SUO: Continuants and Occurrents in 4D
Some people, notably Pat, have complained that Peter Simons' definition
of the distinction between continuants and occurrents cannot be
translated to the 4D point of view. I don't fully agree with that
claim, but in any case, I prefer the approach that Whitehead adopted
with his process philosophy, which is presented in a rather formidable
style in his book _Process and Reality_.
Following is an excerpt from a lecture that Whitehead presented in
1920 (nine years before he had time to invent lots of difficult
terminology). It gives a good summary of his view that processes
and events are the ultimate constituents of reality, and objects
are "recurring event types".
Whitehead's position, which he developed within a 4D framework,
is my preferred view of how continuants should be defined. For a
more nicely formatted version of this paper, see
http://www.bestweb.net/~sowa/ontology/anw_obj.htm
John Sowa
________________________________________________________________________
Objects and Events
by Alfred North Whitehead
In this excerpt, Whitehead summarizes some themes that he developed
more fully in his magnum opus Process and Reality. This lecture is
useful as a brief introduction to his process philosophy, which
treats processes and events as the fundamental constituents of
reality. Objects, in this view, are abstractions from the flux
of experience. They are recurring event types, which give some
degree of permanence and structure to the eternal flux.
Events. To put ourselves in the position to assimilate and to criticise
any change in ultimate scientific conceptions we must begin at the
beginning. So you must bear with me if I commence by making some simple and
obvious reflections. Let us consider three statements:
1. 'Yesterday a man was run over on the Chelsea Embankment,'
2. 'Cleopatra's Needle is on the Charing Cross Embankment,'
3. 'There are dark lines in the Solar Spectrum.'
The first statement about the accident to the man is about what we may term
an 'occurrence,' a 'happening,' or an 'event.' I will use the term 'event'
because it is the shortest. In order to specify an observed event, the
place, the time, and character of the event are necessary. In specifying
the place and the time you are really stating the relation of the assigned
event to the general structure of other observed events. For example, the
man was run over between your tea and your dinner and adjacently to a
passing barge in the river and the traffic in the Strand. The point which I
want to make is this: Nature is known to us in our experience as a complex
of passing events. In this complex we discern definite mutual relations
between component events, which we may call their relative positions, and
these positions we express partly in terms of space and partly in terms of
time. Also in addition to its mere relative position to other events, each
particular event has its own peculiar character. In other words, nature is
a structure of events, and each event has its position in this structure
and its own peculiar character or quality.
Let us now examine the other two statements in the light of this general
principle as to the meaning of nature. Take the second statement,
'Cleopatra's Needle is on the Charing Cross Embankment.' At first sight we
should hardly call this an event. It seems to lack the element of time or
transitoriness. But does it? If an angel had made the remark some hundreds
of millions of years ago, the earth was not in existence, twenty millions
of years ago there was no Thames, eighty years ago there was no Thames
Embankment, and when I was a small boy Cleopatra's Needle was not there.
And now that it is there, we none of us expect it to be eternal. The static
timeless element in the relation of Cleopatra's Needle to the Embankment
is a pure illusion generated by the fact that for purposes of daily
intercourse its emphasis is needless. What it comes to is this: Amidst the
structure of events which form the medium within which the daily life of
Londoners is passed we know how to identify a certain stream of events
which maintain permanence of character, namely the character of being the
situations of Cleopatra's Needle. Day by day and hour by hour we can find a
certain chunk in the transitory life of nature and of that chunk we say,
'There is Cleopatra's Needle.' If we define the Needle in a sufficiently
abstract manner we can say that it never changes. But a physicist who looks
on that part of the life of nature as a dance of electrons, will tell you
that daily it has lost some molecules and gained others, and even the plain
man can see that it gets dirtier and is occasionally washed. Thus the
question of change in the Needle is a mere matter of definition. The more
abstract your definition, the more permanent the Needle. But whether your
Needle change or be permanent, all you mean by stating that it is situated
on the Charing Cross Embankment, is that amid the structure of events you
know of a certain continuous limited stream of events, such that any chunk
of that stream, during any hour, or any day, or any second, has the
character of being the situation of Cleopatra's Needle.
