Philosophy - 750 to 1000 words essay (4 Paragraphs), response to the ALL the prompts

Write an essay of about 750 to 1000 words, or 3 to 4 pages (double- spaced), in response to the ALL the prompts below (4 Paragraphs) .

The relevant texts for Essay are the assigned: * Sorensen, A Brief History of the Paradox, pp. 184- 185 on McTaggart and pp. 173-176 on Augustine’s theory of time as subjective. * David Lewis, “The Paradoxes of Time Travel”. — Do not use any other outside sources! This is not a report on what others have written about McTaggart or Lewis or time travel. This is an exercise in thinking-by-writing!

Consider our discussions of, on one hand, McTaggart’s seemingly paradoxical argument that time is “unreal” and, on the other hand, Lewis’ account of the seemingly paradoxical possibility of time travel.

Write an essay in which you explore the potential “paradoxes” of time we considered in McTaggart’s argument that “time is unreal” and in Lewis’ account of time travel as “possible” in a “strange” possible world (unlike our own). Specifically, structure your narrative in response to the following themes.

Paragraph 1: Explain the distinction between the “A series” and the “B series” of time, as McTaggart introduced these terms. Why did McTaggart think A time is more fundamental than B time? Why did he think A time is impossible?

Paragraph 2: Explain Lewis’ distinction between “external time” and “personal time”. How does Lewis’ distinction compare with McTaggart’s distinction above?

Paragraph 3: Explain how, for Lewis, time travel is possible, even if strange. What is a “person”, for Lewis? What then is “personal identity”? How would the structure of a person over time, as Lewis characterizes this form of personal identity, entail that a person could travel either forward into the future or back into the past and encounter

“himself”/”herself”/”theirself” in a past or a future time?

Paragraph 4: Briefly: Do you find time travel, per Lewis, intuitively possible? You may, if you like, consider the popular film “Back to the Future” (1986), or you may consider how our imagination in science fiction scenarios may address the possibility of time travel.

A U G U S T I N E ’S P R A G M A T I C P A R A D OX E S 173

became more alarming as philosophers became increasingly

persuaded by the negative remarks of both Reid and Mill and

less persuaded by their positive remarks: Yes, phenomenalism

did not give one basis to believe that there are other minds. Yes,

this is not a problem peculiar to phenomenalism. But no,

phenomenalism lacks the resources to justify the inference.

Common sense is equally impotent. Gosh, belief in other minds

seems like a leap of faith! It is a dogma no sane person can

forbear—but it is dogma all the same.

“Do I know that others have minds?” is an example of a

paradox that was posed and carefully answered for fifteen

hundred years prior to being revealed as a paradox. Only in

the nineteenth century did philosophers discover surprisingly

good arguments for a negative answer.

A U G U S T I N E ’ S S U B J E C T I V E T H E O R Y O F T I M E

Augustine deployed Christian dogmas to drown the skeptical

paradoxes. However, Christianity itself generates para-

doxes—at least for Christians. (The phenomenon is general;

introducing almost any apparatus to resolve paradoxes makes

that tool the subject of other paradoxes.)

To oppose the Manichees, Augustine had to portray God

as all-powerful. This generates the problem of evil. If God

knows that there is evil and is able to stop it, then how could

he be all-good if he refrains?

Augustine offers two inharmonious answers. His Neopla-

tonic answer is that, strictly speaking, evil does not exist.

What is real is good. What we call evil (blindness, poverty,

hopelessness) is the absence of certain things. There are degrees of reality; evil is a tear in being.

174 A B R I E F H I S T O R Y O F T H E P A R A D O X

Augustine’s more classically Christian solution is that

human beings are responsible for evil because of their own

freewill. God cedes people control that they frequently abuse.

This freedom does not mean that God is surprised by our

misbehavior. Since God is all-knowing, there was never a

time at which he failed to know that Eve would tempt Adam

to eat an apple from the forbidden Tree of Knowledge. There

was never a time when God did not know the whole course

of human depravity. So why did God make creatures he knew

would disappoint him?

Shipwrights made boats they knew to be vulnerable to

fire. Timber has this engineering limit. Could God be

resigned to limits imposed by raw matter itself?

Not according to Augustine. Deferring to Genesis, he

denies that God made anything from material that predated

his activities as creator. God created the whole world from

nothing. In The Timaeus, Plato allowed that the demiurge began the universe in the sense of organizing a preexisting

state of chaos. But everyone in antiquity agreed that the

universe could not have had a beginning.

The Manichees teased Christians by asking what God

was doing before he created the universe. If God waited, then

he was an idler. And an arbitrary idler at that; there would

be no justification for starting the creation at one point of time

rather than another.

Augustine answers that God created time when he cre-

ated everything else. By this, he does not mean that time

depends on the existence of periodic public phenomena such

as the movement of planets. We can make sense of there

being no physical events occurring. For instance, we can perceive a long silence. What is inconceivable is for time to

pass in the absence of mental change.

A U G U S T I N E ’S P R A G M A T I C P A R A D OX E S 175

Augustine warns that if we think of time as a mind-

independent phenomenon, we fall into a paradox of mea-

surement. The objective present is a boundary between the

past and the future. If that boundary has duration, we can

divide the present’s earlier stage into the past and its later

stage into the future. But what was the case cannot be what is now the case. And what will be the case cannot now be the case. Thus, the objective present must be a durationless

instant. Since the past no longer exists and the future is yet

to exist, things are available only for an instant—according

to the objective mode. But wait! To measure the length of

a spoken sentence, one must hear the beginning of the

sentence and its end. All utterances take longer than an

instant. Therefore, it is impossible to measure the length of

an utterance—or of anything else!

