## 1. Fatalism



Many logical questions about time historically arose from questions
about freedom and determinism--in particular worries about
fatalism. Fatalism can be understood as the doctrine that whatever
will happen in the future is already *unavoidable* (where to
say that an event is unavoidable is to say that no agent is able to
prevent it from occurring). Here is a typical argument for
fatalism:



(1)
There are now propositions about everything that might happen in
the future.
(2)
Every proposition is either true or else false.
(3)
If (1) and (2), then there is now a set of true propositions that,
taken together, correctly predict everything that will happen in the
future.
(4)
If there is now a set of true propositions that, taken together,
correctly predict everything that will happen in the future, then
whatever will happen in the future is already unavoidable.
[?] (5)
Whatever will happen in the future is already unavoidable.


The conclusion appears shocking. Future moral catastrophes are
unavoidable. Every weighty decision that now feels up to you is
already determined.



The argument for fatalism makes some significant metaphysical
assumptions that raise more general questions about logic, time, and
agency.



For example, Premise (1) assumes that propositions describing the
future do not come into or go out of existence. It assumes that there
are propositions now that can accurately represent every future way
things might go. This is a non-trivial logical assumption. You might,
for instance, think that different times becoming present and actual
(like perhaps possible worlds) have different associated sets of
propositions that become present and actual.



Premise (2) appears to be a fundamental principle of semantics,
sometimes referred to as the Principle of Bivalence.



The rationale for premise (4) is that it appears no one is able to
make a true prediction turn out false. (4) assumes that one and the
same proposition does not change its truth value over time. The
shockingness of the conclusion also depends on identifying meaningful
agency with the capacity to make propositions come out true or
false.



A proper discussion of fatalism would include a lengthy consideration
of premises (1) and (4), which make important assumptions about the
nature of propositional content and the nature of agency. That would
take us beyond the scope of this article. For our purposes, it is
important to note that many writers have been motivated by this kind
of fatalist argument to deny (2), the Principle of Bivalence.
According to this line, there are many propositions--namely,
propositions about events that are both in the future and
contingent--that are neither true nor false right now. Consider
the proposition that you will have lunch tomorrow. Perhaps that
proposition either has no truth value right now, or else has a third
truth value: indeterminate. When the relevant time comes, and you
either have lunch or don't, then the proposition will come to be
either true or false, and from then on that proposition will forever
retain that determinate truth value.



This strategy for rejecting fatalism is sometimes referred to as the
"Open Future" response. The Open Future response
presupposes that a proposition can have a truth value, but only
temporarily--truth values for complete propositions can change as
time passes and the world itself changes. This raises further
questions about the correct way to link up propositions, temporal
passage and truth values. For example, which of the following formulas
expresses a genuine proposition about the present?




Tensed Proposition: "Sullivan is eating a burrito".



Tenseless Proposition: "Sullivan eats a burrito at <insert
present time stamp>".




The tensed proposition will no longer be true when Sullivan finishes
her lunch. So it has, at best, a temporary truth value. The tenseless
proposition expresses something like "Sullivan eats a burrito at
3pm on July 20th 2019". That proposition is always true.



Some philosophers argue that only the latter, eternally true kind of
proposition could make sense of how we use propositions to reason over
time. We need propositions to have stable truth values if we are to
use them as the contents of thoughts and communication. Other
philosophers--particularly those who believe that reality itself
changes over time--think that tensed propositions are needed to
accurately reason about the world. We'll return to these issues
in
 Section 4
 and
 Section 5.



**Suggestions for Further Reading:** Aristotle, *De
Interpretatione*, Ch. 9; Barnes and Cameron 2009; Boethius,
*The Consolation of Philosophy*, Book V; Crisp 2007; Evans
1985; Lewis 1986; Markosian 1995; McCall 1994; Miller 2005; Richard
1981; Sullivan 2014; Taylor 1992; Torre 2011; Van Inwagen 1983.


## 2. Reductionism and Platonism with Respect to Time



What if one day things everywhere ground to a halt? What if birds
froze in mid-flight, people froze in mid-sentence, and planets and
subatomic particles alike froze in mid-orbit? What if all change,
throughout the entire universe, completely ceased for a period of,
say, one year? Is such a thing possible?



If the answer to this last question is "yes"--if it
is possible for there to be time without change--then time is in
some important sense independent of the events within time. Other ways
of investigating whether time is independent of the events within time
include asking whether all of the physical processes that happen in
time could happen at a faster or slower rate, and asking whether all
events could have happened slightly earlier or later in time. After
all, if every physical process could suddenly happen twice as fast, or
if every event could take place slightly earlier or later in time,
then it follows that in some important sense time can remain the same
even if the way that events are distributed in time changes
wholesale.



Aristotle and Leibniz, among others, have argued that time is not
independent of the events that occur in time. This view is typically
called either "reductionism with respect to time" or
"relationism with respect to time", since according to
this view, all talk that appears to be about time can somehow be
reduced to talk about temporal relations among things and events. The
opposing view, normally referred to either as "Platonism with
respect to time" or "substantivalism with respect to
time" or "absolutism with respect to time", has been
defended by Plato, Newton, and others. On this view, time is like an
empty container into which things and events may be placed; but it is
a container that is independent of what (if anything) is placed in
it.



Another way to present this distinction is to say that those like
Plato and Newton who think that time is independent of the events that
occur in time believe in "absolute time". Those like
Aristotle and Leibniz, who think that time is not independent of the
events that occur in time, deny the existence of absolute time, though
they still endorse "relative time", where relative time is
nothing over and above the temporal relations between events.



These views about time are closely connected to views about space and
about motion. Most obviously, these views about time have
straightforward spatial analogues--one may be a substantivalist
about space (and thus endorse the existence of absolute space in
addition to spatial relations between things), or one may be a
relationist about space (and thus deny the existence of absolute
space). Substantivalism and relationism about time have traditionally
been taken to stand or fall with their spatial counterparts. In
addition, the choice between substantivalism and relationism about
space and time has consequences for your theory of motion. If you are
a relationist about space and time then you must also be a relationist
about motion: all motion is motion relative to something. If you are a
substantivalist about space and time, you will endorse, in addition to
relative motion, the notion of absolute motion, where absolute motion
is motion relative to absolute space and time. If you are a
substantivalist, in addition to facts about whether and how fast a
train car is moving relative to the track, whether and how fast it is
moving relative to the cars, and so on, there will also be a fact
about whether and how fast the train car is really
moving--whether and how fast it is moving relative to absolute
space and time.