Finally, we come to the third statement, 'There are dark lines in the Solar
Spectrum.' This is a law of nature. But what does that mean? It means
merely this. If any event has the character of being an exhibition of the
solar spectrum under certain assigned circumstances, it will also have the
character of exhibiting dark lines in that spectrum.
This long discussion brings us to the final conclusion that the concrete
facts of nature are events exhibiting a certain structure in their mutual
relations and certain characters of their own. The aim of science is to
express the relations between their characters in terms of the mutual
structural relations between the events thus characterised. The mutual
structural relations between events are both spatial and temporal. If you
think of them as merely spatial you are omitting the temporal element, and
if you think of them as merely temporal you are omitting the spatial
element. Thus when you think of space alone, or of time alone, you are
dealing in abstractions, namely, you are leaving out an essential element
in the life of nature as known to you in the experience of your senses.
Furthermore there are different ways of making these abstractions which we
think of as space and as time; and under some circumstances we adopt one
way and under other circumstances we adopt another way. Thus there is no
paradox in holding that what we mean by space under one set of
circumstances is not what we mean by space under another set of
circumstances. And equally what we mean by time under one set of
circumstances is not what we mean by time under another set of
circumstances.
By saying that space and time are abstractions, I do not mean that they do
not express for us real facts about nature. What I mean is that there are
no spatial facts or temporal facts apart from physical nature, namely that
space and time are merely ways of expressing certain truths about the
relations between events. Also that under different circumstances there are
different sets of truths about the universe which are naturally presented
to us as statements about space. In such a case what a being under the one
set of circumstances means by space will be different from that meant by a
being under the other set of circumstances. Accordingly when we are
comparing two observations made under different circumstances we have to
ask 'Do the two observers mean the same thing by space and the same thing
by time?' The modern theory of relativity has arisen because certain
perplexities as to the concordance of certain delicate observations such as
the motion of the earth through the ether, the perihelion of mercury, and
the positions of the stars in the neighbourhood of the sun, have been
solved by reference to this purely relative significance of space and time.
Objects. I want now to recall your attention to Cleopatra's Needle, which
I have not yet done with. As you are walking along the Embankment you
suddenly look up and say, 'Hullo, there's the Needle.' In other words, you
recognise it. You cannot recognise an event; because when it is gone, it is
gone. You may observe another event of analogous character, but the actual
chunk of the life of nature is inseparable from its unique occurrence. But
a character of an event can be recognised. We all know that if we go to
the Embankment near Charing Cross we shall observe an event having the
character which we recognise as Cleopatra's Needle. Things which we thus
recognise I call objects. An object is situated in those events or in that
stream of events of which it expresses the character.
There are many sorts of objects. For example, the colour green is an object
according to the above definition. It is the purpose of science to trace
the laws which govern the appearance of objects in the various events in
which they are found to be situated. For this purpose we can mainly
concentrate on two types of objects, which I will call material physical
objects and scientific objects. A material physical object is an ordinary
bit of matter, Cleopatra's Needle for example. This is a much more
complicated type of object than a mere colour, such as the colour of
the Needle. I call these simple objects, such as colours or sounds,
sense-objects. An artist will train himself to attend more particularly
to sense objects where the ordinary person attends normally to material
objects. Thus if you were walking with an artist, when you said 'There's
Cleopatra's Needle,' perhaps he simultaneously exclaimed 'There's a nice
bit of colour.' Yet you were both expressing your recognition of different
component characters of the same event. But in science we have found out
that when we know all about the adventures amid events of material physical
objects and of scientific objects we have most of the relevant information
which will enable us to predict the conditions under which we shall
perceive sense-objects in specific situations. For example, when we know
that there is a blazing fire (i.e. material and scientific objects
undergoing various exciting adventures amid events) and opposite to it a
mirror (which is another material object) and the positions of a man's face
and eyes gazing into the mirror, we know that he can perceive the redness
of the flame situated in an event behind the mirror -- thus, to a large
extent, the appearance of sense-objects is conditioned by the adventures of
material objects.