Augustine dismisses this result as absurd. He traces our

false step to the attempt to model measurement in terms of

the objective present. Measurement requires a subjective present—what early-twentieth-century psychologists

called “the specious present.” Some measured its duration

as six seconds, others measured it as twelve seconds. When

a doorbell goes ding-dong you hear the ding and the dong

as a single pattern. Similarly, short melodies and sentences

can be taken in as a single chunk. When the sounds become

too long, you must rely on memory rather than perception.

According to the subjective account of time pioneered by

Augustine, the past corresponds to what we remember, the

present to what we perceive, and the future to what we

anticipate. We can measure intervals in the specious present

because it does have a duration.

Since observers vary in their span of perception, the

meaning of “present” is relative to an observer. Since the

176 A B R I E F H I S T O R Y O F T H E P A R A D O X

human perceptual span is less than a minute, the present is

less than a minute. Much is in the past. Much is in the future.

God has an unlimited perceptual span. Everything is in

the present for him. He grasps the entire history of the

universe in one panoramic glimpse. If we relativize “past” to

God, there is no past. Hence, God cannot literally have waited

to create the world. If we relativize “future” to God, then

there is no future. Hence, God cannot literally have fore- knowledge of Adam and Eve’s wicked decisions. God is

omniscient in virtue of what he perceives, not in virtue of

what he predicts.

We naturally tend to relativize our temporal vocabulary

to a human perspective. This is fine for understanding

ordinary affairs. But if we hope to solve theological paradoxes,

we must scale up to the mind-boggling terrain of eternity.

Augustine agrees this stretch may be too far for a human

being to achieve on his own. But if you put your hand out, the

Lord might take hold and guide you to a vision of eternity.

184 A B R I E F H I S T O R Y O F T H E P A R A D O X

God can help a woman retain her virginity but cannot restore

her virginity. Thus, God’s power is conditioned by time.

Thomists work hard to find consistent interpretations of

Aquinas’s remarks. But I suspect that he is caught by an

underlying schizophrenia in the language of time. This

double nature has been exposed bit by bit since the middle

ages. It was first fully exhibited by a British philosopher

writing seven hundred years after Aquinas.

F L O W I N G T I M E V E R S U S S T A T I C T I M E

Generally, children abandon philosophical questions after

failing to make any progress in answering them. There are a

few exceptions. Like Aquinas, John McTaggart (1866-1925)

was a precociously abstruse boy, shambling about in a cloud

of ruminations about the Almighty. Unlike Aquinas, McTag-

gart became a boy atheist. This caused consternation until

McTaggart’s schoolmates decided he was deranged.

Surprisingly, McTaggart combined his atheism with a

belief in immortality. This conviction was based on mystical

experiences. McTaggart devoted his philosophical career to

devising arguments that would yield the conclusions he took

to have been independently revealed to him.

In 1908, he published “The Unreality of Time.” McTag-

gart points out that our words for time divide into two series.

What he calls the A series is comprised of past, present, and future. McTaggart’s B series is comprised of earlier, simulta- neous, later. He notes that the A series suggests a flow of time whereas the B series is static. What is in the future becomes

present and then becomes past. The A series guides our

emotions. After giving birth, a new mother exclaims “Thank

A Q U I N A S : C A N G O D H A V E A B I O G R A P H Y ? 185

goodness that is over!” She is pleased that her labor is in the

past, not that her labor precedes a particular date. The A series

also guides our actions. Knowing that the baby is scheduled

to be fed at noon leads to action only when coupled with the

belief that it is now noon. McTaggart believes that the A series (past, present,

future) is more fundamental than the B series (earlier, simul- taneous, later). He defines “x is earlier than y” as “Either x is past when y is present, or x is present when y is future.” He then argues that the A series (and therefore the B series) is

subjective. McTaggart agrees with Augustine that the para-

dox of measurement refutes the objectivity of time. But he

thinks Augustine’s equation of past-present-future with the psychological series memory-perception-anticipation makes time viciously subjective. Time cannot vary from mind to mind. If your perceptual span increases from childhood, there

is no corresponding change in the duration of the present. If

there is time, there must be a single perspective from which

all temporal statements can be harmonized. Since there is no

such perspective, time is an illusion.

McTaggart offers a battery of intriguing arguments for

the unreality of time. What binds them together is their

exploitation of tensions between the A series and B series.

Metaphysicians credit McTaggart for specifying the concep-

tual origin of a whole family of temporal paradoxes. In

retrospect many earlier metaphysicians can be seen as

responding to the disharmonies between the A and B series.

Aquinas generally writes in a way that makes the B series

more fundamental than the A series. Most twentieth-century

thinkers share Aquinas’s preference for the B series. They

define the A series in terms of the B series—with the help of

the demonstrative term “this.” Under one scheme “now”

186 A B R I E F H I S T O R Y O F T H E P A R A D O X

means simultaneous with this utterance, “past” means earlier

than this utterance, and “future” means later than this

utterance. Given facts about the speed of light and sound, it

is natural for human beings to organize time in a past-

present-future series. Think of how navigational concerns led

us to develop the longitude-latitude system. This imaginary

grid organizes complicated geographical facts. The relation-

ships between the equator and the prime meridian can be

studied in a precise mathematical way, just like the “logic of

time” implicit in the A series. But the system is a useful fiction

rather than an x-ray of reality.

The Pythagoreans took amenability to mathematical

analysis to be the mark of truth. McTaggart takes the

precision of calendars and stop watches to be a sign of a

fabricated order. The order we “discover” is the order of a

notational scheme that we project onto the world.

This conventionalism already had deep roots in

Aquinas’s era. The medieval nominalists rejected Plato’s

realm of universals and analyzed words as having no more

behind them than custom. They believed we frequently

misconstrue the hand of man as the hand of God. As we shall

see in the next chapter, accusations of this kind of mistake

easily escalate into charges of blasphemy and heresy.

From American Philosophical Quarterly, April 1976, pp. 145-152. © 1976 by North American Philosophical Publications. Re- printed by permission.

