time space and metaphysics dec 2009

TIME, SPACE, AND METAPHYSICS
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Time,Space,and
Metaphysics
BEDE RUNDLE
1
1
Great Clarendon Street, Oxford ox2 6dp
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Time,space,andmetaphysics/BedeRundle.
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Includes bibliographical references and index.
ISBN978–0–19–957511–4 (hardback)
1. Space and time. 2. Metaphysics. I. Title.
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Contents
Preface ix
1. Conceptions of Time and Space 1
1.1 Absolute and relational time 1
1.2 Absolute and relational space 6

1.3 Metrical and non-metrical concepts 10
2. Time, Order, and Direction 18
2.1 Temporal precedence 18
2.2 Causation and order 25
2.3 Order and change 29
3. Time and Tense 34
3.1 Indexicality and tense 35
3.2 Subjectivity and perspective 42
3.3 Tense and tenselessness 49
4. Observer-Dependence 60
4.1 Reality and scepticism 60
4.2 Mind-dependence, indeterminacy, and convention 70
4.3 Temporal parts and temporary intrinsics 78
5. The Past 89
5.1 Present and past reality 89
5.2 McTaggart and the unreality of time 95
5.3 Anti-realism and the past 103
6. The Future 114
6.1 Predictions and truth 115
6.2 Conditionals and modality 119
6.3 Precognition 126
viii Contents
7. Grammar and Ontology 132
7.1 Abstract nouns and clauses 133
7.2 Facts 140
7.3 Instants and the passage of time 149
8. Equality of Time Intervals 156
8.1 Verifiability 156
8.2 Simultaneity 166
8.3 Equality and convention 170

9. Temporal Asymmetries 178
9.1 Time and infinity 178
9.2 Causes, causal conditions, and backwards causation 186
9.3 Time travel 201
10. Space 206
10.1 Absolute space 206
10.2 The reality of space 212
10.3 Space and curvature 223
11. Time and Change 231
11.1 Change and persistence 231
11.2 Temporal vacua 236
11.3 Time, change, and empirical equivalence 247
References 254
Index 261
Preface
Two major theories of time and space have divided philosophers and scientists
over the centuries: the absolute conception of Newton and the relational
theory of Leibniz. The debate between proponents of these views provides
our starting point, and the framework in which much of the subsequent
investigation takes place.
Metaphysics enters in two ways. First, the term may be used with respect
to the investigation and analysis of concepts held to be indispensable to a
description of fundamental and pervasive features of our world. Time and
space are indisputably among such concepts, as also change, identity, objectivity,
memory, facts, causation, and others which we shall encounter along the way.
While most topics which might be expected to figure in a philosophical
investigation of time and space receive some attention, our concern with
more general questions falling under the heading of metaphysics leads us to
range more widely.
Second, metaphysics often enjoys a more contentious status, being con-

cerned with propositions and principles which are not merely basic to our
ways of thinking, but which, while not recording logical truths, purport to
transcend purely experiential knowledge. The very existence of a subject mat-
ter for metaphysics in this sense is a matter of dispute, and the observations
we shall have occasion to make lend no weight to the view that this is a
branch of philosophy with anything to offer, whether concerning time or
others of the topics pursued. Rather, we shall find that, when metaphysics
appears to beckon, what is called for is not an impossible discovery but a
decision to adopt a particular mode of description, a decision to affirm or not
to affirm the disputed propositions. With metaphysics in this sense in mind,
I might equally have called the book ‘Time, Space, and Nonsense’, but not
‘nonsense because unverifiable’. There is ample scope for speaking here of
nonsense without tying meaningfulness to the possibility of verification. A
related negative slant will be found in our diagnoses of depressingly familiar
misconceptions, again with respect both to time and more generally, and
where readers will possibly sense a lack of sympathy with current ways of
thinking. They would be right. However, for the most part, the criticisms
made are made less for themselves, more to prepare the way for a positive
x Preface
resolution of the problems discussed, problems concerning the nature and
reality of time and space, temporal order, temporal parts, verifiability, scepti-
cism, anti-realism and the past, backwards causation, time travel, geometry,
convention, the infinitude of space and time, and the possibility of time
without change. While space as well as time is our concern, it is the latter
that will receive the lion’s share of attention.
The questions which concern us are questions which arise at an elementary
level, and which do not require a knowledge of physics for their formulation.
They persist, however, at more sophisticated levels, and I should like to think
that the clarifications offered throw some light on the more esoteric issues
which physical theory presents.

