Essay instructions and the assigned readings are in the attached file.
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.
1
Philosophy 2: Puzzles and Paradoxes / UCI, Winter Quarter 2020
Professor David Woodruff Smith ( dwsmith@uci.edu ).
Teach Assistants: Joost Ziff
Evan Sommers
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.
2
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
3
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!!!
- Cover Page
- Title Page
- Copyright © 2003 by Oxford University Press, Inc.
- Contents
- List of Figures
- Preface
- 1 Anaximander and the Riddle of Origin
- 2 Pythagoras’s Search for the Common Denominator
- 3 Parmenides on What Is Not
- 4 Sisyphus’s Rock and Zeno’s Paradoxes
- 5 Socrates: The Paradox of Inquiry
- 6 The Megarian Identity Crisis
- 7 Eubulides and the Politics of the Liar
- 8 A Footnote to “Plato”
- 9 Aristotle on Fatalism
- 10 Chrysippus on People Parts
- 11 Sextus Empiricus and the Infinite Regress of Justification
- 12 Augustine’s Pragmatic Paradoxes
- 13 Aquinas: Can God Have a Biography?
- 14 Ockham and the Insolubilia
- 15 Buridan’s Sophisms
- 16 Pascal’s Improbable Calculations
- 17 Leibniz’s Principle of Sufficient Reason
- 18 Hume’s All-Consuming Ideas
- 19 The Common Sense of Thomas Reid
- 20 Kant and the Antinomy of Pure Reason
- 21 Hegel’s World of Contradictions
- 22 Russell’s Set
- 23 Wittgenstein and the Depth of a Grammatical Joke
- 24 Quine’s Question Mark
- Bibliography
- Index
- Book Front and Back Flaps
- Back Cover Page
WHERE DO WE COME FROM?
WHAT IS A PARADOX?
THE OLDEST RECORDED PARADOX
IMPLICATIONS OF THE UNCAUSED CAUSE
WHEN DOES A PARADOX BECOME A FALLACY?
THE MATHEMATICAL SETTING
THE PYTHAGOREANS
THE RELIGION OF DEDUCTION
THE PROBLEM OF NEGATIVE EXISTENTIALS
NEGATION AND TIME
THE RULE OF REASON
REACTION TO PARMENIDES
ZENO’S PARADOXES OF PLURALITY
ZENO’S PARADOXES OF MOTION
ARISTOTLE’S SOLUTION
ZENO’S ARGUMENT AGAINST PLACE
ZENO AND THE MILLET SEED
REACTION TO ZENO
THE SEARCH FOR DEFINITIONS
PROTAGOREAN ORIGINS OF SOCRATIC DIALOGUE
MENO’S PARADOX OF INQUIRY
THE DOCTRINE OF REMINISCENCE
FOLLOWING THE ARGUMENT WHEREVER IT LEADS
THE THEAETETUS FROM A EUCLIDESEAN PERSPECTIVE
HERACLITUS AND THE PARADOX OF CHANGE
KNOWLEDGE AND IDENTITY
THE PARADOX OF ANALYSIS
WAS ARISTOTLE A SPY?
ARISTOTLE’S CONTINUED INFLUENCE
CICERO’S TRADITION
THE ETHICS OF PARADOX
EPIMENIDES AND THE LIAR
THE HORNED MAN
THE SORITES PARADOX
THE TRUTH-TELLER
THE PREFACE PARADOX
JUMBLE ARGUMENTS
THE ELENCHUS PROBLEM
IS THE ELENCHUS NEUTRAL?
THE INALTERABILITY OF THE PAST
THE MASTER ARGUMENT OF DIODORUS CRONUS
VACUOUS FATALISM
ARISTOTLE’S COMMON SENSE
THE MANY BASES OF FATALISM
THE MORAL OBJECTION TO FATALISM
THE GROWING ARGUMENT
STOIC ORGANICISM
DION AND THEON
PARADOXES AND PARADOX TYPES
THERAPEUTIC PYRRHONISM
THE PROBLEM OF THE CRITERION
THE CIRCULARITY OF DIRECT ARGUMENTS
THE PARADOX OF DOGMATISM
A CRITIQUE OF REASON
AUGUSTINE’S COGITO
AUGUSTINE’S SUBJECTIVE THEORY OF TIME
IMMUTABILITY
IS GOD ALIVE?
TIMELESSNESS AND ETERNITY
FLOWING TIME VERSUS STATIC TIME
THE DOCTRINAL STORM OF 1277
WHAT OCKHAM RAZED
OCKHAM’S POLITICS
THE INSOLUBLES
THE ORIGIN OF THE INSOLUBLES
THE EDUCATIONAL SYSTEM
FORCED ERRORS IN A DEBATING GAME
BURIDAN’S BRIDGE
THE MEDIEVAL THEORY OF PROPOSITIONS
BURIDAN ON THE INSOLUBLES
THE DECLINE OF SCHOLASTIC ISM
MINDLESS COMPUTATION AND DESCARTES
EXPERIMENTS ON NOTHING
THE STRUCTURE OF DISORDER
THE MONTY HALL PROBLEM
THE DIVISION PARADOX
PASCAL’S WAGER
THE ST. PETERSBURG PARADOX
THE TWO ENVELOPE PARADOX
LEIBNIZ’S PRINCIPLES
LEIBNIZ’S PREDICTIONS
GEOMETRICAL PROBABILITY
BERTRAND’S PARADOX
LOCKE
BERKELEY
HUME AGAIN
NATURE OF COMMON SENSE
COMMON SENSE AND PHILOSOPHICAL ARGUMENT
FOLLOWING THE ARGUMENT
CRITICISMS OF REID’S CONCEPTION OF COMMON SENSE
THE SCIENTIFIC STUDY OF COMMON SENSE
THE FOUR ANTINOMIES OF PURE REASON
THESIS
PROOF
ANTITHESIS
PROOF
ORIGIN OF THE ANTINOMIES
KANT’S COPERNICAN REVOLUTION
KANT’S CONFLICTING SOLUTIONS
THE HEGELIAN HUNT FOR CONTRADICTIONS
THE SECOND ANALYTIC PHILOSOPHER
LOGICISM AND CANTOR
AFTERMATH
WITTGENSTEIN’S THERAPY
PICTURING WORDS AS NAMES
THE RELEVANCE OF LINGUISTIC ODDITY
SARTRE AND THE SELF- DECEIVED
RULE FOLLOWING
CARTER’S DOOMSDAY ARGUMENT
VERIDICAL AND FALSIDICAL PARADOXES
THE NEW RIDDLE OF INDUCTION
THE ANALYTIC/SYNTHETIC DISTINCTION
RADICAL TRANSLATION
THE ODD UNIVERSE
INTERESTING NUMBERS
ARE PARADOXES SETS?
PARADOXES WITHOUT PREMISES
GRADUALISM ABOUT PARADOXES
A
B
C
D
E
F
G
H,I
J,K,L
M
N,O
P
Q,R
S
T
U
V,W
X,Z