The analysis of these adventures makes us aware of another character of
events, namely their characters as fields of activity which determine the
subsequent events to which they will pass on the objects situated in them.
We express these fields of activity in terms of gravitational,
electromagnetic, or chemical forces and attractions. But the exact
expression of the nature of these fields of activity forces us
intellectually to acknowledge a less obvious type of objects as situated in
events. I mean molecules and electrons. These objects are not recognised
in isolation. We cannot well miss Cleopatra's Needle, if we are in its
neighbourhood; but no one has seen a single molecule or a single electron,
yet the characters of events are only explicable to us by expressing them
in terms of these scientific objects. Undoubtedly molecules and electrons
are abstractions. But then so is Cleopatra's Needle. The concrete facts are
the events themselves -- I have already explained to you that to be an
abstraction does not mean that an entity is nothing. It merely means that
its existence is only one factor of a more concrete element of nature. So
an electron is abstract because you cannot wipe out the whole structure of
events and yet retain the electron in existence. In the same way the grin
on the cat is abstract; and the molecule is really in the event in the same
sense as the grin is really on the cat's face.
Now the more ultimate sciences such as Chemistry or Physics cannot express
their ultimate laws in terms of such vague objects as the sun, the earth,
Cleopatra's Needle, or a human body. Such objects more properly belong to
Astronomy, to Geology, to Engineering, to Archaeology, or to Biology.
Chemistry and Physics only deal with them as exhibiting statistical
complexes of the effects of their more intimate laws. In a certain sense,
they only enter into Physics and Chemistry as technological applications.
The reason is that they are too vague. Where does Cleopatra's Needle begin
and where does it end? Is the soot part of it? Is it a different object
when it sheds a molecule or when its surface enters into chemical
combination with the acid of a London fog? The definiteness and permanence
of the Needle is nothing to the possible permanent definiteness of a
molecule as conceived by science, and the permanent definiteness of a
molecule in its turn yields to that of an electron. Thus science in its
most ultimate formulation of law seeks objects with the most permanent
definite simplicity of character and expresses its final laws in terms of
them.
Event particles. Again when we seek definitely to express the relations of
events which arise from their spatio-temporal structure, we approximate to
simplicity by progressively diminishing the extent (both temporal and
spatial) of the events considered. For example, the event which is the life
of the chunk of nature which is the Needle during one minute has to the
life of nature within a passing barge during the same minute a very complex
spatio-temporal relation. But suppose we progressively diminish the time
considered to a second, to a hundredth of a second, to a thousandth of a
second, and so on. As we pass along such a series we approximate to an
ideal simplicity of structural relations of the pairs of events
successively considered, which ideal we call the spatial relations of the
Needle to the barge at some instant. Even these relations are too
complicated for us, and we consider smaller and smaller bits of the Needle
and of the barge. Thus we finally reach the ideal of an event so restricted
in its extension as to be without extension in space or extension in time.
Such an event is a mere spatial point-flash of instantaneous duration. I
call such an ideal event an 'event-particle.' You must not think of the
world as ultimately built up of eventparticles. That is to put the cart
before the horse. The world we know is a continuous stream of occurrence
which we can discriminate into finite events forming by their overlappings
and containings of each other and separations a spatio-temporal structure.
We can express the properties of this structure in terms of the ideal
limits to routes of approximation, which I have termed event-particles.
Accordingly event-particles are abstractions in their relations to the more
concrete events. But then by this time you will have comprehended that you
cannot analyse concrete nature without abstracting. Also I repeat, the
abstractions of science are entities which are truly in nature, though they
have no meaning in isolation from nature.
