Philosophy of space and time is the branch of philosophy concerned
with the issues surrounding the ontology, epistemology, and character
of space and time. While such ideas have been central to philosophy
from its inception, the philosophy of space and time was both an
inspiration for and a central aspect of early analytic philosophy. The
subject focuses on a number of basic issues, including whether time
and space exist independently of the mind, whether they exist
independently of one another, what accounts for time's apparently
unidirectional flow, whether times other than the present moment
exist, and questions about the nature of identity (particularly the
nature of identity over time).
1 Ancient and medieval views
2 Realism and anti-realism
3 Absolutism and relationalism
3.1 Leibniz and Newton
5 Structure of space-time
5.1 Relativity of simultaneity
5.2 Invariance vs. covariance
5.3 Historical frameworks
6 Direction of time
6.1 Causation solution
6.3 Laws solution
7 Flow of time
9 Presentism and eternalism
Endurantism and perdurantism
11 See also
14 External links
Ancient and medieval views
The earliest recorded
Western philosophy of time was expounded by the
ancient Egyptian thinker
Ptahhotep (c. 2650–2600 BC) who said:
Follow your desire as long as you live, and do not perform more than
is ordered, do not lessen the time of following desire, for the
wasting of time is an abomination to the spirit...
— 11th maxim of
The Vedas, the earliest texts on
Indian philosophy and Hindu
philosophy, dating back to the late 2nd millennium BC, describe
ancient Hindu cosmology, in which the universe goes through repeated
cycles of creation, destruction, and rebirth, with each cycle lasting
4,320,000 years. Ancient Greek philosophers, including Parmenides
and Heraclitus, wrote essays on the nature of time.
Incas regarded space and time as a single concept, named pacha
(Quechua: pacha, Aymara: pacha).
Plato, in the Timaeus, identified time with the period of motion of
the heavenly bodies, and space as that in which things come to be.
Book IV of his Physics, defined time as the number of
changes with respect to before and after, and the place of an object
as the innermost motionless boundary of that which surrounds it.
Book 11 of St. Augustine's Confessions, he ruminates on the nature
of time, asking, "What then is time? If no one asks me, I know: if I
wish to explain it to one that asketh, I know not." He goes on to
comment on the difficulty of thinking about time, pointing out the
inaccuracy of common speech: "For but few things are there of which we
speak properly; of most things we speak improperly, still the things
intended are understood."  But Augustine presented the first
philosophical argument for the reality of Creation (against Aristotle)
in the context of his discussion of time, saying that knowledge of
time depends on the knowledge of the movement of things, and therefore
time cannot be where there are no creatures to measure its passing
Book XI ¶30; City of God
Book XI ch.6).
In contrast to ancient Greek philosophers who believed that the
universe had an infinite past with no beginning, medieval philosophers
and theologians developed the concept of the universe having a finite
past with a beginning, now known as Temporal finitism. The Christian
John Philoponus presented early arguments, adopted by
later Christian philosophers and theologians of the form "argument
from the impossibility of the existence of an actual infinite", which
"An actual infinite cannot exist."
"An infinite temporal regress of events is an actual infinite."
"∴ An infinite temporal regress of events cannot exist."
In the early 11th century, the Muslim physicist Ibn al-Haytham
(Alhacen or Alhazen) discussed space perception and its
epistemological implications in his
Book of Optics
Book of Optics (1021), he also
rejected Aristotle's definition of topos (Physics IV) by way of
geometric demonstrations and defined place as a mathematical spatial
extension. His experimental proof of the intro-mission model of
vision led to changes in the understanding of the visual perception of
space, contrary to the previous emission theory of vision supported by
Euclid and Ptolemy. In "tying the visual perception of space to prior
bodily experience, Alhacen unequivocally rejected the intuitiveness of
spatial perception and, therefore, the autonomy of vision. Without
tangible notions of distance and size for correlation, sight can tell
us next to nothing about such things."
Realism and anti-realism
A traditional realist position in ontology is that time and space have
existence apart from the human mind. Idealists, by contrast, deny or
doubt the existence of objects independent of the mind. Some
anti-realists, whose ontological position is that objects outside the
mind do exist, nevertheless doubt the independent existence of time
Immanuel Kant published the Critique of Pure Reason, one of
the most influential works in the history of the philosophy of space
and time. He describes time as an a priori notion that, together with
other a priori notions such as space, allows us to comprehend sense
experience. Kant denies that either space or time are substance,
entities in themselves, or learned by experience; he holds, rather,
that both are elements of a systematic framework we use to structure
our experience. Spatial measurements are used to quantify how far
apart objects are, and temporal measurements are used to
quantitatively compare the interval between (or duration of) events.
