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-----GROVER MAXWELL------
The Ontological Status of Theoretical Entities
That anyone today should seriously contend that the entities
referred
to by scientific theories are only convenient fictions, or that
talk about
such entities is translatable without remainder into talk about
sense con-
tents or everyday physical objects, or that such talk should be
regarded
as belonging to a mere calculating device and, thus, without
cognitive
con tent-such contentions strike me as so incongruous with the
scientific
and rational attitude and practice that I feel this paper should
turn out
to be a demolition of straw men. But the instrumentalist views
of out-
standing physicists such as Bohr and Heisenberg are too well
known to
be cited, and in a recent book of great competence, Professor
Ernest
Nagel concludes that "the opposition between [the realist and
the in-
slrumentalist] views [of theories] is a conflict over preferred
modes of
sp cch" and "the question as to which of them is the 'corr ect
position'
ha s only terminological interest." 1 The phoenix, it seems, will
not be
laid to rest.
The literature on the subject is, of course, voluminous, and a
compre-
lt nsive treatment of the problem is far beyond the scope of one
essay.
I sl1all limit myself to a small number of constructive
arguments (for a
r lically realistic interpretation of theories) and to a critical
examination
of s me of the more crucial assumptions (sometimes tacit,
sometimes
· pli it) that seem to have generated most of the problems in this
area.2
' fo: . Nngcl, TJ1c Structure of Science (New York: Harcourt,
Brace, and World,
l ') il), h . 6.
1 l•'or th e ge nes is and part of the content of some of the ideas
expressed herein,
I 11n ind ·bled to a number of sources; some of the more
influential are H. Feig!,
" 11: IN! ·11t inl llypotheses," PI1ilosophy of Science, 17 : 35 -
62 ( 1950); P . K. Feyerabend ,
'' 11 Alt · 111pt nt n Rcnlistic Interpretation of Experience,"
Proceedings of the Aristo-
1 / 1111 Soi ty, 58 :144- 170 (1958); N . R . Hanson, Patterns of
Discovery (Cam-
111 ii 1: ,n111hridgc University Press, 1958); E. Nagel, Joe .
cit.; Karl Popper, The
I 11 c• of S ·i 11tilic Dis ovcry (London : Hutchinson, 19 59);
M. Scriven, "Definitions,
f1,ph11111 t i11 11 s 1 :ind Th ·ori ·s," in Miuneso ta Studies
in tlie Philosophy of Science,
3
Grover MaxweII
The Problem
Although this essay is not comprehensive, it aspires to be fairly
self-
contained. Let me, therefore, give a pseudohistorical
introduction to the
problem with a piece of science fiction (or fictional science).
In the days before the advent of microscopes, there lived a Pas
teur-
like scien tist whom, following the usual custom, I shall call
Jon es. Re-
fl ecting on the fact that certain diseases seemed to be
transmitted from
one person to another by means of bodily contact or b y contact
with
articles handled previously by an afHicted person, Jones began
to specu-
late about the mechanism of the transmission. As a "heuristic
crutch,"
he recalled that there is an obvious observable mechanism for
transmis-
sion of certain afHictions (such as body lice), and he postulated
that all,
or most, infectious diseases were spread in a similar manner but
that in
most cases the corresponding "bugs" were too small to be seen
and, pos-
sibly, that some of them lived inside the bodies of their hosts .
Jones pro-
ceeded to develop his theory and to examine its testable
consequences .
Some of these seemed to be of great importance for preventing
the
spread of disease.
After years of struggle with incredulous recalcitrance, Jones
managed
to get some of his preventative measures adopted. Contact with
or prox-
imity to diseased persons was avoided when possible, and
articles which
they handled were "disinfected" (a word coined by Jones) either
by
means of high temperatures or by treating them with certain
toxic prepa-
rations which Jones termed "disinfectants." The results were
spectacular:
within ten years the death rate had declined 40 per cent. Jones
and his
theory received their well-deserved recognition.
However, the "crobes" (the theoretical term coined by Jones to
refer
to the disease-producing organisms) aroused considerable
anxiety among
many of the philosophers and philosophically inclined scientists
of the
day. The expression of this anxiety usually began something
like this:
"In order to account for the facts, Jones must assume that his
crobes
are too small to be seen. Thus the very postulates of his theory
preclude
V~I. IT , TT . Feig!, M . Scri~en ~ and G . ~axw~l.1 '. eds .
(Minneapolis : University of
!"111111. s tn Pre~s. I ?58); W1lfn~ Sellars, Empmc1sm and
the Philosophy of Mind,"
111 M11111 so tn t11d1 cs m the Philosophy of Science, Vol. I,
H. Feig! and M . Scriven
, ~ I s. ( ,M i::n. npo lis: niversity of M in.nesota Press, .19 56),
and " The Language of
111 ·0 11 ~. 111 urr ·11t I ssues m the P/11losophy of Science,
H . Feig! and G . Maxwell,
Is . ( N ·w 0 1 : ll olt, Rin hart, and Win ton, 1961) .
4
THE ONTOLOGICAL STATUS OF THEORETICAL ENTITIES
their being observed; they are unobservable in principle.''
(Recall that
no one had envisaged such a thing as a microscope.) This
common prefa-
tory remark was then followed by a number of different
"analyses" and
"interpretations" of Jones' theory. According to one of these, the
tiny
organisms were merely convenient fictions-fa~ons de parler-
extremely
useful as heuristic devices for facilitating (in the "context of
discovery")
the thinking of scientists but not to be taken seriously in the
sphere of
cognitive knowledge (in the "context of justification"). A
closely related
view was that Jones' theory was merely an instrument, useful
for organ-
izing observation statements and (thus) for producing desired
results,
and that, therefore, it made no more sense to ask what was the
nature
of the entities to which it referred than it did to ask what was
the nature
of the entities to which a hammer or any other tool referred .3
"Yes," a
philosopher might have said, "Jones' theoretical expressions are
just
meaningless sounds or marks on paper which, when correlated
with ob-
servation sentences by appropriate syntactical rules, enable us
to predict
successfully and otherwise organize data in a convenient
fashion ." These
philosophers called themselves "instrumentalists."
According to another view (which, however, soon became
unfashion-
able), although expressions containing Jones '. theoretical terms
were
g nuine sentences, they were translatable without remainder into
a set
(perhaps infinite) of observation sentences. For example, 'There
are
robes of disease X on this article' was said to translate into
something
like this: 'If a person handles this article without taking certain
pre-
autions, he will (probably) contract disease X; and if this article
is
fir t raised to a high temperature, then if a person handles it at
any time
afterward, before it comes into contact with another person with
disease
, he will (probably) not contract disease X; and . . .'
Now virtually all who held any of the views so far noted
granted, even
in istecl, that theories played a useful and legitimate role in the
scientific
·ntcrprise. Their concern was the elimination of "pseudo
problems"
whi ch might arise, say, when one began wondering about the
"reality
f upraempirical entities," etc. However, there was also a school
of
th llght, founded by a psychologist named Pelter, which differed
in an
• 1 hove borrowed the h ammer analogy from E. Nagel, "Science
and [Feigl's]
.'n111nnti Rc:ilism," Philosophy of Science, 17 :174- 181
(1950), but it should be
p11l111 cd 11 t thnt Professor Nagel makes it clear that he does
not necessarily subscribe
lo th vi w whi h he is explaining.
5
Grover Maxwell
interesting manner from such positions as these. Its members
held that
while Jones' crobes might very well exist and enjoy "full -blown
reality,"
they should not be the concern of medical research at all. 'They
insisted
that if Jones had employed the correct methodology, he would
have dis-
covered, even sooner and with much less effort, all of the
observation
laws relating to disease contraction, transmission, etc. without
introduc-
ing superfluous links (the crobes) into the causal chain.
Now, lest any reader find himself waxing impatient, let me
hasten to
emphasize that this crude parody is not intended to convince
anyone,
or even to cast serious doubt upon sophisticated varieties of any
of the
reductionistic positions caricatured (some of them not too
severely, I
would contend) above. I am well aware that there are theoretical
en-
tities and theoretical entities, some of whose conceptual and
theoretical
statuses differ in important respects from Jones' crobes. (I shall
discuss
some of these later.) Allow me, then, to bring the Jonesean
prelude to
our examination of observability to a hasty conclusion .
Now Jones had the good fortune to live to see the invention of
the
compound microscope. His crobes were "observed" in great
detail, and
it became possible to identify the specific kind of microbe (for
so they
began to be called) which was responsible for each different
disease.
Some philosophers freely admitted error and were converted to
realist
positions concerning theories . Others resorted to subjective
idealism or
to a thoroughgoing phenomenalism, of which there were two
principal
varieties. According to one, the one "legitimate" observation
language

had for its descriptive terms only those which referred to sense
data. 1 he
other maintained the stronger thesis that all "factual" statements
were
translatable without remainder into the sense-datum language.
In either
case, any two non-sense data (e.g., a theoretical entity and what
would
ordinarily be called an "observable physical object") had
virtually the
same status. Others contrived means of modifying their views
much less
drastically. One group maintained that Jones' crobes actually
never had
been unobservable in principle, for, they said, the theory did n t
imply
the impossibility of finding a means (e.g., the mi r op ) f b
erving
them . A more radical contention was that th r b s w r not b
erved
at all ; it wa s argued that what was seen by rn an s of th 111i
ros pe was
just a sk1dow or an image rather than a rp r ·n l or •t111i m .
6
THE ONTOLOGICAL STATUS OF THEORETICAL ENTITIES
The Observational-Theoretical Dichotomy
Let us turn from these fictional philosophical positions and
consider
some of the actual ones to which they roughly correspond.
Taking the
last one first, it is interesting to note the following passage from
Berg-
mann: "But it is only fair to point out that if this ...
methodological
and terminological analysis [for the thesis that there are no
atoms] ...
is strictly adhered to, even stars and microscopic objects are not
physical
things in a literal sense, but merely by courtesy of language and
pictorial
imagination. This might seem awkward. But when I look
through a
microscope, all I see is a patch of color which creeps through
the field
like a . hadow over a wall. And a shadow, though real, is
certainly not
a physical thing." 4
I should like to point out that it is also the case that if this
analysis
is strictly adhered to, we cannot observe physical things through
opera
glasses, or even through ordinary spectacles, and one begins to
wonder
about the status of what we see through an ordinary
windowpane. And
what about distortions due to temperature gradients-however
small
and, thus, always present-in the ambient air? It really does
"seem awk-
ward" to say that when people who wear glasses describe what
they see
they are talking about shadows, while those who employ
unaided vision
talk about physical things-or that when we look through a
window-
pane, we can oply infer that it is raining, while if w e raise the
window,
we may "observe directly" that it is. The point I am making is
that there
is, in principle, a continuous series beginning with looking
through a
vacuum and containing these as members: looking through a
window-
pane, looking through glasses, looking through binoculars,
looking
through a low-power microscope, looking through a high-power
micro-
ope, etc., in the order given. The important consequence is that,
so
far, we are left without criteria which would enable us to draw a
non-
nrbitrary line between "observation" and "theory." Certainly, we
will
ften find it convenient to draw such a to-some-extent-arbitrary
line; but
il position will vary widely from context to context. (For
example, if
w are determining the resolving characteristics of a certain
microscope,
w would certainly draw the line beyond ordinary spectacles,
probably
' . Bergmann , " Outline of an Empiricist Philosophy of
Physics," American Jour-
111 1 of Pliysics, 11 : 248- 258; 335-342 (1943), reprinted in
Readings in the Philoso-
/lli y f Science, JI. Feig! and M. Brodbeck, eds. (New York :
Appleton-Century-
:1orl , I 953 ) , pp . 262-287.
