A theorist's philosophy of science


A theorist's philosophy of science
Helier J. Robinson

Citation: Physics Today 37, 3, 24 (1984); doi: 10.1063/1.2916156
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A theorist's philosophy of science
Considerations of perception illuminate and reconcile the issue

that divides theorist and experimentalist in science, rationalist and
empiricist in philosophy, and "airies" and "earthies" in general.

Helier J. Robinson

There is a temperamental difference
among thinkers that has produced a
spectrum of attitudes among them, in
all realms of thought, throughout the
history of ideas. This difference is the
preference, in the one case, for the
concrete over the abstract, and in the
other for the abstract over the concrete.
In science, this temperamental differ-
ence distinguishes experimentalists
and theorists; in mathematics it distin-
guishes applied and pure mathemati-
cians; and in philosophy it distin-
guishes empiricists and rationalists.
Thus experimentalists are concerned
with concrete apparatus in the labora-
tory, or concrete specimens in the field,
while the nearest that theorists get to
experimenting is the "thought experi-
ment," which cannot be performed in
any laboratory. Similarly, although all
mathematics is abstract, applied math-
ematics is less so than pure mathemat-
ics; applied mathematicians are con-
cerned with mathematics that relates
to the concrete world around them,
while extreme pure mathematicians
consider such concrete application un-
important at best and an adulteration
of mathematics at worst.

Helier J. Robinson is professor of philosophy
at the University of Guelph, in Ontario, Can-
ada. Illustrations for this article are by Peter
Bono.

The two temperaments are suffi-
ciently important to be named. The
obvious names, however, are rather
ugly—"concretists" and "abstrac-
tists"—so I propose to call them instead
by the immediately understood terms
earthies and airies.

Each of these terms should be
thought of sympathetically, for the
strength it represents, rather than
contemptuously, for the weakness it
represents. Thus earthies have their
feet on the ground and are practical,
common-sense people, while airies are
impractical and have their heads in the
clouds—at least this is the common-
sense view of the distinction. We
should remember, however, that com-
mon sense is itself earthy and so not
unprejudiced. In fact, the great
strength of common sense is that it is
the cumulative practical wisdom of
millenia of experience, and so, in gen-
eral, highly reliable—which seems to
give lopsided support to the earthies.
However, common sense is not com-
pletely reliable, as the history of ideas
shows. This history is a history of
corrections to common sense, and the
corrections have all been made by
airies. So credence should always be
given to both sides.

It is one of the strengths of science
that the temperamental gap between
earthies and airies is successfully
bridged, and it is one of the weaknesses
of philosophy that the gap is not
bridged—that it remains a gulf of

misunderstanding and mutual con-
tempt. This is important to scientists,
in the realm of the philosophy of their
work, in that a balanced science should
not be backed by an unbalanced philos-
ophy. That is to say, theoretical science
is airy and modern philosophy of
science is earthy, so as a result, modern
philosophy of science cannot do justice
to theory. As with other temperamen-
tal differences, such as those that
separate introverts and extraverts, op-
timists and pessimists, and radicals
and reactionaries, the whole truth
must be a combination of both view-
points. When each side sees the other
as perversely wrong, a sterile contro-
versy results or a one-sided majority
view dominates—a half-truth rather
than a whole truth.

Throughout its history, the philoso-
phy of modern science has been earthy.
It has been dominated by empiricists
who, claiming that science is exclusive-
ly empirical, maintain that philosophy
of science must be so also. In the early
days of science this attitude was quite
reasonable, because no one made the
distinction between empirical science
and theoretical science. Today, how-
ever, it is no longer reasonable, because
theoretical science is clearly distinct
from empiricial science. The philos-
ophers of science have not yet recog-
nized this, and, like Cinderella's step-
sisters, they try to cut theoretical
science down to size so that it will fit
into the glass slipper of empiricism.

2 4 PHYSICS TODAY / MARCH 1984 0031-9228 / 84 / nnnn ? 4 - no / $ m nn m 1984 American Institute of Physics



For example, the predominant philoso-
phy of science in the twentieth century
has been logical positivism in various
forms, all of which insist that theoreti-
cal science is fiction.

In this article I want to correct this
historical neglect of theory. To this end
I shall first examine some of the
differences between earthies and air-
ies, in both philosophy and science.
Then I will present evidence that earth-
ies and airies practice two fundamen-
tally distinct kinds of science, which
are based on two genuinely different
kinds of perception. This will bring us
to the ancient philosophical problem of
the relationship between object and
image, or between observation and
theory. While some may be uncomfor-
table with the solution that I favor, we
will see that it does resolve the problem
of perception and explain science.

