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The Philosophy of the Present
Supplementary Essay 3: Scientific Objects and Experience
III
SCIENTIFIC OBJECTS AND EXPERIENCE
The knowledge process takes a different route for
the scientist from that which it takes for the epistemologist. The scientist
starts with an unquestioned material world and with unquestioned objects
that appear in the problem with which his research is occupied; from
these he proceeds by inference to the formulation of his hypothesis
and the consequences which it involves, and then on to the observation
and experiment by which his hypothesis is tested. Although he criticizes
his perceptual experiences and exhibits the errors and illusions of
perception, his criticism is always founded on objects that are there;
and his criticism does not invalidate these, since he must appeal to
them as tests of the errors he discovers. In the process of thinking
out the hypothesis his ideas symbolize relations in a world that is
there, and he tentatively seeks to find among them such interrelations
as will overcome conflicts between objects and their meanings, or between
different meanings of things. He finally deduces the results that follow
from his hypothetical reconstruction, and by observation and experiment
in an unquestioned world finds, or fails to find, the confirmation he
is seeking. His cognitive proceeding is from an accepted perceptual
world through exceptional instances and conflicting meanings on to the
same world, after its meanings have been reconstructed. That world itself
he never questions.
The epistemologist, on the other hand, proceeds from the fact that
all perceptual experiences are dependent upon the relation of the world
to the organism, and makes use of such (141) experiences
as illusions and perceptual errors in order to locate percepts in a
consciousness entirely separate from the world of objects to which these
percepts refer. This position was strongly fortified by the doctrine
of Renaissance science that secondary qualities cannot belong to the
physical world with which physical science is occupied. Knowledge, as
the epistemologist conceives it, undertakes to proceed from these states
of consciousness, including all perceptual experience, over to an ontologically
separate world to which these states of consciousness seem to refer.
He is thus led to the conclusion that a cognitive reference attaches
to all perceptual experience. The existence of a world to which such
states of consciousness refer becomes the epistemologist's problem.
It is important to place the scientific object in its relation to the
perceptual world, which is, as we have seen, presupposed both in the
scientist's problem and in his experimental data. That object is an
abstraction of that within experience which is subject to exact measurement.
It is furthermore a physical thing, i.e., it occupies a volume of extension
that could conceivably be brought within the range of a manipulatory
experience. Even when we pursue de Broglie's idea and state matter in
terms of wave motion, we must come back to a definable portion of space
which is in so far within our field of conceivable manipulation that
we could measure the waves. The ether, as long as science retained it,
could be conceived of as the stuff occupying this space, and elasticity
and rigidity could be ascribed to it.
If we turn to the experimental findings to which even the most abstruse
hypothesis must appeal, if appeal is by any device possible, we find
that the test takes place within what I have called the manipulatory
area. We are here dealing with pointer readings that reflect changes
lying at a distance from the changes in the apparatus. Within this (142)
manipulatory area visual perspectives disappear, and we can reach a
high degree of accuracy in measurement. Its spatial structure, as we
have seen, is that of the rigid body, and so far as physical tests can
go it is that of Euclidean geometry. What is of peculiar importance
is that it is within this field that we find, directly or indirectly,
our common objects. For example, the penny with which epistemologists
have been so much occupied is the same penny for different observers
at different angles and at different distances in so far as these different
visual pennies are recognized as appearances of one and the same penny
which any of the observers, under the control of his visual experience,
could touch and handle. As a result of a common method of manipulation,
measurement and location, the manipulatory areas of the different observers
thus become identical. It is important to recognize that while each
individual will receive from the penny an experience of pressure, in
a sense peculiar to himself, the method of identifying the penny that
all will experience is not peculiar to himself. It is a logical procedure
whose entities and relations exist only in so far as they constitute
a universal factor in the experience of the individual. The individual,
that is, does not first make his own measurements and reach his own
identifications, and then compare these with those of others in order
to reach a common object; his method of determination is rather in terms
of a language that with its various symbols comes into existence only
through the fact that the individual assumes the attitude common to
all those involved in the common undertaking. This common penny attains
the reality of experimental findings, however, only if it comes back
directly or indirectly to a measurable something in the manipulatory
area. At the basis of the process of measurement, of course, there lies
the fundamental mechanism of perception, in which distance experiences
lead to contact (143) experiences that control the
environment in the interest of the organism. The contact experiences
are the reality of the distance experiences. The physical object, however,
constitutes a break in the primitive biological process that finds its
completion in the consummation which the biological needs of the organism
call for. It is the hand under the control of the eye that is responsible
for the manipulatory area. The handled object comes betwixt and between
the vision of food and its eating. If the biological process, under
the distance stimulation, goes through to consummation without interruption,
no physical object arises in experience. In a biological sense the manipulated
or physical object is thus a mediate reality. In its abstraction from
consummation it is first of all an implement, and then the physical
thing of a later science.