Why would someone endorse the existence of absolute time? One reason
is that the empty container metaphor has a lot of intuitive appeal.
Another reason is that some philosophers have thought that there must
be such a thing as absolute motion--as opposed to merely relative
motion--in order to explain certain physical phenomena, like the
forces felt during acceleration. Newton had an especially famous
argument along these lines involving a spinning bucket of
water--the entry on
 Newton's views on space, time,
 and motion has a careful discussion of this argument.



Why would someone deny the existence of absolute time? Some
relationists have put forward arguments that are supposed to show that
absolute space and time are philosophically problematic in some
important way. Perhaps most famously, Leibniz argued that the
existence of absolute space or time would lead to violations of the
principle of sufficient reason and violations of the identity of
indiscernibles.



In order to see why, consider two ways of describing the way things
could be. On the one hand, everything is as it actually is. On the
other, every event happens one second later than it actually does, but
is otherwise exactly the same. If there is such a thing as absolute
time then these two descriptions would pick out distinct possible
worlds. But this, Leibniz claimed, would violate the principle of
sufficient reason. For given that the actual world and the
one-second-late world are exactly the same except for where things are
located in absolute time, there could not (at least according to
Leibniz) be any reason why one exists rather than the other. Moreover,
Leibniz claimed, the actual world and the one-second-late world are
indistinguishable; so if they were in fact distinct possible worlds,
that would violate the principle that if two things are
indistinguishable, then they are identical.



Leibniz's arguments are examples of arguments that attempt to
identify something philosophically problematic with absolute time and
space. Perhaps more generally, many philosophers have been moved by
the idea that even if absolute time and space are not problematic in a
way that makes them unacceptable, they are still the kinds of things
that we should do without if we can. This kind of attitude can be
motivated by a straightforward kind of parsimony--we should
always make do with the fewest types of entities possible. Or it can
be motivated by a more specific worry about the nature of absolute
space and time. You might, for instance, be especially loath to
admit unobservable entities into your ontology--you are willing
to admit them if you must, but you would rather eliminate them
wherever possible. As absolute space and time are unobservable,
someone who endorses this attitude will be inclined to think there are
no such things.



**Suggestions for Further Reading**: Alexander 1956;
Ariew 2000; Arntzenius 2012; Coope 2001; Mitchell 1993; Newton,
*Philosophical Writings*; Newton-Smith 1980; Shoemaker
1969.


## 3. The Topology of Time



It's natural to think that time can be represented by a line.
But a line has a shape. What shape should we give to the line that
represents time? This is a question about the topology, or structure,
of time.



One natural way to answer our question is to say that time should be
represented by a single, straight, non-branching, continuous line that
extends without end in each of its two directions. This is the
"standard topology" for time. But for each of the features
attributed to time in the standard topology, two interesting questions
arise: (a) does time in fact have that feature? and (b) if time does
have the feature in question, is this a necessary or a contingent fact
about time?



Questions about the topology of time appear to be closely connected to
the issue of Platonism versus relationism with respect to time. For if
relationism is true, then it seems likely that time's
topological features will depend on contingent facts about the
relations among things and events in the world, whereas if Platonism
is true, so that time exists independently of whatever is in time,
then time will presumably have its topological properties as a matter
of necessity. But even if we assume that Platonism is true, it's
not clear exactly what topological properties should be attributed to
time.



Consider the question of whether time should be represented by a line
without a beginning (so a line, rather than a line segment). Aristotle
has argued (roughly) that time cannot have a beginning on the grounds
that in order for time to have a beginning, there must be a first
moment of time, but that in order to count as a moment of time, that
allegedly first moment would have to come between an earlier period of
time and a later period of time, which is inconsistent with its being
the first moment of time. (Aristotle argues in the same way that time
cannot have an end.)



Aristotle's argument may or may not be a good one, but even if
it is unsound, many people will feel, purely on intuitive grounds,
that the idea of time having a beginning (or an end) just does not
make sense. And here we have an excellent illustration of what is at
stake in the controversy over whether time has its topological
properties as a contingent matter or as a matter of necessity. For
suppose we come to have excellent evidence that the universe itself
had a beginning in time. (This seems like the kind of thing that could
be supported by empirical evidence in cosmology.) This would still
leave open the question of whether the beginning of the universe
occurred after an infinitely long period of "empty" time,
or, instead, coincided with the beginning of time itself. There are
interesting and plausible arguments for each of these positions.



It is also worth asking whether time must be represented by a single
line. Perhaps we should take seriously the possibility of time's
consisting of multiple time streams, each one of which is isolated
from each other, so that every moment of time stands in temporal
relations to other moments in its own time stream, but does not bear
any temporal relations to any moment from another time stream.
Likewise we can ask whether time could correspond to a branching line
(perhaps to allow for the possibility of time travel or to model an
open future), or to a closed loop, or to a discontinuous line. And we
can also wonder whether one of the two directions of time is in some
way privileged, in a way that makes time itself asymmetrical. (We say
more about this last option in particular in the section on time and
physics.)



**Suggestions for Further Reading:** (1) On the beginning
and end of time: Aristotle, *Physics*, Bk. VIII; Kant, *The
Critique of Pure Reason* (especially pp. 75ff); Newton-Smith
1980, Ch. V. (2) On the linearity of time: Newton-Smith 1980, Ch. III;
Swinburne 1966, 1968. (3) On the direction of time: Price 1994, 1996;
Savitt 1995; and Sklar 1974. (4) On all of these topics: Newton-Smith
1980.


## 4. McTaggart's Argument



In a famous paper published in 1908, J.M.E. McTaggart argued that
there is in fact no such thing as time, and that the appearance of a
temporal order to the world is a mere appearance. Other philosophers
before and since (including, especially, F.H. Bradley) have argued for
the same conclusion. We will focus here only on McTaggart's
argument against the reality of time, which has been by far the most
influential.