THE PARADOXES OF TIME TRAVEL David Lewis

TIME travel, I maintain, is possible. The paradoxes oftime travel are oddities, not impossibilities. They prove only this much, which few would have doubted: that a possible world where time travel took place would be a most strange world, different in fundamental ways from the world we think is ours.

I shall be concerned here with the sort of time travel that is recounted in science fiction. Not all science fiction writers are clear-headed, to be sure, and inconsistent time travel stories have often been written. But some writers have thought the problems through with great care, and their stories are perfectly consistent.1

If I can defend the consistency of some science fiction stories of time travel, then I suppose parallel defenses might be given of some controversial physical hypothe- ses, such as the hypothesis that time is circular or the hypothesis that there are particles that travel faster than light. But I shall not explore these parallels here.

What is time travel? Inevitably, it involves a discrep- ancy between time and time. Any traveler departs and then arrives at his destination; the time elapsed from de- parture to arrival (positive, or perhaps zero) is the du- ration of the journey. But if he is a time traveler, the separation in time between departure and arrival does not equal the duration of his journey. He departs; he trav- els for an hour, let us say; then he arrives. The time he reaches is not the time one hour after his departure. It is later, if he has traveled toward the future; earlier, if he has traveled toward the past. If he has traveled far to- ward the past, it is earlier even than his departure. How can it be that the same two events, his departure and his arrival, are separated by two unequal amounts of time?

It is tempting to reply that there must be two inde- pendent time dimensions; that for time travel to be pos- sible, time must be not a line but a plane.2 Then a pair

of events may have two unequal separations if they are separated more in one of the time dimensions than in the other. The lives of common people occupy straight diagonal lines across the plane of time, sloping at a rate of exactly one hour of time1 per hour of time2. The life of the time traveler occupies a bent path, of varying slope.

On closer inspection, however, this account seems not to give us time travel as we know it from the stories. When the traveler revisits the days of his childhood, will his playmates be there to meet him? No; he has not reached the part of the plane of time where they are. He is no longer separated from them along one of the two dimensions of time, but he is still separated from them along the other. I do not say that two-dimensional time is impossible, or that there is no way to square it with the usual conception of what time travel would be like. Nevertheless I shall say no more about two-dimensional time. Let us set it aside, and see how time travel is pos- sible even in one-dimensional time.

The world—the time traveler ’s world, or ours—is a four-dimensional manifold of events. Time is one dimen- sion of the four, like the spatial dimensions except that the prevailing laws of nature discriminate between time and the others—or rather, perhaps, between various timelike dimensions and various spacelike dimensions. (Time remains one-dimensional, since no two timelike dimensions are orthogonal.) Enduring things are timelike streaks: wholes composed of temporal parts, or stages, located at various times and places. Change is qualitative difference between different stages—different temporal parts—of some enduring thing, just as a “change” in scenery from east to west is a qualitative difference be- tween the eastern and western spatial parts of the land- scape. If this paper should change your mind about the

possibility of time travel, there will be a difference of opinion between two different temporal parts of you, the stage that started reading and the subsequent stage that finishes.

If change is qualitative difference between temporal parts of something, then what doesn’t have temporal parts can’t change. For instance, numbers can’t change; nor can the events of any moment of time, since they cannot be subdivided into dissimilar temporal parts. (We have set aside the case of two-dimensional time, and hence the possibility that an event might be momentary along one time dimension but divisible along the other.) It is essential to distinguish change from “Cambridge change,” which can befall anything. Even a number can “change” from being to not being the rate of exchange between pounds and dollars. Even a momentary event can “change” from being a year ago to being a year and a day ago, or from being forgotten to being remembered. But these are not genuine changes. Not just any old re- versal in truth value of a time-sensitive sentence about something makes a change in the thing itself.

A time traveler, like anyone else, is a streak through the manifold of space-time, a whole composed of stages located at various times and places. But he is not a streak like other streaks. If he travels toward the past he is a zig-zag streak, doubling back on himself. If he travels toward the future, he is a stretched-out streak. And if he travels either way instantaneously, so that there are no intermediate stages between the stage that departs and the stage that arrives and his journey has zero duration, then he is a broken streak.

I asked how it could be that the same two events were separated by two unequal amounts of time, and I set aside the reply that time might have two independent dimensions. Instead I reply by distinguishing time itself, external time as I shall also call it, from the personal time of a particular time traveler: roughly, that which is meas- ured by his wristwatch. His journey takes an hour of his personal time, let us say; his wristwatch reads an hour later at arrival than at departure. But the arrival is more than an hour after the departure in external time, if he travels toward the future; or the arrival is before the de- parture in external time (or less than an hour after), if he travels toward the past.

That is only rough. I do not wish to define personal time operationally, making wristwatches infallible by definition. That which is measured by my own wrist- watch often disagrees with external time, yet I am no time traveler; what my misregulated wristwatch meas- ures is neither time itself nor my personal time. Instead of an operational definition, we need a functional defi- nition of personal time; it is that which occupies a certain role in the pattern of events that comprise the time trav- eler ’s life. If you take the stages of a common person, they manifest certain regularities with respect to external time. Properties change continuously as you go along, for the most part, and in familiar ways. First come in-

fantile stages. Last come senile ones. Memories accumu- late. Food digests. Hair grows. Wristwatch hands move. If you take the stages of a time traveler instead, they do not manifest the common regularities with respect to ex- ternal time. But there is one way to assign coordinates to the time traveler ’s stages, and one way only (apart from the arbitrary choice of a zero point), so that the regularities that hold with respect to this assignment match those that commonly hold with respect to external time. With respect to the correct assignment properties change continuously as you go along, for the most part, and in familiar ways. First come infantile stages. Last come senile ones. Memories accumulate. Food digests. Hair grows. Wristwatch hands move. The assignment of coordinates that yields this match is the time traveler ’s personal time. It isn’t really time, but it plays the role in his life that time plays in the life of a common person. It’s enough like time so that we can—with due caution— transplant our temporal vocabulary to it in discussing his affairs. We can say without contradiction, as the time traveler prepares to set out, “Soon he will be in the past.” We mean that a stage of him is slightly later in his per- sonal time, but much earlier in external time, than the stage of him that is present as we say the sentence.

