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Time and Persistence: The Two Theories


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Paper for PHIL 3310 that supports Merricks' theory that perduring and enduring things are incompatible and rejects exdurantism

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Time and Persistence: The Two Theories

  1. 1. Hildreth1 Time and Persistence: The Two Theories Heather Hildreth This paper will show that theories on time and persistence in metaphysics boil down totwo distinct and incompatible theories that apply uniformly to things of all possibledimensionality: presentistendurantism and eternalistperdurantism. The paper will rule outHaslanger’sexdurantism as a viable persistence theory, and show that it is persistence thatimplies time, as it is impossible to separate the idea of persistence from the idea of time. Thispaper does not attempt to commit to one of the two final theories.Theories on Time The theories of time are explained before those of persistence because it is easier toseparate the idea of time from persisting objects, not because it is these theories of time thatentail certain theories of persistence. There are two main theories of the existence of time,presentism and eternalism, and these can be distinguished in how each one presents the motionand extension of time.Presentism The Stanford Encyclopedia of Philosophy (SEP)defines presentism as the belief that theonly time that exists is the present, and the past and future are non-existent (Markosian, “Time”).Since the only time that exists is “now,” the only properties an object has are the ones itcurrently has. This definition is consistent with definitions given by other philosophers, likeMerricks in his On the Incompatibility of Enduring and Perduring Entities and Haslanger in herPersistence Through Time.It is clear that this view sees time as a constantly moving arrow thatpoints to the present moment, as past moments are immediately swept out of existence as thearrow progresses to the present.
  2. 2. Hildreth2Eternalism SEP and others define the other view, eternalism (or indexicalism, in Merricks), as thebelief that past, present, and future times equally coexist, so past properties an object has exist atthe same time properties the object has now and has in the future (Markosian).Haslanger notesthat this view of time is more stationary. The arrow of time has a fixed set of times that it canindicate as the present, and once it picks out a new temporal place to point to as the present, anyprevious points it indicated still exist along with the future points to which it has yet to point.Theories on Persistence defines persistence as “continued existence or occurrence.” Explainingtheories of persistence in a way that distinguishes them from theories of time is rathercomplicated, as it requires time by its definition; an object persists if it survives an interval oftime. The different theories of persistence explain different ways an object survives this interval.Endurantism According to the SEP, endurantism interprets persistence as wholly enduring throughtime; an object persists if it wholly exists at one time and wholly exists at a different time(Hawley, “Temporal Parts”). The object must wholly exist at all times between these two times;otherwise there is a discontinuity.Endurantism is synonymous with three-dimensionalismin lightof physical, ordinary objects because, as Merrickspoints out, “enduring objects lack temporalextent” (p. 525), so only their three spatial dimensionsfill the entirety of theirexistence.Dimensionalism refers to a certain extent of an object. An object having one spatialdimension is an object that has spatial extent in one direction, like a line. An object having onetemporal dimension is an object that has temporal extent in one direction.Merricks is careful toaccount for certain dimensionless entities (extensionless points, souls) that endure because while
  3. 3. Hildreth3they do not fill space, they exist only and wholly in the present. He is also careful to account forphysics theories (for example, string theory) that claim multiple spatial dimensions. In this case,he notes that “physical entities would have as many dimensions as space”(p.525). Endurantismcan be generalized in terms of dimensionalism with the view that athingendures by wholly existing in the present in as many spatial dimensions it fills. A physical,ordinary object endures by wholly existing in allof the spatial dimensions available in space(Merricksp. 525). A soul or extensionless point endures by wholly existing, but has nodimensions. An event also endures in endurantism. Consider a scene of three-dimensionalobjects in conventional space.The scene is made up of a collection of three-dimensional, whollyexisting objects and perhaps some zero-dimensional wholly existing points or souls. Althoughthis scene is composed of a collection of these 3-D objects, the dimensions do not add up tomake it more than 3-dimensional.An “event” is merely a scene that endures a change, whichmeans that one of the objects that composes the scene endures a change.Since these objects arewholly enduring and the scene is wholly enduring, the event is wholly enduring.Merrickssupports the idea of an event that wholly endures (p.529).For general space, perhaps S-dimensionalism is a better term than three-dimensionalism.Perdurantism According to the SEP, perdurantism interprets persistence as perduring through temporalparts that make up time; an object persists if it partly exists at t1 and t1 + dt (Hawley). Unlikeendurantism, an object never wholly exists at any one time; rather, it partially exists at each time.To get the wholly existing object, one must integrate it over a space-time hypervolume to get thesum of its spatial parts and temporal parts. Perdurantism is synonymous with four-dimensionalism in light of physical objects because, as Merricksnotes, these objects do have a