McTaggart begins his argument by distinguishing two ways in which
positions in time can be ordered. First, he says, positions in time
can be ordered according to their possession of properties like being
two days future, being one day future, being present, being one day
past, etc. These properties are often referred to now as
"*A* properties" because McTaggart calls the series
of times ordered by these properties "the *A*
series". But he says that positions in time can also be ordered
by two-place relations like two days earlier than, one day earlier
than, simultaneous with, etc. These relations are now often called
"*B* relations" because McTaggart calls the series of
times ordered by these relations "the *B*
series".



McTaggart argues that the *B* series alone does not constitute a
proper time series; the *A* series is essential to time. His
reason for this is that he assumes change is essential to time, and
the *B* series without the *A* series does not involve
genuine change (since *B* series positions are forever
"fixed", whereas *A* series positions are constantly
changing).



McTaggart also argues that the *A* series is inherently
contradictory. For, he says, the different *A* properties are
incompatible with one another. No time can be both future and past,
for example. Nevertheless, he insists, each time in the *A*
series must possess all of the different *A* properties, since a
time that is future will be present and then will be past. McTaggart
concludes that, since neither the A-series nor the B-series can order
the time series, time is unreal.



One response to this argument that McTaggart anticipates involves
claiming that it's not true of any time, *t*, that *t*
is both future and past. Rather, the objection goes, we must say that
it *was* future at some moment of past time and *will
be* past at some moment of future time. But this objection fails,
according to McTaggart, because the additional times that are invoked
in order to explain *t*'s possession of the incompatible
*A* properties must themselves possess all of the same *A*
properties (as must any further times invoked on account of these
additional times, and so on *ad infinitum*). Thus, according to
McTaggart, we never resolve the original contradiction inherent in the
*A* series, but, instead, merely generate an infinite regress of
more and more contradictions.



McTaggart's argument has had staying power because it organizes
crucial debates about the metaphysics of temporal passage, because it
hints at how those debates connect to further debates about where
evidence for the time series and the nature of change come from, and
because the difference between A-theoretic and B-theoretic approaches
to the debate has continued in the intervening century.



**Suggestions for Further Reading:** Bradley 1893; Dyke
2002; McTaggart 1908; Mellor 1998; Prior 1967, 1968.


## 5. The A-Theory and the B-Theory



In
 Section 1,
 we introduced the distinction between a tensed proposition and a
tenseless proposition. Tensed propositions can fully and accurately
describe the world, but nevertheless change truth value over time.
Tenseless propositions, on the other hand, are always true or always
false--they reference a particular time in the proposition and
never change. Propositions represent ways reality could be. So, which
view of propositions we adopt depends on what we think it means for
reality itself to undergo change.



In
 section 4,
 we discussed McTaggart's distinction between time conceived of
as a B-series (events ordered by which come before and which come
after) and time conceived of as an A-series (events ordered by which
are present, which are past, and which are future). Though not
particularly creative as names, the A/B distinction has stuck around
as a way of classifying theories of change.



B-theorists think all change can be described in before-after terms.
They typically portray spacetime as a spread-out manifold with events
occurring at different locations in the manifold (often assuming a
substantivalist picture). Living in a world of change means living in
a world with variation in this manifold. To say that a certain autumn
leaf changed color is just to say that the leaf is green in an earlier
location of the manifold and red in a later location. The locations,
in these cases, are specific times in the manifold. And all of the
metaphysically important facts about change can be captured by
tenseless propositions like "The leaf is red at October 7,
2019". "The leaf is not red at September 7,
2019".



A-theorists, on the other hand, believe that at least some important
forms of change require classifying events as past, present or future.
And accurately describing this kind of change requires some tensed
propositions--there is a way reality is (now, presently) which is
complete but *was* different in the past and also *will
be* different in the future. These tensed propositions also
explain why we tend to attribute significance to the
past-present-future distinction. For example, you might think the
A-theorist is in a better position to explain why we care whether a
horrible event is already in the past versus still in the future. Some
A-theorists will argue that we aren't concerned with
location--we care that the event is over with in reality.



Note, also, there is a significant range of views within the A-theory
camp about whether there is a spacetime manifold (Moving Spotlighters
think there is), or whether only present events are real (the
presentist view), or whether only present and past events are real
(the Growing Block view). We say more about all of these views below.
A-theorists also debate whether objects themselves undergo A-theoretic
change or whether it is only entire regions of spacetime that change
this way.



A-theorists and B-theorists appeal to different sources of evidence
for their different views of passage. A-theorists typically emphasize
how psychologically we seem to perceive a world of robust passage or
"flow" of time. In physics, the laws of thermodynamics
seem to imply a strong past-to-future direction to time. And quantum
mechanics seems to identify an important sense of simultaneity, which
could be identified with presentness (see
 section 11
 below). Finally many commonsense ways of thinking of change seem to
rely on A-theory descriptions of passage. For instance, they will use
the fact that we care so much about whether bad events are past as
evidence that there are ineliminable tensed propositions and those
propositions represent ineliminable A-properties.



B-theorists typically emphasize how special relativity eliminates the
past/present/future distinction from physical models of space and
time. Thus what seems like an awkward way to express facts about time
in ordinary English is actually much closer to the way we express
facts about time in physics. Moreover, thinking of change in tenseless
terms makes it easier to describe in a logically consistent way how
objects survive change--objects have properties only relative to
particular times, so there is no worry about attributing absolutely
inconsistent properties to anything. We'll consider some of
these arguments in more detail in the remaining sections of this
entry, as we consider more specific variations on A-theories and
B-theories of time.



**Suggestions for Further Reading:** For general
discussion of The *A* theory and The *B* theory: Emery 2017;
Le Poidevin 1998; Le Poidevin and McBeath 1993; Markosian 1993;
Maudlin 2007 (especially Chapter 4); Mellor 1998; Paul 2010; Prior
1959 [1976], 1962 [1968], 1967, 1968, 1970, 1996; Sider 2001; Skow
2009; Smart 1963, 1949; Smith 1993; Sullivan 2012a; Williams 1951;
Zimmerman 2005; Zwart 1976.