7
Grover Maxwell
beyond simple magnifying glasses, and possibly beyond another
micro-
scope with a lower power of resolution.) But what ontological
ice does
a mere methodologically convenient observational-theoretical
dichotomy
cut? Does an entity attain physical thinghood and/or "real
existence" in
one context only to lose it in another? Or, we may ask, recalling
the con-
tinuity from observable to unobservable, is what is seen through
pecta-
cles a "little bit less real" or does it "exist to a slightl y less
extent" than
what is observed by unaided vision? 5
However, it might be argued that things seen through sp tacles
and
binoculars look like ordinary physical objects, while those seen
through
microscopes and telescopes look like shadows and patches of li
ght. I can
only reply that this does not seem to me to be the case,
p::irticularly
when looking at the moon, or even Saturn, through a telescope
or when
looking at a small, though "directly observable," physical objc t
thro ugh
a low-power microscope. Thus, again, a continuity appears.
"But," it might be objected, "theory tells us that wh::it we ce by
means of a microscope is a real image, which is certainly clistin
t from
the object on the stage." Now first of all, it should be remark d
that it
seems odd that one who is espousing an austere empiri ism
which re-
quires a sharp observational-language/theoretical-langua g di
tinction
(and one in which the former language has a privileged ta u )
hould
need a theory in order to tell him what is observable . But, l
lling this
pass, what is to prevent us from saying that we still ob erve th
object
on the stage, even though a "real image" may be involved?
therwise,
we shall be strongly tempted by phenomenalistic demons, and at
this
point we are considering a physical-object observation language
rather
than a sense-datum one. (Compare the traditional puzzles: o I
see one
physical object or two when I punch my eyeball? Does one obj
ec t split
into two? Or do I see one object and one image? Etc.)
Another argument for the continuous transition from the
observable
to the unobservable (theoretical) may be adduced from
theoretical con-
• r. am not attributing to Professor Bergmann the absurd views
sugges ted by th ese
q11 cs l1ons. Ile seems to take a sense-datum language as his
observation language (the
!ins' or wl ~nt he called " the empirical hi~rarchy") , and, in
some ways, such a position
is mor'~ difTi ult to refu te than one which purports to take an
"observable-physical-
ohjt•< I" vi ·w. I low •vcr, I beli eve that demolishing the straw
men with which I am
11 ow <k1 11i11 f: umo1111 ls lo de irable preliminary
"therapy." Some nonrealist interpreta-
11 1111 ol I h '<>ii« wld It mbody the presupposition that the
observable- theoretical
cli 111H I 1111 I 111 11 p 11 11 d ont ologi ally crucial seem
to me to entail positions which
< 111 1 !'~ po11tl lo 11 < It f1 uw 111 · 11 rn th r losely.
THE ONTOLOGICAL STATUS OF THEORETICAL ENTITIES
siderations themselves. For example, contemporary valency
theory tells
us that there is a virtually continuous transition from very small
mole-
cules (such as those of hydrogen) through "medium-sized" ones
(such
as those of the fatty acids, polypeptides, proteins, and viruses)
to ex-
tremely large ones (such as crystals of the salts, diamonds, and
lumps
of polymeric plastic). The molecules in the last-mentioned
group are
macro, "directly observable" physical objects but are,
nevertheless, genu-
ine, single molecules; on the other hand, those in the first
mentioned
group have the same perplexing properties as subatomic
particles (de
Broglie waves, Heisenberg indeterminacy, etc.). Are we to say
that a
large protein molecule (e.g., a virus) which can be "seen" only
with an
electron microscope is a little less real or exists to somewhat
less an ex-
tent than does a molecule of a polymer which can be seen with
an
optical microscope? And does a hydrogen molecule partake of
only an
infinitesimal portion of existence or reality? Although there
certainly is
a continuous transition from observability to unobservability,
any talk
of such a continuity from full-blown existence to nonexistence
is, clearly,
nonsense.
Let us now consider the next to last modified position which
was
adopted by our fictional philosophers. According to them, it is
only
those entities which are in principle impossible to observe that
present
special problems . What kind of impossibility is meant here?
Without
going into a detailed discussion of the various types of
impossibility,
about which there is abundant literature with which the reader is
no
doubt familiar, I shall assume what usually seems to be granted
by most
philosophers who talk of entities which are unobservable in
principle-
i.e., that the theory ( s) itself (coupled with a physiological
theory of
perception, I would add) entails that such entities are
unobservable.
We should immediately note that if this analysis of the notion of
un-
observability (and, hence, of observability) is accepted, then its
use as
n means of delimiting the observation language seems to be
precluded
for those philosophers who regard theoretical expressions as
elements of
calculating device-as meaningless strings of symbols. For
suppose they
wi bed to determine whether or not 'electron' was a theoretical
term .
Fir t, they must see whether the theory entails the sentence
'Electrons
r unobservable.' So far, so good, for their calculating devices
are said
to be able to select genuine sentences, provided they contain no
theo-
ti l terms. But what about the selected "sentence" itself?
Suppose
9
Grover Maxwell
that 'electron' is an observation term. It follows that the
expression is a
genuine sentence and asserts that electrons are unobservable.
But this
entails that 'electron' is not an observation term. Thus if
'electron' is
an observation term, then it is not an observation term.
Therefore it is
not an observation term. But then it follows that 'Electrons are
un-
observable' is not a genuine sentence and does not assert that
electrons
are unobservable, since it is a meaningless string of marks and
does not
assert anything whatever. Of course, it could be stipulated that
when a
theory "selects" a meaningless expression of the form 'Xs are
unobserv-
able,' then 'X' is to be taken as a theoretical term. But this
seems rather
arbitrary.
But, assuming that well-formed theoretical expressions are
genuine
sentences, what shall we say about unobservability in principle?
I shall
begin by putting my head on the block and argue that the
present-day
status of, say, electrons is in many ways similar to that of Jones'
crobes
before microscopes were invented. I am well aware of the
numerous
theoretical arguments for the impossibility of observing
electrons. But
suppose new entities are discovered which interact with
electrons in
such a mild manner that if an electron is, say, in an eigenstate
of posi-
tion, then, in certain circumstances, the interaction does not
disturb it.
Suppose also that a drug is discovered which vastly alters the
human
perceptual apparatus-perhaps even activates latent capacities so
that
a new sense modality emerges. Finally, suppose that in our
altered state
we are able to perceive (not necessarily visually) by means of
these new
entities in a manner roughly analogous to that by which we now
see by
means of photons. To make this a little more plausible, suppose
that
the energy eigenstates of the electrons in some of the
compounds pres-
ent in the relevant perceptual organ are such that even the weak
inter-
action with the new entities alters them and also that the cross
sections,
relative to the new entities, of the electrons and other particles
of the
gases of the air are so small that the chance of any interaction
here is
negligible. Then we might be able to "observe directly" the
position and
possibly the approximate diameter and other properties of some
elec-
tron s. It would follow, of course, that quantum theory would
have to
b alt r d in some respects, since the new entities do not conform
to
rill ils prin ipl s. But however improbable this may be, it does
not, I
111ni11Lni11 , involv any logical or conceptual absurdity.
Furthermore, the
10
THE ONTOLOGICAL STATUS OF THEORETICAL ENTITIES
modification necessary for the inclusion of the new entities
would not
necessarily change the meaning of the term 'electron.' 6
Consider a somewhat less fantastic example, and one which
does not
involve any change in physical theory. Suppose a human mutant
is
born who is able to "observe" ultraviolet radiation, or even X
rays, in
the same way we "observe" visible light.
Now I think that it is extremely improbable that we will ever
observe
electrons directly (i.e., that it will ever be reasonable to assert
that we
have so observed them). But this is neither here nor there; it is
not the
purpose of this essay to predict the future development of
scientific
theories, and, hence, it is not its business to decide what
actually is ob-
servable or what will become observable (in the more or less
intuitive
sense of 'observable' with which we are now working). After all,
we are
operating, here, under the assumption that it is theory, and thus
science
itself, which tells us what is or is not, in this sense, observable
(the 'in
principle' seems to have become superfluous). And this is the
heart of
the matter; for it follows that, at least for this sense of
'observable,' there
are no a priori or philosophical criteria for separating the
observable from
the unobservable. By trying to show that we can talk about the
possi-
bility of observing electrons without committing logical or
conceptual
blunders, I have been trying to support the thesis that any (
nonlogical)
term is a possible candidate for an observation term.
There is another line which may be taken in regard to
delimitation
f the observation language. According to it, the proper term
with which
l work is not 'observable' but, rather 'observed.' There
immediately
mes to mind the tradition beginning with Locke and Hume (No
idea
without a preceding impression!), running through Logical
Atomism
nd the Principle of Acquaintance, and ending (perhaps) in
contempo-
ry positivism. Since the numerous facets of this tradition have
been
tensively examined and criticized in the literature, I shall limit
myself
re to a few summary remarks.
Again, let us consider at this point only observation languages
which
ntnin ordinary physical-object terms (along with observation
predi-
s, etc., of course). Now, according to this view, all descriptive
terms
tu observation language must refer to that which has been
observed.
• F r nrgumcnts that it is possible to alter a theory without
altering the meanings
t t m1 , see my "Meaning Postulates in Scientific Theories," in
Current Issues in
1 I lJ1il p l1 y of Science, Feig! and Maxwell, eds .
11
Grover Maxwell
How is this to be interpreted? Not too narrowly, presumably,
otherwise
each language user would have a different observation
language. The
name of my Aunt Mamie, of California, whom I have never
seen, would
not be in my observation language, nor would 'snow' be an
observation
term for many Floridians. One could, of course, set off the
observation
language by means of this awkward restriction, but then,
obviously, not
being the referent of an observation term would have no bearing
on the
ontological status of Aunt Mamie or that of snow.
Perhaps it is intended that the referents of observation terms
must be
members of a kind some of whose members have been observed
or in-
stances of a property some of whose instances have been
observed. But
there are familiar difficulties here. For example, given any
entity, we can
always find a kind whose only member is the entity in question;
and
surely expressions such as 'men over 14 feet tall' should be
counted as
observational even though no instances of the "property" of
being a man
over 14 feet tall have been observed. It would seem that this
approach
must soon fall back upon some notion of simples or
determinables vs.
determinates. But is it thereby saved? If it is held that only
those terms
which refer to observed simples or observed determinates are
observation
terms, we need only remind ourselves of such instances as
Hume's no-
torious missing shade of blue. And if it is contended that in
order to be
an observation term an expression must at least refer to an
observed de-
terminable, then we can always find such a determinable which
is broad
enough in scope to embrace any entity whatever. But even if
these diffi-
culties can be circumvented, we see (as we knew all along) that
this
approach leads inevitably into phenomenalism, which is a view
with
which we have not been concerning ourselves .
Now it is not the purpose of this essay to give a detailed
critique of
phenomenalism. For the most part, I simply assume that it is
untenable,
at least in any of its translatability varieties.7 However, if there
are any
unreconstructed phenomenalists among the readers, my purpose,
insofar
as they are concerned, will have been largely achieved if they
will grant
what I suppose most of them would stoutly maintain anyway,
i.e., that
theoretical entities are no worse off than so-called observable
physical
object.
' Th r ad r is no doubt familiar with the abundant literature
concerned with this
i ~ 11 • S ·,, f r xnmple, Sellars' "Empiricism and the
Philosophy of Mind," which
nl , o 011 l n 111 ~ r f r ·nee to other pertinent works.
12
THE ONTOLOGICAL STATUS OF THEORETICAL ENTITIES
Nevertheless, a few considerations concerning phenomenalism
and re-
lated matters may cast some light upon the observational -
theoretical
dichotomy and, perhaps, upon the nature of the "observation
language."
As a preface, allow me some overdue remarks on the latter.
Although I
have contended that the line between the observable and the
unobserv-
able is diffuse, that it shifts from one scientific problem to
another, and
that it is constantly being pushed toward the "unobservable" end
of the
spectrum as we develop better means of observation-better
instruments
-it would, nevertheless, be fatuous to minimize the importance
of the
observation base, for it is absolutely necessary as a
confirmation base for
statements which do refer to entities which are unobservable at
a given
time. But we should take as its basis and its unit not the
"observational
term" but, rather, the quickly decidable sentence. (I am indebted
to
Feyerabend, Joe. cit., for this terminology.) A quickly decidable
sentence
(in the technical sense employed here) may be defined as a
singular,
nonanalytic sentence such that a reliable, reasonably
sophisticated lan-
guage user can very quickly decide 8 whether to assert it or
deny it when
he is reporting on an occurrent situation. 'Observation term' may
now .
be defined as a 'descriptive (nonlogical) term which may occur
in a
quickly decidable sentence,' and 'observation sentence' as a
'sentence
whose only descriptive terms are observation terms.'