  4. 4. Hildreth4temporal extent(p. 524). Merricks is again careful to account for certain entities lacking spatialdimension that perdure because while they do not fill space, they could be smeared out overtime, as a soul (p.525).Using the same logic he used for endurantism, one can account forphysics theories (for example, M-Theory) that claim multiple temporal dimensions, such thatphysical entities would have as many dimensions as space and as time. Perdurantismcan be generalized in terms of dimensionalism with the view that a thingpersists by perduring in as many spatial dimensions it fills through as many temporal dimensionsit fills. A physical, ordinary object partially exists at one time in allof the spatial dimensionsavailable in space, and perdures by existing in all of the spatial dimensions available through allof the temporal dimensions available in space. A soul or extensionless pointperdures through allof the temporal dimensions available, but fills none of the spatial dimensions; so a soul has asmany dimensions as time has. An event in perdurantism, like endurantism, has as manydimensions as thewhole object, which, if the object is ordinary and resides in conventional space-time, has four dimensions due to its temporal parts. The dimensions of all of the objects in acollection do not add up to make it more than 4-dimensional. A whole eventhere is the sceneintegrated over time, and can be thought of as a collection of whole objects (occupying the sametime interval), or Haslanger’s “worms” (explained in the next paragraph). An event, then, is four-dimensional in conventional space-time and perdures.For general space, perhaps S-T-dimensionalism is a better term than four-dimensionalism.Exdurantism In explaining persistence theories, Haslanger is careful to distinguish between twopersistence theoriesthat use temporal parts: perdurantism (worm theory) and exdurantism (stagetheory). She claims that perdurantism interprets “persisting things [as] temporally extended
  5. 5. Hildreth5composites, also known as space-time worms” (p. 318).Haslanger’s space-time worms are thehypervoluminousobjects in S-T-dimensionalism, and her definition of perdurantism is consistentwith the one above. She claims that exdurantism, on the other hand, interprets persisting thingsas not only temporal but also spatial stages; an object does not perdure or endure through time, ithas instantaneous counterparts: “ordinary objects are stages and…only exist momentarily,they…persist by virtue of having counterpart antecedent and/or successor stages” (p. 318). Theintegral object as a whole, as in perdurantism, does not exist; for example, a ball is not the sumof all of its counterparts; a ball is an object that exists instantaneously and is then followed byanother, different ball that exists in the very next moment. It is through these stages that theball(s) persists by exduring.Supporters will argue that the ball survives to the next moment intime by having a counterpart at that time1. Exduring objects do not have temporal parts in thesame way that perduring objects do; they have temporal counterparts. The ordinary objects(balls) are wholly S-dimensional objects without temporal extent. Exdurantism differs fromendurantism because the counterparts are temporal and spatial, and the ball at t1 is not the sameas the ball at t1 + dt, so it does not wholly endure. The “events” must also exdure; for example, apass of the ball(s). Since each ball is different, each event is different and exdures by having arelated counterpart. So, which ball is it that “exdures”? Allof the ballsexdure by having counterparts that existat different times. Problems arise inexdurantism when looking at how these distinct balls areconnected to each other and how they change. The term counterpart is a bit misleading because itis associated with Lewis’s “A Philsopher’s Paradise: The Plurality of Worlds” in his On thePlurality of Worlds. Summarizing Lewis, objects existing in this world have counterparts inother worlds simply by sharing a similar relation. For example, person A, a philosophy teacher,
  6. 6. Hildreth6in world W has a counterpart A’, a physics teacher, in world W’; A is similar to A’ because theyare both teachers orhumans, or because they have similar appearances, or because they sharesome other relation. In stage theory, a person or object A at t1 exdures by having a counterpartA’ at t2; they are counterparts because they share all or most of the same properties, except thetime at which they exist. However, when analyzing cause and effect relations, the analogy breaksdown and the term “counterpart” comes to mean a different thing. Suppose person A at t1 istortured. Person A’ at t2 feels pain. Suppose person A in world W is tortured. Person A’ in worldW’ does not feel pain. Why should he? He is spatiotemporally distinct. Person A’ at t2 issomehow distinct from Person A at t1, but it receives the effects of Person A. Some might objectto this analogy by claiming that people are different from objects, but the same idea could beapplied to a ball at t1 that is marked with a sharpie and a ball’ at t2 that shows the mark. How does one know if A’ is a counterpart to A? One could limit the term “counterpart”in such a way that A’ is related to A because it experiences all of its