## 6. Presentism, Eternalism, and the Growing Block Theory



A further question that you might ask about time is an ontological
question. Does whether something is past, present, or future make a
difference to whether it exists? And how do these ontological theses
connect to debates about the A-theory and the B-theory?



According to presentism, only present objects exist. More precisely,
presentism is the view that, necessarily, it is always true that only
present objects exist. Even more precisely, no objects exist in time
without being present (abstract objects might exist outside of time).
(Note that some writers have used the name differently, and unless
otherwise indicated, what is meant here by "present" is
temporally present, as opposed to spatially present.) According to
presentism, if we were to make an accurate list of all the things that
exist--i.e., a list of all the things that our most unrestricted
quantifiers range over--there would be not a single merely past
or merely future object on the list. Thus, you and the Taj Mahal would
be on the list, but neither Socrates nor any future Martian outposts
would be included. (Assuming, that is, both (i) that each person is
identical to his or her body, and (ii) that Socrates's body
ceased to be present--thereby going out of existence, according
to presentism--shortly after he died. Those who reject the first
of these assumptions should simply replace the examples in this
article involving allegedly non-present people with appropriate
examples involving the non-present bodies of those people.) And it is
not just Socrates and future Martian outposts, either--the same
goes for any other putative object that lacks the property of being
present. No such objects exist, according to presentism.



There are different ways to oppose presentism--that is, to defend
the view that at least some non-present objects exist. One version of
non-presentism is eternalism, which says that objects from both the
past and the future exist. According to eternalism, non-present
objects like Socrates and future Martian outposts exist now, even
though they are not currently present. We may not be able to see them
at the moment, on this view, and they may not be in the same
space-time vicinity that we find ourselves in right now, but they
should nevertheless be on the list of all existing things.



It might be objected that there is something odd about attributing to
a non-presentist the claim that Socrates exists now, since there is a
sense in which that claim is clearly false. In order to forestall this
objection, let us distinguish between two senses of "*x*
exists now". In one sense, which we can call the temporal
location sense, this expression is synonymous with "*x* is
present". The non-presentist will admit that, in the temporal
location sense of "*x* exists now", it is true that
no non-present objects exist now. But in the other sense of
"*x* exists now", which we can call the ontological
sense, to say that "*x* exists now" is just to say
that *x* is now in the domain of our most unrestricted
quantifiers. Using the ontological sense of "exists", we
can talk about something existing in a perfectly general sense,
without presupposing anything about its temporal location. When we
attribute to non-presentists the claim that non-present objects like
Socrates exist right now, we commit non-presentists only to the claim
that these non-present objects exist now in the ontological sense (the
one involving the most unrestricted quantifiers).



According to the eternalist, temporal location does not affect
ontology. But according to a somewhat less popular version of
non-presentism, temporal location does matter when it comes to
ontology, because only objects that are either past or present exist.
On this view, which is often called the growing block theory, the
correct ontology is always increasing in size, as more and more things
are added on to the leading "present" edge (temporally
speaking). (Note, however, that the growing block theory does not
involve any commitment to four-dimensionalism as discussed in
 section 7.
 In this way, the name "growing block" is somewhat
misleading and the view is probably better described as the growing
universe theory.) Both presentism and the growing block theory are
versions of the A-theory.



Despite the claim by some presentists that theirs is the commonsense
view, it is pretty clear that there are some major problems facing
presentism (and, to a lesser extent, the growing block theory; but in
what follows we will focus on the problems facing presentism). One
problem has to do with what appears to be perfectly meaningful talk
about non-present objects, such as Socrates and the year 3000. If
there really are no non-present objects, then it is hard to see what
we are referring to when we use expressions such as
"Socrates" and "the year 3000".



Another problem for the presentist has to do with relations involving
non-present objects. It is natural to say, for example, that Abraham
Lincoln was taller than Napoleon Bonaparte, and that World War II was
a cause of the end of The Depression. But how can we make sense of
such talk, if there are no non-present objects to be the relata of
those relations?



A third problem for the presentist has to do with the very plausible
principle that for every truth, there is a truth-maker--something
whose existence suffices for the truth of the proposition or
statement. If you are a presentist, it is hard to see what the
truth-makers could be for truths such as that there were dinosaurs and
that there will be Martian outposts.



Finally, the presentist, in virtue of being an A-theorist, must deal
with the arguments against the A-theory that were mentioned above,
including especially the worry that the A-theory is incompatible with
special relativity. We will discuss these physics-based objections
below.



**Suggestions for Further Reading:** Adams 1986; Bourne
2006; Bigelow 1996; Emery 2020; Hinchliff 1996; Ingram 2016; Keller
and Nelson 2001; Markosian 2004, 2013; McCall 1994; Rini and Cresswell
2012; Sider 1999, 2001; Sullivan 2012b; Tooley 1997; Zimmerman 1996,
1998.


## 7. Three-Dimensionalism and Four-Dimensionalism



In
 Section 4
 and
 Section 5
 we saw that there have been two main theories developed in response
to McTaggart's Argument: The A-theory and The B-theory. Then, in
 Section 6
 we saw that there are two main ways of thinking about the relation
between ontology and time: presentism and eternalism. (There was also
a third way, The Growing Block Theory, which we will mainly set aside
for the sake of simplicity in this section.) Two main ways of thinking
about time emerge from these discussions. On the one hand, A-theorists
and presentists think that our pre-theoretical idea of time as flowing
or passing, and thus being very different from the dimensions of
space, corresponds to something objective and real. B-theorists and
eternalists, on the other hand, reject the idea of time's
passage and instead embrace the idea of time as being a dimension like
space. There is another important way in which philosophers in the
second camp (the B-theory/eternalist camp) think time is like space,
and it has to do with how objects and events persist over time. The
debate typically centers around the doctrine of "temporal
parts", which those in the B-theory/eternalist camp tend to
accept while those in the A-theory/presentist camp tend to reject.