The question of illusion
The basic positions of empiricism and

rationalism are frequently expressed
by their opponents as caricatures. Em-
piricism is said to be the doctrine that
all knowledge, without exception, is
obtained empirically, that is, through
the senses. Rationalism is said to be
the doctrine that all knowledge—true
knowledge, that is, for the empirically
known is not really knowledge because
of illusion—is known by reasoning
about the way the world must be. If
these caricatures were true, then no
empiricist could allow any generaliza-
tion of empirical data into empirical
law, because no generalizations are
known through the senses. And every
rationalist would be nothing but an
armchair scientist, reasoning a priori
about the nature of reality without any
reference to empirical fact.

These caricatures arise in the first
place because each side is wary of the
weaknesses of the other side's position
and seeks to defend the truth from this
weakness. The weakness in the empiri-
cist position stems from the existence of
illusion: Not all that we perceive
around us is really so. To correct
illusion rationally is to replace an
empirical observation with a rational

PHYSICS TODAY / MARCH 1984 2 5



belief—for example, that railroad
tracks do not really meet in the dis-
tance—which is what the rationalists
want to do. The weakness of the
rationalist position is that, historically,
they disagreed so much among them-
selves as to what these rational beliefs
should be (to say nothing of their
weakness for falling back on authority
rather than reason) that one cannot
help but regard this disarray as evi-
dence of a failure of method.

The point of departure between em-
piricists and rationalists is indeed on
the question of illusion. The empiri-
cists believe that what we perceive
around us is reality. The rationalists,
because of the fact of illusion, believe
that what we perceive around us is not
necessarily reality, and that to know
reality we must substitute rational
belief for perception. In consequence,
there are two definitions of reality, an
earthy one and an airy one. It what
follows it will be most important that
they be explicit.

Empirical reality is denned as all
that we perceive around us—with two
provisos. One is that the purely private
is not empirically real; it is, rather, a
product of the perceiver's unconscious
mind, projected into the world. Beauty
and sex-appeal in a lover, glory in a
hero and evil in an enemy are common
examples. Hence we can say that the
empirically real must be public. (This
includes potential publicity, of course:
If what one perceives is private merely
because no one else is around to per-
ceive it, this does not mean that it is
unreal.) The second proviso is that not
everything public is empirically real,
because illusions are both public and
unreal. During a solar eclipse, for
example, the Sun and the Moon appear
to be the same size, an appearance that
is both public and an illusion. No
illusions are real—the stick half-im-
mersed in water is not really bent, for
example—so empirical reality is all
that we perceive around us, provided
that it is public and nonillusory. The
reason for calling this empirical reality
is that we know it empirically. It is the
reality that we know through our
senses.

Theoretical reality, on the other
hand, is denned as all that exists
independently of being perceived. If
something continues to exist when no
one is perceiving it any longer, or it
exists even though no one can perceive
it at all, then it is theoretically real.
Conversely, if something exists only
while perceived—as in a dream or
hallucination—then it is unreal. The
reason for calling this theoretical rea-
lity is that no one can perceive any-
thing existing while unperceived, so
such existence is nonempirical, hence
theoretical.

These two definitions of reality are

usually regarded as equivalent, even
though no one has ever been able to
prove that they are. However, I shall
keep them distinct, at least for the
present.

A second major point of disagree-
ment between earthies and airies is on
the question of whether or not there
are such things as abstract ideas. The
notion of an abstract idea was invented
to explain our use of abstract language.
For each abstract word an abstract idea
is supposed to exist, and to be the
meaning of that word. A structure of
abstract ideas—a proposition—is sup-
posed to be the meaning of an abstract
sentence. Those who accept the exis-
tence of abstract ideas and propositions
are called conceptualists, while those
who deny their existence are called
nominalists. Not surprisingly, earthies
are generally nominalists and airies
are generally conceptualists. (The two
most important nominalists of the
twenthieth century were David Hilbert
and Ludwig Wittgenstein.) In the past,
nominalists supposed that the mean-
ings of abstract words were the words
themselves: "Words are the counters
of the mind" and "All thought is silent
speech" were two ways of expressing
this. However, this leads to difficulties
in explaining such things as abstract
synonyms and translation of abstract
sentences from one language to an-
other without loss of meaning.

The strength of the earthies' position
with regard to nominalism is that one
cannot discover abstract ideas empiri-
cally—that is, in this case, introspec-
tively. The airies do not worry about
this, however. Their view is that we
suppose many things to exist even
though we cannot have direct empiri-
cal experience of them—wavefunc-
tions, for example, or force fields. The
reason for supposing such things to
exist is that they have great explana-
tory power.