effects, but consider thefollowing scenario. Person A and Person B are both punched at t1. Person C and Person D bothfeel pain at t2. Since both Person C and Person D feel the effect of a punch, which one is thecounterpart to Person A? Lewis’s worlds allow a person A in W to have multiple counterparts A’and A’’ in W’ without an issue. An object having multiple temporal counterparts, however,creates problems for how something persists. It would be absurd to say that Person A survivesthrough both Person C and Person D, because if Person C and Person D have different, say,physical properties, there is a contradiction in saying that Person A survives by having Person Cand Person D counterparts both at t2. Believing Person A survives through two people Person Cand Person D may be plausible in terms of brain splitting (Parfit), but it should not occur becausetwo separate people happen to have experiences with identical effects; in this case, Person A
  7. 7. Hildreth7does not split into two, its counterpart becomes indistinguishable with the counterpart of aseparate entity. Perhaps the term “counterpart” is further limited such that A and A’ are counterpartsbecause A’ feels the effects of A, and A’ shares most of the same properties with A. In this case,suppose Person A and Person B from the example above are identical twins. The same problemarises. What makes A and A’ similar enough to be related? One could keep limiting theconditions to avoid the problem (A and A’ share most of the same space, A and A’ are closeenough in time), but the more these limitations are imposed, the more the theory approachesendurantism until finally, A and A’ relate to each other in exactly the same way that A at t1relates to A at t2 in endurantism. I will dismiss exdurantism as a persistencetheory in light of thisproblem, and not examine its possible combinations with the theories of time.Persistence Theories Combined with Time Theories Does the concept of persistence itself imply a certain passage of time? Once thepersistence theories were introduced, there was a need to establish the dimensionalism of objectsand events. In fact, Haslanger’s language in her distinction between the two theories withtemporal parts seems to connect to a distinction in the concept of time: her space-time worms aretemporally extended composites, and so concern a static interval of time. It would appear in thisway that perdurantism (worm theory) implies an acceptance of eternalism. However, sheelaborates later on her view of the compatibility of worm theory and stage theory with boththeories of time when she considers various combinations of presentism, eternalism,endurantism, perdurantism, and exdurantism: the more interesting combinations which should bescrutinized are presentistperdurantismand eternalistendurantism.PresentistPedurantism
  8. 8. Hildreth8 Presentistperdurantism and presentistexdurantism rely, according to Haslanger, onwhether or not the presentist view can accept temporal parts. In making perdurantism compatiblewith presentism, she argues: “a presentist could say that a persisting candle consists of thepresent candle-stage and those stages of it that already were and those that will be” (p.325).Presentistperdurantism says only the present stage exists, but the object is a composite ofpast and future stages, which is how it persists by perduring. Unfortunately, it becomes clear that if past and future stages don’t exist, the composite ofan S-T-dimensional object or event is not whole. Merricks uses this idea toargue that presentismrules out perdurantism: If presentism is true, then those parts of an objectwhich do not exist at the present time do not exist at all. So if presentism is true, a perduring object has some parts—the vast majority of its parts, in fact—which do not exist…We can, therefore, conclude that if presentism is true, there are no perduring objects (p. 525).While this quote refers to “objects,” he also shows that it applies to events, as well. Thisargument makes sense, since events fill the same dimensions as objects in both perdurantism andendurantism. A mathematical interpretation of Merrick’s argument is: in integrating an S-dimensional, partially existing thing over its temporal dimensions, the integral is equivalent to anintegralonly over that one moment in time, since all times (and those parts of the thing at thosetimes) before and after do not exist, so there is no “volume” to sum up at those times. The resultis the same S-dimensional slice of a partially existing thing and not the whole thing, because thewhole thing has S + T dimensions. Presentism, then, rules out perdurantism because all there isof a thing is an infinitesimal fraction. If perdurantism is not consistent with presentism, it shouldbe consistent with eternalism, since that is the opposite of presentism. Note that Merricks argues