Trinity College
Oxford
1
Conceptions of Time and Space
Time is often perceived as having a dynamic quality, as something which
moves and for which a stream provides a familiar, and a fitting, metaphor. Is
it also, like a stream, to be thought of as a quantity in its own right, a quantity
which exists side by side with events and changes, or is it just an aspect of
such happenings, so that, when talking about time, we are simply talking in
a more roundabout way about clocks, seasons, sunrises, and sunsets? Given
that we may speak of having or not having enough time to do something,
time must be a quantity of some kind, but does it compare with other
quantities, as quantities of a gas or a liquid? A feature of these is that they
qualify as substances. Not just substances in the ordinary sense of ‘stuffs’,
but substances in the traditional philosophical sense of items enjoying an
independent existence. For time, independence would mean independence
of events or changes, such as the movements of the hands of a clock, a status
which need owe nothing to such happenings or indeed to anything else which
exists or takes place in time. On that conception, it is not that periods of
time are ultimately determined by clocks or other regularities, but time is
a self-sufficient quantity which clocks may, rightly or wrongly, measure or
record.
1.1 ABSOLUTE AND RELATIONAL TIME
Two conceptions of time, the absolutist or substantivalist view of Isaac
Newton and the relational or relative view of Gottfried Wilhelm Leibniz,
can be distinguished by the answers which they give to these questions. Since
the seventeenth century, western thought about time has been dominated by
these conceptions, and much of our discussion will bear upon questions at
issue in the debate between their past and present proponents. We shall begin
with a brief sketch of what each involves.

2 Time,Space,andMetaphysics
According to Newton,
Absolute, true, and mathematical time, in and of itself and of its own nature,
without reference to anything external, flows uniformly and by another name is
called duration. Relative, apparent, and common time is any sensible and external
measure (precise or imprecise) of duration by means of motion; such a measure—for
example, an hour, a day, a month, a year—is commonly used instead of true time.
(Newton 1999: 408)
Absolute time equates to duration, and relative time is a measure of duration,
and hence of absolute time. It is right to distinguish time as a measure and
time as what is measured, but while the concepts may be different, a period
of time may be both what measures and what is measured. So when we say
that the task took a whole day, day serves to give a measure, but we may also
determine the length of a day by making use of a timekeeper, in which case
day serves to specify what is measured. In speaking of our sensible measure
of time as being used instead of true time, Newton implies that true or
absolute time itself provides a measure. However, it is not as if relative time
werenecessarilyaroughandreadymeasure,sinceitisallowedthatitcan
be precise—so, let us say, does not always have the variable character of a
month or a year—in which case does it not then give the true time?
That is surely so, but relative time remains susceptible of variation and
inaccuracy in a way that is excluded for absolute time:
In astronomy, absolute time is distinguished from relative time by the equation
of common time. For natural days, which are commonly considered equal for the
purpose of measuring time, are actually unequal. Astronomers correct this inequality
in order to measure celestial motions on the basis of a truer time. It is possible that
there is no uniform motion by which time may have an exact measure. All motions
can be accelerated and retarded, but the flow of absolute time cannot be changed. The
duration or perseverance of the existence of things is the same, whether their motions
are rapid or slow or null; accordingly, duration is rightly distinguished from its

sensible measures and is gathered from them by means of an astronomical equation.
Moreover, the need for using this equation in determining when phenomena occur
is proved by experience with a pendulum clock and also by eclipses of the satellites
of Jupiter.
(Newton 1999: 410)
In this translation, ‘equation’ renders aequationem. The sense is better
conveyed by replacing ‘the equation of common time’ by ‘equating it with
common time’. The constancy of absolute time is contrasted here with the
Conceptions of Time and Space 3
variability of relative time, these features being what is distinctive of each.
Our various measures may not do justice to this constancy, days of relative
time being liable to variation when set against days of absolute time. Absolute
time is said to flow uniformly or equably (aequabiliter). What does that mean?
Not to speed up or slow down, one might think, but that is a matter of the
same amount of time passing in a given time, and, to ensure accuracy, what
qualifies as the true time would surely have to be determined by absolute
time itself, which leaves us with absolute time providing its own measure.
Not only is it not clear that absolute time can be coherently enlisted to this
end, but if absolute time is to furnish a measure, it would appear that it
must be objectively divided, or at least divisible, into hours, seconds, and any
other units we might happen to make use of. How could such divisions be
effected in the absence of suitable periodic changes, as might be given by a
clock, ‘a measure of duration by means of motion’? The natural thought is
that constancy or uniformity of time requires regularity of changes, rather
than that changes are seen to be regular through their accord with absolute
time, but for Newton that priority is reversed: even a perfect clock does
not determine true time, but the dependence goes in the other direction,
our clock having to be tested against true time and passing the test only if
it is faithful to the equable or uniform flow which time in itself possesses.
Intervals or periods of time require termini, temporal points, which we might