To get an intuitive idea of what temporal parts are supposed to be,
think of a film strip depicting you as you walk across a room. It is
made up of many frames, and each frame shows you at a moment of time.
Now picture cutting the frames, and stacking them, one on top of
another. Finally, imagine turning the stack sideways, so that the
two-dimensional images of you are all right-side-up. Each image of you
in one of these frames represents a *temporal part* of you, in
a specific position, at a particular location in space, at a single
moment of time. And what you are, on this way of thinking, is the
fusion of all these temporal parts. You are a "spacetime
worm" that curves through the four-dimensional manifold known as
*spacetime*. Moreover, on this view, what it is to have a
momentary property at a time is to have a temporal part at the time
that has the property in question. So you are sitting right now in
virtue of the fact that your current temporal part is sitting.



The doctrine of temporal parts that B-theorists and eternalists tend
to like can be stated like this:




**Four-Dimensionalism:** Any physical object that is
located at different times has a different temporal part for each
moment at which it is located.




On this view you have a temporal part right now, which is a
three-dimensional "time slice" of you. And you have a
different temporal part at noon yesterday, but no temporal parts in
the year 1900 (since you are not located at any time in 1900). Also on
this view, the physical object that is you is a fusion of all of your
many temporal parts. (Note: there is a variation on the standard
four-dimensional view, which is sometimes called "the worm
view". The variation, known as "the stage view",
holds that names and personal pronouns normally refer, not to entire
fusions of temporal parts but, rather, to the individual
person-stages, each of which is located at just an instant of time,
and each of which counts as a person, rather than a mere part of a
person).



The opposing view is three-dimensionalism, which is just the denial of
the claim that temporally extended physical objects must have temporal
parts. Here is a formulation of the view:




**Three-Dimensionalism:** Any physical object that is
located at different times is wholly present at each moment at which
it is located.




According to three-dimensionalism, the thing that was doing whatever
you were doing at noon yesterday was you. It was you who was doing
that, and now you are doing something different (namely, reading this
sentence). So the relation between "you then" and
"you now" is *identity*. According to
four-dimensionalism, on the other hand, the thing that was doing
whatever you were doing at noon yesterday was an earlier temporal part
of the thing that is you, and the thing that is doing what you are
doing now is the present temporal part of you. The relation between
"you then" and "you now" is the *temporal
counterpart* relation. (This is similar to the relation between
your left hand and your right hand, which is the *spatial
counterpart* relation. Your two hands are distinct parts of a
bigger thing that contains them both.)



David Lewis, one of the main proponents of four-dimensionalism,
suggests that the principal reason to accept the view is to solve what
he calls "the problem of temporary intrinsics". How can a
single thing--Lewis, for example--have different intrinsic
properties--like being straight, while he is standing, and then
being bent, while seated--at different times? Not by standing in
different relations--the *being straight at* and *being
bent at* relations--to different times, he argues. (Since, he
says, *being straight* and *being bent* are genuine
properties rather than disguised relations.) And not in virtue of
there being only one reality--such as the time when Lewis is
bent--so that reality consists of Lewis, and every other thing,
being the way it is now and not any other way. (For Lewis points out
that we all believe we have a past and a future, in addition to a
present.) So Lewis suggests that the best answer to the question about
how a single thing can have different intrinsic properties at
different times is that such an object has different temporal parts
which themselves have the different intrinsic properties.



There is, however, a natural three-dimensionalist response to this
argument. It involves appealing to a certain way of thinking about
time, truth, and propositions that we touched on briefly in
 Section 1,
 namely, the idea that propositions are in some way
"tensed" as opposed to "tenseless". Here is a
way to formulate the relevant semantic thesis:




**The Tensed Conception of Semantics**


1. Propositions have truth values at times rather than
*simpliciter* and can, in principle, change their truth values
over time.
2. We cannot eliminate verbal tenses like *is*, *was*,
and *will be* from an ideal language.




On this view, a sentence like "Sullivan is eating a
burrito" expresses a proposition that used to be true, but is
false now.



The alternative to the tensed conception of semantics is *the
tenseless conception of semantics*. On the latter view, an
utterance of a sentence like "Sullivan is eating a
burrito" expresses a proposition about a B-relation between
events--it says that Sullivan's eating a burrito is
simultaneous with the utterance itself (or perhaps with the time of
the utterance). Here is a way of stating this view:




**The Tenseless Conception of Semantics**


1. Propositions have truth values *simpliciter* rather than at
times, and so cannot change their truth values over time.
2. We can in principle eliminate verbal tenses like *is*,
*was*, and *will be* from an ideal language.




Consideration of Lewis's argument from temporary intrinsics has
shown that a three-dimensionalist should probably endorse the tensed
conception of semantics, in order to account for changing truths about
the world and its objects. And once we have seen this, it also becomes
clear that A-theorists, presentists, and proponents of the growing
block theory all have similar reasons for adopting the tensed
conception of semantics. For the A-theorist is committed to there
being changing truths about which times and events are future, which
are present, and which are past; and presentists and growing block
theorists are both committed to there being changing truths about what
exists.



**Suggestions for Further Reading:** Hawley 2004 [2020];
Lewis 1986; Sider 2001; Thomson 1983; van Inwagen 1990


## 8. The Dynamic and the Static Theory



Many of the above considerations--especially those about
McTaggart's Argument; the A-theory and the B-theory; presentism,
eternalism, and the growing block theory; and the dispute between
three-dimensionalism and four-dimensionalism--suggest that there
are, generally speaking, two very distinct ways of thinking about the
nature of time. The first is the Static Theory of Time, according to
which time is like space, and there is no such thing as the passage of
time; and the second is the Dynamic Theory of Time, according to which
time is very different from space, and the passage of time is a real
phenomenon. These two ways of thinking about time are not the only
such ways, but they correspond to the two most popular combinations of
views about time to be found in the literature, which are arguably the
most natural combinations of views on these issues. In this section we
will spell out these two popular combinations, mainly as a way to
synthesize much of the preceding material, and also to allow the
reader to appreciate in a big-picture way how the different disputes
about the nature of time are normally taken to be interrelated.