  9. 9. Hildreth9that presentism rules out a persistence theory but does not directly entail the other; presentismonly entails endurantism because it rules out its opposite, S-T dimensionalist theory. It is not,then, the qualities of presentism that lead to a persistence theory but rather the requirement oftemporal extent in perdurantism that leads to eternalism. Expanding upon Merrick’s argument, one could say that in order for a combination of atemporal theory and a persistence theory to work, one must get 100% (one whole) of that thing;not less, and not more. Applying his process to a spatially dimensionless soul that extends overtime (T-dimensional), it’s less obvious that the result is only a fraction of the thing, because interms of space, it would seem that the sum of zero is still zero, and so the result would be thewhole, zero-dimensional object. However, the point or soul extends over time and in fact has atleast one dimension- S is equal to zero, so it has T dimensions. The integral in presentism timeyields something that only partially exists and has no temporal dimension, as the integral againwould be over the time interval from t1 to t1.The result of this summation, like that of thephysical, S-dimensional filling object, gives one less dimension than perdurantism claims thesoul actually has, so there is a contradiction, and presentism is again not compatible withperdurantism in the realm of extensionless points or souls spread out in time. The samecontradiction arises for things that fill some of the space dimensions but not all, like a 2-Dprojected image or shadow in a 3-D spatial and 1-D temporal world; the integral will yield onlythe 2-D shadow and not the 2-D spatial plus 1-D temporal shadow.So, for objects with at leastone temporal dimension, presentism rules out perduratism becauseperdurantism requires theextended temporal extent available in eternalism. Zero-demensional things in perdurantism referto instantaneous points that do not survive a time interval and have no temporal extent, so it is
  10. 10. Hildreth10not worth trying to figure out if presentism and perdurantism are compatible in this context, sincethere is no persistence. Haslangerargues against Merrick’s idea that an object can’t be composed of non-existentparts by claiming the presentist should be able to account for claims such as “my maternalgrandmother is part of my family even though she does not (presently) exist” by accounting forcross-temporal relations. There are many possible ways to interpret this statement. One couldattack the meaning of “part of” in this sentence1. Is a grandmother part of a family the way anarm is part of a body?1She certainly isn’t physically attached to the family, and a person whosays that she is physically a part of the composition that makes up the family must commit to aview of unrestricted composition, as the arrangement of family members does not change thestatus of the family. Is a grandmother part of a family the way a temporal part is part of aperduring object?1If she is, this again implies that the family is composed of a bunch of parts, butthe progression of temporal parts does seem to matter in creating the 4-D worm, while again, thearrangement of family matters should not matter. In these examples, there seems to be differentmeanings of “part of”; one can interpret it such that A is a part of B if A is a smaller part of Band continuously connected to its other physical parts, or one can interpret it such that A is a partof B if A helps to define what is meant by B. Since “part of” can have multiple interpretations, itis unfair to claim that the presentist must account for statements like the grandmother statement. Suppose the meaning of “part of” is broadened such that A is a part of B if A is anecessary component in describing B.In terms of ordinary, physical objects, one could interpret“grandmother” as a physical, human body and “family” as a collection of bodies, but this wouldmean that the “grandmother” does in fact exist with the property of being dead. Using thisinterpretation, it would be unfair to say that the presentist should be able to account for this
  11. 11. Hildreth11statement because it is contradictory; the grandmother exists, “even though she does not(presently) exist.” In another interpretation using physical objects, “grandmother” is a physical,human body that does not presently exist because it was smushed, invoking Gibbard’s statue andclay problem in the form of grandmother and human flesh. Using this interpretation, it would beunfair to require presentists to accept this statement, because it is asking them to accept co-location. Both of these interpretations are also unfair because it forces the presentist to accept thestatement by thinking of a “family” as an ordinary, physical object when most people do notthink of “family” this way1. The interpretation that’s left is in terms of spatially absent souls: “grandmother” meansthe soul that once lived inside the grandmother’s body and “family” as a collection of souls.Using this interpretation, Haslanger claims that the collection of souls that presently exist in thefamily includes a soul that does not presently exist.It is unfair to require presentists to accountfor the statement in light of this interpretation because it requires them to accept the existence ofsouls.While Haslanger defends presentistperdurantism by claiming a presentist should be able toaccount for statements like “my maternal grandmother is part of my family even though she doesnot (presently) exist”, it seemsthis requirement of presentists is not fair in all possibleinterprations of “grandmother” and “family.”EternalistEndurantism In exploring the eternalistendurantist combination,Haslanger considers thispossibility: “past, present, and future objects all exist; ordinary objects persist by enduring” (p.324). One objection to the entire idea of eternalistendurantism is denying that an object can exist100% at one time and also exist 100% at another. If something exists in more than one place, ithas spatial parts, so if something exists in more than one time, it has temporal parts. If one were