again look to events to furnish, but Newton regards moments or instants of
absolute time—‘indivisible moments of duration’—as depending only on
God, not on events (1999: 941).
We can perhaps extract a minimal absolutist thesis from the preceding
passages to the effect that, whatever the variations and inaccuracies in our
customary measures of time, there is such a thing as true time, in the sense
of time which can be partitioned into objectively equal units or intervals.
Whether this is correct, and whether it takes an absolutist conception to
ground such equality, will be considered later. There is also controversy in
the supposed possibility of time in the absence of change, a possibility which,
while it does not figure in the initial characterization of absolute time, is
sanctioned in the last passage: ‘The duration or perseverance of the existence
of things remains the same, whether the motions are swift or slow, or null’.
It has been argued that Newton is misrepresented when it is said that he
allows the possibility of a totally empty universe in which time none the less
passes. However, while, given God’s omnipresence, there can for Newton be
no such universe, change does not come with the same inescapability.
4 Time,Space,andMetaphysics
The problem of explaining how true or absolute time has priority over
relative time does not arise for the relationist account championed by Leibniz,
and which was already to be glimpsed in Aristotle with his conception of time
as the measure of change with respect to earlier and later (1984: 220
a
25).
The relationist insists that time does not enjoy the independence accorded
it by Newton, that in the absence of events and their relations it has no
reality (Alexander 1956: 25–6). If there were no phenomena succeeding one
another, there would be no time, time being, in Leibniz’s view, nothing more
than the order of succession among events. It is not: time makes change
possible—as if time could be antecedent to change, a feature of the universe

that rendered it fit for the occurrence of events. Rather, time supervenes
upon, indeed is created by, change. We may expound this view in the
following way.
Time, it is said, is a great healer; it is something we spend, gain, and
waste; it marches on and it waits for no man. Take the first of these ways of
speaking. This is not, for the relationist, an observation about a healing agent,
time, but it amounts to saying that various wounds and injuries, setback and
sufferings, mend or lessen as the years go by. True, there is metaphor here,
but the same style of breakdown is supposedly possible for more literal forms.
One event goes on for a longer time than another if there are more swings
of the pendulum while the one unfolds as against the other. Once more, no
substance or entity, time, needs to be invoked, but the sense is conveyed by
an appeal to regularities and periodic processes. Again, we say ‘Time passes’.
A seeming platitude, but not to be interpreted as a platitude about a quantity
or entity, time, which may be set alongside weekends, opportunities, storms,
and so forth, as yet another, independent, phenomenon that may be said to
pass. Rather, ‘Time passes’ is to be thought of as reducible to a proposition
about what may befall the other members of this list, a matter of events
generally taking place in succession.
In focussing on the ‘order of succession among events’, Leibniz is giving
a central place to temporal precedence, to before and after,butonlyan
incidental place, if any, to temporal periods or intervals, to the notion of
duration. A melody may be played fast on a musical instrument, it may
be played slow; the same ordering of the notes, but that ordering does
not determine the differing durations of the piece as played. We have just
represented the relationist as invoking periods marked out by the swings of
a pendulum, but this procedure relies on the periods being equal in length.
Consider some protracted event, an event which goes on for a long time,
Conceptions of Time and Space 5
and suppose that a long time is understood in terms of a large number