The guiding thought behind the Static Theory of Time is that time is
like space. Here are six ways in which this thought is typically
spelled out. (Note: The particular combination of these six theses is
a natural and popular combination of related claims. But it is not
inevitable. It is also possible to mix and match from among the tenets
of the Static Theory and its rival, the Dynamic Theory.)




**The Static Theory of Time**


1. The universe is spread out in four similar dimensions, which
together make up a unified, four-dimensional manifold, appropriately
called *spacetime*.
2. Any physical object that is located at different times has a
different temporal part for each moment at which it is located.
3. There are no genuine and irreducible A-properties; all talk that
appears to be about A-properties can be correctly analyzed in terms of
B-relations. Likewise, the temporal facts about the world include
facts about B-relations, but they do not include any facts about
A-properties.
4. The correct ontology does not change over time, and it always
includes objects from every region of spacetime.
5. Propositions have truth values *simpliciter* rather than at
times, and so cannot change their truth values over time. Also, we can
in principle eliminate verbal tenses like *is*, *was*,
and *will be* from an ideal language.
6. There is no dynamic aspect to time; time does not pass.




Static Theorists of course admit that time *seems* special to
us, and that it seems to pass. But they insist that this is just a
feature of consciousness--of how we perceive the world--and
not a feature of reality that is independent of us.



The second of the main ways of thinking about time is the Dynamic
Theory of Time. The guiding thought behind this way of thinking is
that time is very different from space. Here are six ways in which
this thought is typically spelled out. (Note: The particular
combination of these six theses is a natural and popular combination
of related claims. But, like the Static Theory, it is not inevitable.
It is also possible to mix and match from among the tenets of the
Dynamic Theory and the Static Theory.)




**The Dynamic Theory of Time**


1. The universe is spread out in the three dimensions of physical
space, and time, like modality, is a completely different kind of
dimension from the spatial dimensions.
2. Any physical object that is located at different times is wholly
present at each moment at which it is located.
3. There are genuine and irreducible A-properties, which cannot be
correctly analyzed in terms of B-relations. The temporal facts about
the world include ever-changing facts involving A-properties,
including facts about which times are past, which time is present, and
which times are future.
4. The correct ontology changes over time, and it is always true that
only present objects exist.
5. Propositions have truth values at times rather than
*simpliciter* and can, in principle, change their truth values
over time. Also, we cannot eliminate verbal tenses like *is*,
*was*, and *will be* from an ideal language.
6. The passage of time is a real and mind-independent
phenomenon.




Opponents of the Dynamic Theory (and sometimes proponents as well)
like to characterize the theory using the metaphor of a moving
spotlight that slides along the temporal dimension, brightly
illuminating just one moment of time, the present, while the future is
a foggy region of potential and the past is a shadowy realm of what
has been. The moving spotlight is an intuitively appealing way to
capture the central idea behind the Dynamic Theory, but in the end, it
is just a metaphor. What the metaphor represents is the idea that
A-properties like *being future*, *being present*, and
*being past* are objective and metaphysically significant
properties of times, events, and things. Also, the metaphor of the
moving spotlight represents the fact that, according to the Dynamic
Theory, each time undergoes a somewhat peculiar but inexorable
process, sometimes called *temporal becoming*. It goes from
being in the distant future to the near future, has a brief moment of
glory in the present, and then recedes forever further and further
into the past.



Despite its being intuitively appealing (especially for Static
Theorists, who see it as a caricature of the Dynamic Theory), the
moving spotlight metaphor has a major drawback, according to some
proponents of the Dynamic Theory: it encourages us to think of time as
a fourth dimension, akin to the dimensions of space. For many
proponents of the Dynamic Theory, this way of
thinking--"spatializing time"--is a mistake.
Instead, we should take seriously the ways that time seems completely
different from the dimensions of space--for instance,
time's apparent directionality, and the distinctive ways that
time governs experience.



**Suggestions for Further Reading:** Hawley 2001; Lewis
1986; Markosian 1993; Markosian 2004; Markosian (forthcoming); Moss
2012; Price 1977; Prior 1967; Prior 1968; Sider 2001; Smart 1949;
Sullivan 2012a; Thomson 1983; and Williams 1951.


## 9. The Moving Spotlight Theory



Above we mentioned that a metaphor sometimes used to characterize the
Dynamic Theory is that of a moving spotlight that slides along the
temporal dimension and that is such that only objects within the
spotlight exist. A similar sort of metaphor can also be used to
characterize the Moving Spotlight Theory, which is an interesting
hybrid of the Static Theory and the Dynamic Theory. Like the Static
Theory, the Moving Spotlight Theory incorporates the idea of spacetime
as a unified manifold, with objects spread out along the temporal
dimension in virtue of having different temporal parts at different
times, and with past, present, and future parts of the manifold all
equally real. But like the Dynamic Theory, it incorporates the thesis
that A-properties are objective and irreducible properties, as well as
the idea that time genuinely passes. The metaphor that characterizes
the Moving Spotlight Theory is one on which there is a moving
spotlight that slides along the temporal dimension and that is such
that only things that are within the spotlight are present (but things
that are outside the spotlight still exist).



Thus the Moving Spotlight Theory is an example of an eternalist
A-theory that subscribes to the dynamic thesis. Unlike presentist or
growing block theories, spotlighters deny that any objects come into
or out of existence. Unlike the B-theories, however, spotlighters
think that there is an important kind of change that cannot be
described just as mere variation in a spacetime manifold. Spotlighters
think instead that there is a spacetime manifold, but one particular
region of the manifold is objectively distinguished--the present.
And this distinction is only temporary--facts about which region
of spacetime count as the present change over time. For example, right
now a region of 2019 is distinguished as present. But in a year, a
region of 2020 will enjoy this honor. The term "moving spotlight
theory" was coined by C.D. Broad--himself a growing
blocker--because he thought this view of time treated passage on
the metaphor of a policeman's "bull's eye"
scanning regions in sequence and focusing attention on their
contents.