Although space and time are held to be transcendentally ideal in this
sense, they are also empirically real—that is, not mere illusions.
Idealist writers, such as
J. M. E. McTaggart
J. M. E. McTaggart in The Unreality of Time,
have argued that time is an illusion (see also The flow of time,
The writers discussed here are for the most part realists in this
regard; for instance,
Gottfried Leibniz held that his monads existed,
at least independently of the mind of the observer.
Absolutism and relationalism
Leibniz and Newton
The great debate between defining notions of space and time as real
objects themselves (absolute), or mere orderings upon actual objects
(relational), began between physicists
Isaac Newton (via his
spokesman, Samuel Clarke) and
Gottfried Leibniz in the papers of the
Arguing against the absolutist position, Leibniz offers a number of
thought experiments with the purpose of showing that there is
contradiction in assuming the existence of facts such as absolute
location and velocity. These arguments trade heavily on two principles
central to his philosophy: the principle of sufficient reason and the
identity of indiscernibles. The principle of sufficient reason holds
that for every fact, there is a reason that is sufficient to explain
what and why it is the way it is and not otherwise. The identity of
indiscernibles states that if there is no way of telling two entities
apart, then they are one and the same thing.
The example Leibniz uses involves two proposed universes situated in
absolute space. The only discernible difference between them is that
the latter is positioned five feet to the left of the first. The
example is only possible if such a thing as absolute space exists.
Such a situation, however, is not possible, according to Leibniz, for
if it were, a universe's position in absolute space would have no
sufficient reason, as it might very well have been anywhere else.
Therefore, it contradicts the principle of sufficient reason, and
there could exist two distinct universes that were in all ways
indiscernible, thus contradicting the identity of indiscernibles.
Standing out in Clarke's (and Newton's) response to Leibniz's
arguments is the bucket argument: Water in a bucket, hung from a rope
and set to spin, will start with a flat surface. As the water begins
to spin in the bucket, the surface of the water will become concave.
If the bucket is stopped, the water will continue to spin, and while
the spin continues, the surface will remain concave. The concave
surface is apparently not the result of the interaction of the bucket
and the water, since the surface is flat when the bucket first starts
to spin, it becomes concave as the water starts to spin, and it
remains concave as the bucket stops.
In this response, Clarke argues for the necessity of the existence of
absolute space to account for phenomena like rotation and acceleration
that cannot be accounted for on a purely relationalist account. Clarke
argues that since the curvature of the water occurs in the rotating
bucket as well as in the stationary bucket containing spinning water,
it can only be explained by stating that the water is rotating in
relation to the presence of some third thing—absolute space.
Leibniz describes a space that exists only as a relation between
objects, and which has no existence apart from the existence of those
objects. Motion exists only as a relation between those objects.
Newtonian space provided the absolute frame of reference within which
objects can have motion. In Newton's system, the frame of reference
exists independently of the objects contained within it. These objects
can be described as moving in relation to space itself. For many
centuries, the evidence of a concave water surface held authority.
Another important figure in this debate is 19th-century physicist
Ernst Mach. While he did not deny the existence of phenomena like that
seen in the bucket argument, he still denied the absolutist conclusion
by offering a different answer as to what the bucket was rotating in
relation to: the fixed stars.
Mach suggested that thought experiments like the bucket argument are
problematic. If we were to imagine a universe that only contains a
bucket, on Newton's account, this bucket could be set to spin relative
to absolute space, and the water it contained would form the
characteristic concave surface. But in the absence of anything else in
the universe, it would be difficult to confirm that the bucket was
indeed spinning. It seems equally possible that the surface of the
water in the bucket would remain flat.
Mach argued that, in effect, the water experiment in an otherwise
empty universe would remain flat. But if another object were
introduced into this universe, perhaps a distant star, there would now
be something relative to which the bucket could be seen as rotating.
The water inside the bucket could possibly have a slight curve. To
account for the curve that we observe, an increase in the number of
objects in the universe also increases the curvature in the water.