Returning to phenomenalism, let me emphasize that I am not
among
those philosophers who hold that there are no such things as
sense con-
tents (even sense data), nor do I believe that they play no
important
role in our perception of "reality." But the fact remains that the
refer-
nts of most (not all) of the statements of the linguistic
framework
u ed in everyday life and in science are not sense contents but
rather
l hysical objects and other publicly observable entities. Except
f~r pains:
dors, "inner states," etc., we do not usually observe sense
contents; and
lthough there is good reason to believe that they play an
indispensable
l in observation, we are usually not aware of them when we
visually
tactilely) observe physical objects. For example, when I observe
a
'storted, obliquely reflected image in a mirror, I may seem to be
seeing
l nby elephant standing on its head; later I discover it is an
image of
11 le harles taking a nap with his mouth open and his hand in a
· uliar position. Or, passing my neighbor's home at a high rate
of
' W may . say "~oninferent~lly" decide, provided this is
interpreted liberally
n h to avoid startmg the entire controversy about observability
all over again.
13
Grover Maxwell
speed, I observe that he is washing a car. If asked to report th ·s
· oh · r
vations I could quickly and easily report a baby elephant and n
wn sliin
of a car; I probably would not, without subsequent obsc rvaliou
s, h • uhl
to report what colors, shapes, etc. (i.e., what sense data) w •r ·
involv •<1.
Two questions naturally arise at this point. How is ii tl111l w ·
ran
(sometimes) quickly decide the truth or falsity of a pert i 11
•111 oh1.t•1 vn
tion sentence? and, What role do sense contents play in Iii ·
app1opdnl ·
tokening of such sentences? The heart of the matter is tlrnl 111 .
., · 111
primarily scientific-theoretical questions rather than "p 111 ·ly
1011it1 1' ,"
"purely conceptual," or "purely epistemological." If the r I i · ii
I l1 y~i<'s,
psychology, neurophysiology, etc., were sufficiently advan •cl ,
W(' ('()11 ld
give satisfactory answers to these questions, using, in all Ii k
·lil1ood , 111
physical-thing language as our observation language and tr "" i
111: ,(" 11 ~ :1 ·
tions, sense contents, sense data, and "inner states" as t/1 ·c11
·t i(':i/ ( l'S,
theoretical!) entities.9
It is interesting and important to note that, even bcf or · W('
i:iw <'<1 111
pletely satisfactory answers to the two questions consid ·1 ·cl
1hoV<', w ·
can, with due effort and reflection, train ourselves lo "obs ·1
v<• di11 ·c t ly"
what were once theoretical entities-the sense conlcnls (C'o lo1
M' 11 1 d 1011 s,
etc.)-involved in our perception of physical things. As !i ns
1>1· ·11 po11il ·d
out before, we can also come to observe other kind s of
1·111ii1<' wl11d1
were once theoretical. Those which most readil y c 111 • lo
111111d 111volv ·
the use of instruments as aids to observation . Ind · d, """I: 011
1 pain·
fully acquired theoretical knowledge of the world, w co 1111·
lo I'<' lliul
we "directly observe" many kinds of so-called thcor ·li ·1 1'
111111 1: . All ·r
listening to a dull speech while sitting on a hard h ncli , W<'
liq:111 Io h •
come poignantly aware of the presence of a consid •rahly .
11011111:111viln·
tional field, and as Professor Feyerabend is fond of poi111i111:
rnll , ii w
were carrying a heavy suitcase in a changing gravi tali o11 11 I
flC'lcl , we• c 011ld
observe the changes of the Gµ.v of the metric tensor.
I conclude that our drawing of the obscrvatio1111l I li
c011·1111 1' li111• at
any given point is an accident and a function of 0111 pl1 wloi: r
11 11111k .
•C f. Sellars, "Empiricism and the Philosophy of Mi11 I " A 1 1
111f1,~111 S •llnrs
points out, this is the crux of the "other-minds" p1ohlc111 , Sr n
111 1111 1111tl 111111 tut e
(r~lativc to nn i'.~tcrsubjc~ti~~ observation l:mgu:iric, I
w1111ld 11 dd) 1111 11111111 t 111 1 t•n.
~111.cs (n 11d 1·h.'Y. really exist ) and not mer ly o ·111 11 l
1111d/111  "'~~l tit l11l111v111 S111 ly
1t is 11 ~ · 1111w1ll111gncss to countena nce th or lira I ·111
it 1·~ I 11 1111111 t 11111 1·vny ·n·
t ·1.1c· 1 ~ I 11111slatnhl '. 11 01'. on ly int? som ohsc1~11 t i
~> 11 li111111111H• li11t 11111 t 111 phyNi1. l·
I h111 g !:11.11:11111: wh1 ·h 1s r ·spons1blc for th 10111<
111 lir l111 v 111 - 111 " 111 1111 11ro Witt·
fll' n ~ I t•11 11 1 111 ~ .
THE ONTOLOGICAL STATUS OF THEORETICAL ENTITIES
up, our current state of knowledge, and the instruments we
happen to
have available and, therefore, that it has no ontological
significance what-
ever.
What If We COULD Eliminate Theoretical Terms?
Among the candidates for methods of eliminating theoretical
terms,
three have received the lion's share of current attention: explicit
defin-
ability, the Ramsey sentence,10 and implications of Craig's
theorem.11
Today there is almost (not quite) universal agreement that not
all theo-
retical terms can be eliminated by explicitly defining them in
terms of
observation terms . It seems to have been overlooked that even
if this
could be accomplished it would not necessarily avoid reference
to un-
observable (theoretical) entities. One example should make this
evident.
Within the elementary kinetic theory of gases we could define
'mole-
cules' as 'particles of matter (or stuff), not large enough to be
seen even
with a microscope, which are in rapid motion, frequently
colliding with
each other, and are the constituents of all gases.' All the (
nonlogical)
terms in the definiens are observation terms, and still the
definition it-
self, as well as kinetic theory (and other theoretical
considerations), im-
plies that molecules of gases are unobservable (at least for the
present).
It seems to me that a large number-certainly not all, however;
for
example, 'photon,' 'electromagnetic field,' 'if-function'-of
theoretical
terms could be explicitly defined wholly in terms of observation
terms,
but this would in no way avoid a reference to unobservable
entities. This
important fact seems to have been quite generally overlooked. It
is an
important oversight because philosophers today are devoting so
much
nltention to the meaning of theoretical terms (a crucially
important
pr blem, to be sure), while the ontological stomach-aches
(ultimately
unjustifiable, of course) concerning theories seem to have arisen
from
I h • fact that the entities rather than the terms were
nonobservational.
Implicit, of course, is the mistaken assumption that terms
referring to
1111ob crvable entities cannot be among those which occur in
the ob-
c'IVnlion language (and also, perhaps, the assumption that the
referent
of 11 defined term always consists of a mere "bundle" of the
entities
~ Iii ·h nrc referents of the terms of the definiens).
'" l•' 111nk P. Ramsey, The Foundations of Mathematics (New
York: Humanities
11111 ) . ,
" Wlllinrn rnig, "Replacement of Auxiliary Expressions,"
Philosophical Review
r1 Ill ~~ ( 1956). '
15
Grover Maxwell
Surprisingly nough, both the Ramsey sentence and Craig's
theorem
provid e us with gen uine (in principle) methods for eliminating
theo-
reti al term s provided we are interested only in the deductive
"observa-
ti nal" onscq uences of an axiomatized theory. That neither can
provide
a viable method for avoiding reference to theoretical entities
has been
pointed out clearly by both Hempel and Nagel.1 2 I shall
discuss these
two devices only briefly.13
The first step in forming the Ramsey sentence of a theory is to
take
the conjunction of the axioms of the theory and conjoin it with
the
so-called correspondence rules (sentences containing both
theoretical
and observational terms-the "links" between the "purely
theoretical"
and the observational). This conjunction can be represented as
follows:
---P---Q--- . . .
where the dashes represent the sentential matrixes (the axioms
and C-
rules) containing the theoretical terms (which are, of course,
almost
always predicates or class terms) 'P,' 'Q,' ' .. .';the theoretical
terms are
then "eliminated" by replacing them with existentially
quantified vari-
ables . The resulting "Ramsey sen tence" is represented, then,
by
(3f)(3g) ... (---f---g--- . .. ) .
Or, consider an informal illustration. Let us represent
schematically an
oversimplified axiomatization of kinetic theory by
All gases are composed entirely of molecules. The molecules
are
in rapid motion and are in frequent collision, etc., etc.
And for simplicity's sake, suppose that 'molecules' is the only
theoretical
term. The Ramsey sentence would be something like the
following:
There is a kind of entity such that all gases are composed
entire-
ly of these entities . They are in rapid motion and are in
frequent
collision, etc., etc.
Now it is a simple matter to demonstrate that any sentence
containing
only observation (and logical) terms which is a deductive
consequence
of the original theory is also a deductive consequence of its
Ramsey
sentence (see, for example, Rozeboom's article in this volume);
thus,
:is for as any deductive systemization is concerned, any theory
may be
" nrl ,. IT mp I, "The Theoretician's Dilemma," in Minnesota
Studies in Phi-
losoi11ty I. i nee, Vol. II, Feig!, Scriven, and Maxwell, eds.
Nagel, Joe. cit.
' For nn · l nd d nsiderntion of the Ramsey sentence see
Professor William
Hoi ·hoo111' s ny 111 thi volume.
16
THE ONTOLOGICAL STATUS OF THEORETICAL ENTITIES
eliminated and its Ramsey sentence used instead. However, it is
also
easy to prove (if indeed it is not obvious) that if a given theory
(or a
theory together with other considerations, theoretical or
observational)
entails that there exist certain kinds of unobservable entities,
then the
appropriate Ramsey sentence will also entail that there exist the
same
number of kinds of unobservable entities.14 Although, insofar
as deduc-
tive systemization is concerned, the Ramsey sentence can avoid
the use
of theoretical terms; it cannot, even in letter, much less in spirit
(Hem-
pel, Ioc. cit., was too charitable), eliminate reference to
unobservable
(theoretical) entities.
The Craig result, like the Ramsey sentence, provides a "
method" of
reaxiomatizing a postulate set so that any arbitrarily selected
class of
terms may be eliminated, provided one is interested only in
those theo-
rems which contain none of these terms . Its "advantages" over
the
Ramsey sentence are that it does not quantify over predicates
and class
terms and that its final reaxiomatization eliminates reference
both in
spirit and in letter to unobservable entities. However, its
shortcomings
(for the purposes at hand) render it useless as an instrument of
actual
scientific practice and also preclude its having, even in
principle, any
implications for ontology. The resulting number of axioms will,
in gen-
eral, and particularly in the case of the empirical sciences, be
infinite in
number and practicably unmanageable.
But if the practical objections to the use of Craig's method as a
means
for elimination of theoretical terms are all but insurmountable,
there are
objections of principle which are even more formidable. Both
Craig's
method and the Ramsey device must operate upon theories
(containing,
of course, theoretical terms) which are "already there." They
eliminate
theoretical terms only after these terms have already been used
in inter-
" The proof may be sketched as follo ws: Let 'T' designate the
theory (conjoined,
i( nc essary, with other statements in the accepted body of
knowledge ) which entails
Iii 1t the kinds of entities C, D, ... are not observable, i.e ., T
entails that
(3 x)( 3 y) ... (Cx·Dy .. . xis not observable•y is not observable
. . . ) which in turn entails
(3f)(3 g) . .. (3x)(3y) ... (fx•gy ... x is notobservable•yisnot
observable . . . ) .