When the Michelson-Morley experiment and the difficulties brought to
light by the lack of invariance in the Maxwell equations of electro-magnetism
had ejected ether as a physical thing, the ether of "stuff,"
or, to use Whitehead's term, the event, was substituted for it, and
time entered as a dimension of the physical thing. We have already seen
that in the perceptual world space and time are inevitably separated.
Motion involves a something that moves which is irrelevant to the temporal
process. An event always happens to something. A striking result of
recent changes in physical science, and of the new theories to which
these changes have given rise, is that the event has taken the place
of the physical thing. In the perceptual world and in the world of masses
in motion events happen to things. Over against change there are unchanged
things which are the conditions of change. That is, in the perceptual
world space and time are necessarily separate. Space-time cannot be
the form of perceptual experience. We can shift from one perspective
to another, and realize that what from one standpoint (144)
is rest, from another is motion; but in each perspective there are permanent
things, irrelevant to time, that give meaning to the changes that go
on within time. If perspectives can be reduced to diverse appearances
of things that have remained the same during all changes, relativity
will not bite into the nature of the things; but if the nature of things
is found in process, in a system of changes, the different values which
this process takes on from the various standpoints of different but
related observers must affect the natures of the things themselves.
Yet we cannot really reduce things to processes, for it is not possible
that processes should go on that are not processes of things, and measurements
can only be made in a situation within which something abides irrelevant
to time.
While the event is taking place we watch it or listen to it or feel
it; but if we can complete the behavior it initiates, we isolate the
thing to which the event is happening. But from the standpoint of relativity
no physical object can be isolated from what is happening to it. If
it is at rest in one consentient set under the measurement of a scientist,
it is moving in another set; and not only are its measurements in time
and space shifting with the relative velocities of the sets, but its
inner content of mass varies also. There is nothing that can be laid
hold of except the transformations of these measurements from one set
to another and the coincidences of events in an absolute space. Now
what this amounts to is that we have no sooner got hold of the thing
in a permanent space within which we can measure it and determine its
inner mass-content than we must put ourselves at a distance from it
in another space and determine its changes due to the relative velocities
of these two spaces and their consentient sets.
We have thus reversed the fundamental order of our behavior and have
made the "what a thing is" a distance (145)
experience instead of a contact experience. The reason for this shifting
is evident. The object in the manipulatory area belongs to the perspective
of the individual, and, in so far as this manipulatory area can be determined
by measurements which are common to all members of the community to
which he belongs, to the space and time of the consentient set of which
his organism as a physical thing is a member. It is only by putting
ourselves in the distant consentient set that we can realize that the
distortions the objects of that set suffer are the same as those our
set undergoes when seen from that standpoint. Since there is no absolute
space to which these differing standpoints can be referred, as the perspectives
of vision can be referred to a common manipulatory area, there can be
no manipulatory area to which these perspectives or frames of reference
may be referred. The measuring-rod and the clock that gives the local
time belong to the manipulatory area, and the quantities they measure
will vary from one set to another. There is no common measuring rod,
and no common clock, that all can accept. The different observers can
only make use of formulae of transformation by which measurements made
in one set can be read into those of another. We are left therefore
with a language of distance light-signals which can refer to no object
common to the experience of all. It is true that by application of the
formulae we can isolate a constant value for the interval between the
coincidences of events in a Minkowski space-time, and that this constant
value may be regarded as the common reality to which all the different
measurements, made from the standpoints of various perspectives, ultimately
refer. This space-time, however, abstracts from every character in the
distance experience whose meaning lies in its reference to a common
physical object. Only those character-, in the distance experience are
left that refer to a single form of calculation (146)
common to all the different perspectives. It is this abstraction that
makes it possible to assimilate time to space as a fourth dimension.