Just as there are different understandings of presentism and
eternalism, there are different versions of the moving spotlight
theory. Some versions think that even though the present is
distinguished, there is still an important sense in which the past and
future are concrete. Other versions (like Cameron 2015) treat the
spotlight theory more like a variant of presentism--past and
future objects still exist, but their intrinsic properties are
radically unlike those of present objects. Fragmentalists (see Fine
2005) think that there is a spacetime manifold but that every point in
the manifold has its own type of objective presentness, which defines
a past and future relative to the point.



Why be a spotlighter? Advocates think it combines some of the best
features of eternalism while still making sense of how we seem to
perceive a world of substantive passage. It also inherits some of the
counterintuitive consequences of eternalism (i.e., believing dinosaurs
still exist) and the more complicated logic of the A-theories (i.e.,
it requires rules for reasoning about tensed propositions involving
the spotlight).



**Suggestions for Further Reading:** Broad 1923; Cameron
2015; Fine 2005; Hawley 2004 [2020]; Lewis 1986 (especially Chapter
4.2); Sider 2001; Skow 2015; Thomson 1983; Van Inwagen 1990; Zimmerman
1998.


## 10. Time Travel



We are all familiar with time travel stories, and there are few among
us who have not imagined traveling back in time to experience some
particular period or meet some notable person from the past. But is
time travel even possible?



One question that is relevant here is whether time travel is permitted
by the prevailing laws of nature. This is presumably a matter of
empirical science (or perhaps the correct philosophical interpretation
of our best theories from the empirical sciences). But a further
question, and one that falls squarely under the heading of philosophy,
is whether time travel is permitted by the laws of logic and
metaphysics. For it has been argued that various absurdities follow
from the supposition that time travel is (logically and
metaphysically) possible. Here is an example of such an argument:



(1)
If you could travel back in time, then you could kill your
grandfather before your father was ever conceived. (For what's
to stop you from bringing a gun with you and simply shooting
him?)
(2)
It's not the case that you could kill your grandfather
before your father was ever conceived. (Because if you did, then you
would ensure that you never existed, and that is not something that
*you* could ensure.)
[?] (3)
You cannot travel back in time.


Another argument that might be raised against the possibility of time
travel depends on the claim that presentism is true. For if presentism
is true, then neither past nor future objects exist. And in that case,
it is hard to see how anyone could travel to the past or the
future.



A third argument, against the possibility of time travel to the past,
has to do with the claim that backward causation is impossible. For if
there can be no backward causation, then it is not possible that, for
example, your pushing the button in your time machine in 2020 can
cause your appearance, seemingly out of nowhere, in, say, 1900. And
yet it seems that any story about time travel to the past would have
to include such backward causation, or else it would not really be a
story about time travel.



Despite the existence of these and other arguments against the
possibility of time travel, there may also be problems associated with
the claim that time travel is *not* possible. For one thing,
many scientists and philosophers believe that the actual laws of
physics are in fact compatible with time travel. And for another
thing, as we mentioned at the beginning of this section, we often
think about time travel stories; but when we do so, those thoughts do
not have the characteristic, glitchy feeling that is normally
associated with considering an impossible story. To get a sense of the
relevant glitchy feeling, consider this story: *Once upon a time
there was a young girl, and two plus two was equal to five*. When
you try to consider that literary gem, you mainly have a feeling that
something has gone wrong (you immediately want to respond, "No,
it wasn't"), and the source of that feeling seems to be
the metaphysical impossibility of the story being told. But nothing
like this happens when you consider a story about time travel
(especially if it is one of the logically consistent stories about
time travel, such as the one depicted in the movie *Los
Cronocrimenes (Timecrimes)*). One task facing the
philosopher who claims that time travel is impossible, then, is to
explain the existence of a large number of well-known stories that
appear to be specifically about time travel, and that do not cause any
particular cognitive dissonance.



**Suggestions for Further Reading:** Bernstein 2015,
2017; Dyke 2005; Earman 1995; Markosian (forthcoming); Meiland 1974;
Miller 2017; Sider 2001; Thorne 1994; Vihvelin 1996; Yourgrau
1999.


## 11. Time and Physics



Our best physical theories have often had implications for the nature
of time, and by and large, it is assumed that philosophers working on
time need to be sensitive to the claims of contemporary physics. One
example of the interaction between physics and philosophy of time that
was mentioned in
 Section 2
 was Newton's bucket argument, which used the observed effects
of acceleration to argue for absolute motion (and thus absolute space
and time). Another example mentioned above was the worry that the
A-theory conflicted with special relativity. The latter has proved
especially influential in contemporary metaphysics of time and so
deserves some further discussion.



According to standard presentations of special relativity, there is no
fact of the matter as to whether two spatially separated events happen
at the same time. This principle, which is known as the *relativity
of simultaneity*, creates serious difficulty for the A-theory in
general and for presentism in particular. After all, it follows from
the relativity of simultaneity that there is no fact of the matter as
to what is present, and according to any A-theory there is an
important distinction between what is present and what is merely past
or future. According to presentism, that distinction is one of
existence--only what is present exists.



A different way of describing the relativity of simultaneity involves
the combination of two claims:


1. the claim that whether two spatially separated events happen at
the same time depends on the reference frame you use to describe them,
and
2. the claim that no reference frame is privileged.



This way of putting the relativity of simultaneity requires a new bit
of technical jargon: the notion of a reference frame. For our
purposes, a *reference frame* is nothing more than a coordinate
system that is used to identify the same point in space at different
times. Someone on a steadily moving train, for instance, will
naturally use a reference frame that is different from someone who is
standing on the station platform, since it is natural for the person
on the train to think of themselves as stationary, while for the
person on the platform it seems obvious that they are moving.



