events implies the temporal location of their participants, and transcendentism becomes untenable. This means that transcendentism is committed to a rejection of such a construal, which we take to be independently unappealing – both because parts of a football match are its two halves, and not its participants, and because the fact that a whole is located at a region does not imply the fact that its parts are located at some sub-regions of it (think of mereological sums of entities that are in space and entities that are not, if such sums are possible). 3. Miller's semantic worries Let us now turn to Miller's remarks concerning the transcendentist semantics. As she correctly points out, transcendentism comes with an appropriate semantics, according to which several temporal claims about objects are made true by the fact that they participate in events. Thus, the proposition that an object exists at a time is made true by the fact that it participates in an event which is located at that time. Moreover, the proposition attributing a temporary intrinsic property to an object at a time is made true by the fact that the object participates in an event of a given kind that is located at that time. After having defined the transcendentist semantics accordingly, Miller remarks that such a semantics is compatible not only with the transcendentist metaphysics – according to which objects are not located at times – but also with the opposite metaphysics view according to which objects are located at times – i.e. the immanentist metaphysics. A concrete example of the latter case goes as follows. If objects are sums of events, and events are located at times, it is plausibly the case that (i) many claims about objects are made true by the events that compose them, and (ii) objects themselves, insofar as they have parts that are located at times – events – will also be located at times (Miller 2013). Miller's claim sounds legitimate. In a sense, one could legitimately think that the transcendentist semantics is compatible with a plethora of different metaphysical options – immanentism included. However, we do not see in which sense this should count as an objection against transcendentism. It comes as no surprise that transcendentism, as any other theory of persistence, consists of some parts that, taken separately, may be consistent with theories that are at odds with transcendentism taken as a whole. Compare the present case with multilocationism and perdurantism, which agree on immanentism. Or, to give an example concerning a theory composed of a metaphysical and a semantic part, take the case of the class nominalism. The semantics usually associated with class nominalism implies that the proposition 'x is red' is true just in case x belongs to the class of red objects. Of course, this semantic claim does not in itself exclude the possibility that in addition to particulars and class thereof, there also are universals, so that the class nominalist semantics, or at leas a part of it, seems to be compatible with the realist's metaphysics. Still, nobody would take this as a shortcoming of class nominalism of its semantics. Similarly, while the semantics of an ersatzist about possible worlds is consistent with the assumption that concrete possible worlds exist, nobody would take this as evidence against ersatzism about possible worlds. Hence, to go back to our case, we do not see why the consistency of the transcendentist semantics with the immanentist metaphysics should count as an objection against transcendentism. A second objection that Miller moves against the transcendentist semantics is that it is not sufficiently motivated. In particular, she thinks that further semantic evidence should be offered in favour of the idea that objects are not located at times. We agree with Miller that a theory that departs from the philosophical literature as transcendentism does should be well motivated. Yet, we do not think that it is the transcendentist semantics alone that needs to be justified, and that such a justification should come from semantics alone (Miller 2013, 226). Rather, we think that it is the whole transcendentist theory that needs to be justified. Since transcendentism is primarily a metaphysical thesis about the relation between objects and time, one would expect it to be primarily justified on a metaphysical basis. The aim of the next section is to offer such a further justification. 4. In favour of transcendentism What reasons do we have to prefer the transcendentist theory of persistence to its rivals? In order to answer this question, let us take a step back and clarify the general perspective we assume on the whole debate. We interpret it as originating from the apparent contradiction between two theses. First, there is an intuition about location. According to it, every located entity has at most one exact location, r say, and has a part for any subregion r' of r. For example, Mary's life, which is an event, has an interval, and only that interval, as its exact location, and has a part, a phase of this life, for any subregion of that interval. Second, there is an intuition about persisting objects, namely that every persistent object is the proper subject of attribution of the attributes that characterize it across time. For example, if Mary is sitting at t and standing at t', Mary herself is the proper subject of attribution of the two attributes standing and sitting. Locative thesis (LT) Every located entity has at most one exact location, r say, and has a part for any subregion r' of r. Persistence thesis (PT) Every persistent object is the proper subject of attribution of the attributes that characterize it across time. Now, none of the current theories of persistence enable us to maintain both the locative and the persistence intuitions. On the one hand, perdurantism and exdurantism preserve LT, but reject the PT. According to them, that the proper subject of some attributes of Mary are temporal parts or counterparts of her, respectively. On the other hand multilocationism and extended atoms theory6, preserve PT, but reject LT. According to them, entities have multiple locations or fail to have parts for each subregion of their exact location. However, it is crucial noting that even if the locative and persistence intuitions appear