The earthy-airy preferences are very
clear on the question of abstract ideas.
If abstract ideas exist then they are
abstract entities. In the earthy view, no
abstract entities exist and nominalism
is true (and theories using wavefunc-
tions and force fields are fiction), while
in the airy view there is no objection to
abstract entities and conceptualism is
accepted.

Two kinds of science
When it comes to earthy-airy prefer-

ences is science, it might seem at first
that the existence of two kinds of
science, empirical and theoretical, is
due entirely to this temperamental
difference among scientists. But this is
not in fact so. I am not here siding with
the empiricist philosophers, who most-
ly claim that there is really only one
kind of science. Rather, I want to
emphasise that there definitely are two

kinds of science. A particular scientist
may favor experimental or theoretical
science, according as he is an earthy or
an airy, but this is not the reason why
there are two kinds of science. There
are in fact at least four reasons for
distinguishing them. These distinc-
tions are usually denied or discounted
by earthy philosophers of science, who
regard theories and empirical laws as
the same thing, on the supposition that
both are generalizations from empiri-
cal data; but this is untenable, as the
following discussion will show.

Perceptible or imperceptible? The first
difference between empirical and theo-
retical science follows immediately
from their descriptions. Empirical
science deals with empirical data and
theoretical science does not. "Theoreti-
cal" means "nonempirical," meaning
that the entities of theoretical science
cannot be perceived, by anyone, ever.
We are quite used to believing other-
wise on this, because for several centur-
ies many earthy philosophers have
been insisting on it. They have been
insisting that theoretical science is
really empirical and hence, if theoreti-
cal entities exist at all, then they are
perceptible.

One way they justify this is with a
doctrine of "indirect perception." It is
supposed that to perceive an effect
directly is to perceive its cause indirect-
ly. "Directly" here means to be direct-
ly conscious of it. Thus, to perceive a
table directly is to be directly conscious
of its color, shape, number of legs, and
so on, and indirectly conscious of the
molecules that cause these direct per-
ceptions. If we put a piece of paper over
a magnet and sprinkle iron filings on it,
then we are directly conscious of a
pattern to those filings and hence
indirectly conscious of the magnetic
field that causes the pattern. Again, if
we directly perceive forces of weight or
of inertia, then we indirectly perceive
mass, and if we directly perceive sensa-
tions of warmth or see thermometer
readings, then we indirectly perceive
molecular kinetic energy. Thus, if
theoretical entities are indirectly per-
ceived, then they are perceived, in
which case they are empirical.

A little thought shows, however, that
we never perceive molecules, force
fields, mass, kinetic energy or any
other theoretical entity. The doctrine
of indirect perception is a camouflaged
description of belief. To say that we
indirectly perceive the magnetic field
when we directly perceive the iron
filings means that as we see the filings
we believe that there exists a magnetic
field that causes the pattern. Similar-
ly, we believe in the existence of mole-
cules, mass and all the other accepted
entities of theoretical science. Belief is
a substitute for perception. Whenever
our perception fails us, for any reason

2 6 PHYSICS TODAY / MARCH 1984



whatever—horizons, darkness, uncon-
sciousness, limitations of our sense
organs, and so on—we substitute a
belief. We believe in these theoretical
causes of empirical effects because they
explain these effects, as I will show
shortly.

The fact that we believe (at best) in
the existence of theoretical entities
proves their nonempirical status. That
the doctrine of indirect perception is a
doctrine of disguised belief is shown by
the fact that as beliefs change, so do the
things supposedly indirectly perceived.
If there really is indirect perception,
then we have to say that medieval
astronomers indirectly perceived an-
gels guiding the planets in their orbits
and the alchemists indirectly perceived
phlogiston whenever they saw fire.
The distinction here is quite sharp:
Everything empirical is perceived by
someone, sometime, and nothing theo-
retical is perceived by anyone, ever.

The sharpness of this distinction is

frequently denied by means of a doc-
trine of "degrees of perception." The
fewer causal steps between the object
and its perceptible effects, the more
directly the object is supposed to be
perceived. Thus, things are seen most
directly with the naked eye, less direct-
ly through a microscope or telescope,
less directly still through an electron
microscope, and quite indirectly as
tracks in bubble chambers or as pointer
readings; and all of these are rendered
even less direct if they are seen in the
form of photographs or television pic-
tures. Given this doctrine, everything
theoretical is empirical to some degree,
provided that there is some empirical
evidence for it. In fact, however, it
makes no difference whether indirect-
ness of perception is a two-valued
property or is a matter of degree: This
doctrine of perception remains a cir-
cumlocution for belief in a strictly
imperceptible cause.