For this calculation what is a timeinterval in one perspective is a
space-interval in another. It would, however, be a mistake to assume
that we have thus passed into a field of communication in which our
symbols have lost all significance except that of reference to a common
referent. In fact we are still in a visual world, with a finite value
for the velocity of light; only the physical thing to which that visual
experience refers is stated in terms of a calculation-value common to
an indefinite number of diverse visual experiences.
A similar criticism may be made of the view that would regard energy
as constituting the nature of the physical thing. For the perceptual
world there must be a system of things, and energy is the measure of
the changes brought about in this system when a force is brought to
bear upon it from without. Experiments, and the mathematical formulation
in which thermodynamics has clothed the results of these experiments,
however, have justified the conclusion that such measurement reveals
only the potential energy within the system. How widely we are justified
in spreading the generalization of the conservation of energy has been
made the subject of dispute, though, as Poincaré has pointed out, we
can always assume potential energy to keep the doctrine intact. When,
however, we make this energy the nature of the thing, we are as necessarily
passing out of the perceptual world as when we substitute space-time
for space and time.
Energy, like space-time, is a transformation value. We select a process
in the manipulatory field-the amount of work done-as the measure of
energy; but what is measured is not stated as a function of the mass
of the body, on the contrary mass itself is stated in terms of energy.
Thus, (147) when we reduce physical things either
to space-time or to energy, we are in either case utilizing a process
of measurement in a perceptual, manipulatory area to give the nature
of the physical thing, while the nature thus ascribed to the physical
thing does not belong to the field of the measurement. In the one case
instead of the thing we set up an event located in a space-time that
lies outside of experience; in the other, we appeal, as in Ostwald's
view, to a metaphysical field equally remote from experience.
Reduction of mass to electro-magnetism. would provide us with a further
illustration, for electro-magnetism and light have thus been brought
back to the same process, viz., that which relates an organism to distant
objects. If mass could be stated in electro-magnetic terms we should
have substituted the distance-value of the object for its manipulatory
value. That it should be so stated, however, presupposes that we are
using the wave formulation and not the corpuscular formulation for electro-magnetism,
and that we are not driven to introduce the corpuscular concept - the
photon, into the theory of light.
This brings us to Professor Bridgman's program of rigidly reducing
all our physical concepts to the operations we make use of in measurement.[1]
His proposal seems to amount to an undertaking to bring the object back
to the manipulatory area, but not to interpret the physical thing as
a volume of mass in motion, but rather to redefine the physical thing
of the manipulatory area in terms of its uses in scientific measurement.
The simple Newtonian doctrine interpreted the light and heat of the
sun as evidence of molecules of massive elements in violent motions;
but the elements have now become particles of electricity that can conceivably
be defined entirely in electro-magnetic terms, and this means (148)
that we can define them only in terms of mathematical formulations whose
constants are certain pointer-readings. The mathematical formulations
fix as exactly as possible the conditions under which we can obtain
these pointer readings. We are thus getting a picture, not of the movements
of manipulatory things, which, within the realm of our observations,
are the conditions of our distance experiences, but of ideal conditions
of control of manipulatory situations in which these distance experiences
can be reproduced. If we conceive the sun as made up of electrons and
protons, we can present in an imagined manipulatory area the movements
of these particles, with their distances from each other and their velocities.
We can present the electron and the proton as pressing toward each other
and as held apart by the centrifugal force of the incredible velocity
with which the electron revolves about the proton. But if we go on to
picture the electron and proton as crushed together in the center of
the sun, thus setting free, in the form of radiation, the electro-magnetic
energy, including that of mass, which is the "what it is"
of these electrical particles, we have transformed the stuff or manipulatory
content of the thing into distance experience. The indestructibility
of Newtonian mass reflected our fundamental attitude that what we get
hold of is the permanent reality of what we see, hear and otherwise
sense at a distance. If this permanent reality disappears in radiation,
and this comes to us, say, in heat and light, or in the form of cosmic
rays, it is no longer a distance experience of anything. The
same is true of fields of force. We may say that they are events but
there are no things to which the events happen at the location where
they are.