The reason why it is worth introducing this bit of jargon is that once
you present the relativity of simultaneity as the combination of
claims (i) and (ii), you can also note that the motivation for claim
(i) is importantly different from the motivation for claim (ii). The
motivation for (i) is a series of empirical results at the end of the
nineteenth and beginning of the twentieth century, including, most
famously, the Michelson-Morley experiment. No one should deny this
part of the relativity of simultaneity. The motivation for (ii), by
contrast, is less often explicitly discussed, and seems to involve the
commitment to some sort of general extra-empirical principle like
"eliminate unobservable entities whenever possible", or
"eliminate excess spacetime structure whenever possible".
This means that presentists and other A-theorists have a way of
avoiding the worry from relativity without any conflict with empirical
results--they can reject whatever extra-empirical principle
motivates (ii). Whether you think the costs associated with this move
are worth paying will depend on your degree of commitment to the
A-theory, what exactly you think of the relevant extra-empirical
principle supporting (ii), and whether that principle plays an
important role elsewhere in physics.



It is often said that philosophers should defer to physics with
respect to what the latter says about time. But the interaction
between the A-theory and special relativity illustrates one way in
which that claim is more complicated than it first appears. Must
philosophers respect *both* the empirical and the
extra-empirical aspects of our best physical theories? Or is it
sufficient that they respect the former?



Another way in which this assumption is complicated is that different
physical theories often seem to imply different things about the
nature of time. Consider, for instance, the fact that in general
relativity there is sometimes (though not always!) a preferred way of
"foliating" spacetime into instants of time and thus
reintroducing a notion of absolute simultaneity, or the fact that on
some interpretations of quantum mechanics, the dynamical laws seem to
require a notion of absolute simultaneity.



Two additional questions about the nature of time that have been
especially influenced by contemporary physics have to do with the
arrow of time and the extent to which time itself might be
emergent.



To motivate the first question, start from the observation that the
order in which events happen in time seems to matter a great deal.
There seems to be an important difference, for instance between a
train traveling from Boston to Providence and a train traveling from
Providence to Boston. This is because, even though both of these
sequences may be constituted by the very same events, those events are
in a different order in each sequence. In the former sequence the
train being in Boston happens earlier than the train being in
Providence. In the latter, the train being in Boston happens
later.



These straightforward observations show that we experience time as
having a direction. This is what philosophers call "the arrow of
time". But is the arrow of time a fundamental feature of the
world? Or can it be reduced to some other feature, thus simplifying
our metaphysics as a whole?



One way to try to eliminate the arrow of time at the fundamental level
is to make use of certain interpretations of statistical mechanics
inspired by Ludwig Boltzmann's work. Imagine the history of the
universe as a long timeline, but with no indication of which end of
the time line represents the first moment of time and which end
represents the last moment. It follows from certain interpretations of
statistical mechanics that there is a physical quantity, the
*entropy* of the universe, that will be relatively low at one
end of the timeline and relatively high at the other end and will
always increase as you move from the former end of the timeline to the
latter. (More carefully, the entropy will almost always increase or at
least stay constant.) The thought, then, is that we might be able to
reduce the arrow of time to this entropy gradient. Earlier moments of
time are just moments of time when the entropy of the universe is
lower.



This way of eliminating the arrow of time from the fundamental level
is promising, but has at least some unintuitive consequences. For
instance, it seems natural to think that entropy could have decreased
over time, instead of increasing over time as it actually does. But
given the reduction described above, it is not in fact possible for
entropy to decrease over time.



The second question mentioned above is a question about whether time
itself--as opposed to just some particular feature of time, like
time's arrow--might merely be an emergent feature of the
world. This question has become especially pressing as philosophers of
physics have turned their attention to theories of quantum gravity in
which there does not seem to be anything like temporal structure at
the fundamental level. Work in this area is nascent, but some of the
questions of interest include: Does quantum gravity eliminate time
entirely or does it merely make time a non-fundamental feature of the
world? What would it mean for something temporal to be grounded in
something atemporal and what sort of grounding relation would be
involved? What is the distinction between causal structure (especially
the causal structure in causal set theory--one approach to
quantum gravity) and temporal structure? And how can a theory that
eliminates time entirely be empirically confirmed or disconfirmed?



**Suggestions for Further Reading:** Albert 2000; Emery
2019 & forthcoming; Godfrey-Smith 1979; Healey 2002; Huggett and
Wuthrich 2013; Knox 2013; Markosian 2004; Maxwell 1985; Monton
2006; Price 1996; Putnam 1967; Rovelli 2017; Savitt 2000; Stein 1968,
1970; Weingard 1972; Wuthrich and Callender 2017.


## 12. Time and Rationality



A final important question concerns how considerations about the
nature of time ought to impact the ways that we reason about time. For
example, if it turns out that a B-theory is true, and there is no
metaphysically important difference between the past and future, then
should we adopt a more neutral attitude about events in our personal
past and future? Epicurean philosopher Lucretius famously suggested
that if there is no substantive difference between the times in the
past before we came to exist and the times in the future after we die,
we should care much less about the deprivation that death will bring.
But we may think that even if the B-theory can describe everything
that is metaphysically important without positing an important
difference between the past and future, there is still an
indispensable psychological importance to the past/future distinction
that rational agents honor. Still other A-theorists argue that while
there is an important metaphysical distinction between the past and
future, the distinction has no normative importance.



If we deny three-dimensionalism and instead view ourselves as objects
that persist through time by having temporal parts, then does that
justify caring less about temporal parts in the distant future that
are less strongly linked with our present part? Derek Parfit famously
argued that a proper understanding of what we care about when we care
about our own future persistence should motivate us to be less
self-interested and more interested in redistributing resources to
others. Endurantists have argued that facts about how we persist
through time underwrite a strong distinction between moral principles
(which concern what we owe to others now) and prudential rationality
(which concerns what we owe to our future selves).



Another interesting line of research uses empirical work in psychology
to better understand what is happening cognitively when we judge time
as passing. This is especially pressing for B-theorists, who must
explain why time seems to pass in psychologically or rationally
significant ways, even though all passage is really just variation in
an eternal manifold. Some B-theorists explain the apparent passage of
time as an illusion of flow caused by perceptual processes that
attribute apparent motion to events that happen in sequence. Another,
compatible approach considers the way that evolutionary pressures
might have shaped emotions and cognitive heuristics to give us a
strong past/future distinction in our reasoning.



**Suggestions for Further Reading:** Brink 2003; Suhler
and Callender 2012; Parfit 1971; Paul 2010; Prosser 2016; Sullivan
2018.