Ramsey result holds for any arbitrary division of nonlogical
terms into two
1 l.1, r , 6 we may put 'observable' into the class with the
observation terms, so that
lltr h1 tt <•r formalized statement may be treated as an
"observational" consequence
111 ' I' ( I 111 itivity of entailment). But then it is also a
consequence of the Ramsey
111 l 1 1H' f T . Q. • .D.
17
Grover Maxwell
mediary steps. Neither provides a method for axio1n ut izu ti n
ab initio
or a recipe or guide for invention of new theo ri es. 0 11 . qn
•11tly neither
provides a method for the elimination of th co rcli ul I •rn1 s in
the all-
important "context of discovery." 1 5 It might be argu cl th ut t-
hi s objec-
tion is not so telling, after all, for we also lack any re ·i I f r lh
c inven-
tion of theories themselves, and it is logically poss ibl lh:it w
should
discover, without the use of theories as intermediari es, Rams ·y
se n tences
or Craig end products which are just as useful for xpl ai nin a
nd pre-
dicting observations as the theories which we happ 11 to ha ve
(acci-
dently) adduced. It might be added that it is al so logica ll y
poss ible that
we should discover just those observation statement ( in cl ncl
iu g pre-
dictions, etc.) which happen to be true without th e use of a 11 y
i nstru-
mental intermediaries.
We must reply that the accomplished fact that it is th eo ri es,
referrin g to
unobservables, which have been invented for thi s pmposc and
tl1 at many
of them serve it so admirabl y-this fa ct, itself, cri es out for
expl anation.
To say that theories are designed to accompli sh thi task is no r
pl y un-
less at least a schema of an instrum entalist recipe for su h cl
signin g is
provided. As far as I know thi s has not been don . Th e th sis
t·hat theo-
retical entities are "really" just "bundles" of obscrva hl bj ts or
of
sense data would, if tru e, p~ovicle an explanati on; but it is not
taken very
seriously by most philosophers today- for th e very good r ason
tha t it
seems to be fal se. The only reasonable explanati on for th e
success of
theories of which I am aware is that well-confirmed th eo ri es
arc con-
junctions of well-confirmed, genuine statements and that th e cn
ti ti c to
which they refer, in all probability, exist. That it is
psychologica ll y pos-
sible for us to invent such theories is explained by the fa ct that
many
of th e entities to which they refer resemble in many respects
(although
. ',: T he Ramsey sentence is intuitively tractable enough so that
ve ry simple " theo-
ri es . might be mvented as full-blown Ramsey sentences
without the use of inter-
mec!1ary ~crms. However'. Craig's theorem provides no means
of operating ab initio.
ra 1g points out ( Joe. cit. ) that once the original theory is "
there," reference in
I ·11 ·r, 1·0 theoret ical e.ntities in the application of his
method may be avoided by u; ing
l!ll' ,11 11 111 ·s of t~1 coret1 ca l terms rather t~an using the
terms themselves (i.e . by men-
l1011111 g, lh ·or l1 cnl term s ra ther than usmg them) . But
surely only a diehard instru-
11 1 c· 11 l 1 il 1 ~ I • 111 l:ik : more than very scant comfort
from this. The qu es tion would still
11' 11 1111 11 : h ·r did th theory come fr om in th e first place,
and why are the names
ol th C' ~ ci p11il i(o 11l 11 I ·n 11s arra ng cl in this particu
lar ma nn er such admirable "instru-
11 11•11I H" 101 <• p l 11 11 1 ~ 1 ion . nn I pr ·di tio1.1 of ob
crvat ions? Whatever ontological im-
pl 111 11011 I I ii ~ 111 odif1 c11 11 011 of t he ra1g m ·thod
may have, they seem to be exactly
t li 1 11 11 1 11 lh <l'I(' of i11 Nl1 u111 ·nt: il is111 pr p •r.
18
THE ONTOLOGICAL STATUS OF THEORETICAL ENTITIES
they may differ radically from them in others) the entities which
we
have already observed.
It should also be remembered, at this point, that theories, even
as
instruments, are important not only for deductive systemization
but also
for inductive systemization (see Hempel, Joe. cit.) . We often
reason
theoretically using induction, and the conclusions may be either
obser-
vational or theoretical. Thus we might infer from the facts that a
certain
substance was paramagnetic, that it catalyzed the recombination
of free
radicals, and that it probably contained a " one-electron" bond;
and we
might go on to infer, again inductively, that it would probably
catalyze
the conversion of orthohydrogen to parahydrogen. The Craig
result ap-
plies only to deductive systemization and, thus, cannot, even in
its Pick-
wickian fashion, eliminate theoretical terms where inductive
theoretical
reasoning is involved . Although Craig's theorem is of great
interest for
formal logic, we must conclude, to use Craig's (Joe. cit.) own
words,
"[as far as] the meaning [and, I would add, the referents] of
such ex-
pressions [auxiliary expressions (theoretical terms)] . . . [is
concerned]
the method . . . fails to provide any . . . clarification."
We have seen that the elimination of theoretical terms, even by
ex- -'
plicit definition, would not necessarily eliminate reference to
theoretical
(unobservable) entities. We have also seen that, even if
reference to
theoretical entities could be eliminated after the theories
themselves
have been used in such an elimination (for example, by a device
such
n Craig's), the reality (existence) of the theoretical entities is
not there-
by militated against. But the most crucial point follows. Even if
we do
me up with a gimmick-a prediction machine or "black box" -into
whi ch we can feed data and grind out all the completely
veridical ob-
N rvational predictions which we may desire, the possibility-I
should
1y the likelihood-of the existence of unobserved causes for the
ob-
•rv cl events would still remain . For unless an explanation of
why any
lL li ction machine or " calculating device" in terms of the
established ...
ul · of explanation, confirmation, etc., were forthcoming, the
task of
·i •n c would still be incomplete.
'fltis brings us to another mistaken assumption that has been
responsi-
k. f r much mischief in considerations concerning the cognitive
status
tl1 · ries-th e assumption that science is concerned solely with
the
'' tutful" orga ni za tion of observational data or, more
specifically, with
· ·ss fnl predi ction. Surel y the main concerns of, say, a
theoretical
19
Grover Maxwell
physicist involve such things as the actual properties and vari
ties of
subatomic particles rather than the mere predictions abo ut
where and
how intense a certain spectral line will be. The instrum ntalist
has the
picture entirely reversed; as far as pure science is con crned,
most ob-
servational data-most predictions-are mere instrum ents and are
of
value only for their roles in confirming theoretical principles.
Even if
we obtain the prediction machine, many of the theoric ex tant
today
are well confirmed enough to argue strongly for the reality of th
eoretical
entities. And they are much more intellectually satisfactory, for
they pro-
vide an explanation of the occurrence of the observational
events which
they predict. And-equally important-an explanation for th e fact
that
theories "work" as well as they do is, as already noted, also
forth coming;
it is simply that the entities to which they refer exist.
"Criteria" of Reality and i nstrum en talism
It was pointed out in the beginning of this article that Professor
Ernest Nagel considers the dispute between realists and
instrumentalists
to be merely a verbal one.16 There follows here a brief and
what I hope
is a not too inaccurate summary of his argument. Various
criteria of
'real' or 'exist' (runs the argument) are employed by scientists,
philoso-
phers, etc., in their considerations of the "reality problem."
(Among
these. criteria-some of them competing, some compatible with
each
other-are public perceivability, being mentioned in a generally
accepted
law, being mentioned in more than one law, being mentioned in
a
"causal" law, and being invariant "under some stipulated set of
trans-
formation, projections, or perspectives." 17 ) Since, then (it
continues)
any two disputants will, in all probability, be using 'real' or
'exist' in two
different senses, such disputes are merely verbal. Now someone
might
anticipate the forthcoming objections to this argument by
pointing out
that the word 'criteria' is a troublesome one and that perhaps,
for Nagel,
the connection between criteria and reality or existence is a con
tingent
one rather than one based on meaning. But a mom ent's reA tion
makes
it obvious that for Nagel's argument to have for e, ' rit ri,' must
be
tak n in the latter sense; and, indeed, Nagel xpli ·itl y 1 ak for
the
0 1111 1·i n between criteria and th e "sen es [ i I] f ' r nl' r
'exist.' " 18
•• p. it., pp . 141- 152 .
"Nn11 ·I, op. it., pp . 145- 150.
,. p. it., p. 151.
2
THE ONTOLOGICAL STATUS OF THEORETICAL ENTITIES
n fore proceeding to a criticism of these arguments, let me point
out that
Professor Gustav Bergmann, completely independently, treats
ontologi-
al questions in a similar manner. Rather than criteria, he speaks
of "pat-
terns," although he does say that he "could instead have spoken
of
riteria," and he makes explicit reference to various "uses" of
'exist.' 19
There are two main points that I wish to make regarding this
kind of
approach to ontological issues. First, it seems to me that it
commits the
Id mistake of confusing meaning with evidence. To be sure, the
fact
that a kind of entity is mentioned in well-confirmed laws or that
such
entities are publicly perceptible, etc.-such facts are evidence
(very good
evidence!) for the existence or "reality" of the entities in
question. But
I cannot see how a prima-facie-or any other kind of-case can be
made
for taking such conditions as defining characteristics of
existence.
The second point is even more serious . One would hope that
(Pro-
fess or Norman Malcolm notwithstanding) over nine hundred
years of
debate and analysis have made it clear that existence is not a
property.
Now surely the characteristics of being mentioned in well -
confirmed
laws, being publicly perceptible, etc ., are properties of sorts;
and if these
omprised part of the meaning of 'exists,' then 'existence' would
be a
predicate (and existence a property) .
Thus it is seen that the issue between instrumentalism and
realism
' an be made into a merely verbal one only by twisting the
meanings of
'existence' and 'reality,' not only beyond their "ordinary"
meaning but,
al o, far beyond any reasonable meanings which these terms
might be
•iven. In fact, it seems not too much to say that such an
interpretation
f the "reality problem" commits a fallacy closely akin to that of
the
ntological Argument.
What can be said about the meanings of 'real' and 'exists'? I
submit
1hnt in "ordinary language," the most usual uses of these terms
are such
Iha
<I>. are real =dr <I>. exist
md that
<I>. exist = dr there are <I> 8
ll l l that the meanings of these definiens are clear enough so
that no
111 lh r xplication is seriously needed . (In most "constructed
languages,"
''l'h are iJl.' would, of course, be expressed by ' ( 3x) ( <I>x) .')
Thus, if
••" Phy i ond Ontology," Pl1ilosopl1y of Science, 28 : 1-14 (
196 1).
21
Grover Maxwell
we have a well-confirmed set of statements (laws or theories
plus initial
conditions) which entail the statement 'There are cf!.' (or ' ( 3x)
( cf!x )'),
then it is well confirmed that cf!. are real-full stop!
In summary, let us recall three points concerning
instrumentalism.
First, as is shown above, it cannot be excused on the grounds
that it
differs from realism only in terminology. Second, it cannot
provide an
explanation as to why its "calculating devices" (theories) are so
success-
ful. Realism provides the very simple and cogent explanation
that the
entities referred to by well-confirmed theories exist. Third, it
must be
acutely embarrassing to instrumentalists when what was once a
" purely"
theoretical entity becomes, due to better instruments, etc., an
observ-
able one.20
The Ontological Status of Entities-Theoretical and Otherwise
As I have stated elsewhere (see the second reference in footnote
22),
the key to the solution of all significant problems in ontology
can be
found in Carnap's classic article, "Empiricism, Semantics, and
Ontol-
ogy.''21 Taking this essay as our point of departure, we may say
that in
order to speak at all about any kind of entities whatever and
thus, a for-
tiori, to consider their existence or nonexistence, one must first
accept
the "linguistic framework" which ... troduces the entities." 22
This sim-
ply means that in order to understand considerations concerning
the
existence of any kind of entities one must understand the
meanings of
the linguistic expressions (sentences and terms) referring to
them-and
that such expressions have no meaning unless they are given a
place in
a linguistic framework which "talks about the world" and which
has at
least a minimum of comprehensiveness . (Since I am interested,
here,
primarily in empirical science, I neglect universes of discourse
containing
only "purely mathematical" or "purely logical" entities.)