I am not voicing a hankering after the fleshpots of what Whitehead
has called the materialism of the Newtonian period. That view was afflicted
by the bifurcation that (149) Whitehead deplored,
and harbored the whole nest of epistemological problems that Lovejoy
has extensively spread before us.[2] I am only insisting
that whatever view we may take of the momentous changes that science
has brought in its wake since electro-magnetism. began to dominate its
research and doctrine, we cannot get away from the perceptual findings
that all science accepts as its most fundamental criterion of reality.
The appeal of science to its perceptual findings as its criterion evidently
involves more than any mere confirmation of distance experience by contact
experience; the appeal is rather to the perceptual occurrence of events
predicted on the basis of an hypothesis, in order to confirm that hypothesis.
The importance of the perceptually real thing of the manipulatory area
appears when an object of this sort can be identified under observation
and experiment in an exceptional instance; consider, for example, the
radiation of black bodies where the reality of the object as a perceptual
thing must be accepted, wholly in advance of any further interpretation
of it that a later hypothesis may give. Here we reach a something that
maintains itself as an object that can be felt as seen. It is further
evident that the reliability of measurements-of pointer readings-must
be assured within this same perceptual field. Even if we can neither
spread out the space and time of this area into the Euclidean space
of the Newtonian doctrine, nor subdivide its perceptual things into
Newtonian mass-particles, we nevertheless in some fashion relate the
assumed reality of a universe that goes way beyond the boundaries of
our perceptual experience to the decisive reality of the scientist's
findings.
Even if we reduce our physical concepts to operational processes, we
must confess that our physical things belong (150)
to the field of our control-the field of measurement of changes in our
experience. The causal antecedents of these changes can no longer be
stated in terms of physical things, in the sense that they are conceivable
permanent contactexperiences referred to by distance-experiences; but
our relevant measurements must still take place by means of physical
things. The causal antecedent may, for example, be both physical and
mental. It may be an event with adjectives supplied by ingression from
a world of eternal objects or universals. Or the expression for it may
be an elaborate mathematical apparatus for carrying out exact measurements
within the field of experiment and observation, as in Bridgman's Logic
of the Physical Sciences. Or again it may be a logical pattern
corresponding to some structure in a metaphysical world beyond experience-an
absolute world of space-time whose coincidences of events and the intervals
between them cannot appear in our relative spaces and times. But in
no case can the nature of these elements of the subatomic, electro-magnetic
world take the place of the physical mass-particles of Newtonian doctrine
which could be conceived of as subdivisions of the massive objects that
come under our own hands.
The breakdown of the Newtonian mechanical system was reached when,
with the development of the laws of thermodynamics and of the theory
of electro-magnetism, that meaning of physical things which fits our
perceptual experience could no longer be applied to the so-called material
universe. We now find that exactly determined distance-experiences occur,
which answer to something going on-something, however, that cannot be
stated in terms of changes among manipulatory things. In fact, we now
postulate in our physical hypotheses, as the inner nature of the things
referred to by the earlier distance experiences, other distance experiences,
such as energies, or radiations. In the account (151)
given of the pressure of gases, on the other hand, we present to ourselves
a picture of mass-particles bombarding each other and the walls of the
container. Here the ultimate elements are physical things conceived
in perceptual terms. But when we speak of the content of the electrons
and protons as an energy which may take the form of radiation, we are
describing them in terms of another distance experience-one which, moreover,
can refer to no conceivable contact-experience. We cannot however simply
brush to one side the whole of perceptual experience with the claim
that we are dealing rather with the conceptual objects of science, for
both our problems and our observations and experiments are stated in
perceptual experience.
There are two sides to the question. I think we must admit that the
distance-experience does and must imply that what is going on there
would be responsible for contact-experiences if the organism could
be at the place where the process responsible for the distance experience
is going on, and were provided with the appropriate sensitivity. The
other side of the question is, why do we state the nature of the object
not in these terms but in terms of distance-experience? I assume that
the reason for this is that the scientist is seeking for what is permanent,
that he finds this in the uniformities of the processes, that it is
in terms of these uniformities that he defines his objects, and that
this therefore is what he means when he speaks of conceptual objects.