We may assign locations in the time traveler ’s per- sonal time not only to his stages themselves but also to the events that go on around him. Soon Caesar will die, long ago; that is, a stage slightly later in the time trav- eler ’s personal time than his present stage, but long ago in external time, is simultaneous with Caesar ’s death. We could even extend the assignment of personal time to events that are not part of the time traveler ’s life, and not simultaneous with any of his stages. If his funeral in ancient Egypt is separated from his death by three days of external time and his death is separated from his birth by three score years and ten of his personal time, then we may add the two intervals and say that his funeral follows his birth by three score years and ten and three days of extended personal time. Likewise a bystander might truly say, three years after the last departure of another famous time traveler, that “he may even now—if I may use the phrase—be wandering on some plesiosau- rus-haunted oolitic coral reef, or beside the lonely saline seas of the Triassic Age.”3 If the time traveler does wan- der on an oolitic coral reef three years after his departure in his personal time, then it is no mistake to say with respect to his extended personal time that the wandering is taking place “even now”.

We may liken intervals of external time to distances as the crow flies, and intervals of personal time to dis- tances along a winding path. The time traveler ’s life is like a mountain railway. The place two miles due east of here may also be nine miles down the line, in the westbound direction. Clearly we are not dealing here with two independent dimensions. Just as distance along the railway is not a fourth spatial dimension, so a time traveler ’s personal time is not a second dimension of

time. How far down the line some place is depends on its location in three-dimensional space, and likewise the locations of events in personal time depend on their lo- cations in one-dimensional external time.

Five miles down the line from here is a place where the line goes under a trestle; two miles further is a place where the line goes over a trestle; these places are one and the same. The trestle by which the line crosses over itself has two different locations along the line, five miles down from here and also seven. In the same way, an event in a time traveler ’s life may have more than one location in his personal time. If he doubles back toward the past, but not too far, he may be able to talk to himself. The conversation involves two of his stages, separated in his personal time but simultaneous in external time. The location of the conversation in personal time should be the location of the stage involved in it. But there are two such stages; to share the locations of both, the con- versation must be assigned two different locations in per- sonal time.

The more we extend the assignment of personal time outwards from the time traveler ’s stages to the surround- ing events, the more will such events acquire multiple locations. It may happen also, as we have already seen, that events that are not simultaneous in external time will be assigned the same location in personal time—or rather, that at least one of the locations of one will be the same as at least one of the locations of the other. So extension must not be carried too far, lest the location of events in extended personal time lose its utility as a means of keeping track of their roles in the time trav- eler ’s history.

A time traveler who talks to himself, on the telephone perhaps, looks for all the world like two different people talking to each other. It isn’t quite right to say that the whole of him is in two places at once, since neither of the two stages involved in the conversation is the whole of him, or even the whole of the part of him that is located at the (external) time of the conversation. What’s true is that he, unlike the rest of us, has two different complete stages located at the same time at different places. What reason have I, then, to regard him as one person and not two? What unites his stages, including the simultaneous ones, into a single person? The problem of personal identity is especially acute if he is the sort of time traveler whose journeys are instantaneous, a broken streak consisting of several unconnected segments. Then the natural way to re- gard him as more than one person is to take each segment as a different person. No one of them is a time traveler, and the peculiarity of the situation comes to this: all but one of these several people vanish into thin air, all but an- other one appear out of thin air, and there are remarkable resemblances between one at his appearance and another at his vanishing. Why isn’t that at least as good a descrip- tion as the one I gave, on which the several segments are all parts of one time traveler?

I answer that what unites the stages (or segments) of a time traveler is the same sort of mental, or mostly men- tal, continuity and connectedness that unites anyone else. The only difference is that whereas a common person is connected and continuous with respect to external time, the time traveler is connected and continuous only with respect to his own personal time. Taking the stages in order, mental (and bodily) change is mostly gradual rather than sudden, and at no point is there sudden change in too many different respects all at once. (We can include position in external time among the respects we keep track of, if we like. It may change discontinu- ously with respect to personal time if not too much else changes discontinuously along with it.) Moreover, there is not too much change altogether. Plenty of traits and traces last a lifetime. Finally, the connectedness and the continuity are not accidental. They are explicable; and further, they are explained by the fact that the properties of each stage depend causally on those of the stages just before in personal time, the dependence being such as tends to keep things the same.4

To see the purpose of my final requirement of causal continuity, let us see how it excludes a case of counterfeit time travel. Fred was created out of thin air, as if in the midst of life; he lived a while, then died. He was created by a demon, and the demon had chosen at random what Fred was to be like at the moment of his creation. Much later someone else, Sam, came to resemble Fred as he was when first created. At the very moment when the resemblance became perfect, the demon destroyed Sam. Fred and Sam together are very much like a single per- son: a time traveler whose personal time starts at Sam’s birth, goes on to Sam’s destruction and Fred’s creation, and goes on from there to Fred’s death. Taken in this order, the stages of Fred-cum-Sam have the proper con- nectedness and continuity. But they lack causal continu- ity, so Fred-cum-Sam is not one person and not a time traveler. Perhaps it was pure coincidence that Fred at his creation and Sam at his destruction were exactly alike; then the connectedness and continuity of Fred-cum-Sam across the crucial point are accidental. Perhaps instead the demon remembered what Fred was like, guided Sam toward perfect resemblance, watched his progress, and destroyed him at the right moment. Then the connect- edness and continuity of Fred-cum-Sam has a causal ex- planation, but of the wrong sort. Either way, Fred’s first stages do not depend causally for their properties on Sam’s last stages. So the case of Fred and Sam is rightly disqualified as a case of personal identity and as a case of time travel.