Although wide latitude in choosing and constructing
frameworks is
permissible, any satisfactory framework will embody, at the
very least,
•
20 ".'-!though I cannot agree with all the conclusions of
Professor Feycrabend 's essay
111 this volume, the reader 1s referred to it for an interesting
critique of instrumen-
talism .
" R. a map, Meaning and Necessity, 2nd ed. (Chicago: Univers
ity of Chicago
Pr ss, 19 59 ) .
" fo'or n mor cl ctailccl discussion of linguistic frameworks as
well as th eir releva nce
for nn tn lop i(•nl probl ms, sec Carnap, ibid .; and G . Maxw II
, "Theories, Frameworks,
11 11 <1 )11tolor,y,' Pl1ilosop hy of Science, vol. 28 (1961 ).
For an elaboration of the
li11 11 11i NI i · I Ii ·scs pr •s 11ppos d by th e fatter article
and, to some extent, by this essay,
22
THE ONTOLOGICAL STATUS OF THEORETICAL ENTITIES
I h ' f II owing features: ( 1) the usual L ( ogical )-formation
and L-trans-
fo1 n1ation rules and the corresponding set of L-true sentences
which
I Ii y generate; ( 2) a set of confirmation rules, whose nature I
shall not
di · n s here but which I shall assume are quite similar to those
actually
11 , d in the sciences; ( 3) a set of sentences whose truth value
is quickly
d idable on other than purely linguistic grounds-these
correspond to
"s i11 gular observation statements," but, of course, as we have
seen, it is
11 ithcr necessary nor desirable that such statements be
incorrigible or
i11dubitable or that a sharp distinction between observation and
theory
h ' drawn; and ( 4) a set of law like sentences, which, among
other things,
provide that component of meaning which is nonostensive for
every
d s riptive ( nonlogical) term of the framework. (I have argued
in the
1· •f rcnces given in footnote 22 that every descriptive term has
a mean-
i11 omponent which is nonostensive.23 Even a term such as
'red' has
I art of its meaning provided by, for example, the lawlike
sentence 'No
snrfoce can be both red and green all over at the same time.'
Such a
vi •w is sometimes stigmatized by the epithet 'holism.' But if
there is
111 y holi sm involved in the view I am advocating, it is
completely con-
ptual or epistemological and not ontological. Just what relations
are
pr ' nt, or absent, between the actual entities of the "real world"
is an
·111pirical question and must be decided by considerations
within a de-
s ·ri ptivc linguistic framework rather than by consideration
about such
f1t11n works.)
this point, two views may be mentioned . I will omit
consideration
o xpli citly defined terms, since they are, in principle, always
eliminable.
· · rcling to one view, it is always a proper subset of the lawlike
sen-
t · 11 ontaining a given term which contributes to the term's
meaning.
' I 'Ii · s n tcnces in this subset are A-true 24 (analytic in a
broad sense)
111d :ir · totally devoid of any factual content-their only
function is to
I 1 ovid part of the meaning of the term in question. The
situation is
111111 ·n cly com plicated by the fact that when actual usage is
considered,
11 •• Maxwell and H. F eig!, "Why Ordinary Language Needs
Reforming," Journal
11/ l '/1ilosop hy, 58: 488-498 (1961); G. Maxwell, "Meaning
Postulates in Scientific
' l'll('oii ·s," in Current Issues in the Philosophy of Science,
Feigl and Maxwell, eds.; and
111 hd •f nrti le, "Th e N ecessary and the Contingent," in this
volume.
r. nlso the writi ngs of Wilfrid Sellars, for example in "Some
Reflections on
I .111111111H a mes," Pl1iloso pl1y of Science, 21 : 204-228 (
1954 ).
1 S • · ll. amnp, " Bcobachtun gsprache und theoretisch
Sprache," Dialectica,
I ~ 2<18 ( 1957); as we ll as the referen ces in fn . 22 .
23
Grover Maxwell
a sentence which is A-true in one context may be contingent in
another
and that even in a given context it is, more often than not, not
clear,
unless the context is a rational reformation, whether a given
sentence
is being used as A-true or as contingent. This confusion can be
avoided
by engaging in rational reformation, i.e., by stipulating (subject
to cer-
tain broad and very liberal limitations) which sentences are to
be taken
as A-true and which as contingent. Needless to say, this is the
viewpoint
which I prefer.
The complication just mentioned, however, has led many
philoso-
phers, including Professor Putnam 25-to say nothing of W. V.
Quine-
to the other viewpoint. According to it, no segregation of the
relevant
lawlike sentences into A-true and contingent should be
attempted; each
law like sentence plays a dual role : ( 1) it contributes to the
meanings
of its descriptive terms and (2) it provides empirical
information. For-
tunately, we do not have to choose between these two
viewpoints here,
for the thesis of realism which I am advocating is (almost)
equally well
accommodated by either one.
Now when we engage in any considerations about any kinds of
en-
tities and, a fortiori, considerations about the existence of
theoretical
entities, it is to the lawlike sentences mentioning the entities-for
theo-
retical entities, the theoretical postulates and the so-called
correspond-
ence rules-to which we turn. These sentences tell us, for
example, how
theoretical entities of a given kind resemble, on the one hand,
and differ
from, on the other, the entities with which we happen to be
more fa-
miliar. And the fact that many theoretical entities, for example
those of
quantum theory, differ a great deal from our ordinary everyday
physical
objects is no reason whatever to ascribe a questionable
ontological status
to them or to contend that they are merely "calculating devices."
After
all, the very air we breathe as well as such things as shadows
and mir-
ror images are entities of quite different kinds from chairs and
tables,
but this provides no grounds for impugning their ontological
status. The
fa ct that molecules, atoms, etc., cannot be said in any non-
Pickwickian
sense to have a color has given some philosophers ontological
qualms.
But, of course, the air has no color (unless we invoke the color
of the
sky); and a transparent object whose refractive index was the
same as
t li a t of air would be completely invisible, although it would
have all
• S h is essay in this volume.
24
THE ONTOLOGICAL STATUS OF THEORETICAL ENTITIES
I he other properties of ordinary physical objects. Molecules,
for exam-
pl e, are in about the same category; they are physical things
which pos-
' some but not all of the properties of everyday physical things.
A : Do molecules exist?
B: Certainly. We have an extremely well-confirmed theory,
which when conjoined with other true sentences such as
'There are gases' entails that there are molecules.
A: But are they real?
B: What do you mean?
A: Well, I'm not sure. As a starter : Are they physical objects?
B: Certainly the large ones are. Take, for example, that dia-
mond in your ring. As for those which are submicroscopic
but still large enough to have large quantum numbers, it
seems that in almost any reasonable reformation they would
be classified as physical objects. It would seem unjustifiable
to withhold from them this status simply because they can-
not be said to have a color in any straightforward fa shion .
In fact, I would even be inclined to call the smallest, the
molecule of hydrogen, a physical object. It has mass, a
reasonably determinate diameter, and, usually, something
which approximates simple location, etc.
A: How about electrons?
B : The decision here is more difficult. We might find it neces -
sary to try several reformations, taking into account many
facets of contemporary physical theory, before we arrived
at the most satisfactory one. It would also be helpful to
have a more specific problem in view than the one which
we are now considering. At any rate, we might begin by
pointing out that electrons do have mass, even rest mass.
111ey can be simply located at the expense of refraining
from ascribing to them a determinate momentum . They
ca~ be said to causally interact with "bona fide" physical
ob1 ec ts, even by those who have a billiard-ball notion of
ca usality. The important point is that the question 'Are elec-
tron s physical objects?' is a request for a rational reformation
of a very thoroughgoing variety. For most purposes, a ra-
tion al reformation would not need to answer it. For your
purposes, wh y not be content to learn in what ways elec-
trons are similar to, and in what ways they differ from , what
yo u would call "ordinary physical objects"? This will enable
you to avoid conceptual blunders.
A: Perh aps you are right. However, I am genuinely puzzled
nhoul fi eld s, and even photons.
25
Grover Maxwell
B: Take the last first. We would probably never call them
physical objects. For example, they have no rest mass and
it would be a conceptual mistake to ask, except in a Pick-
wickian sense, What is their color? However, it would be
reasonable to say that they are a sort of physical continuant;
and they can even interact with electrons in a billiard-ball
manner. At any rate, we must agree, speaking loosely, that
they are "every bit as real" as electrons. The concepts of field
theories are so open textured that it is difficult to decide
what kinds of reformations one should adopt here. And it
is virtually impossible to find similar kinds of entities with
which one is prescientifically familiar. Perhaps these theories
will someday be enriched until decisions concerning the
most appropriate rational reformations are easier to make-
perhaps not. But even here, the meanings of the terms in-
volved are usually sufficiently clear to avoid conceptual
blunders and ontological anxieties. You might like to con-
sider the "lines of force," which are often spoken of in con-
nection with fields. These are often used as a paradigm of
the "convenient fiction" by those who hold such a view of
theories. 26 But though convenient, lines of force are not
fictions. They "really exist." Let me try to make this a little
more plausible. Consider the isobars of meteorology, or the
isograms which connect points of equal elevation above sea
level. Now at this very moment, the 1017 millibar isobar,
i.e., the line along which the barometric pressure is 1017
millibars, exists right here in the United States. Its location
can even be determined "operationally." And all of this is
true whether anyone ever draws, or ever has drawn, a weather
map. Since a well-confirmed theory (plus, perhaps, other
"°Cf. B. Mayo, "The Existence of Theoretical Entities," Science
News, 32: 7-18
(1954), and "More about Theoretical Entities," ibid., 39:42-55
(1956) . For a
critique of these articles and for excellent constructive remarks
concerning theoretical
entities, see J. J. C . Smart, "The Reality of Theoretical
Entities," Austrafasian Journal
of Philosophy, 34 :1-12 (1956).
In connection with convenient fictions, we might consider such
entities as ideal
gases and bodies uninfluenced by external forces. These
actually are fictions. But no
theory (or theory plus true sentences) entails that there are such
things . To under-
sta nd their function, we need only recourse to the notion of a
limit, often used in
mathematics. Roughly speaking, what we actually do when we
use theories involving
s11 ch "fictions" is to assume, for example, that the influence of
external forces on the
body in question is very, very small, or that the behavior of the
gas with which we
:11 011 ·crnccl is approximately given by 'PV = nRT,' or, in
early kinetic theory, that
t Ii ~· di:1111 ·1 ·r of ~ molecule is very, very small compa red
to the distance between mole-
c·11l<·s. Nol· th nt lind van clcr Waals taken the calculating-
device or convenient-fiction
vi •w, Ii · p1ohahly wou ld not ha ve developed his equation
which embodies a correction
for th · d i n ·! d11l0 lo Ili c finite (greater than zero) diameter
of molecules.
26
THE ONTOLOGICAL STATUS OF THEORETICAL ENTITIES
well-confirmed sentences) entails that there are lines of force,
lines of force exist. To be sure, they are very different from
everyday physical objects. But as long as we are clear about
this, what metaphysical-what ontological-problems re-
main?
ne of the exciting aspects of the development of science has
been
I It emergence of reference to strikingly new kinds of entities.
This is
p:irticularly true in field theories and quantum theory. The great
differ-
•ncc between these and the old, familiar categories seems to
have caused
111any philosophers and philosophically inclined scientists to
despair of
·ff cting a satisfactory conceptual analysis of these powerful
new con-
. ptual tools. The attitude too often has been, "Let us proceed to
use
I ho e new devices and, if necessary for heuristic reasons, even
to behave
is it they consisted of genuine sta~ements about real entities.
But let us
1 ·member that, in the last analysis, they are only meaningless
calculating
I 'vices, or, at best, they talk only of convenient fictions, etc.