The scientist seems thus to have transcended the perceptual field. He
seems to be dealing no longer either with distance-or with contact-experience,
but rather with an organized system of changes which may in perceptual
experience reflect themselves in either of these categories, but which
is really entirely independent of such experience. The door thus is
thrown open to the representative theory of perception. The perceptual
content of the object comes (152) to be defined in
terms of sense-data, which are correlated with scientific objects, but
have their proper locus in a consciousness, or else lie somewhere between
the mind and nature.
There are two reasons why the scientist does not make use of this realm
of consciousness, either in terms of consciousness or in terms of sense
data. The first is that the world which is out there in his observations
and experiments is the world of reality. No satisfactory line can be
drawn that will leave what is real for him on one side and sense-data
on the other. This fact becomes particularly evident when we consider
what we term the meanings of things. These are inextricably
interwoven with what must be termed consciousness; yet these meanings
are the very nature of the scientific objects. The other reason is that
so-called consciousness has now been brought within the range of biologic
science. Mind can no longer be put outside of nature.
As long as the scientist could be at home in a world of Newtonian mechanics,
before the atom disintegrated into particles of electricity, he could
look with Du Bois-Reymond's telescopic eye through the masses of things
down to ultimate particles whose motions followed relatively simple
laws. The connection of scientific with perceptual objects was close
enough to make him feel that his observations and experiments were in
the same world with the objects of his science. It is true that the
so-called sensory qualities, whether secondary or primary, could not
be the actual characters of the object; but the agreement between the
Euclidean space of science and that of perception was adequate, and
the correlation of weight with mass was so complete that the imaginary
subdivision of the matter of sense-perception still paralleled the analyses
of physics. The scientist was compelled, of course, so far as he considered
the matter, to locate all secondary qualities in consciousness, (153)
since the mechanical universe consisted simply of mass-particles in
motion, and of ether waves. In the physical world it was types of motion
that corresponded to color, sound, taste, odor and temperature. If the
scientist had been consistent he would have had to relegate to consciousness
the resistances of things as well; but as a matter of fact nothing interfered
with his building up mechanical models of mass-particles in his perceptual
imagination of what was going on in nature. Lord Kelvin is an excellent
example of the scientist of the period that had come to terms with thermo-dynamics
and electro-magnetism, yet still sought to preserve in the vortices
and stresses of the ether a mechanical picture of the anatomy of the
universe within which the perceptual imagination could be at home. Millikan's
oil-drops, Rutherford's photographs of the bombardment of atoms by alpha-particles,
and the models of the Bohr atom, seemed to connect the galaxies of the
submicroscopical world with those of stellar space. As long as pushing
and resistant things with calculable velocities could be located in
space, scientific imagination did not leave the world of perception.
It is relativity that changed all this. In the geometry of a Minkowski
space-time perceptual motion disappears. The ether has vanished, and
events take the place of physical things. Time is assimilated to space,
and the mind with its own spatial frame of reference adventures into
this space-time whose curvature corresponds to the gravitational constant.
The result is to carry the whole world of perception and perceptual
imagination into perspectives that exhibit only a logical correlation
between patterns affected with transformation formulae and events in
a four dimensional time-space and intervals between them. By definition
both events and intervals here lie outside of any experience. We reach
them by way of the reference in the knowledge process (154)
to something beyond itself, and by a theory of probability. In our mathematical
formulations of scientific experience we have come upon a cipher that
seems to refer to inexperiencable entities and their mutual relations;
and this hypostasized structure of logical entities satisfies our desire
for an absolute reality to which our confessedly relative experience
shall refer.