We might expect that when a time traveler visits the past there will be reversals of causation. You may punch his face before he leaves, causing his eye to blacken cen- turies ago. Indeed, travel into the past necessarily in- volves reversed causation. For time travel requires personal identity—he who arrives must be the same per- son who departed. That requires causal continuity, in

which causation runs from earlier to later stages in the order of personal time. But the orders of personal and external time disagree at some point, and there we have causation that runs from later to earlier stages in the or- der of external time. Elsewhere I have given an analysis of causation in terms of chains of counterfactual depend- ence, and I took care that my analysis would not rule out casual reversal a priori.5 I think I can argue (but not here) that under my analysis the direction of counterfac- tual dependence and causation is governed by the direc- tion of other de facto asymmetries of time. If so, then reversed causation and time travel are not excluded al- together, but can occur only where there are local excep- tions to these asymmetries. As I said at the outset, the time traveler ’s world would be a most strange one.

Stranger still, if there are local—but only local—causal reversals, then there may also be causal loops: closed causal chains in which some of the causal links are nor- mal in direction and others are reversed. (Perhaps there must be loops if there is reversal: I am not sure.) Each event on the loop has a causal explanation, being caused by events elsewhere on the loop. That is not to say that the loop as a whole is caused or explicable. It may not be. Its inexplicability is especially remarkable if it is made up of the sort of causal processes that transmit information. Recall the time traveler who talked to him- self. He talked to himself about time travel, and in the course of the conversation his older self told his younger self how to build a time machine. That information was available in no other way. His older self knew how be- cause his younger self had been told and the information had been preserved by the causal processes that consti- tute recording, storage, and retrieval of memory traces. His younger self knew, after the conversation, because his older self had known and the information had been preserved by the causal processes that constitute telling. But where did the information come from in the first place? Why did the whole affair happen? There is simply no answer. The parts of the loop are explicable, the whole of it is not. Strange! But not impossible, and not too dif- ferent from inexplicabilities we are already inured to. Al- most everyone agrees that God, or the Big Bang, or the entire infinite past of the universe, or the decay of a trit- ium atom, is uncaused and inexplicable. Then if these are possible, why not also the inexplicable causal loops that arise in the time travel?

I have committed a circularity in order not to talk about too much at once, and this is a good place to set it right. In explaining personal time, I presupposed that we were entitled to regard certain stages as comprising a single person. Then in explaining what united the stages into a single person, I presupposed that we were given a personal time order for them. The proper way to proceed is to define personhood and personal time simultaneously, as follows. Suppose given a pair of an aggregate of persona-stages, regarded as a candidate for personhood, and an assignment of coordinates to those

stages, regarded as a candidate for his personal time. If the stages satisfy the conditions given in my circular ex- planation with respect to the assignment of coordinates, then both candidates succeed: the stages do comprise a person and the assignment is his personal time.

I have argued so far that what goes on in a time travel story may be a possible pattern of events in four-dimen- sional space-time with no extra time dimension; that it may be correct to regard the scattered stages of the al- leged time traveler as comprising a single person; and that we may legitimately assign to those stages and their surroundings a personal time order that disagrees some- times with their order in external time. Some might con- cede all this, but protest that the impossibility of time travel is revealed after all when we ask not what the time traveler does, but what he could do. Could a time traveler change the past? It seems not: the events of a past moment could no more change than numbers could. Yet it seems that he would be as able as anyone to do things that would change the past if he did them. If a time traveler visiting the past both could and couldn’t do something that would change it, then there cannot possibly be such a time traveler.

Consider Tim. He detests his grandfather, whose suc- cess in the munitions trade built the family fortune that paid for Tim’s time machine. Tim would like nothing so much as to kill Grandfather, but alas he is too late. Grandfather died in his bed in 1957, while Tim was a young boy. But when Tim has built his time machine and traveled to 1920, suddenly he realizes that he is not too late after all. He buys a rifle; he spends long hours in target practice; he shadows Grandfather to learn the route of his daily walk to the munitions works; he rents a room along the route; and there he lurks, one winter day in 1921, rifle loaded, hate in his heart, as Grandfather walks closer, closer,. . . .

Tim can kill Grandfather. He has what it takes. Con- ditions are perfect in every way: the best rifle money could buy, Grandfather an easy target only twenty yards away, not a breeze, door securely locked against intrud- ers. Tim a good shot to begin with and now at the peak of training, and so on. What’s to stop him? The forces of logic will not stay his hand! No powerful chaperone stands by to defend the past from interference. (To imag- ine such a chaperone, as some authors do, is a boring evasion, not needed to make Tim’s story consistent.) In short, Tim is as much able to kill Grandfather as anyone ever is to kill anyone. Suppose that down the street an- other sniper, Tom, lurks waiting for another victim, Grandfather ’s partner. Tom is not a time traveler, but oth- erwise he is just like Tim: same make of rifle, same mur- derous intent, same everything. We can even suppose that Tom, like Tim, believes himself to be a time traveler. Someone has gone to a lot of trouble to deceive Tom into thinking so. There’s no doubt that Tom can kill his vic- tim; and Tim has everything going for him that Tom

does. By any ordinary standards of ability, Tim can kill Grandfather.