The character of the spatio-temporal structure of events can be fully
expressed in terms of relations between these more abstract
event-particles. The advantage of dealing with event-particles is that
though they are abstract and complex in respect to the finite events which
we directly observe, they are simpler than finite events in respect to
their mutual relations. Accordingly they express for us the demands of an
ideal accuracy, and of an ideal simplicity in the exposition of relations.
These event-particles are the ultimate elements of the four-dimensional
space-time manifold which the theory of relativity presupposes. You will
have observed that each event-particle is as much an instant of time as it
is a point of space. I have called it an instantaneous point-flash. Thus in
the structure of this space-time manifold space is not finally
discriminated from time, and the possibility remains open for diverse modes
of discrimination according to the diverse circumstances of observers. It
is this possibility which makes the fundamental distinction between the new
way of conceiving the universe and the old way. The secret of understanding
relativity is to understand this. It is of no use rushing in with
picturesque paradoxes, such as 'Space caught bending,' if you have not
mastered this fundamental conception which underlies the whole theory. When
I say that it underlies the whole theory, I mean that in my opinion it
ought to underlie it, though I may confess some doubts as to how far all
expositions of the theory have really understood its implications and its
premises.
Measurements. Our measurements when they are expressed in terms of an
ideal accuracy are measurements which express properties of the space-time
manifold. Now there are measurements of different sorts. You can measure
lengths, or angles, or areas, or volumes, or times. There are also other
sorts of measures such as measurements of intensity of illumination, but I
will disregard these for the moment and will confine attention to those
measurements which particularly interest us as being measurements of space
or of time. It is easy to see that four such measurements of the proper
characters are necessary to determine the position of an event-particle in
the space-time manifold in its relation to the rest of the manifold. For
example, in a rectangular field you start from one corner at a given time,
you measure a definite distance along one side, you then strike out into
the field at right angles, and then measure a definite distance parallel to
the other pair of sides, you then rise vertically a definite height and
take the time. At the point and at the time which you thus reach there is
occurring a definite instantaneous point-flash of nature. In other words,
your four measurements have determined a definite event-particle belonging
to the four-dimension space-time manifold.
These measurements have appeared to be very simple to the land-surveyor and
raise in his mind no philosophic difficulties. But suppose there are beings
on Mars sufficiently advanced in scientific invention to be able to watch
in detail the operations of this survey on earth. Suppose that they
construe the operations of the English land-surveyors in reference to the
space natural to a being on Mars, namely a Martio-centric space in which
that planet is fixed. The earth is moving relatively to Mars and is
rotating. To the beings on Mars the operations, construed in this fashion,
effect measurements of the greatest complication. Furthermore, according to
the relativistic doctrine, the operation of time-measurement on earth will
not correspond quite exactly to any timemeasurement on Mars.
I have discussed this example in order to make you realise that in thinking
of the possibilities of measurement in the space-time manifold, we must not
confine ourselves merely to those minor variations which might seem natural
to human beings on the earth. Let us make therefore the general statement
that four measurements, respectively of independent types (such as
measurements of lengths in three directions and a time), can be found such
that a definite event-particle is determined by them in its relations to
other parts of the manifold.