Mach argued that the momentum of an object, whether angular or linear,
exists as a result of the sum of the effects of other objects in the
universe (Mach's Principle).
Albert Einstein proposed that the laws of physics should be based on
the principle of relativity. This principle holds that the rules of
physics must be the same for all observers, regardless of the frame of
reference that is used, and that light propagates at the same speed in
all reference frames. This theory was motivated by Maxwell's
equations, which show that electromagnetic waves propagate in a vacuum
at the speed of light. However,
Maxwell's equations give no indication
of what this speed is relative to. Prior to Einstein, it was thought
that this speed was relative to a fixed medium, called the
luminiferous ether. In contrast, the theory of special relativity
postulates that light propagates at the speed of light in all inertial
frames, and examines the implications of this postulate.
All attempts to measure any speed relative to this ether failed, which
can be seen as a confirmation of Einstein's postulate that light
propagates at the same speed in all reference frames. Special
relativity is a formalization of the principle of relativity that does
not contain a privileged inertial frame of reference, such as the
luminiferous ether or absolute space, from which Einstein inferred
that no such frame exists.
Einstein generalized relativity to frames of reference that were
non-inertial. He achieved this by positing the Equivalence Principle,
which states that the force felt by an observer in a given
gravitational field and that felt by an observer in an accelerating
frame of reference are indistinguishable. This led to the conclusion
that the mass of an object warps the geometry of the space-time
surrounding it, as described in Einstein's field equations.
In classical physics, an inertial reference frame is one in which an
object that experiences no forces does not accelerate. In general
relativity, an inertial frame of reference is one that is following a
geodesic of space-time. An object that moves against a geodesic
experiences a force. An object in free fall does not experience a
force, because it is following a geodesic. An object standing on the
earth, however, will experience a force, as it is being held against
the geodesic by the surface of the planet. In light of this, the
bucket of water rotating in empty space will experience a force
because it rotates with respect to the geodesic. The water will become
concave, not because it is rotating with respect to the distant stars,
but because it is rotating with respect to the geodesic.
Einstein partially advocates
Mach's principle in that distant stars
explain inertia because they provide the gravitational field against
which acceleration and inertia occur. But contrary to Leibniz's
account, this warped space-time is as integral a part of an object as
are its other defining characteristics, such as volume and mass. If
one holds, contrary to idealist beliefs, that objects exist
independently of the mind, it seems that relativistics commits them to
also hold that space and temporality have exactly the same type of
The position of conventionalism states that there is no fact of the
matter as to the geometry of space and time, but that it is decided by
convention. The first proponent of such a view, Henri Poincaré,
reacting to the creation of the new non-Euclidean geometry, argued
that which geometry applied to a space was decided by convention,
since different geometries will describe a set of objects equally
well, based on considerations from his sphere-world.
This view was developed and updated to include considerations from
relativistic physics by Hans Reichenbach. Reichenbach's
conventionalism, applying to space and time, focuses around the idea
of coordinative definition.
Coordinative definition has two major features. The first has to do
with coordinating units of length with certain physical objects. This
is motivated by the fact that we can never directly apprehend length.
Instead we must choose some physical object, say the Standard Metre at
Bureau International des Poids et Mesures
Bureau International des Poids et Mesures (International Bureau of
Weights and Measures), or the wavelength of cadmium to stand in as our
unit of length. The second feature deals with separated objects.
Although we can, presumably, directly test the equality of length of
two measuring rods when they are next to one another, we can not find
out as much for two rods distant from one another. Even supposing that
two rods, whenever brought near to one another are seen to be equal in
length, we are not justified in stating that they are always equal in
length. This impossibility undermines our ability to decide the
equality of length of two distant objects. Sameness of length, to the
contrary, must be set by definition.
Such a use of coordinative definition is in effect, on Reichenbach's
conventionalism, in the General Theory of Relativity where light is
assumed, i.e. not discovered, to mark out equal distances in equal
times. After this setting of coordinative definition, however, the
geometry of spacetime is set.
As in the absolutism/relationalism debate, contemporary philosophy is
still in disagreement as to the correctness of the conventionalist
Structure of space-time
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Building from a mix of insights from the historical debates of
absolutism and conventionalism as well as reflecting on the import of
the technical apparatus of the General Theory of Relativity, details
as to the structure of space-time have made up a large proportion of
discussion within the philosophy of space and time, as well as the
philosophy of physics. The following is a short list of topics.