Tim cannot kill Grandfather. Grandfather lived, so to kill him would be to change the past. But the events of a past moment are not subdivisible into temporal parts and there- fore cannot change. Either the events of 1921 timelessly do include Tim’s killing of Grandfather, or else they timelessly don’t. We may be tempted to speak of the “original” 1921 that lies in Tim’s personal past, many years before his birth, in which Grandfather lived; and of the “new” 1921 in which Tim now finds himself wait- ing in ambush to kill Grandfather. But if we do speak so, we merely confer two names on one thing. The events of 1921 are doubly located in Tim’s (extended) personal time, like the trestle on the railway, but the “original” 1921 and the “new” 1921 are one and the same. If Tim did not kill Grandfather in the “original” 1921, then if he does kill Grandfather in the “new” 1921, he must both kill and not kill Grandfather in 1921—in the one and only 1921, which is both the “new” and the “original” 1921. It is logically impossible that Tim should change the past by killing Grandfather in 1921. So Tim cannot kill Grandfather.

Not that past moments are special; no more can any- one change the present or the future. Present and future momentary events no more have temporal parts than past ones do. You cannot change a present or future event from what it was originally to what it is after you change it. What you can do is to change the present or the future from the unactualized way they would have been without some action of yours to the way they ac- tually are. But that is not an actual change: not a differ- ence between two successive actualities. And Tim can certainly do as much; he changes the past from the un- actualized way it would have been without him to the one and only way it actually is. To “change” the past in this way, Tim need not do anything momentous; it is enough just to be there, however unobtrusively.

You know, of course, roughly how the story of Tim must go on if it is to be consistent: he somehow fails. Since Tim didn’t kill Grandfather in the “original” 1921, consistency demands that neither does he kill Grandfa- ther in the “new” 1921. Why not? For some common- place reason. Perhaps some noise distracts him at the last moment, perhaps he misses despite all his target practice, perhaps his nerve fails, perhaps he even feels a pang of unaccustomed mercy. His failure by no means proves that he was not really able to kill Grandfather. We often try and fail to do what we are able to do. Success at some tasks requires not only ability but also luck, and lack of luck is not a temporary lack of ability. Suppose our other sniper, Tom, fails to kill Grandfather ’s partner for the same reason, whatever it is, that Tim fails to kill Grandfather. It does not follow that Tom was unable to. No more does it follow in Tim’s case that he was unable to do what he did not succeed in doing.

We have this seeming contradiction: “Tim doesn’t, but can, because he has what it takes” versus “Tim doesn’t, and

can’t, because it’s logically impossible to change the past.” I reply that there is no contradiction. Both conclusions are true, and for the reasons given. They are compatible be- cause “can” is equivocal.

To say that something can happen means that its hap- pening is compossible with certain facts. Which facts? That is determined, but sometimes not determined well enough, by context. An ape can’t speak a human lan- guage—say, Finnish—but I can. Facts about the anatomy and operation of the ape’s larynx and nervous system are not compossible with his speaking Finnish. The cor- responding facts about my larynx and nervous system are compossible with my speaking Finnish. But don’t take me along to Helsinki as your interpreter: I can’t speak Finnish. My speaking Finnish is compossible with the facts considered so far, but not with further facts about my lack of training. What I can do, relative to one set of facts, I cannot do, relative to another, more inclu- sive, set. Whenever the context leaves it open which facts are to count as relevant, it is possible to equivocate about whether I can speak Finnish. It is likewise possible to equivocate about whether it is possible for me to speak Finnish, or whether I am able to, or whether I have the ability or capacity or power or potentiality to. Our many words for much the same thing are little help since they do not seem to correspond to different fixed delineations of the relevant facts.

Tim’s killing Grandfather that day in 1921 is compos- sible with a fairly rich set of facts: the facts about his rifle, his skill and training, the unobstructed line of fire, the locked door and the absence of any chaperone to defend the past, and so on. Indeed it is compossible with all the facts of the sorts we would ordinarily count as relevant is saying what someone can do. It is compossi- ble with all the facts corresponding to those we deem relevant in Tom’s case. Relative to these facts, Tim can kill Grandfather. But his killing Grandfather is not com- possible with another, more inclusive set of facts. There is the simple fact that Grandfather was not killed. Also there are various other facts about Grandfather ’s doings after 1921 and their effects: Grandfather begat Father in 1922 and Father begat Tim in 1949. Relative to these facts, Tim cannot kill Grandfather. He can and he can’t, but under different delineations of the relevant facts. You can reasonably choose the narrower delineation, and say that he can; or the wider delineation, and say that he can’t. But choose. What you mustn’t do is waver, say in the same breath that he both can and can’t, and then claim that this contradiction proves that time travel is impossible.

Exactly the same goes for Tom’s parallel failure. For Tom to kill Grandfather ’s partner also is compossible with all facts of the sorts we ordinarily count as relevant, but not compossible with a larger set including, for in- stance, the fact that the intended victim lived until 1934. In Tom’s case we are not puzzled. We say without hesi- tation that he can do it, because we see at once that the

facts that are not compossible with his success are facts about the future of the time in question and therefore not the sort of facts we count as relevant in saying what Tom can do.

In Tim’s case it is harder to keep track of which facts are relevant. We are accustomed to exclude facts about the future of the time in question, but to include some facts about its past. Our standards do not apply un- equivocally to the crucial facts in this special case: Tim’s failure, Grandfather ’s survival, and his subsequent do- ings. If we have foremost in mind that they lie in the external future of that moment in 1921 when Tim is al- most ready to shoot, then we exclude them just as we exclude the parallel facts in Tom’s case. But if we have foremost in mind that they precede that moment in Tim’s extended personal time, then we tend to include them. To make the latter be foremost in your mind, I chose to tell Tim’s story in the order of his personal time, rather than in the order of external time. The fact of Grandfa- ther ’s survival until 1957 had already been told before I got to the part of the story about Tim lurking in ambush to kill him in 1921. We must decide, if we can, whether to treat these personally past and externally future facts as if they were straightforwardly past or as if they were straightforwardly future.