The only
r •nl entities are the good old familiar ones which we sense
directly every-
da y." To turn the purpose of a saying of Bertrand Russell's
almost com-
pl Lely about-face: such a view has advantages-they are the
same as
I hose of theft over honest toil. The compulsion toward
metaphysical
1s ·p is which appears to have been the motivation for the
espousal of
1rn1n y of these reductionistic philosophies seems, itself, to
have arisen
I 10111 a preoccupation with metaphysical pseudo problems,
e.g., the con-
j ·t ion that there are very few ontologically legitimate kinds of
entities,
l •rhaps only one.
27
03.jpg04.jpg06.jpg08.jpg10.jpg12.jpg14.jpg16.jpg18.jpg20.jpg2
2.jpg24.jpg26.jpg
80 Scientific American, August 2011
Fractals, such as this stack
of spheres created using
3-D modeling software, are
one of the mathematical
structures that were invent-
ed for abstract reasons yet
manage to capture reality.
© 2011 Scientific American
August 2011, ScientificAmerican.com 81Illustration by Tom
Beddard
Mario Livio is a theoretical astrophysicist at the Space
Telescope
Science Institute in Baltimore. He has studied a wide range of
cosmic phenomena, ranging from dark energy and super nova
explosions to extrasolar planets and accretion onto white
dwarfs,
neutron stars and black holes.
Is math invented or discovered?
A leading astrophysicist suggests that the answer
to the millennia-old question is both
By Mario Livio
M
ost of us take it for granted
that math works—that sci-
entists can devise formulas
to describe subatomic events
or that engineers can calcu-
late paths for space craft. We
accept the view, initially es-
poused by Galileo, that mathematics is the language of
science and expect that its grammar explains experi-
mental results and even predicts novel phenomena.
The power of mathematics, though, is nothing short of
astonishing. Consider, for example, Scottish physicist
James Clerk Maxwell’s famed equations: not only do
these four expressions summarize all that was known
of electromagnetism in the 1860s, they also anticipat-
ed the existence of radio waves two decades before
German physicist Heinrich Hertz detected them. Very
few languages are as effective, able to articulate vol-
umes’ worth of material so succinctly and with such
precision. Albert Einstein pondered, “How is it possi­
ble that mathematics, a product of human thought
that is independent of experience, fits so excellently
the objects of physical reality?”
As a working theoretical astrophysicist, I encoun-
ter the seemingly “unreasonable effectiveness of math­
ematics,” as Nobel laureate physicist Eugene Wigner
called it in 1960, in every step of my job. Whether I am
struggling to understand which progenitor systems
produce the stellar explosions known as type Ia super-
novae or calculating the fate of Earth when our sun ul-
timately becomes a red giant, the tools I use and the
models I develop are mathematical. The uncanny way
I N B R I E F
The deepest mysteries are often the things
we take for granted. Most people never
think twice about the fact that scientists
use mathematics to describe and explain
the world. But why should that be the case?
Math concepts developed for purely ab-
stract reasons turn out to explain real phe-
nomena. Their utility, as physicist Eugene
Wigner once wrote, “is a wonderful gift
which we neither understand nor deserve.”
Part of the puzzle is the question of wheth-
er mathematics is an invention (a creation
of the human mind) or a discovery (some-
thing that exists independently of us). The
author suggests it is both.
Math
P H I L O S O P H Y O F S C I E N C E
Works
Why
© 2011 Scientific American
82 Scientific American, August 2011
ED
W
A
RD
C
H
A
RL
ES
L
E
G
RI
CE
G
et
ty
Im
ag
es
that math captures the natural world has fascinated me through-
out my career, and about 10 years ago I resolved to look into
the
issue more deeply.
At the core of this mystery lies an argument that mathemati-
cians, physicists, philosophers and cognitive scientists have had
for centuries: Is math an invented set of tools, as Einstein be-
lieved? Or does it actually exist in some abstract realm, with
hu-
mans merely discovering its truths? Many great mathemati-
cians—including David Hilbert, Georg Cantor and the group
known as Nicolas Bourbaki—have shared Einstein’s view,
associ-
ated with a school of thought called Formalism. But other
illustri-
ous thinkers—among them Godfrey Harold Hardy, Roger Pen-
rose and Kurt Gödel—have held the opposite view, Platonism.
This debate about the nature of mathematics rages on today
and seems to elude an answer. I believe that by asking simply
whether mathematics is invented or discovered, we ignore the
possibility of a more intricate answer: both invention and dis-
covery play a crucial role. I posit that together they account for
why math works so well. Although eliminating the dichotomy
between invention and discovery does not fully explain the un-
reasonable effectiveness of mathematics, the problem is so pro-
found that even a partial step toward solving it is progress.
INVENTION AND DISCOVERY
mathematics is unreasonably effective in two distinct ways, one
I
think of as active and the other as passive. Sometimes scientists
create methods specifically for quantifying real-world phenome-
na. For example, Isaac Newton formulated calculus for the pur-
pose of capturing motion and change, breaking them up into in-
finitesimally small frame-by-frame sequences. Of course, such
ac-
tive inventions are effective; the tools are, after all, made to
order.
What is surprising, however, is their stupendous accuracy in
some
cases. Take, for instance, quantum electrodynamics, the mathe-
matical theory developed to describe how light and matter inter-
act. When scientists use it to calculate the magnetic moment of
the electron, the theoretical value agrees with the most recent
experimental value—measured at 1.00115965218073 in the ap-
propriate units in 2008—to within a few parts per trillion!
Even more astonishing, perhaps, mathematicians sometimes
develop entire fields of study with no application in mind, and
yet
decades, even centuries, later physicists discover that these very
branches make sense of their observations. Examples of this
kind
of passive effectiveness abound. French mathematician Évariste
Galois, for example, developed group theory in the early 1800s
for
the sole purpose of determining the solvability of polynomial
equations. Very broadly, groups are algebraic structures made
up
of sets of objects (say, the integers) united under some
operation
(for instance, addition) that obey specific rules (among them the
existence of an identity element such as 0, which, when added
to
any integer, gives back that same integer). In 20th-century
phys-
ics, this rather abstract field turned out to be the most fruitful
way of categorizing elementary particles—the building blocks
of
matter. In the 1960s physicists Murray Gell-Mann and Yuval
Ne’eman independently showed that a specific group, referred
to
as SU(3), mirrored a behavior of subatomic particles called had-
rons—a connection that ultimately laid the foundations for the
modern theory of how atomic nuclei are held together.
The study of knots offers another beautiful example of passive
effectiveness. Mathematical knots are similar to everyday knots,
except that they have no loose
ends. In the 1860s Lord Kelvin
hoped to describe atoms as knot-
ted tubes of ether. That misguid-
ed model failed to connect with
reality, but mathematicians con-
tinued to analyze knots for many
decades merely as an esoteric
arm of pure mathematics. Amaz-
ingly, knot theory now pro vides
important insights into string
theory and loop quantum gravi-
ty—our current best attempts at
articulating a theory of space-
time that reconciles quantum
mechanics with general relativi-
ty. Similarly, English mathemati- Similarly, English
mathemati-Similarly, English mathemati-
cian Hardy’s discoveries in num­
ber theory advanced the field of
cryptography, despite Hardy’s
earlier proclamation that “no one
has yet discovered any warlike purpose to be served by the
theo-
ry of numbers.” And in 1854 Bernhard Riemann described non­
Euclidean geo met ries— curious spaces in which parallel lines
converge or diverge. More than half a century later Einstein in-
voked those geometries to build his general theory of relativity.
A pattern emerges: humans invent mathematical concepts
by way of abstracting elements from the world around them—
shapes, lines, sets, groups, and so forth—either for some
specific
purpose or simply for fun. They then go on to discover the con-
nections among those concepts. Because this process of
inventing
and discovering is man-made—unlike the kind of discovery to
which the Platonists subscribe—our mathematics is ultimately
based on our perceptions and the mental pictures we can
conjure.
For instance, we possess an innate talent, called subitizing, for
in-
stantly recognizing quantity, which undoubtedly led to the con-
cept of number. We are very good at perceiving the edges of
indi-
vidual objects and at distinguishing between straight and curved
lines and between different shapes, such as circles and
ellipses—
abilities that probably led to the development of arithmetic and
geometry. So, too, the repeated human experience of cause and
ef-
fect at least partially contributed to the creation of logic and,
with
it, the notion that certain statements imply the validity of
others.
SELECTION AND EVOLUTION
michael atiyah, one of the greatest mathematicians of the 20th
century, has presented an elegant thought experiment that re-
veals just how perception colors which mathematical concepts
we
embrace—even ones as seemingly fundamental as numbers.
Ger-
man mathematician Leopold Kronecker famously declared,
“God
created the natural numbers, all else is the work of man.” But
imagine if the intelligence in our world resided not with human-
kind but rather with a singular, isolated jellyfish, floating deep
in
the Pacific Ocean. Everything in its experience would be
continu-
ous, from the flow of the surrounding water to its fluctuating
tem-
perature and pressure. In such an environment, lacking
individu-
al objects or indeed anything discrete, would the concept of
num-
ber arise? If there were nothing to count, would numbers exist?
Like the jellyfish, we adopt mathematical tools that apply to
The universe
has regularities,
known as
symmetries, that
let physicists
describe it
mathematically.
And no one
knows why.
© 2011 Scientific American
August 2011, ScientificAmerican.com 83
our world—a fact that has undoubtedly contributed to the per-
ceived effectiveness of mathematics. Scientists do not choose
an-
alytical methods arbitrarily but rather on the basis of how well
they predict the results of their experiments. When a tennis ball
machine shoots out balls, you can use the natural numbers 1, 2,
3,
and so on, to describe the flux of balls. When firefighters use a
hose, however, they must invoke other concepts, such as volume
or weight, to render a meaningful description of the stream. So,
too, when distinct subatomic particles collide in a particle
accel-
erator, physicists turn to measures such as energy and momen-
tum and not to the end number of particles, which would reveal
only partial information about how the original particles collid-
ed because additional particles can be created in the pr ocess.
Over time only the best models survive. Failed models—such
as French philosopher René Descartes’s attempt to describe the
motion of the planets by vortices of cosmic matter—die in their
infancy. In contrast, successful models evolve as new
information
becomes available. For instance, very accurate measurements of
the precession of the planet Mercury necessitated an overhaul of
Newton’s theory of gravity in the form of Einstein’s general
rela-
tivity. All successful mathematical concepts have a long shelf
life:
the formula for the surface area of a sphere remains as correct
to-
day as it was when Archimedes proved it around 250 b.c. As a
re-
sult, scientists of any era can search through a vast arsenal of
for-
malisms to find the most appropriate methods.
Not only do scientists cherry-pick solutions, they also tend to
select problems that are amenable to mathematical treatment.
There exists, however, a whole host of phenomena for which no
accurate mathematical predictions are possible, sometimes not
even in principle. In economics, for example, many variables—
the
detailed psychology of the masses, to name one—do not easily
lend themselves to quantitative analysis. The predictive value of
any theory relies on the constancy of the underlying relations
among variables. Our analyses also fail to fully capture systems
that develop chaos, in which the tiniest change in the initial
condi-
tions may produce entirely different end results, prohibiting any
long-term predictions. Mathematicians have developed statistics
and probability to deal with such shortcomings, but mathematics
itself is limited, as Austrian logician Gödel famously proved.
SYMMETRY OF NATURE
this careful selection of problems and solutions only partially
accounts for mathematics’s success in describing the laws of na­
ture. Such laws must exist in the first place! Luckily for
mathema-
ticians and physicists alike, universal laws appear to govern our
cosmos: an atom 12 billion light-years away behaves just like
an
atom on Earth; light in the distant past and light today share the
same traits; and the same gravitational forces that shaped the
universe’s initial structures hold sway over present­day
galaxies.
Mathematicians and physicists have invented the concept of
sym-
metry to describe this kind of immunity to change.
The laws of physics seem to display symmetry with respect to
space and time: They do not depend on where, from which an-
gle, or when we examine them. They are also identical to all ob-
servers, irrespective of whether these observers are at rest, mov-
ing at constant speeds or accelerating. Consequently, the same
laws explain our results, whether the experiments occur in Chi-
na, Alabama or the Andromeda galaxy—and whether we con-
duct our experiment today or someone else does a billion years
from now. If the universe did not possess these symmetries, any
attempt to decipher nature’s grand design—any mathematical
model built on our observations—would be doomed because we
would have to continuously repeat experiments at every point in
space and time.