  12. 12. Hildreth12to view the whole, eternalist time, the summation of all of these times produces more than thewhole existence of the thing, whether it is an object, event, shadow, or dimensionless soul. Thesupporter of eternalistendurantism would point out, however, that one can imagine an objectwholly existing in more than one region of space, not by being spread out in the space, but byhaving a twin counterpart in that region1. Applying this idea to time, one can imagine the objecthaving a twin counterpart in another moment of time1. This view might sound like exdurantism,but as shown earlier, it collapses to endurantism because the two counterparts are the same exactobject; that is how the object endures. The eternalistendurantism view produces a problem of change that Haslanger points out:if an object exists at t1 and changes at t2, that object is not identical with itself because it hasincompatible properties. Merricks summarizes this contradiction well: “Given indexicalism, wecan conclude that if a single object is F at one time, and is not-F at another, then that object bothis and is not F” (526-527). The object both is and is not F because not only do t1 and t2 exist, theobject at t1 and the object at t2 exist, as well (“past, present, and future objects all exist”). Haslanger claims that one can avoid this contradiction with a relational approach totemporal qualification; using her example, she argues that the statements “The candle is bent inthe morning” and “The candle is bent in the afternoon” does not create a contradiction because ofthe qualifiers “in the morning” and “in the afternoon” (328). Haslanger admits that the biggestobjection to this relational approach involves temporary intrinsics, which claims that temporalrelations are not intrinsic properties of an object (329). In avoiding this objection, one couldinterpret that the candle in the morning is not the same as the candle in the afternoon, but thiswould not allow for endurantism, as the object endures by existing wholly in the times it exists.
  13. 13. Hildreth13 So, if one commits to eternalistendurantism, one must commit to temporal qualificationin avoiding the contradiction that comes with change and thus must accept the idea that objectshave no intrinsic properties.Summarizing another paper by Merricks, Persistence, Parts, andPresentism, if objects have no intrinsic properties, or properties simpliciter, they also cannothave parts simpliciter and instead these parts must be modified with temporal qualifiers, muchlike the properties are modified. In other words, these parts become temporal parts. If an objectwholly exists at t1, which it must for it to be an enduring object, how can it have other parts atother times? His argument goes back to the initial objection to the entire idea ofeternalistendurantism; if an object wholly exists at t1, its parts must also wholly exist at t1 andnot elsewhere. So, an enduring object must have its parts simpliciter and not parts qualified bytime. This argument is stronger than his previous argument because it attacks the temporalqualifier supporters of eternalistendurantism need to use, and in this argument, it was thepersistence theory of endurantism that led to the presentist theory on time.PresentistEndurantism and EternalistPerdurantism Knocking out presentistperdurantism and eternalistendurantism gives two theories:presentistendurantism and eternalistperdurantism. Presentistendurantism is a theory ofmovement; not only of time, but also of the object itself as it endures. One can think of a whollyexisting object as one that propagates at “the speed of time”- if the object is at rest, it willpropagate through time at c.Eternalistperdurantism is a theory of stillness; time is stagnant and sois the object, since all of its parts always exist, there is not one thing that endures through time.Rather, the object perdures in its temporal parts.Incompatibility of the Theories
  14. 14. Hildreth14 Merricks’s paper concludes that these two theories are incompatible: “a single worldcannot contain both temporally extended, perduringevents and three-dimensional, enduringobjects” (2) because either presentism or eternalism is true, and presentism rules outperdurantism and eternalism rules out endurantism. His claim reinforces the idea that eventsalways have the same dimensionality as objects and that the combinations of presentism andendurantism and then eternalism and perdurantism are compatible for entities of all possiblepersisting dimensions; from souls and extensionless points to events. While the incompatibility of the two theories in Merricks stems from the incompatibilityof the two time theories, it is also clear that they are incompatible due to the persistence ofobjects and their motion through time. Many claim that eternalists view time as analogous tospace, while presentists see time very differently from space. When contemplating the two finaltheories, it is clear that both view time as analogous to space in different respects. Theeternalistperdurantist sees time as analogous to space in terms of an object’s location orextension: a whole cube is the sum of its spatial parts extending through space and its temporalparts extending through time. The presentistendurantist sees time as analogous to space in termsof an object’s motion: once a cube moves from point A to point B, it no longer exists at point Band once a cube moves from t1 to t2, it no longer exists at t1. The Heisenberg uncertaintyprinciple states that when more is known about an object’s position, less is known about itsmotion.It is impossible to know exactly both its position and motion, so we cannot have bothpresentistendurantism and eternalistperdurantism because presentistendurantism yields exactcertainty to an object’s motion through time, while eternalistperdurantism gives exact certaintyto an object’s extent or location in time.