Fatalists—the best of them—are philosophers who take facts we count as irrelevant in saying what someone can do, disguise them somehow as facts of a different sort that we count as relevant, and thereby argue that we can do less than we think—indeed, that there is noth- ing at all that we don’t do but can. I am not going to vote Republican next fall. The fatalist argues that, strange to say, I not only won’t but can’t; for my voting Repub- lican is not compossible with the fact that it was true already in the year 1548 that I was not going to vote Republican 428 years later. My rejoinder is that this is a fact, sure enough; however, it is an irrelevant fact about the future masquerading as a relevant fact about the past, and so should be left out of account in saying what, in any ordinary sense, I can do. We are unlikely to be fooled by the fatalist’s methods of disguise in this case, or other ordinary cases. But in cases of time travel, precognition, or the like, we’re on less familiar ground, so it may take less of a disguise to fool us. Also, new methods of disguise are available, thanks to the device of personal time.

Here’s another bit of fatalist trickery. Tim, as he lurks, already knows that he will fail. At least he has the where- withal to know it if he thinks, he knows it implicitly. For he remembers that Grandfather was alive when he was a boy, he knows that those who are killed are thereafter not alive, he knows (let us suppose) that he is a time traveler who has reached the same 1921 that lies in his personal past, and he ought to understand—as we do— why a time traveler cannot change the past. What is known cannot be false. So his success is not only not compossible with facts that belong to the external future

and his personal past, but also is not compossible with the present fact of his knowledge that he will fail. I reply that the fact of his foreknowledge, at the moment while he waits to shoot, is not a fact entirely about that moment. It may be divided into two parts. There is the fact that he then believes (perhaps only implicitly) that he will fail; and there is the further fact that his belief is correct, and correct not at all by accident, and hence qualifies as an item of knowledge. It is only the latter fact that is not compossible with his success, but it is only the former that is entirely about the moment in question. In calling Tim’s state at that moment knowledge, not just belief, facts about personally earlier but externally later moments were smuggled into consideration.

I have argued that Tim’s case and Tom’s are alike, ex- cept that in Tim’s case we are more tempted than usual— and with reason—to opt for a semi-fatalist mode of speech. But perhaps they differ in another way. In Tom’s case, we can expect a perfectly consistent answer to the counterfactual question: what if Tom had killed Grand- father ’s partner? Tim’s case is more difficult. If Tim had killed Grandfather, it seems offhand that contradictions would have been true. The killing both would and wouldn’t have occurred. No Grandfather, no Father; no Father, no Tim; no Tim, no killing. And for good measure: no Grandfather, no family fortune; no fortune, no time machine; no time machine, no killing. So the supposition that Tim killed Grandfather seems impossible in more than the semi-fatalistic sense already granted.

If you suppose Tim to kill Grandfather and hold all the rest of his story fixed, of course you get a contradic- tion. But likewise if you suppose Tom to kill Grandfa- ther ’s partner and hold the rest of his story fixed—including the part that told of his failure—you get a contradiction. If you make any counterfactual sup- position and hold all else fixed you get a contradiction. The thing to do is rather to make the counterfactual sup- position and hold all else as close to fixed as you con- sistently can. That procedure will yield perfectly consistent answers to the question: what if Tim had not killed Grandfather? In that case, some of the story I told would not have been true. Perhaps Tim might have been the time-traveling grandson of someone else. Perhaps he might have been the grandson of a man killed in 1921 and miraculously resurrected. Perhaps he might have been not a time traveler at all, but rather someone cre- ated out of nothing in 1920 equipped with false memo- ries of a personal past that never was. It is hard to say what is the least revision of Tim’s story to make it true that Tim kills Grandfather, but certainly the contradictory story in which the killing both does and doesn’t occur is not the least revision. Hence it is false (according to the unrevised story) that if Tim had killed Grandfather then contradictions would have been true.

What difference would it make if Tim travels in branching time? Suppose that at the possible world of Tim’s story the space-time manifold branches; the

branches are separated not in time, and not in space, but in some other way. Tim travels not only in time but also from one branch to another. In one branch Tim is absent from the events of 1921; Grandfather lives; Tim is born, grows up, and vanishes in his time machine. The other branch diverges from the first when Tim turns up in 1920; there Tim kills Grandfather and Grandfather leaves no descendants and no fortune; the events of the two branches differ more and more from that time on. Cer- tainly this is a consistent story; it is a story in which Grandfather both is and isn’t killed in 1921 (in the dif- ferent branches); and it is a story in which Tim, by killing Grandfather, succeeds in preventing his own birth (in one of the branches). But it is not a story in which Tim’s killing of Grandfather both does occur and doesn’t: it simply does, though it is located in one branch and not the other. And it is not a story in which Tim changes the past. 1921 and later years contain the events of both branches, coexisting somehow without interaction. It re- mains true at all the personal times of Tim’s life, even after the killing, that Grandfather lives in one branch and dies in the other.6

Princeton University Received September 4, 1975

Notes 1. I have particularly in mind two of the time travel stories of Robert

A. Heinlein: “By His Bootstraps” in R. A. Heinlein, The Menace from Earth (Hicksville, N.Y., 1959), and “—All You Zombies—,” in R. A. Heinlein, The Unpleasant Profession of Jonathan Hoag (Hicksville, N.Y., 1959).

2. Account of time travel in two-dimensional time are found in Jack W. Meiland, “A Two-Dimensional Passage Model of Time for Time Travel,” Philosophical Studies, vol. 26 (1974), pp. 153–173; and in the initial chapters of Isaac Asimov, The End of Eternity (Garden City, N.Y., 1955). Asimov’s denouement, however, seems to re- quire some different conception of time travel.

3. H. G. Wells, The Time Machine, An Invention (London, 1895), epi- logue. The passage is criticized as contradictory in Donald C. Williams, “The Myth of Passage,” The Journal of Philosophy, vol. 48 (1951), p. 463.