Yet, however far the scientists' procedure may go it never reaches
any situation except one in which a transformation , or a possible transformation,
takes place. If we ask for what lies back of all transformations, we
are asking for something outside of any experience, whether actual or
imaginary. We do, for example, postulate stages of development of the
universe which antedate any possible human experience, but in imagination
these are spread before an inner eye, or at least before a mind. If
we exclude the imagination, we have the abstractions of symbolic analysis,
which are of the same logical character as the transformation formulae
to which I have referred. If I say that this is a color, and hold this
color in its universality before my mind, I am isolating that which
enables me to reduce any other visual experience to the present experience
in so far as this is occupied with visual as distinct from auditory
or sensuous qualities of things. There is a common way of acting toward
all qualities that exist for the eye, as there is another way of acting
toward those that exist for the ear; and the isolation of this typical
reaction enables me to "transform" my conduct toward red into
that toward blue, in so far as I am able to react to color by one response
and to sound by another.
What we designate as "mental" is this attitude of isolation
of common features that call out identical responses provided that we
have symbols by which we refer to them. To set up a world of essences
or universals or eternal objects within (155) which
these entities subsist or exist is parallel to the procedure of setting
up a Minkowski space-time or a four dimensional aggregate of events.
Presumably objects in motion with reference to us have different values
spatially, temporally and in terms of mass from those at rest; and if
we are to measure them as we measure objects at rest about us we must
isolate the common feature-viz., the relational character of space and
time common to the two situations of rest and motion. The expression
of this common feature in the transformation formulae that Larmor and
Lorentz worked out in order to give invariance to the Maxwell equations
carries with it most interesting implications, especially with reference
to the constant velocity of light; but it does not change the fact that
what is going on is measurement in one situation of something whose
measurable characters are partly dependent upon the fact that it is
in another situation as well. It does not carry with it the necessity
of setting up a space-time realm. The postulation of such a realm rests
upon the assumption that because the same object may be dealt with either
as at rest or in motion, it must therefore be affected with the coordinate
of time in the same fashion in each situation. This assumption consequently
wipes out motion and substitutes for it geometrical determination in
a four dimensional realm outside of any possible experience.
It all comes back to this; the separation of space and time is essential
to the perceptual fact of motion. There must be a timeless space within
which motion takes place. But timeless spaces differ according as the
individual or "percipient event" is in motion or at rest.
If, as in the example of the railway train, we transfer ourselves from
the space of the compartment within the train to that of the landscape,
then the space of the compartment within the train is in motion, and
that space, if measured, will be measured in units- differing from those
of the space of the (156) landscape. The same is true
of the times. Given the relational character of space and time, their
structural characters differ according to what may be called the temporal
perspective of the individual. And, as Whitehead insists, these differences
belong to nature. They are not subjective. But the scientist is satisfied
with the transformation from one situation to another. Whether he accepts
a geometry of space-time or not, his operation is occupied only with
the transformation and does not require the assumption of a transcendent
space-time. The physicist's aim is an invariant set of equations that
will formulate the conditions under which we may control our physical
conduct. In order to reach an invariance for the Maxwell equations,
and to interpret the Michelson-Morley experiment, it became necessary
to work out transformations from one temporal perspective to another.
The possibility of successful formulae of transformation involves numerical
statements identical for all different perspectives. These can be expressed
in terms of intersections of events, and intervals between them, in
an absolute space-time; but such a formulation is not made use of in
the physicist's transformations. In every instance the physicist is
in a perceptual world, transforming, so far as may be necessary, one
perceptual perspective into another. Nor is the situation changed when
we pass from the special to the general principle of relativity. In
the application of the special theory the coordinates have immediate
physical significance, denoting measures expressed in terms of standard
measuring-rods and clocks, while in the general theory the numbers refer
to a continuum lying, as we have seen, outside of any possible experience.
The constants remain therefore mere numbers in terms of which natural
laws can be so expressed that they hold in any frame of reference, that
a transformation of axes of coordinate systems may be substituted for
a field of gravitational (157) force, and, in general,
that the metrical properties of space are wholly determined by the masses
of bodies. Einstein's genius has on the basis of these principles elaborated
a physical theory which not only carries through to logical completeness
the relativity of space and time, but also gives a more perfect and
accurate formulation of physical processes--one, moreover, that has
stood the test of observation and experiment at those points at which
it could be brought to the test. In the special theory we are formulating
measurable values-in terms of different systems of coordinates -- for
one perceptual perspective in terms of another perceptual perspective,
i.e., we are dealing with local times and local measuring rods. The
numbers have physical significance. In the general theory we obtain
equations that are covariant, i.e., we do not transform from one set
of coordinates to another, but obtain expressions that hold for all
possible sets of coordinates. The numbers evidently cannot express the
measures of time and space in any one coordinate system, as distinct
from another. They arise out of the possibility of transformation from
any possible set to any other possible set. They are reached by the
use of a Riemannian geometry of a four-dimensional manifold, and tensor
mathematics. These provide the mathematical apparatus for the measurement
of the intervals in a continuum however it may be deformed -- a continuum,
in this case, of space-time, and determine the form which equations
that express natural laws must have if they are to hold for every set
of coordinates.