  15. 15. Hildreth15 Furthermore, the two theories must view “change” in two incompatible ways, asdiscussed in Merrick’s class lectures. In presentistendurantism, an object changes by gaining orlosing a property. In eternalistperdurantism, an object cannot gain or lose a property, because itexists at all times, so the whole object still has the properties. Instead, a new time-slice isobserved because that is where the arrow of time now points. Enduring objects change bygaining or losing a property; that is why there was a contradiction in eternalistendurantism.Perduring objects change by having unequal temporal parts; that is, the part at t1 may have aproperty that t2 lacks. Enduring objects move in space by gaining a position and losing anotherone. Perduring objects move in space by having two temporal parts located at different positions.Enduring objects move through time by not existing at past times, and perduring objects movethrough time simply by having temporal parts. Change and movement, as discussed in Merrick’s class lectures, mean two differentthings for enduring and perduring objects1. These two views are incompatible because anenduring object will lose a property during change, while a perduring object will always havethat property in a temporal part. An object cannot both lose a property and retain it, so an objecteither endures or perdures. Events, then, must also either endure or perdure, and since events arecollections of objects, all the objects in a single event must either endure or perdure. So, theincompatible views of change support the idea thatperduring and enduring objects, events, andother things of varying dimensionality are incompatible with those that perdure.Persistence before Time It makes sense to start off with the theories of time because they are obviouslycontradictory; the past and future cannot both exist (as in eternalism) and both not exist (as inpresentism). The persistence theories are not as obviously contradictory, and so it is more
  16. 16. Hildreth16complicated to start there. However, a change in an object is more noticeable than how timeflows, especially if it is this static, eternalist kind. In fact, most people naturally infer time bypersistence of objects and the changes those objects survive; for example, the sun movingposition or a person aging. In Stephen Hawking’s A Brief History of Time, he asks why one can remember the pastbut not the future (Hawking p.148). He then invokes the second law of thermodynamics, statingthat time increases as entropy does. Additionally, the physical act of making and storing amemory increases entropy because it releases heat, so a person remembers things in order fromleast chaotic to most chaotic. Even if events actually occurred in decreasing entropy order (hisexample is a smashed glass falling up to the table to be restored to its un-smashed state), anobserver would still remember these events in increasing entropy order (the glass falling off thetable); thus his account of persistence dictates where the arrow of time points. So, it ispersistence of things that creates the need to define an arrow of time, and how all things persistcan be uniformly described by either of the two distinct and incompatible theories ofpresentistendurantism and eternalistperdurantism. Works Cited Thank you to Jess Hrebinka and Professor Merricks for providing helpful comments on this paper1 Brought to attention in helpful comments by MerricksHaslanger, Sally 2003: “Persistence Through Time”. The Oxford Handbook of Metaphysics p. 315-354.Hawking, S. W. A Brief History of Time. New York: Bantam Books, 1992.Hawley, Katherine, "Temporal Parts", The Stanford Encyclopedia of Philosophy (Winter 2010
  17. 17. Hildreth17 Edition), Edward N. Zalta (Ed.), temporal-parts/.Lewis, David 1968: “A Philosopher’s Paradise: The Plurality of Worlds”. On the Plurality of Worlds. Rpt. in Metaphysics: An Anthology, (Second Edition),Jaegwon Kim, Daniel Z. Korman, and Endest Sosa (Eds.). Blackwell Publishing Ltd., 2012. Print.Markosian, Ned, "Time". The Stanford Encyclopedia of Philosophy (Winter 2010 Edition), Edward N. Zalta (Ed.),, Trenton 1995: “On the Incompatibility of Enduring and Perduring Entities”. Mind 104, p. 523-531. incompatibility-of-enduring-and-perduring-entities.pdf.Merricks, Trenton 1999: “Persistence, Parts, and Presentism”. Noûs 33, p. 421-438. presentism.pdf.Merricks, Trenton. Class Lecture. Philosophy 3310: Metaphysics. University of Virginia, Charlottesville, Virginia. Fall 2012.Parfit, Derek. “Personal Identity”.Rpt. In Metaphysics: An Anthology, (Second Edition), Jaegwon Kim, Daniel Z. Korman, and Endest Sosa (Eds.). Blackwell Publishing Ltd., 2012. Print."persistence." The Free On-line Dictionary of Computing. Denis Howe. 12 Nov. 2012.