of swings of a pendulum. That will not do, according to the absolutist,
since the interval between the swings may be vanishingly short. So, whether
it is the equality of the intervals or their length, the requirement is for
intervals that are objectively equal and objectively long when measured
against time.
Leibniz has an answer, but it does not improve upon an appeal to such
examples, as when he argues in response to Newton’s follower, Samuel
Clarke:
The author objects here, that time cannot be an order of successive things, because
the quantity of time may become greater or less, and yet the order of successions
continue the same. I answer; this is not so. For if the time is greater, there will be
more successive and like states interposed; and if it be less, there will be fewer.
(Alexander 1956: 89–90)
The difficulty with this rejoinder lies with ‘like states interposed’. How
is the likeness of states, their comparability in terms of duration, to be
determined? This is a problem for Leibniz, but it is not as if Newton solves
it. For the absolutist, even if all periodic changes in the universe are to
some degree irregular, we can supposedly make sense of the identity of
temporal intervals in terms of this more basic reality, time itself, which, in
Newton’s words, ‘flows uniformly, without reference to anything external’.
As it is, equal divisions in absolute time are not detectable, so it remains a
metaphysical hypothesis whether a clock keeps true time. For the relationist,
the only comparisons can be between different regularities, as with one
clock and another. The very notion of true time may be rejected, perhaps
because it is thought metaphysical, or it may be claimed that true time can
be secured by making use of nothing more than inter-clock comparisons,
or at least by finding some suitable relation between clocks and events in
time, but not between clocks and time itself. If no definitive comparison is
deemed possible, the relationist may adopt some form of conventionalism,
the search for a perfect timekeeper terminating, not in a discovery of a

natural or artificial rhythm forever assured of that virtue, but in a decision
to adopt one or more of the natural or artificial rhythms available: a chosen
regularity wins out because it makes for the most self-consistent measure
and the simplest physics, but it is a matter of an agreement to opt for that
regularity as determining equality, rather than an incontrovertible proof that
it does so.
6 Time,Space,andMetaphysics
1.2 ABSOLUTE AND RELATIONAL SPACE
The absolute and relational views of space largely mirror their temporal
counterparts. Newton’s Principia is again the locus classicus for the former:
Absolute space, of its own nature without reference to anything external, always
remains homogeneous and immovable. Relative space is any movable measure or
dimension of this absolute space; such a measure or dimension is determined by
our senses from the situation of the space with respect to bodies and is popularly
used for immovable space, as in the case of space under the earth or in the air or
in the heavens, where the dimension is determined from the situation of the space
with respect to the earth. Absolute and relative space are the same in species and in
magnitude, but they do not always remain the same numerically. For example, if the
earth moves, the space of our air, which in a relative sense and with respect to the
earth always remains the same, will now be one part of the absolute space into which
the air passes, now another part of it, and thus will be changing continually in an
absolute sense.
(Newton 1999: 408–9)
The space between the driver’s seat of a car and the car’s dashboard moves
about as the car moves, but it moves against the background of a fixed
space, being located now in one region, now in another of this unmoving
and immovable setting. The car and its contained space move relatively to
absolute space. The fixity of absolute space, as illustrated in this contrast,
appears to be the leading idea in Newton’s conception, but it brings with it
a notion of the identity of points or regions of absolute space which, as with

time, is determined by their immutable order (Alexander 1956: 154). So,
our moving car can be said to move back to the same part of space which
it occupied before, where this sameness is not defined by physical objects,
such as a garage from which the car began its journey, since these, too, might
have moved on. Such movement is indeed an inescapable consequence of
the perpetual rotation of the earth on its axis and around the sun, but where
everything is in flux, absolute space stands fast, providing a fixed setting or
background to any and every change of position.
This fixity leads on to the idea that absolute space, having no need of bodies
to define its various parts or regions, can exist independently of any objects
and, though it cannot exist without God, could well have been or become
completely empty. It is, for Newton, a vast receptacle into which the universe
was placed, a void replete with its own spatial points. These points being fixed
Conceptions of Time and Space 7
and immovable, we can allow the possibility of a universe containing a single
body in motion, since the object could be moving relatively to such points,
points which are truly at rest. If we can posit a plethora of points dispersed
throughout space without having to respect any observational constraints,
why should we not admit all manner of geometrical figures? And this Newton
does indeed allow:
there are everywhere all kinds of figures, everywhere spheres, cubes, triangles, straight
lines, circles, ellipses, parabolas, and all the rest, and of all shapes and sizes, even
though they are not delineated to sight. For the material delineation of a figure
is not a new production of that figure with respect to space, but only a corporeal
representation of it, so that what was formerly insensible in space now appears to the
senses to exist.
(Newton 1962: 100, 133)
Could we say that the figures are in space in the same way that they may
be in a block of marble? But it is a marble sphere that is sculpted from
the block, whereas a figure which takes shape in space does not consist