Description or explanation? The sec-
ond difference between em-

pirical and t h e o r e t i c a l
science arises from the

well-known distinction
t h a t empirical
science describes the
world and theoretical
science explains it.
Explanation is caus-
al. To describe a
cause is to explain its

effect. This is putting it very simply, of
course, because most effects are com-
plex, and result from complex causes.
Philosophers tend to speak of causes
and effects as single events, while
scientists speak in terms of processes.
However, a process is a complex series
of events, so the difference in approach
is not fundamental. Theoretical
science, then, describes the causes of
what empirical science describes. This
is emphasized by another well known
saying: Theoretical science explains by
describing the underlying causes of
phenomena, which is to say, by describ-
ing imperceptible causes.

A third well-known saying seems to
disagree with this: Explanation is de-
ductive. This needs a little explication,
for which an actual example is best. In
empirical science, data are formulated
and, if the formulas warrant it, they
are generalized into empirical laws.
Boyle's law and Charles's law are well-
known examples. They are combined
into the ideal gas law, PV = nRT,
where P is the pressure, V the volume,
n the mass of the gas in moles, R the
universal gas constant and T the abso-
lute temperature. (The law is only
approximately true, but we can ignore
that.) The quantities P, V, n, R and T
are measured, empirical quantities.
This law is explained in statistical
mechanics by assuming that gases con-
sist of a statistically significant number
of molecules that obey the laws of
mechanics. The quantity V is then
denned as the volume occupied by
these molecules, T as their average
kinetic energy and P as the average
force of reaction as they bounce on
their container. It is then possible to
deduce, within this theory, that
PV = nRT. When an empirical law is
deduced within a theory in this way,
the theory is said to have explained the
law. Although this seems to contradict
the earlier claim that all explanation is
causal, it does not in fact do so, as I will
show later. It is worth mentioning,
however, that a widely accepted empir-
icist doctrine that all explanation is
deductive in this way—it's called the
doctrine of covering law explanation—
stands or falls on whether deductive
explanation is not, or is, a special case
of causal explanation.

Laboratory or armchair? The third
difference between empirical and theo-
retical science lies in their methods.
Philosophers of science have long been
fascinated by scientific method, for the
simple reason that science is spectacu-
larly successful, so that if this success is
due to method, then specification of the
method should allow its application in
other fields—with equal success. Var-
ious analyses have been undertaken;
the best known was that by John
Stuart Mill, resulting in the famous
Mill's Methods. These are all various

PHYSICS TODAY / MARCH 1984 2 7



ways of discovering empirical correla-
tions which, if they warrant it, may be
generalized into empirical laws.

It is quite significant that Mill ig-
nored theoretical science entirely.
This was not merely because he was an
earthy—he was, in fact, one of the most
extreme of all empiricists—but because
no one has ever been able to formulate
a method for theoretical science. The
reason for this is quite simple. Theo-
retical science is invented, and this
requires creativity, for which there is
no known method. A major theory in
science, just like a major work of art,
requires creativity to produce it. A
computer can discover correlations but
it cannot be creative. This is the
difference in method between empiri-
cal and theoretical science, according
to Mill's analysis.

Even more significant than Mill's
neglect of theory is the fact that empiri-
cal science does not in fact consist of the
blind groping after correlations that
Mill's Methods make of it. As Karl

Popper has pointed out, empirical
science is almost always a matter of
testing theories. Whenever a theory
predicts something novel, an experi-
ment is required to test the prediction.
Such experiments have to be designed,
and their design requires as much
creative genius as does the invention of
theories. Strictly speaking, then,
neither empirical nor theoretical
science has a formal method. Nonethe-
less, they do differ in their methods, in
a fashion that is obvious once it is
pointed out. Empirical science takes
place in a laboratory, an observatory or
in the field, and theoretical science
does not. Theories can be created
anywhere, even in an armchair.
Hence, theoretical science could be
called armchair science, without any
disrespect, while empirical science de-
finitely is not armchair science.

Repetition or novelty? Fourth, empiri-
cal and theoretical science differ in the
kind of predictions they make. Empiri-
cal science makes predictions of repeti-

tion and theoretical science makes
predictions of novelty. Empirical pre-
dictions result from the fact that em-
pirical laws are generalizations of
empirical formulas, and this general-
ization includes generalization into the
future—which is prediction. Thus, if
PV = nRT is true now, then it will be
true tomorrow.