4. I discuss the relation between personal identity and mental con- nectedness and continuity at greater length in “Survival and Identity” in The Identity of Persons, ed. by Amelie Rorty (forth- coming).

5. “Causation,” The Journal of Philosophy, vol. 70 (1973), pp. 556–567; the analysis relies on the analysis of counterfactuals given in my Counterfactuals (Oxford, 1973).

6. The present paper summarizes a series of lectures of the same title, given as the Gavin David Young Lectures in Philosophy at the University of Adelaide in July, 1971. I thank the Australian- American Educational Foundation and the American Council of Learned Societies for research support. I am grateful to many friends for comments on earlier versions of this paper; especially Philip Kitcher, William Newton-Smith, J. J. C. Smart, and Donald Williams.

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Philosophy 2: Puzzles and Paradoxes / UCI, Winter Quarter 2020 Professor David Woodruff Smith ( [email protected] ). Teach Assistants: Joost Ziff <[email protected]>, Louis Doulas <[email protected]>, Evan Sommers <[email protected]>. February 10, 2020 Professor Notes: Re McTaggart and time McTaggart’s paradox of time. J. M. E. McTaggart offered a metaphysical theory of time in “The Unreality of Time” (1908). According to his theory, time is unreal (a kind of subjective illusion). But McTaggart’s argument for his theory has been seen as presenting a paradox. Here is a particular formulation of McTaggart’s paradox of time. McTaggart’s theory begins with a fundamental distinction. As he notes, we treat time as ordered in two ways. The A series of times is structured as moving from past to present to future. The B series of times is structured as before or after. Given this distinction, McTaggart argued that time itself is unreal. McTaggart’s argument, reconstructed: 1. Time follows an A series: time moves from past to present to future — so that, inversely, a given time is future, then present, then past. 2. Time follows a B series: one time is before another — or, inversely, the latter time is after the former. 3. The A series is more fundamental than the B series — that is, what makes one time before another is whether it is past relative to the other (etc.). 4. A given time cannot be past, present, and future — that is, first future, then present, then past. 5. Therefore, time is unreal. We might say: The B series is developed as an objective measure of the flow of time, where for any two times one is before the other. By contrast, the A series is developed around a special property of what is “now”. Logically, the A series defines a special property of a time, its being “now” or “present”, whereas the B series defines a special relation between times. Suppose I find a journal, a book, specifying events on each day observed, say, April 1, then April 2, and so on … As I read this book, turning from one page to another, I cannot tell of any day described whether it is “now”, “today”, “present”. So we are not done with our account of time given the day-to-day journal. We are now puzzled about the nature of time: what is “the present”? McTaggart argues that any given time T (note: objectively specified, as in the B series) cannot (logically?, metaphysically?) be Past and Present and Future.

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Yet (by our own experience) this moment T is “now” — so it is not “past” (now) or “future” (then). … So McTaggart holds. Paradoxically: because we clearly think that this time T really fits into both a B series and an A series. But, per McTaggart, this cannot be. Reconstructing: There is a deep problem in combining the A series with the B series. !!! Where, then, are we in our reflections on the nature of space and time? McTaggart raised a new problem regarding time. How can we square our A-series order of time (past – present – future) with our B-series order of time (T1 is before T2, etc.)? The problem seems to be: If time is objectively ordered as in the B series (physics assumes such an order, as does our everyday sense of the passage of time), how can we say which time T is now, i.e. “present”, as in the A series? Given his argument, McTaggart held that time is unreal. However, we seem to observe things happening in time, as we see or hear things happening “now”. In effect, then, McTaggart held that time is fundamentally subjective, appearing in our experience as “now” (in the A-series — with the B-series founded on the A-series according to McTaggart). Now, Sorenson noted that Augustine held such a view of time: in perception we experience something that is “now”, in memory something that is “past”, in anticipation something that is “future”. This form of time (the A-series) is something we directly experience, as a subjective structure of time, but that is different from the objective structure of time (the B- series), which we assume in physics and already find in everyday life as clock time. So: What we learn from McTaggart’s theory of time, arguably, is that there are both an objective form of time and a subjective form of time. Well, then: Time is ordered in an objective continuum, but standing out from that stream of time is “now”. The present “now” is something altogether different: seemingly out of place in the continuity of time (in the B-series). And as with the present, so too with the past and the future (in the A-series): for the Augustine-McTaggart theory, the experience of time becomes subjective, even illusory. The problem of the here and now: Which time (objectively defined) is “now’? Which spatial location (objectively defined) is “here”? In this way we can turn McTaggart loose on Zeno. Thus, we find a further and perhaps deeper problem lurking in each of our Zeno-style arguments about motion or space or time. Which point of motion is “actual”, really happening “now” and indeed “here”? Which point of space is “here”? Which point of time is “now”? We may think of “A” time as an active structure (“active” now) and “B” time as one of four dimensions in a block structure (each time t being part of a point of space-time <x,y,z,t> ).

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The turn to “indexical” forms. The terms “this”, “that”, “here”, “there”, “I”, “she”, and “now” — also “today”, “yesterday”, “tomorrow” — are called indexical terms (they point toward something, as we do with the “index” finger). We use such terms to indicate or point toward something in the context of utterance. Without a given context, these terms do not succeed in referring to anything. Suppose we read in a journal, “Today I saw a whale jumping in the ocean.” Without the actual context of the author’s report in her journal, there is no telling which day is “today”. Similarly, the statement “it is now raining” does not specify a time of precipitation without a context of uttering, as the speaker announces the rain. Similarly, “here” does not specify a particular location in space all by itself. Nor does “I” specify any individual unless the speaker reports, “Today I saw a whale”. The problem is not only one of language, of logic or semantics. We have found the problem in the theory of space and time themselves! That is where we found a problem in the seeming paradox of time, where A time does not seem to fit in with B time: in the world!!!