just of space. Very well, but suppose we sketch out a sphere in space
using lines or paths. Lines and paths have the virtue of not being of space,
yet not being bodies either. This gives a meaning to what Newton says,
though it is perhaps too figurative to capture his thought: the figures are
actually, not merely potentially there; it is just that they are insensible.
We may grant that points and lines are truly in space, in that they have
spatial co-ordinates, but this falls short of ascribing a metaphysical status
to them.
According to Newton, the parts of immovable space in which bodies truly
move ‘make no impression on the senses’ (Newton 1999: 414). However,
it would be premature to take unobservability to show the non-existence of
parts, regions, or points of space, or the meaninglessness of their postulation,
since it is as yet not clear what it is that is being alleged to be unobservable,
what it would be to observe such parts, as understood by Newton. As we
shall see, arguments in this area which conform to the pattern, ‘unobservable,
hence meaningless’, should give way to considerations concerning definition,
in a broad sense of the term. So, it is sometimes claimed that, because absolute
motion in space is undetectable, it does not exist, whereas what should be
said is that, because absolute motion in space is undefined, the question of
its existence or occurrence does not arise. We shall have occasion to revisit
this issue.
8 Time,Space,andMetaphysics
The relationist rejects the conception of space as a possibly empty container,
construing it as a system of relations between objects. Thus Leibniz: ‘I have
said more than once, that I hold space to be something merely relative, as
time is; that I hold it to be an order of coexistences, as time is an order
of successions. For space denotes, in terms of possibility, an order of things
which exist at the same time, considered as existing together’ (Alexander
1956: 25–6). So, all movement is with respect to things in space, not to
space itself. Take away all bodies, and space itself is no more.

Newton wrote:
The parts of duration and space are only understood to be the same as they really are
because of their mutual order and position; nor do they have any hint of individuality
apart from that order and position which consequently cannot be altered.
(Newton 1962: 126)
So, the identity of a part of space or time—what makes it that part—is
constituted by its order and position; and what is important about order and
position is that they are not in turn determined by bodies or events, but
are as they are irrespectively of whether the latter exist. But do spaces and
intervals of time come in predetermined volumes or lengths enjoying such
independence? We can define a region of space as, say, the space bounded by
these walls, floor and ceiling; that is, we define a space. What is problematic is
the conception of this region as a space having an identity which owes nothing
to anything in space; as though it had a determinate location, though not in a
reference-frame defined by any body or bodies. What, we may wonder, would
constitute the axes with respect to which the co-ordinates could be defined?
If space were empty—a possibility that Newton allows—there would be
nothing that provided an origin, or any other reference point.
For Leibniz, the only identity which points of space and time enjoy is what
is conferred upon them by the bodies and events in terms of which they are
defined or identified. Space is not real in itself, but ‘is nothing at all without
bodies, but the possibility of placing them’, and instants, ‘consider’d without
the things, are nothing at all; and they consist only in the successive order
of things’ (Alexander 1956: 26–7; cf. 76–7). To say that space is relative
is to deny it an existence independent of that of bodies, but Leibniz’s more
positive characterization of space needs refining. The grammar does not allow
the simple identification of ‘space’ and ‘the possibility of placing bodies’,
but the translation has to be more roundabout: space (is what) makes possible
the placing of bodies; or: there is a space between A and B if and only if it
Conceptions of Time and Space 9