Theoretical science, on the other
hand, predicts not only this, but also
experimental results never before per-
ceived. Sometimes these predictions
are spectacular, as in the case of
Maxwell's equations leading to Hertz's
discovery of radio and Einstein's
E = me2 leading to atomic energy.
Most of the time, however, theoretical
predictions of novelty are predictions of
new empirical data that, when tested
by experimentalists, serve either to
verify or to falsify the theory. Indeed,
this kind of interaction between theory
and experiment is the mark of sophisti-
cated science. It is also the supreme
example of successful cooperation

28 PHYSICS TODAY / MARCH 1984



between earthies and airies in science,
a cooperation whose success is shown
by major advances in the sciences that
manage to achieve it. So successful is
the cooperation in these sciences, that
all research experiment is concerned
with testing theories and all theories
must be empirically testable to be
theories. Physics and chemistry are
examples of such successful sciences.

A second point about prediction of
novelty is the curious fact that only
mathematical theories are capable of
it. The theory of evolution, for exam-
ple, although an excellent theory, is not
a mathematical theory and does not
make predictions of novelty. The the-
ory does predict that, given time, new
species will arise; but this is only
generalization into the future, from the
fact that in the past new species have
evolved. This is prediction of repeti-
tion, not prediction of novelty in the
sense of predicting precisely what the
new species will be.

Thus, philosophers of science have a
problem. It is, in my opinion, the most
important problem in all of philosophy
of science. What do the mathematical
theories of science (and nothing else
that we know of) have that enables
them to predict empirical novelty, suc-
cessfully and often? Poets cannot do
this nor astrologers nor soothsayers
nor prophets nor think tanks nor biolo-
gists nor social scientists nor empirical
scientists. Mathematical theories
must have some special relationship to
reality that enables them to predict
successfully, and it is an exceedingly
interesting question to ask what this
relationship is. We will return to this
later.

Two kinds of perception
I have said enough, I believe, to show

that empirical science and theoretical
science are distinct, and that earthy
philosophers of science either discount
or deny this distinction. Let us turn
next to the question: Why are there
two kinds of science? This question is
important because it concerns a duality
that is one facet of a much more
general duality. Other facets are some
of the dualities that we have already
met, and that we may equally question.
Why are there two kinds of reality,
empirical and theoretical? Why is
there the distinction between descrip-
tion and explanation? Why are the
entities of empirical science always
perceptible and the entities of theoreti-
cal science always imperceptible? Why
are there two kinds of prediction—of
repetition and of novelty? Why are
there two methods in science—experi-
mental and armchair? There is also a
duality of two kinds of publicity. The
Moon is public, according to common
sense, because we all perceive the one
Moon, whereas the contents of news-

papers are public because all copies of
one edition have the same contents.
The first is publicity by singularity and
the second is publicity by similarity—a
distinction that will be relevant later.

Why are there all these dualities?
The answer is that all of these dualities
are caused by a more general one: the
duality between two kinds of percep-
tion. These may appropriately be
called empirical and theoretical per-
ception. As one might expect, earthies
prefer to view perception as being
empirical perception, and airies prefer
to view it as being theoretical percep-
tion.

Before explaining these two kinds of
perception, we should note that percep-
tion, and the philosophic problems of
perception, are bound to come into any
sound philosophy of science. Not only
is science observer-dependent and so
perception-dependent, but its founda-
tion on the authority of empirical data
is a foundation on perception.

Empirical perception is perception as
we all know it from experience. In it
we are directly conscious of material
objects around us. Theoretical percep-
tion is the scientific explanation of
empirical perception, in terms of reflec-
tion and refraction of light, acoustical
vibrations, diffusion of olfactory mole-
cules, and neural physiology. In theo-
retical perception a reproduction, im-
age or representation of the external
object is conveyed into the brain of the
perceiver. Theoretical perception thus
has a duality of object and image. The
object is external to the head of the
perceiver, theoretically real (because it
continues to exist when unperceived),
public and material (as opposed to
mental). The image is internal and
mental, hence not theoretically real
(because it exists only while perceived)
and not public.

I emphasize these four differences
between object and image to demon-
strate that the duality is a genuine one
rather than merely verbal. The point
is important because empirical percep-
tion does not have this duality. When
we empirically perceive objects, quali-
ties or relations around us, we are
directly conscious of objects only, not of
objects and images.