Even more subtle symmetries, called gauge symmetries,
prevail within the laws that describe the subatomic world. For
instance, because of the fuzziness of the quantum realm, a giv-
en particle can be a negatively charged electron or an electri-
cally neutral neutrino, or a mixture of both—until we measure
the electric charge that distinguishes between the two. As it
turns out, the laws of nature take the same form when we inter-
change electrons for neutrinos or any mix of the two. The same
holds true for interchanges of other fundamental particles.
Without such gauge symmetries, it would have been very diffi-
cult to provide a theory of the fundamental workings of the
cosmos. We would be similarly stuck without locality—the fact
that objects in our universe are influenced directly only by their
immediate surroundings rather than by distant phenomena.
Thanks to locality, we can attempt to assemble a mathematical
model of the universe much as we might put together a jigsaw
puzzle, starting with a description of the most basic forces
among elementary particles and then building on additional
pieces of knowledge.
Our current best mathematical attempt at unifying all inter-
actions calls for yet another symmetry, known as supersymme-
try. In a universe based on supersymmetry, every known parti-
cle must have an as yet undiscovered partner. If such partners
are discovered (for instance, once the Large Hadron Collider at
CERN near Geneva reaches its full energy), it will be yet
another
triumph for the effectiveness of mathematics.
I started with two basic, interrelated questions: Is mathemat-
ics invented or discovered? And what gives mathematics its ex-
planatory and predictive powers? I believe that we know the an-
swer to the first question. Mathematics is an intricate fusion of
inventions and discoveries. Concepts are generally invented,
and
even though all the correct relations among them existed before
their discovery, humans still chose which ones to study. The
sec-
ond question turns out to be even more complex. There is no
doubt that the selection of topics we address mathematically has
played an important role in math’s perceived effectiveness. But
mathematics would not work at all were there no universal fea-
tures to be discovered. You may now ask: Why are there univer-
sal laws of nature at all? Or equivalently: Why is our universe
governed by certain symmetries and by locality? I truly do not
know the answers, except to note that perhaps in a universe
without these properties, complexity and life would have never
emerged, and we would not be here to ask the question.
M O R E T O E X P L O R E
The Unreasonable Effectiveness of Mathematics in the Natural
Sciences. Eugene Wigner
in Communications in Pure and Applied Mathematics, Vol. 13,
No. 1, pages 1–14; February 1960.
Pi in the Sky: Counting, Thinking, and Being. John D. Barrow.
Back Bay Books, 1992.
Creation v. Discovery. Michael Atiyah in Times Higher
Education Supplement; Septem-
ber 29, 1995.
Is God a Mathematician? Mario Livio. Simon & Schuster, 2010.
SCIENTIFIC AMERICAN ONLINE
Is mathematics invented, discovered, both or neither? See
examples of remarkable math-
ematical structures that invite this question at
ScientificAmerican.com/aug11/livio
© 2011 Scientific American
McMullin’s Inference: A Case for Realism?
with Bas C. van Fraassen, “Scientific Realism and the
Empiricist Challenge: An
Introduction to Ernan McMullin’s Aquinas Lecture”; and Ernan
McMullin, “The
Inference that Makes Science”
SCIENTIFIC REALISM AND THE EMPIRICIST
CHALLENGE: AN INTRODUCTION TO ERNAN
MCMULLIN’S AQUINAS LECTURE
by Bas C. van Fraassen
Abstract. In The Inference That Makes Science, Ernan
McMullin
recounts the clear historical progress he saw toward a vision of
the
sciences as conclusions reached rationally on the basis of
empirical
evidence. Distinctive of this vision was his view of science as
driven by
a specific form of inference, retroduction. To understand this
properly,
we need to disentangle the description of retroductive inference
from
the claims made on its behalf. To end I will suggest that the real
rival to
McMullin’s vision of science is not the methodologies he
criticizes so
successfully but a more radical empiricist alternative in
epistemology.
Keywords: abduction; empiricism; induction; Ernan McMullin;
retroduction; scientific realism
In The Inference That Makes Science, Ernan McMullin takes us
on a fabulous
journey through the history of philosophy of science, displaying
clear
progress toward a vision of the sciences as conclusions reached
rationally
on the basis of empirical evidence.1 This is McMullin’s vision,
distinctively
his, though in large outlines shared by the twentieth-century
philosophers
to whom he refers, in the last few pages, as scientific realists.
And surely, in
large outlines, though with characteristic qualifications, it is
also shared by
those to whose contrasting points of view he refers there as
instrumentalist.
For on all hands, the empirical sciences are accepted as a
paradigm of
rational inquiry into what our world is like.
But the title itself announces what is distinctive of McMullin’s
view:
the sciences are driven by a specific form of inference that
accounts for
Bas C. van Fraassen is a professor of philosophy at San
Francisco State University and
may be contacted at the Department of Philosophy, San
Francisco State University, 1600
Holloway Avenue, San Francisco, CA 94132, USA; e-mail:
[email protected]
Unless otherwise noted, page references will be to the text of
The Inference That Makes
Science (originally McMullin 1992) which is reprinted in this
issue of Zygon: Journal of
Religion and Science.
[Zygon, vol. 48, no. 1 (March 2013)]
C© 2013 by the Joint Publication Board of Zygon ISSN 0591-
2385 www.zygonjournal.org
131
132 Zygon
their success, and is indeed the hallmark of the scientific
approach to
any subject. As the history unfolds we see the attempts, one
after the other
found wanting, to identify that form of inference, until its final
articulation
as a process of (as McMullin decides to call it) retroductive
inference.
Aristotle, Grosseteste, Aquinas, Galileo, Zabarella, the late me-
dieval nominalists and Francis Bacon, Isaac Newton’s
methodological
vacillations, . . . the story reads as well and as fluently as a
mystery novel,
and is as engaging. What I shall comment on here is not
McMullin’s
excursions into history, however, though they were certainly for
me the
most fascinating part. My concern will instead be with
McMullin’s project,
the project to characterize the sciences as, in essence, a practice
identified
by a form of inference.
CONTRASTING MCMULLIN’S VISION WITH RIVAL
EPISTEMOLOGIES
McMullin does enough to discredit some alternative projects
with a similar
aim, such as attempts to define induction as a method for
science. Today
other projects of that sort exist as well, drawing in one way or
another on
the concept and theories of probability, notably varieties of
Bayesianism
or a more liberal probabilism. It would be of interest to ask
how, or
to what extent, such alternatives could do justice to the insights
that
support McMullin’s concept of retroduction as the crucial or
central form
of scientific inference. I will leave that aside as well. The more
interesting
question, for me, is rather whether scientific practice, the
enterprise of
science, is best characterized in that sort of form at all.
McMullin does not have an overriding ambition in this project.
He
emphasizes that it was “not intended to furnish a criterion of
demarcation
between science and non science [ . . . .] retroductive inference
makes use
of ingredients that are commonplace in human reason generally”
(144).
In good human reasoning to be sure; McMullin mentions
approvingly the
detective and the journalist. But retroduction is easily discerned
in not so
good human reasoning as well, when conspiracy theorists are
retroductively
inferring from the facts in evidence to their weird or wonderful
causal
explanation. So it seems at least at first blush as if the hallmark
of scientific
inquiry will not be that the form of inference is different, but
rather how
well it is employed:
What is distinctive about the way in which explanatory theories
are constructed
and tested in natural science is the precision, as well as the
explicitness, with which
retroductive inference is deployed. (146)
But that is too modest. It is not just a matter of doing it better,
not just a
matter of greater precision and explicitness, because McMullin
emphasized
features of the practice that are not captured by such earlier
accounts as
Bas C. van Fraassen 133
were focused on deduction, induction, or even Peircean
abduction. The
details emerge for McMullin after a long scrutiny of errors and
insights
accumulating through some twenty centuries of reflection on the
matter,
and they are not simple or neat, let alone algorithmic.
As a process of inference, retroduction “is not rule-governed as
deduction
is, nor regulated by technique as induction is” (183). McMullin
elaborates
on this elsewhere, indicating a strong difference from another
rival that
was much in the limelight in the closing decades of the
twentieth century:
retroduction [ . . . ] is not a strict form of rule-governed
reasoning, or at least,
it is not as long as it isn’t equated with the easily-criticized
“inference to best
explanation.” [ . . . .] The vulnerability of such an inference
need hardly be
emphasized. (McMullin 2007, 175)
These are important differences, and it is a characteristically
twentieth-
century insight that rational change in view is not a matter of
rule following,
that rules of right reason cannot be dictates, only guidelines.
But something
is needed beyond this negative point.
MCMULLIN’S ACCOUNT OF RETRODUCTIVE INFERENCE
It is in fact not easy to disentangle the points that allow us to
recognize
a process of retroductive inference from the claims McMullin
makes
concerning this sort of inference. We must concentrate on the
definitive
account that McMullin provides in the last 5 pages (in the
reprint that
follows) of The Inference That Makes Science, but it may help
to look
first at a formulation McMullin provided in a later publication,
as a short
summary:
Retroduction, argument from observed data to an explanatory
causal structure
which may itself be unobserved though not necessarily
unobservable is of its
essence tentative. It terminates in likelihood (in the everyday
sense of that term,
not the sense given it in probability theory). It allows for the
gradual mounting of
evidence of all sorts: increasingly troublesome anomalies
eliminated, ambiguities
resolved, new evidence successfully incorporated, and the rest.
Above all, under
certain circumstances it encourages more and more persistent
questioning of the
assumption that the paradigm in possession is beyond challenge
or that a potential
rival is, on the face of it, absurd. There is a lot of room here
between strict reason
and credo quia absurdum, the room afforded by an ever-
increasing likelihood that
may begin from a very low level indeed. (McMullin 2007, 176)
To what extent is this a description, such as a neutral observer
of scientific
practices might give, and to what extent does it involve claims
about the
adequacy or rationality or truth-conduciveness of this form of
inference?
First: that in such an inference we are “led backwards” from
effect
to cause, for example, we can read as merely describing the
form (from
premises about what happens to conclusions about what causes
them).
But we can also read it as a claim that what happens is al ways
in fact an
134 Zygon
effect, that is, an event that has causes, and in addition that
these causes
are discovered by retroductive inference. That this composite
claim is in
fact part of what McMullin maintains becomes quickly evident
toward the
end of his Aquinas lecture.
That McMullin is making a strong claim on behalf of this form
appears
also earlier in his critique of Newton, whom he describes as
having been
misled by the “quasi-demonstrative” form of his own writings,
and as
having had a distorting influence on eighteenth century
methodological
reflection, which
was to have negative repercussions for decades to come, until
the atoms and ether-
vibrations of the early nineteenth century once and for all
showed causal inference
to underlying structure to be indispensable to the work of the
physical scientist.
(180)
Second: one feature McMullin lists, which clearly distinguishes
this
retroductive inference, is the creation of new concepts. We can
imagine a
situation in which all attempts at explanation fail, within the
conceptual
framework that has been actualized so far. In that case—and
surely there
are famous historical cases of this sort—a smaller or larger
conceptual
revolution is the only way forward. As a distinguishing mark of
retroductive
inference, though, it has its limits; for this feature is one that
may be present,
and certainly is not always involved.
Once again, Newton furnishes the bad example of a misdirected
empiricism. The need for new concepts and new language
appears to
be ruled out by Newton’s Third Rule of Reasoning which
postulated that
the relevant properties of all bodies would be those accessible
to the human
senses. And this was not incidental, Newton “needed this
restriction . . . in
order that induction might be, as he claimed, the all-sufficient
method of
natural science” (185).