to be jointly inconsistent, they actually are not. They appear to be so only as long as immanentism is assumed, i.e. as long as it is implicitly assumed that for an object to exist at a time is for it to be somehow located at that time, so that for an object to persist is for it to be somehow located at an extended region of time. Without this assumption there simply is no way to get a real inconsistency here. Transcendentism has the undeniable advantage of eluding the inconsistency by denying that persistence has to be construed as temporal location. After all, there is no reason to think that the fact that an object persists through time cannot be construed as a complex state of affairs. Moreover, there is nothing mysterious in the transcendentist semantics. In fact, from the semantic point of view, the sense of the proposition "object x persists" is simply the way in which the corresponding state of affairs is presented and the truth condition of the proposition is stated following Tarski's biconditionals: the proposition that "object x persists" is true iff x persists, where persisting coincides with participating in an event which is located at that time. In so doing, transcendentism preserves both the locative thesis and the persistence thesis. First, it preserves the locative thesis because it need not deny that located entities have at most one exact location, or that objects have parts for each subregion of their exact location. Second, it preserves the persistence thesis because it does not deny that e.g. Mary itself, and not parts or counterparts thereof, is the proper subject of the attributes standing and sitting, by participating in some appropriate events at t and t'. In our opinion, this fact 6 See Giordani and Costa (2013) for definitions of the view and Gilmore (2006), Parsons (2007), Miller (2009) and Daniels (2014) for discussion. suffices, if not to prefer transcendentism to its rivals, to take it a strong competitor in the persistence debate and to investigate it in more detail. 5. APPENDIX: classification of the views In order to provide a general classification of the positions in the current debate about persistence, we exploit the parallel between identity through times and identity through worlds and distinguish five different theories of persistence, that are related in different ways with three different theories of location and that provide different interpretation to statements about temporal and modal states of affairs. In particular, with respect to the identity through times and worlds, we distinguish • a metaphysical thesis concerning the relation of occupation (MTO) • a metaphysical thesis concerning temporal existence (MTT) • a metaphysical thesis concerning modal existence (MTM) • a semantic thesis concerning temporal discourses (STT) • a semantic thesis concerning modal discourses (STM) Here is the classification. 1. Classical uni-locationist immanentist theories: MTO 1: (classical unilocationism) entities exactly occupy a single region and occupy each proper subregion thereof by having a proper part that exactly occupies that region. MTT 1: (perdurantism: uni-located objects): persisting objects are classically unilocated at a single extended temporal region. MTM 1: (modal uni-located objects): objects in different worlds are classically unilocated at a single extended modal region. The metaphysical theses provide a direct support for the following semantic theses: STT 1: <x was P >, uttered at t, is true just in case there is a temporal part xi of x such that xi is exactly located before t and xi is P. STM 1: <x can be P >, uttered at w, is true just in case there is a modal part xi of x such that xi is exactly located in a different world and xi is P. 2. Bare uni-locationist immanentist theories: MTO 12: (bare unilocationism) entities exactly occupy a single region, but do so without having proper parts that occupy any proper subregion of that region. MTT 2: (endurantism: uni-located atomic objects): persistent objects are barely unilocated at a single extended temporal region. MTM 2: (modal uni-located atomic objects): objects in different worlds are barely uni-located at a single extended modal region. The metaphysical theses provide a direct support for the following semantic theses: STT 2: <x was P >, uttered at t, is true just in case there is a temporal region ri before t such that ri is not free of x and x is P at ri. STM 2: <x can be P >, uttered at w, is true just in case there is a world wi different from w such that wi is not free of x and x is P at wi. 3. Multi-locationist immanentist theories: MTO 3: (multilocationism) entities exactly occupy more than one region and can occupy each proper subregion of the regions they occupy by having a proper part that exactly occupies it. MTT 3: (endurantism: multi-located objects): persistent objects are multilocated at several extended / non-extended temporal regions. MTM 3: (modal multi-located objects): objects in different worlds are multilocated at several extended / non-extended modal regions. The metaphysical theses provide a direct support for the following semantic theses: STT 3: <x was P >, uttered at t, is true just in case there is a temporal region ri before t such that x exactly occupy ri and x is P at ri. STM 3: <x can be P >, uttered at w, is true just in case there is a world wi different from w such that x exactly occupy wi and x is P at wi. 4. Classical uni-locationist immanentist stage theory of persistence: MTO 4: (classical unilocationism) entities exactly occupy a single region and occupy each proper subregion thereof by having a proper part that exactly occupies that region. MTT 4: (exdurantism: uni-located stage objects): persistent objects are momentary classically uni-located at a single non-extended region of time. MTM 4: (modal uni-located stage objects): objects in different worlds are classically uni-located at a single world. The metaphysical theses provide a direct support for the following semantic theses: STT 4: <x was P >, uttered at t, is true just in case there is a temporal counterpart xi of x before t such that xi is P. STM 4: <x can be P >, uttered at w, is true just in case there is a modal counterpart xi of x in a different world such that xi is P. 5. 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