Thus theoretical perception has a
duality and empirical perception does
not, so they are two distinct kinds of
perception. There have been many
attempts to identify them. These all
involve describing a duality within
empirical perception and claiming that
it is identical with that of theoretical
perception. The most common is the
claim that a memory is an image of a
perceived object and so is the image of
theoretical perception. Another is dua-
lity of object of perception and act of
perception. Another is that of object
and belief about that object. None of

these works, for a very simple reason:
In theoretical perception the object is
theoretical and the image is empirical.
This means that the object is impercep-
tible and the image is perceptible. But
in empirical perception it is the object
that is perceptible. If the two kinds of
perception are to be combined, then
that of which we are conscious must be
the same in each case, meaning that
the object of empirical perception must
be the image of theoretical perception.
However, we have just seen that the
first is external, real and public while
the second is internal, unreal and
private. What has gone wrong?

The problem
We are here involved in an ancient

philosophical problem. Long before
there was a scientific theory of percep-
tion there was a theory that postulated
a duality of object and image. This
theory arose because of the simple fact
of illusion. We know of illusions be-
cause they are contradictions between
different sensations or between present
sensations and normal experience. For
example, the half-immersed stick is
bent to the sight and straight to the
touch, and visual size diminishes with
distance from the perceiver, contrary
to our general experience of the world.

A contradiction is a necessary falsity,
and illusions are thus false perceptions.
There is only one possibility of explain-
ing false perceptions, namely, the false
perception is an image of reality, and
false insofar as it is dissimilar to that
reality. Dissimilarity is a matter of
degree, varying from perfect dissimi-
larity, or complete falsity, to perfect
similarity, or complete truth. Because
we do not know of anything empirically
perceived that is completely and wholly
nonillusory, we have to say that every-
thing empirically perceived is an im-
age, or a copy or a representation or a
reproduction—the actual term used to
describe it does not matter. This Re-
presentational Theory of Perception, as
it is called, goes back at least as far as
Plato and the fifth century BC.

The modern scientific theory of per-
ception—theoretical perception—in-
cludes the representational theory
within it. Indeed, theoretical percep-
tion explains most illusions in consider-
able detail, but always in terms of
images that are dissimilar to reality.
The basic logic here is simple: Dissimi-
larity cannot be reflexive, it must have
a duality. One thing cannot be dissimi-
lar to what it is. Because illusions are
dissimilar to reality, perception must
consist of a duality of reality and image
of reality.

We can now state our problem more
clearly. We have three things: the
theoretical object, which is wholly non-
illusory; the theoretical image, which is
(usually) partly illusory; and the em-

PHYSICS TODAY / MARCH 1984 2 9



pirical object, which is also partly
illusory. Put in this way, it is clear that
the empirical object must be the theo-
retical image, and cannot be the theo-
retical object. However, this is con-
trary to all our beliefs, and also leads to
the quadruple contradiction between
theory and observation, where the em-
pirically perceived object is internal,
private, unreal and mental, as well as
external, public, real and material.
This may be more clear if it is stated as
follows. What we empirically perceive
is very clearly outside our heads, as
opposed to the images inside, and so is
real. But what we empirically perceive
is also partly illusory, and so is an
unreal image. How can it be both?

As we will see later, the difficulty
here is due to two earthy common-sense
beliefs that are false. This has hap-
pened often before in the history of
ideas, and improved beliefs have usual-
ly resolved the problem. However, the
resolution always involved bitter con-
troversy between the advocates of the
new and the defenders of the old.
Copernicus's heliocentric theory and
Darwin's theory of evolution are the
most notable examples. In the present
case, however, the adjustment to estab-
lished belief is considerably more diffi-
cult than Copernicus or Darwin re-
quired.

The solution to the problem is so
difficult that most people do not even
suspect that it exists, even though it is
highly probable that Plato taught it in
his Academy, Gottfried Wilhelm Leib-
niz (co-inventor of the calculus) pub-

lished it in the seventeenth century
and Bertrand Russell published it
again in this century. To be sure,
Plato, having witnessed the death of his
teacher Socrates (condemned for cor-
rupting the youth of Athens), did not
make the solution explicit in his pub-
lished works—although they contain a
fair amount of evidence that he knew of
it. Leibniz, aware that Giordano Bruno
had only recently been burned at the
stake, and that Galileo had been con-
demned to house arrest for life—be-
cause they published theories upsetting
to established belief—was careful not
to draw attention to the solution in his
published works, although it is there
for all to see. (In this vein, it is worth
noting that both Copernicus and Dar-
win cautiously postponed publishing
their theories for as long as possible.)
In fact, no one noiticed Leibniz's solu-
tion until early in this century, when
Russell published his own version of it
and acknowledged Leibniz's priority.
Unfortunately, Russell's early version
used a six-dimensional space, which
very few of his readers understood. By
the time he published a later version in
1948, almost all philosophers had con-
signed his theory to limbo.