It is as if we should take the formula by which we transform the value
of the dollar in 1913 into that of 1930, and into that of any other
possible date in human history, and should pass over from the constants
of food, clothing and the like and what they will exchange for, to a
generalized economic field in which the distances between the exchangeable
(158) goods we possess and those we want could be
expressed in a certain formula which would serve in any possible situation.
If we should set up such a world of determined intervals between abstract
values, and if in our effort to give our economic laws such a formulation
that they would obtain in any possible situation, we should state the
values in terms of their scarcity, i.e., in terms of the intervals-if
we succeeded in this undertaking, we might conceive of this abstract
economic world as the world of real valuation, of which our experienced
economic situations were subjective reflections. The orthodox school
of economics did in a manner thus reduce all values to the work necessary
for their production, that is, to the economic interval between the
raw material and the finished product, and sought thus within an economic
process to obtain more exact laws of exchange such as should be capable
of universal application within all economic situations. The Austrian
school, however, brought out the unique character of the want that lies
behind the valuation, which therefore could not be dissolved into the
abstract formulae of exchange.
I do not wish to pursue too far a somewhat far-fetched analogy; yet
it may serve to bring out the fallacy of reference common to both cases.
The constants that appear in formulae of exchange or transformation
refer not to entities that can be defined in terms of symbols of exchange
or transformation, but to such uniformities in these processes as enable
us to give them the widest generalization. I make bold to say that the
successful development of the theory of general relativity, with its
seeming reference beyond experience, is due to the power of its mathematical
apparatus, which has exploited the conception of the "field,"
taken from electro-magnetism and carried over to gravitation. The generalization
belonging to the, Riemannian geometry, the Gaussian coordinates, and
the Tensor Mathematics, applied (159) to the field
of physics, introduce a new entity only in so far as their application
presupposes a four-dimensional manifold within which time is one dimension.
The assimilation of time to space, as we have seen, divests reality
of the character of novelty inherent in change. It relegates change,
including motion, to subjective experience, and substitutes for it a
geometry of space-time within which every event is inexorably charted.
In the Newtonian mechanics, given uniformities of nature such as the
law of gravitation, a like determination of physical events was involved;
but the determination did not flow from formal characters in which a
lapse of time could be equated with a spatial extent, or in which spatial
and temporal extents fell together as predetermined numbers in the determination
of an interval. Space, whether Euclidean or non-Euclidean, was a necessary
frame-work within which change must take place, and the changes that
had taken place could be spatially charted and geometrically described;
but none of this necessity spread over into the causes of motion. The
mind might be wholly possessed by a faith that the laws of change were
as inexorable as were the structural characters of space; but it was
a faith, resting at best upon an induction that could never go beyond
a presumption. A change might always conceivably be other than it is.
A geometrical structure and what follows from that structure can never
conceivably be other than it is. In a space-time whose structure is
once given nothing could conceivably be other than it is. As long, then,
as nature appears in experience with the brute constants we discover,
which change under our further investigation, the reference of formulae
such as those of generalized relativity will always be to a situation
that may conceivably be other than it is. They can never disappear,
in our thinking of the world, into the geometry of a space-time. For
example, it will always be conceivable that the
(160) constant of gravitation will prove to be such
as not to resolve itself into curvatures of space-time. I recur to the
statement I made earlier, that the reference of general relativity as
well as that of special relativity is to the field of experience within
which scientific problems, observations and experiments lie.
Endnotes
- "The Logic of Modem Physics," especially chapter 1.
- "The Revolt Against Dualism," passim.
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