Co-ordinates. If (p1, p2, p3, p4) be a set of measurements of this system,
then the event-particle which is thus determined will be said to have p1,
p2, p3, p4 as its co-ordinates in this system of measurement. Suppose that
we name it the p-system of measurement. Then in the same p-system by
properly varying (p1, p2, p3, p4) every event-particle that has been, or
will be, or instantaneously is now, can be indicated. Furthermore,
according to any system of measurement that is natural to us, three of the
co-ordinates will be measurements of space and one will be a measurement of
time. Let us always take the last co-ordinate to represent the
time-measurement. Then we should naturally say that (p1, p2, p3) determined
a point in space and that the event-particle happened at that point at the
time p4. But we must not make the mistake of thinking that there is a space
in addition to the space-time manifold. That manifold is all that there is
for the determination of the meaning of space and time. We have got to
determine the meaning of a space-point in terms of the event-particles of
the four-dimensional manifold. There is only one way to do this. Note that
if we vary the time and take times with the same three space co-ordinates,
then the eventparticles, thus indicated, are all at the same point. But
seeing that there is nothing else except the eventparticles, this can only
mean that the point (p1, p2, p3) of the space in the p-system is merely the
collection of event-particles (p1, p2, p3, [p4]), where p4 is varied and
(p1, p2, p3) is kept fixed. It is rather disconcerting to find that a point
in space is not a simple entity; but it is a conclusion which follows
immediately from the relative theory of space.
Furthermore the inhabitant of Mars determines event-particles by another
system of measurements. Call his system the q-system. According to him (q1,
q2, q3, q4) determines an event-particle, and (q1, q2, q3) determines a
point and q4 a time. But the collection of event-particles which he thinks
of as a point is entirely different from any such collection which the man
on earth thinks of as a point. Thus the q-space for the man on Mars is
quite different from the p-space for the land-surveyor on earth.
Timeless and Instantaneous Space. So far in speaking of space we have been
talking of the timeless space of physical science, namely, of our concept
of eternal space in which the world adventures. But the space which we see
as we look about is instantaneous space. Thus if our natural perceptions
are adjustable to the p-system of measurements we see instantaneously all
the event-particles at some definite time p4, and observe a succession of
such spaces as time moves on. The timeless space is achieved by stringing
together all these instantaneous spaces. The points of an instantaneous
space are event-particles, and the points of an eternal space are strings
of event-particles occurring in succession.
But the man on Mars will never perceive the same instantaneous spaces as
the man on the earth. This system of instantaneous spaces will cut across
the earth-man's system. For the earth-man there is one instantaneous space
which is the instantaneous present, there are the past spaces and the
future spaces. But the present space of the man on Mars cuts across the
present space of the man on the earth. So that of the event-particles which
the earth-man thinks of as happening now in the present, the man on Mars
thinks that some are already past and are ancient history, that others are
in the future, and others are in the immediate present. This break-down in
the neat conception of a past, a present, and a future is a serious
paradox. I call two event-particles which on some or other system of
measurement are in the same instantaneous space 'co-present'
event-particles. Then it is possible that A and B may be co-present, and
that A and C may be co-present, but that B and C may not be co-present. For
example, at some inconceivable distance from us there are events co-present
with us now and also co-present with the birth of Queen Victoria. If A and
B are co-present there will be some systems in which A precedes B and some
in which B precedes A. Also there can be no velocity quick enough to carry
a material particle from A to B or from B to A.
These different measure-systems with their divergences of time-reckoning
are puzzling, and to some extent affront our common sense. It is not the
usual way in which we think of the Universe. We think of one necessary
time-system and one necessary space. According to the new theory, there are
an indefinite number of discordant time-series and an indefinite number of
distinct spaces. Any correlated pair, a time-system and a space-system,
will do in which to fit our description of the Universe. We find that under
given conditions our measurements are necessarily made in some one pair
which together form our natural measure-system. The difficulty as to
discordant time-systems is partly solved by distinguishing between what I
call the creative advance of nature, which is not properly serial at all,
and any one time series. We habitually muddle together this creative
advance, which we experience and know as the perpetual transition of nature
into novelty, with the single-time series which we naturally employ for
measurement. The various time-series each measure some aspect of the
creative advance, and the whole bundle of them express all the properties
of this advance which are measurable.
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The full text of this lecture, which Whitehead presented to the students of
the Chemical Society of Imperial College, London, in 1920, has been
reprinted as Chapter VII of The Concept of Nature, by A. N. Whitehead,
Cambridge University Press. This web page was reformatted with subheadings
added by John F. Sowa.