The solution
This problem is not logically difficult,

it is only psychologically difficult.
There are two incompatible proposi-
tions, and we want both to be true.
What we perceive directly in empirical
perception is
• outside our heads, and therefore real

objects
• partly illusory, and therefore unreal
images, inside our heads.

Earthy common sense has its cake
and eats it on this question by stating
that when we perceive illusions we
perceive images, and that otherwise we
perceive real objects. We are so used to
thinking this way that we do not
normally recognize its inconsistency.
In empirical perception everything we
perceive is outside our heads and there-
fore real, while in theoretical percep-
tion everything we perceive is an image.
Therefore, if we perceive a mixture of
reality and images of reality, both of
these accounts of perception are false.
Earthies usually avoid this problem by
using the empty concept of "projec-
tion," in which we "project" illusory
images onto real objects. This concept
is empty because it is a metaphor that
cannot work. The word "projection"
has three meanings: mechanical, opti-
cal and geometrical, and none can
apply here. Furthermore, how can
private mental content be projected
into public space and remain private?

We do want both empirical percep-
tion and theoretical perception to be
true. Empirical perception is the foun-
dation of science, and without theoreti-
cal perception illusions are impossible.
How, then, can what we perceive be
both inside our heads and outside? We
can consider the possibility of this most
easily with an analogy. Suppose we are
told that the apple is in the box and also
that the apple is outside the box. The
only way to make both of these true at

3 0 PHYSICS TODAY / MARCH 1984



once is to allow two apples or two boxes
or both. Thus we can have one box,
with an apple inside it and an apple
outside it; or two boxes, one inside the
other, with the apple inside the outer
and outside the inner; or both of
these—for example, two boxes, one
inside the other, with an apple between
them and an apple outside both. In the
same way, when we want the empirical
object to be both outside and inside the
head, we must allow either two ob-
jects—object and image—or two
heads— empirical head and theoretical
head—or both. As it turns out, the
facts of perception require that we have
both. Indeed, it is the understanding of
one key point here that leads to the
Leibniz-Russell solution.

Suppose everything empirical is an
image of a theoretical reality, as theo-
retical perception requires. Then one
very special empirical object that each
of us knows is his own head. One's own
empirical head is thus an image of one's
own theoretical head. This simple
observation has extraordinary and far-
reaching consequences. The most
striking of these comes from asking
where this theoretical head is. The
answer is simple: Because everything
empirical is an image inside one's
theoretical head, it follows that this
theoretical head must be outside every-
thing empirically perceived. This
means that beyond the limits of your
empirical perception—that is, beyond
the blue sky on a clear day or beyond
the dome of visible stars on a clear
night—is the inside surface of your own
theoretical skull.

Many people find this so emotionally
appalling that they react to it as
creationists do to evolution, with pas-
sionately closed minds. However, a
willing suspension of disbelief will
quickly show the value of the Leibniz-
Russell theory. Its value lies in resolv-
ing the problem of perception and in
explaining science.

Thus, everything you empirically
perceive, including your own body, is
an image of parts of the theoretically
real world. As such, it is partly similar
and partly dissimilar to that reality—
that is, it is partly true and partly
illusion. Insofar as it is true, it is
empirically real. Insofar as other peo-
ple have similar images, what is em-
pirically perceived is public by similar-
ity. And these images are outside the
image of your own body. Thus, what is
empirically perceived is external, real
and public—as empirical perception
requires. At the same time, all these
images are inside your theoretical
skull, so they are theoretically unreal
and private. Thus, what is theoretical-
ly perceived is internal, unreal and
private—as theoretical perception re-
quires. These seeming contradictions
are resolved because what you empiri-

cally perceive is external to your em-
pirical head but internal to your theo-
retical head, empirically real but
theoretically unreal, and public by
similarity but private by plurality.

The significance of all this for science
is considerable. I propose to examine
only three consequences here. There
are many others, which I have dealt
with in my Renascent Rationalism.1

Consequences for science
The first consequence is the obvious

relationship between empirical and
theoretical science. Empirical science
tries to describe the true features of
empirical worlds, and theoretical
science tries to describe the theoretical
world. This is why the content of
empirical science is perceptible and the
content of theoretical science is strictly
imperceptible, or "underlying." Be-
cause the theoretical world is the cause
of empirical worlds, theoretical science
describes the cause of what empirical
science describes. However, to describe
a cause is to explain its effect, so
theoretical science explains empirical
science.