Relativity of simultaneity
According to special relativity each point in the universe can have a
different set of events that compose its present instant. This has
been used in the
Rietdijk–Putnam argument to demonstrate that
relativity predicts a block universe in which events are fixed in four
Invariance vs. covariance
Bringing to bear the lessons of the absolutism/relationalism debate
with the powerful mathematical tools invented in the 19th and 20th
century, Michael Friedman draws a distinction between invariance upon
mathematical transformation and covariance upon transformation.
Invariance, or symmetry, applies to objects, i.e. the symmetry group
of a space-time theory designates what features of objects are
invariant, or absolute, and which are dynamical, or variable.
Covariance applies to formulations of theories, i.e. the covariance
group designates in which range of coordinate systems the laws of
This distinction can be illustrated by revisiting Leibniz's thought
experiment, in which the universe is shifted over five feet. In this
example the position of an object is seen not to be a property of that
object, i.e. location is not invariant. Similarly, the covariance
group for classical mechanics will be any coordinate systems that are
obtained from one another by shifts in position as well as other
translations allowed by a Galilean transformation.
In the classical case, the invariance, or symmetry, group and the
covariance group coincide, but, interestingly enough, they part ways
in relativistic physics. The symmetry group of the general theory of
relativity includes all differentiable transformations, i.e., all
properties of an object are dynamical, in other words there are no
absolute objects. The formulations of the general theory of
relativity, unlike those of classical mechanics, do not share a
standard, i.e., there is no single formulation paired with
transformations. As such the covariance group of the general theory of
relativity is just the covariance group of every theory.
A further application of the modern mathematical methods, in league
with the idea of invariance and covariance groups, is to try to
interpret historical views of space and time in modern, mathematical
In these translations, a theory of space and time is seen as a
manifold paired with vector spaces, the more vector spaces the more
facts there are about objects in that theory. The historical
development of spacetime theories is generally seen to start from a
position where many facts about objects are incorporated in that
theory, and as history progresses, more and more structure is removed.
For example, Aristotelian space and time has both absolute position
and special places, such as the center of the cosmos, and the
circumference. Newtonian space and time has absolute position and is
Galilean invariant, but does not have special positions.
With the general theory of relativity, the traditional debate between
absolutism and relationalism has been shifted to whether spacetime is
a substance, since the general theory of relativity largely rules out
the existence of, e.g., absolute positions. One powerful argument
against spacetime substantivalism, offered by
John Earman is known as
the "hole argument".
This is a technical mathematical argument but can be paraphrased as
Define a function d as the identity function over all elements over
the manifold M, excepting a small neighbourhood H belonging to M. Over
H d comes to differ from identity by a smooth function.
With use of this function d we can construct two mathematical models,
where the second is generated by applying d to proper elements of the
first, such that the two models are identical prior to the time t=0,
where t is a time function created by a foliation of spacetime, but
differ after t=0.
These considerations show that, since substantivalism allows the
construction of holes, that the universe must, on that view, be
indeterministic. Which, Earman argues, is a case against
substantivalism, as the case between determinism or indeterminism
should be a question of physics, not of our commitment to
Direction of time
The problem of the direction of time arises directly from two
contradictory facts. Firstly, the fundamental physical laws are
time-reversal invariant; if a cinematographic film were taken of any
process describable by means of the aforementioned laws and then
played backwards, it would still portray a physically possible
process. Secondly, our experience of time, at the macroscopic level,
is not time-reversal invariant. Glasses can fall and break, but
shards of glass cannot reassemble and fly up onto tables. We have
memories of the past, and none of the future. We feel we can't change
the past but can influence the future.
One solution to this problem takes a metaphysical view, in which the
direction of time follows from an asymmetry of causation. We know more
about the past because the elements of the past are causes for the
effect that is our perception. We feel we can't affect the past and
can affect the future because we can't affect the past and can affect
There are two main objections to this view. First is the problem of
distinguishing the cause from the effect in a non-arbitrary way. The
use of causation in constructing a temporal ordering could easily
become circular. The second problem with this view is its explanatory
power. While the causation account, if successful, may account for
some time-asymmetric phenomena like perception and action, it does not
account for many others.