makes sense to speak of placing a body between A and B (without displacing
anything). We are talking about what is describable, rather than physically
possible. Leibniz’s positive account of instants is also in need of a more
accurate formulation.
Space and time are to be thought of as relations. In Leibniz’s scheme
this means that they are ideal things, though this is not a categorization
which renders them subjective, nor threatens the truth of attributions of
duration or spatial, or temporal order (cf. Ishiguro 1972: 106–10). In
modern terminology, we might say that for Leibniz space and time are
logical constructions out of bodies and events. Equivalently, we could give
the following explanation. It was said above that, for the relationist, time is
created by change. How, it may be wondered, could that possibly be? We
may seem to go too far in speaking of creation, but this is simply a matter of
making certain descriptions possible. Given change we have a foundation for
speaking of when something happened, of its continuing to be; given bodies,
we have what is needed to allow us to speak of space and spatial extension.
In passing, Leibniz appears to suppose that he has refuted absolute space,
or the view that space is a substance, by showing that its existence would
conflict with the principles of the identity of indiscernibles—‘There is no
such thing as two individuals indiscernible from each other’—and sufficient
reason—‘nothing happens without a reason why it should be so, rather than
otherwise’ (Alexander 1956: 36, 16). God could be accused of locating the
universe where it is, rather than a mile to the left, for no good reason, if
there were such a thing as absolute space. Leibniz holds that, since God
cannot do anything without sufficient reason, there cannot be absolute space,
but his central objection undercuts this charge: there is no threat to God’s
observance of that principle, since the alternative which absolute space would
sanction—location of the universe in one place rather than another—is no
real alternative at all, so the question of God’s acting arbitrarily or otherwise
does not even arise.

We might try to bring together Leibniz’s two lines of reasoning by taking
him as holding that there is no real difference between the supposedly distinct
possibilities, which therefore fail to yield a differentiating reason on which
God might act. However, if the identity of indiscernibles is sufficient to settle
the matter, the reference to God is unnecessary, yet here and elsewhere in
the correspondence with Clarke, Leibniz places less emphasis on that more
basic consideration, more on the way God’s choices are determined by the
principle of sufficient reason.
10 Time,Space,andMetaphysics
Leibniz’s argument concerning a displacement in time follows the same
lines, but presents us with a more complex issue. It may be argued that, if it
has been in existence for an infinite time, the universe could not have been in
existence for a shorter or longer time up to the present, and even if its history
is finite, it could not have been in existence for a shorter or longer time in
the sense that more or less time might have lapsed before it began, since the
passage of time could not antedate the beginning of the universe. But could
we not allow that the universe might have been older without supposing a
time before it began, thus keeping time within the universe? True, questions
of identity arise. If events are individuated by the date and place of their
occurrence, it might seem that a current eclipse, say, could not have occurred
at a different time, so not at a later or earlier time since the universe began.
However, we can surely say that a longer period of time might have preceded
the current eclipse, the eclipse we are now observing. Supposing t
0
the first
moment of time, it is not a matter of going back in time beyond t
0
,butof
increasing the lapse of time between t
0

and the eclipse.
Some relationists feel obliged to say that an empty space is simply nothing,
or, with Einstein (1993: x), that ‘empty space’ has no meaning, but while
itmaybeagreedthatthewholeofspacecouldnotbeempty,thespaces
that can exist between bodies would not seem to equate literally to nothing.
That there should be an empty space appears possible. That time should be
empty, in the sense that there might never be any events occurring, is highly
questionable, but so too is the suggestion that there could be even a period
or interval of time devoid of all change. We shall return to these issues.
1.3 METRICAL AND NON-METRICAL CONCEPTS
Absolute time, thought of as a quantity possessed of its own intrinsic
subdivisions, intervals against which our clocks are, ideally, to be judged, is
difficult to fathom: divisions arise only with events which mark their termini,
as with the arrival of the clock hands at a point on the dial. On the other hand,
time as duration owes nothing to the existence of clocks, an independence
that is shared by many of our temporal concepts, so perhaps something of
the absolute conception is to be found in pursuing the respects in which such
independence arises. We shall now develop this contrast.
Consider simultaneity and temporal precedence. Simultaneity would nor-
mally be explained in terms of events taking place at the same time, where
Conceptions of Time and Space 11
the significance of this latter phrase lies in what it presupposes by way of
a system of timekeeping. So the wedding and the funeral having both got
under way at 3.00 p.m., they began at the same time. However, instead
of mapping events onto a common time, we may compare them directly,
as when we observe two runners leave their starting blocks together, and,
without making use of a clock, we can appreciate that two extended events,
as a wedding and a funeral, take place concurrently, given that they both
begin and end together. Take an event which encompasses another event,
as a downpour might encompass rumbles of thunder and flashes of light-