The second consequence of the Leib-
niz-Russell theory concerns the crite-
ria for good empirical science. The
most important of these are:
• The scientist must be objective.
• Data should be quantitative rather
than qualitative.
• Experiments should be repeatable.
These are all explained in terms of
publicity. We saw that publicity, or
potential publicity, of empirical worlds
is a necessary condition for their con-
tent being true. That is, publicity is a
necessary condition for empirical rea-
lity (by definition) and empirical rea-
lity is the truth of empirical worlds
(truth by the similarity between each
person's empirical world and the theo-
retical world). It follows that if empiri-
cal science concentrates on public data
then it has the best chance of being
true, in the sense of similarity to the
theoretical world.

That objectivity in science is atten-
tion to the public is obvious as soon as it
is realized that subjectivity is attention
to the private. What the scientist does
in being objective is exclude from
consideration everything private—
such as prejudice, personal wishes and
vanity.

That quantitative data are more
public than qualitative data is shown
by the fact that all qualitative data are
a matter of what Galileo and John
Locke called secondary qualities.
These are qualities, such as color, that
are produced by the sense organs at the
earliest and so are unreal in the sense
of existing only when perceived. When
we ask if the grass is really green, the
answer is that the green we see when
we look at grass is empirically real

insofar as it truly represents the molec-
ular structure of the theoretical grass,
but it is not theoretically real, because
it is a secondary quality. Although the
color is widely believed to be public,
this cannot be properly established
because we cannot compare, interper-
sonally, our color sensations. Properly
obtained quantitative data, on the oth-
er hand, are thoroughly public.

Finally, that experiments must be
repeatable is quite clearly a require-
ment that their results be publicly
verifiable.

There are two further significances
of publicity in science. One is that if we
ask about the most public content of
minds (as opposed to empirical worlds)
then the answer is rational thought—
logic and mathematics. That these are
necessary in science hardly needs to be
said. Second, Einstein's principle of
relativity, from which the special and
general theories of relativity were de-
rived, is the principle that all the basic
laws of science must be true for all
observers, no matter how they are
moving relative to one another. This
requires no more than that these laws
be public to all observers.

The third consequence of the Leib-
niz-Russell theory is that we can now
explain that most important feature of
theoretical science: its frequent and
successful prediction of empirical no-
velty. There are two main features in
the process of successful prediction:
making the prediction, and its coming
true. The key to understanding these
features is the concept of necessity.
Nominalist earthies tend to discount
necessity because it is an abstract
thing. They claim that it is merely a
property of language, or else a name for
what is empirically always so. But it is
more than both of these. Necessity can
be defined as singular possibility.
Whenever, in a given situation, the
next possibility is the only one, then
that posssibility must occur, which is to
say that it is necessitated by that
situation. We are familiar with two
kinds of necessity, logical and causal.
Thus logically the outcome of adding
two and two is the singular possibility,
four; and the outcome of accelerating
an electric charge is the singular possi-
bility, electromagnetic radiation. We
use logical necessity to make the pre-
diction: We deduce the prediction
within the theory. The theoretical
world causally necessitates the predic-
tion coming true: It comes true be-
cause theoretical reality makes it do so.
These two necessities are related in
that they are similar. As we have seen,
such similarity between the theory and
theoretical reality is truth.

Thus, this explanation of prediction
works only if three conditions are
fulfilled: The theory is true, logical
necessity enables the prediction to be

PHYSICS TODAY / MARCH 1984 3 1



deduced and causal necessity in the
theoretically real world makes it come
true. Other explanations are possi-
ble—the predictions come true by a
long series of coincidences, or miracu-
lously, by God who is testing our faith
or by Satan who is trying to deceive
us—but none of them is plausible. This
explanation does require the Leibniz-
Russell distinction between empirical
realities and theoretical reality, be-
cause, as David Hume pointed out long

ago, there are no empirical necessities:
We never perceive necessity around us.

Finally, we can account for the fact
that only mathematical theories suc-
ceed in predicting novelties. Because
prediction of novelty requires a theory
to be true by similarity to reality,
mathematical theories must succeed
because reality is mathematical. "All
is number," as Pythagoras said two and
a half millennia ago. This airy claim
was endorsed by Plato, Galileo, Des-

cartes, Spinoza, Leibniz and Newton, to
name only the most famous.

Thus we have an outline of an airy
philosophy of science, the result of
giving theoretical science, and, in parti-
cular, theoretical perception, its due.

Reference
1. H. J. Robinson, Renascent Rational-

ism, second edition, Speedside Publish-
ing, Fergus, Ont., Canada (1982) D

3 2 PHYSICS TODAY / MARCH 1984