However, asymmetry of causation can be observed in a non-arbitrary way
which is not metaphysical in the case of a human hand dropping a cup
of water which smashes into fragments on a hard floor, spilling the
liquid. In this order, the causes of the resultant pattern of cup
fragments and water spill is easily attributable in terms of the
trajectory of the cup, irregularities in its structure, angle of its
impact on the floor, etc. However, applying the same event in reverse,
it is difficult to explain why the various pieces of the cup should
fly up into the human hand and reassemble precisely into the shape of
a cup, or why the water should position itself entirely within the
cup. The causes of the resultant structure and shape of the cup and
the encapsulation of the water by the hand within the cup are not
easily attributable, as neither hand nor floor can achieve such
formations of the cup or water. This asymmetry is perceivable on
account of two features: i) the relationship between the agent
capacities of the human hand (i.e., what it is and is not capable of
and what it is for) and non-animal agency (i.e., what floors are and
are not capable of and what they are for) and ii) that the pieces of
cup came to possess exactly the nature and number of those of a cup
before assembling. In short, such asymmetry is attributable to the
relationship between temporal direction on the one hand and the
implications of form and functional capacity on the other.
The application of these ideas of form and functional capacity only
dictates temporal direction in relation to complex scenarios involving
specific, non-metaphysical agency which is not merely dependent on
human perception of time. However, this last observation in itself is
not sufficient to invalidate the implications of the example for the
progressive nature of time in general.
The second major family of solutions to this problem, and by far the
one that has generated the most literature, finds the existence of the
direction of time as relating to the nature of thermodynamics.
The answer from classical thermodynamics states that while our basic
physical theory is, in fact, time-reversal symmetric, thermodynamics
is not. In particular, the second law of thermodynamics states that
the net entropy of a closed system never decreases, and this explains
why we often see glass breaking, but not coming back together.
But in statistical mechanics things become more complicated. On one
hand, statistical mechanics is far superior to classical
thermodynamics, in that thermodynamic behavior, such as glass
breaking, can be explained by the fundamental laws of physics paired
with a statistical postulate. But statistical mechanics, unlike
classical thermodynamics, is time-reversal symmetric. The second law
of thermodynamics, as it arises in statistical mechanics, merely
states that it is overwhelmingly likely that net entropy will
increase, but it is not an absolute law.
Current thermodynamic solutions to the problem of the direction of
time aim to find some further fact, or feature of the laws of nature
to account for this discrepancy.
A third type of solution to the problem of the direction of time,
although much less represented, argues that the laws are not
time-reversal symmetric. For example, certain processes in quantum
mechanics, relating to the weak nuclear force, are not
time-reversible, keeping in mind that when dealing with quantum
mechanics time-reversibility comprises a more complex definition. But
this type of solution is insufficient because 1) the time-asymmetric
phenomena in quantum mechanics are too few to account for the
uniformity of macroscopic time-asymmetry and 2) it relies on the
assumption that quantum mechanics is the final or correct description
of physical processes.
One recent proponent of the laws solution is
Tim Maudlin who argues
that the fundamental laws of physics are laws of temporal evolution
(see Maudlin ). However, elsewhere Maudlin argues: "[the]
passage of time is an intrinsic asymmetry in the temporal structure of
the world... It is the asymmetry that grounds the distinction between
sequences that runs from past to future and sequences which run from
future to past" [ibid, 2010 edition, p. 108]. Thus it is arguably
difficult to assess whether Maudlin is suggesting that the direction
of time is a consequence of the laws or is itself primitive.
Flow of time
The problem of the flow of time, as it has been treated in analytic
philosophy, owes its beginning to a paper written by J. M. E.
McTaggart. In this paper McTaggart proposes two "temporal series". The
first series, which means to account for our intuitions about temporal
becoming, or the moving Now, is called the A-series. The A-series
orders events according to their being in the past, present or future,
simpliciter and in comparison to each other. The B-series eliminates
all reference to the present, and the associated temporal modalities
of past and future, and orders all events by the temporal relations
earlier than and later than.
McTaggart, in his paper "The Unreality of Time", argues that time is
unreal since a) the A-series is inconsistent and b) the B-series alone
cannot account for the nature of time as the A-series describes an
essential feature of it.
Building from this framework, two camps of solution have been offered.