ning. What we have is, say, rain under way and no lightning followed
by rain and lightning co-present, then rain continuing unaccompanied by
lightning. Our ability to become apprised of, and to recall, these succes-
sive states puts us in a position to say such things as that the downpour
preceded and outlasted the lightning, and we can say this without mak-
ing use of a concept of time which presupposes a means of keeping or
measuring time.
Before the introduction of clocks we could speak of one event as going
on for just as long as another when their end points coincided, and we
could reckon one event as going on for longer than another when the one
occurred within the temporal span of the other. But suppose that the rain
comes on and stops, and only then does the wind get up, and eventually
die down. Could the question meaningfully arise as to which went on for
longer? With spatial length there is the possibility of relating objects to a
common measuring rod and arriving at an answer in terms of their measured
lengths. Alternatively, we may dispense with the measure and compare the
two directly: we stand the man up against the door to see which is the taller.
With temporal comparisons there is nothing corresponding to the latter when
the events lack any temporal overlap, so if there is no temporal measure onto
which both events can be mapped, it might appear that the question of their
relative lengths would have no application.
That would, however, be an overhasty conclusion. We confidently pro-
nounce some events to be much briefer than others without the benefit of an
inclusion of the one within the span of the other. Witness our example of
the tune played fast and the same tune played slowly. We are even happy to
speak of sameness of length or duration with respect to events separated by a
lapse of time, in neither case thinking it necessary to have recourse to a clock.
Take a sequence of knocks on a door or chimes of a bell, where the interval
between successive sounds is so brief there is little scope for significant error
12 Time,Space,andMetaphysics

in judging them equally spaced, each sound being seemingly identical with,
and running on almost immediately from, its predecessor. We are not, of
course, concerned to answer to the nanosecond exactitude of measurements
in particle physics. As the intervals between the sounds become greater we
become less assured of their equality unless, for instance, we can interpose
sequences of the kind just considered, as when, hearing the tick of a clock,
we may go ‘tick, two, three, four, tick, two, three, four’, and so on. But do
we have a criterion for being right in such cases? Even if we forgo complete
accuracy, our mere say-so does not give the assurance that two episodes
are of equal duration which we may have when their end points coincide.
Wittgenstein’s observation appears to be pertinent: ‘One would like to say:
whatever is going to seem right to me is right. And that only means that here
we can’t talk about ‘‘right’’ ’ (1958: §258).
The question of making sense of relative length in the absence of a system
of timekeeping will be taken further later. Certainly, the utility of clocks in
enabling us to extend our temporal comparisons to non-overlapping events is
evident, though the comparisons which can be made without clocks are the
more basic. For instance, simultaneity as directly apprehended is not a notion
that introduction of a system of chronometry will oblige us to abandon
in favour of another, more sophisticated alternative, but it is incorporated
into the eventual metrical scheme. The cases of simultaneity which Einstein
counts on as being relatively unproblematic are precisely those where we
have clock readings and events in the immediate vicinity of the observer
and judged coincident by him—much as clear cases of spatial measurement
are those in which we can bring measure and object measured into close
spatial proximity. After all, timing an event is just a particular case of our
basic comparison, its distinctive feature being simply that the events being
correlated with the beginning and end of what is to be timed are events
generated by a clock or other timekeeper. Accounts of time in relativity
theory give clocks a fundamental role, but their very use presupposes a

non-metrical conception. Thus, e
1
and e
2
are deemed to occur at the same
time if, in suitable circumstances, they can be mapped onto the same clock
reading, but if the event of the clock signalling midday occurs simultaneously
with event e
1
,thisisnottobethoughtofascallingforasecondclock
giving the same time for these two events. Again, on our account of the
basic level at which our temporal concepts operate, we can render ‘Events
e
1
and e
2
take place at different times’ as ‘When e
1
takes place, different
things are happening from when e
2
takes place’. The different things could
Conceptions of Time and Space 13
be different clock readings, but there are not further things, times, there to
be invoked.
Clocks are not needed in order to make sense of simultaneity or temporal
precedence, nor for us to know that such relations obtain. Suppose you
experience a flash followed by a bang. How do you know that it is the flash
that takes place first? I am not concerned with uncertainties which may be
prompted by questions about the speeds at which sound and light travel,

but the question is, rather: how do you know that the one occurred before
the other within your experience? One response is to claim that we just
do know, that we have to do here with a bedrock form of knowledge that
cannot be further explained. Another suggestion might be that we depend on
atemporalsense.Thiscannotbeoneofthemoreusualfive,sinceweorder
events perceived by different senses, as with our flash and bang, but it must be
a sense which integrates temporally the deliverances of the others. However,
to postulate a sense with no known organ, no known mode of function, looks
to be no real advance on saying that we just do know. The right answer, it
would appear, requires us to consider the different states of mind associated
with the two experiences being ordered: when the flash occurs we have no
consciousness of the bang, whereas at the time of the bang’s occurrence we
have a lingering awareness of the flash. Such a situation is not one where we
should most naturally speak of memory, given the recentness of the earlier
occurrence, but we note that memory gives us something of the character
of the postulated sense, in that it shares with this construct the capacity to
embrace the deliverances of any of the acknowledged senses. And, of course,
talk of memory becomes more apposite the further removed from one another
in time the two events become.
While a community of speakers possessing only non-metrical temporal
notions can have the conception of one event as simply having occurred,
or as having occurred before another, this is, once more, not necessarily a
conception of one event as having occurred at an earlier time,oratanearlier
time than another event, since this would require them to map events onto
a temporal series, and such a development would be yet to come. Indeed,
we may even hesitate to speak in terms of a concept of time in their regard,
since any term equivalent to our ‘time’ is clearly dispensable, and they are
not in a position to make use of such phrases as ‘at a time’, ‘for a time’,
‘the right time’, ‘in time’, and so forth. Again, it will not be appropriate to
expand ‘e

1
occurred before e
2
’as‘e
1
occurred at a time before e
2
’, and while,
for us, to say that an event occurred then may be to say that it occurred at
14 Time,Space,andMetaphysics
that time, where this is a matter of time as given by a clock, for the speaker
of the more primitive language, the temporal reference will be as determined
directly by some past event, rather than by the time onto which this might
in turn be mapped, ‘at that time’ being, even for us, just one among the
paraphrases possible for ‘then’. Note the analogy between points of time and
points of space. ‘a is above b’ is not to be explained as ‘a is situated at a point
above b’, since there being a point above b will be an instance of the former
relation.
It is of interest to consider how much of our temporal vocabulary
presupposes a chronometry, a system of timekeeping. Not as much as one
might suppose, I am inclined to say, for a reason already glimpsed: points and
periods are specifiable by singling out certain events, such as the movements of
the hands of a clock, but events are still there to furnish points of reference even
if systematization into a temporal scheme has not taken place. Consider some
of the relevant vocabulary, as ‘always’, ‘never’, ‘seldom’, ‘often’, ‘again’, and
‘occasionally’. The sentence, ‘She has never mentioned the possibility’, is
naturally paraphrased as ‘She has at no time mentioned the possibility’, but
it could equally be rendered as ‘On no occasion has she mentioned the
possibility’. Occasions may be specified by means of temporal clauses—‘On
that occasion—when, that is, she was receiving her degree’—but the identity

of the occasion can be determinate without our having to introduce a time
or date into its specification. As just illustrated, a clause beginning ‘when ’
can fix a temporal reference without explicit or implicit reference to clock
time, and we may observe ‘as’ in a similar role: ‘He fell as he was approaching
the house’. In ‘At this point the chairman interrupted’, ‘at this point’, like
‘at this juncture’, would not naturally pick out a time, but we could again
enlarge upon its reference with a temporal clause, ‘when the speaker started
to ramble’. ‘Always’ is often ‘at all times’, but the reference would be more
restricted with ‘He is always complaining’, and here a phrase beginning
‘whenever ’, with appropriate occasions specified, may be usable in its
stead. Think, too, how qualifications such as ‘incessantly’ and ‘invariably’
may be enlisted.
There are many uses of ‘time’ itself which can often be understood without
the benefit of a chronometry, as with ‘for the last time’, ‘several times’,
‘sometimes’, and ‘time and time again’. If we were to say ‘The children were
alltalkingatthesametime’,weshouldbeunlikelytobethinkingofatimeas
given by a clock; it is a matter of the children all talking together, or at once.
With respect to some uses there may be uncertainty whether a system of