The first, the A-theorist solution, takes becoming as the central
feature of time, and tries to construct the B-series from the A-series
by offering an account of how B-facts come to be out of A-facts. The
second camp, the B-theorist solution, takes as decisive McTaggart's
arguments against the A-series and tries to construct the A-series out
of the B-series, for example, by temporal indexicals.
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Quantum field theory
Quantum field theory models have shown that it is possible for
theories in two different space-time backgrounds, like
T-duality, to be equivalent.
Presentism and eternalism
Presentism (philosophy of time) and Eternalism
(philosophy of time)
According to Presentism, time is an ordering of various realities. At
a certain time some things exist and others do not. This is the only
reality we can deal with and we cannot for example say that Homer
exists because at the present time he does not. An Eternalist, on the
other hand, holds that time is a dimension of reality on a par with
the three spatial dimensions, and hence that all things—past,
present, and future—can be said to be just as real as things in the
present. According to this theory, then,
Homer really does exist,
though we must still use special language when talking about somebody
who exists at a distant time—just as we would use special language
when talking about something far away (the very words near, far,
above, below, and such are directly comparable to phrases such as in
the past, a minute ago, and so on).
Endurantism and perdurantism
Endurantism and Perdurantism
The positions on the persistence of objects are somewhat similar. An
endurantist holds that for an object to persist through time is for it
to exist completely at different times (each instance of existence we
can regard as somehow separate from previous and future instances,
though still numerically identical with them). A perdurantist on the
other hand holds that for a thing to exist through time is for it to
exist as a continuous reality, and that when we consider the thing as
a whole we must consider an aggregate of all its "temporal parts" or
instances of existing.
Endurantism is seen as the conventional view
and flows out of our pre-philosophical ideas (when I talk to somebody
I think I am talking to that person as a complete object, and not just
a part of a cross-temporal being), but perdurantists have attacked
this position. (An example of a perdurantist is David Lewis.) One
argument perdurantists use to state the superiority of their view is
that perdurantism is able to take account of change in objects.
The relations between these two questions mean that on the whole
Presentists are also endurantists and Eternalists are also
perdurantists (and vice versa), but this is not a necessary connection
and it is possible to claim, for instance, that time's passage
indicates a series of ordered realities, but that objects within these
realities somehow exist outside of the reality as a whole, even though
the realities as wholes are not related. However, such positions are
Arrow of time
Being and Time
The End of Time
Eternalism (philosophy of time)
Identity and change
Presentism (philosophy of time)
Process and Reality
Time travel in science and time travel in fiction
William Lane Craig
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Debate in Cosmology. Springer. ISBN 978-3642232589.
Hans Reichenbach (1958) The
Space and Time. Dover
Hans Reichenbach (1991) The Direction of Time. University of
Rochelle, Gerald (1998) Behind Time. Ashgate.
Lawrence Sklar (1976) Space, Time, and Spacetime. University of
Turetzky, Philip (1998) Time. Routledge.
Bas van Fraassen, 1970. An Introduction to the
Time. Random House.
Gal-Or, Benjamin "Cosmology, Physics and Philosophy". Springer-Verlag,
New York, 1981, 1983, 1987 ISBN 0-387-90581-2
Ahmad, Manzoor (May 28, 1998). "XV: The Notion of Existence". In Naeem
Ahmad; George F McClean.
Philosophy in Pakistan. Department of
Philosophy, University of Punjab, Lahore, Punjab Province of Pakistan:
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Retrieved 4 July 2012.
Stanford Encyclopedia of Philosophy:
"Time" by Ned Markosian;
Being and Becoming in Modern Physics" by Steven Savitt;
"Absolute and Relational Theories of
Space and Motion" by Nick Huggett
and Carl Hoefer.
Internet Encyclopedia of Philosophy: "Time" by Bradley Dowden.
Brown, C.L., 2006, "What is Space?" A largely Wittgensteinian,
approach towards a dissolution of the question: "What is space?"
Rea, M. C., "Four Dimensionalism" in The Oxford Handbook for
Metaphysics. Oxford Univ. Press. Describes presentism and
Time and Temporality Research Center. "
Time and Temporality".
http://www.exactspent.com/philosophy_of_space_and_time.htm and related
"Gods and the
Universe in Buddhist Perspective, Essays on Buddhist
Cosmology" by Francis Story.
Mark P. de Munnynck (1913). "Space". In Herbermann, Charles.
Catholic Encyclopedia. New York: Robert Appleton Company.
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