Third: that the product of retroduction is a theory which
presents a
causal explanation, distinct from the sort of empirical law that
registers a
regularity, is crucial. We can perhaps typically see the feature
of causal
“explanatoriness” at a glance, and if so it can serve as a
hallmark to
recognize retroduction. But even here a claim of adequacy or
efficacy, not
just something offered as description, is entangled with the
description:
The language here is, of course, that of scientific realism. It is
because the cause is,
in some sense however qualified, affirmed as real cause, that
retroduction functions
as a distinct form of inference. (184)
Here, after all, Newton appears as on the side of the angels. For
this phrasing
echoes Newton’s First Rule of Reasoning, the “vera causa”
principle. What
I will suggest though is that inductivism in the naı̈ ve form that
Newton
may have preached, if not practiced, is in any case not the most
important
rival to McMullin’s view of science.
Bas C. van Fraassen 135
AN ANALOGY, TO ARRIVE AT WHAT MAY BE
DISTINCTIVELY
DIFFERENT
As an analogy, suppose that someone wanted to construct an
account not of
what science is but of business, commerce. If someone starts a
business, he
will begin by amassing some capital, acquire a place of
business, equipment,
inventory, employees, and begin to advertise. As the business
gets going he
has to look ahead, plan replenishing his stock, have reserve
funds for repair
and for salary, including his own, when receipts are lagging.
What is the
inference that makes business?
Certainly inference is involved. Evidence of demand for his
goods or
services needs to be available before he can set out at all. A
record of the
expenses and receipts, and the timing of each, forms a growing
base of
evidence that he needs to consult continually, not simply to
assess how
well he is doing but to assess what is needed to go on. This
assessment is a
process of arriving at some conclusion that, though perhaps not
logically
derivable from that evidence, is at least sufficiently likely to
him in the light
of that evidence. That process is a process of inference. So yes,
inference is
involved.
But this we could say of almost any form of intentional activity
or
practice. In order to characterize business in a way that
distinguishes it
from other human practices, is looking for a distinctive form of
the sort
of inference involved the right thing to do? Is business
distinguished by
a special form of inference? Is engaging in that sort of inference
precisely
what it is to do business?
McMullin’s concentration on inference in developing his view
of science,
in continuation with the tradition he explores, suggests that we
should
assume science to be distinguished from such other practices as
business
and commerce in these terms. Science, not business or
commerce or the
like, is distinguished by a special form of inference. But it takes
patience
and willingness to look for differences, partly differences of
degree and
partly of kind, to elucidate what is special about that special
form.
We can go back at this point to the early pages of McMullin’s
Aquinas
lecture and remember that the ingredients of retroductive
inference, as
present in science, are commonplace in human reason generally.
That all
sorts of rational ways to reach conclusions are involved in
business, and that
this should be a common feature of business practice and
scientific practice,
should come as no surprise. It may well be in addition that in
business
sometimes the way to victory over rivals, to commercial
success, can only
come through the creation of new, novel concepts. A new
invention,
conceptually novel, may open an opportunity for a business to
take on
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-----GROVER MAXWELL------The Ontological Status of Theoret

  • 1. -----GROVER MAXWELL------ The Ontological Status of Theoretical Entities That anyone today should seriously contend that the entities referred to by scientific theories are only convenient fictions, or that talk about such entities is translatable without remainder into talk about sense con- tents or everyday physical objects, or that such talk should be regarded as belonging to a mere calculating device and, thus, without cognitive con tent-such contentions strike me as so incongruous with the scientific and rational attitude and practice that I feel this paper should turn out to be a demolition of straw men. But the instrumentalist views of out- standing physicists such as Bohr and Heisenberg are too well known to be cited, and in a recent book of great competence, Professor Ernest Nagel concludes that "the opposition between [the realist and the in- slrumentalist] views [of theories] is a conflict over preferred modes of sp cch" and "the question as to which of them is the 'corr ect position' ha s only terminological interest." 1 The phoenix, it seems, will not be
  • 2. laid to rest. The literature on the subject is, of course, voluminous, and a compre- lt nsive treatment of the problem is far beyond the scope of one essay. I sl1all limit myself to a small number of constructive arguments (for a r lically realistic interpretation of theories) and to a critical examination of s me of the more crucial assumptions (sometimes tacit, sometimes · pli it) that seem to have generated most of the problems in this area.2 ' fo: . Nngcl, TJ1c Structure of Science (New York: Harcourt, Brace, and World, l ') il), h . 6. 1 l•'or th e ge nes is and part of the content of some of the ideas expressed herein, I 11n ind ·bled to a number of sources; some of the more influential are H. Feig!, " 11: IN! ·11t inl llypotheses," PI1ilosophy of Science, 17 : 35 - 62 ( 1950); P . K. Feyerabend , '' 11 Alt · 111pt nt n Rcnlistic Interpretation of Experience," Proceedings of the Aristo- 1 / 1111 Soi ty, 58 :144- 170 (1958); N . R . Hanson, Patterns of Discovery (Cam- 111 ii 1: ,n111hridgc University Press, 1958); E. Nagel, Joe . cit.; Karl Popper, The I 11 c• of S ·i 11tilic Dis ovcry (London : Hutchinson, 19 59); M. Scriven, "Definitions, f1,ph11111 t i11 11 s 1 :ind Th ·ori ·s," in Miuneso ta Studies in tlie Philosophy of Science,
  • 3. 3 Grover MaxweII The Problem Although this essay is not comprehensive, it aspires to be fairly self- contained. Let me, therefore, give a pseudohistorical introduction to the problem with a piece of science fiction (or fictional science). In the days before the advent of microscopes, there lived a Pas teur- like scien tist whom, following the usual custom, I shall call Jon es. Re- fl ecting on the fact that certain diseases seemed to be transmitted from one person to another by means of bodily contact or b y contact with articles handled previously by an afHicted person, Jones began to specu- late about the mechanism of the transmission. As a "heuristic crutch," he recalled that there is an obvious observable mechanism for transmis- sion of certain afHictions (such as body lice), and he postulated that all, or most, infectious diseases were spread in a similar manner but that in most cases the corresponding "bugs" were too small to be seen and, pos- sibly, that some of them lived inside the bodies of their hosts . Jones pro-
  • 4. ceeded to develop his theory and to examine its testable consequences . Some of these seemed to be of great importance for preventing the spread of disease. After years of struggle with incredulous recalcitrance, Jones managed to get some of his preventative measures adopted. Contact with or prox- imity to diseased persons was avoided when possible, and articles which they handled were "disinfected" (a word coined by Jones) either by means of high temperatures or by treating them with certain toxic prepa- rations which Jones termed "disinfectants." The results were spectacular: within ten years the death rate had declined 40 per cent. Jones and his theory received their well-deserved recognition. However, the "crobes" (the theoretical term coined by Jones to refer to the disease-producing organisms) aroused considerable anxiety among many of the philosophers and philosophically inclined scientists of the day. The expression of this anxiety usually began something like this: "In order to account for the facts, Jones must assume that his crobes are too small to be seen. Thus the very postulates of his theory preclude V~I. IT , TT . Feig!, M . Scri~en ~ and G . ~axw~l.1 '. eds .
  • 5. (Minneapolis : University of !"111111. s tn Pre~s. I ?58); W1lfn~ Sellars, Empmc1sm and the Philosophy of Mind," 111 M11111 so tn t11d1 cs m the Philosophy of Science, Vol. I, H. Feig! and M . Scriven , ~ I s. ( ,M i::n. npo lis: niversity of M in.nesota Press, .19 56), and " The Language of 111 ·0 11 ~. 111 urr ·11t I ssues m the P/11losophy of Science, H . Feig! and G . Maxwell, Is . ( N ·w 0 1 : ll olt, Rin hart, and Win ton, 1961) . 4 THE ONTOLOGICAL STATUS OF THEORETICAL ENTITIES their being observed; they are unobservable in principle.'' (Recall that no one had envisaged such a thing as a microscope.) This common prefa- tory remark was then followed by a number of different "analyses" and "interpretations" of Jones' theory. According to one of these, the tiny organisms were merely convenient fictions-fa~ons de parler- extremely useful as heuristic devices for facilitating (in the "context of discovery") the thinking of scientists but not to be taken seriously in the sphere of cognitive knowledge (in the "context of justification"). A closely related view was that Jones' theory was merely an instrument, useful for organ- izing observation statements and (thus) for producing desired results,
  • 6. and that, therefore, it made no more sense to ask what was the nature of the entities to which it referred than it did to ask what was the nature of the entities to which a hammer or any other tool referred .3 "Yes," a philosopher might have said, "Jones' theoretical expressions are just meaningless sounds or marks on paper which, when correlated with ob- servation sentences by appropriate syntactical rules, enable us to predict successfully and otherwise organize data in a convenient fashion ." These philosophers called themselves "instrumentalists." According to another view (which, however, soon became unfashion- able), although expressions containing Jones '. theoretical terms were g nuine sentences, they were translatable without remainder into a set (perhaps infinite) of observation sentences. For example, 'There are robes of disease X on this article' was said to translate into something like this: 'If a person handles this article without taking certain pre- autions, he will (probably) contract disease X; and if this article is fir t raised to a high temperature, then if a person handles it at any time afterward, before it comes into contact with another person with disease
  • 7. , he will (probably) not contract disease X; and . . .' Now virtually all who held any of the views so far noted granted, even in istecl, that theories played a useful and legitimate role in the scientific ·ntcrprise. Their concern was the elimination of "pseudo problems" whi ch might arise, say, when one began wondering about the "reality f upraempirical entities," etc. However, there was also a school of th llght, founded by a psychologist named Pelter, which differed in an • 1 hove borrowed the h ammer analogy from E. Nagel, "Science and [Feigl's] .'n111nnti Rc:ilism," Philosophy of Science, 17 :174- 181 (1950), but it should be p11l111 cd 11 t thnt Professor Nagel makes it clear that he does not necessarily subscribe lo th vi w whi h he is explaining. 5 Grover Maxwell interesting manner from such positions as these. Its members held that while Jones' crobes might very well exist and enjoy "full -blown reality," they should not be the concern of medical research at all. 'They
  • 8. insisted that if Jones had employed the correct methodology, he would have dis- covered, even sooner and with much less effort, all of the observation laws relating to disease contraction, transmission, etc. without introduc- ing superfluous links (the crobes) into the causal chain. Now, lest any reader find himself waxing impatient, let me hasten to emphasize that this crude parody is not intended to convince anyone, or even to cast serious doubt upon sophisticated varieties of any of the reductionistic positions caricatured (some of them not too severely, I would contend) above. I am well aware that there are theoretical en- tities and theoretical entities, some of whose conceptual and theoretical statuses differ in important respects from Jones' crobes. (I shall discuss some of these later.) Allow me, then, to bring the Jonesean prelude to our examination of observability to a hasty conclusion . Now Jones had the good fortune to live to see the invention of the compound microscope. His crobes were "observed" in great detail, and it became possible to identify the specific kind of microbe (for so they began to be called) which was responsible for each different disease. Some philosophers freely admitted error and were converted to
  • 9. realist positions concerning theories . Others resorted to subjective idealism or to a thoroughgoing phenomenalism, of which there were two principal varieties. According to one, the one "legitimate" observation language had for its descriptive terms only those which referred to sense data. 1 he other maintained the stronger thesis that all "factual" statements were translatable without remainder into the sense-datum language. In either case, any two non-sense data (e.g., a theoretical entity and what would ordinarily be called an "observable physical object") had virtually the same status. Others contrived means of modifying their views much less drastically. One group maintained that Jones' crobes actually never had been unobservable in principle, for, they said, the theory did n t imply the impossibility of finding a means (e.g., the mi r op ) f b erving them . A more radical contention was that th r b s w r not b erved at all ; it wa s argued that what was seen by rn an s of th 111i ros pe was just a sk1dow or an image rather than a rp r ·n l or •t111i m . 6 THE ONTOLOGICAL STATUS OF THEORETICAL ENTITIES
  • 10. The Observational-Theoretical Dichotomy Let us turn from these fictional philosophical positions and consider some of the actual ones to which they roughly correspond. Taking the last one first, it is interesting to note the following passage from Berg- mann: "But it is only fair to point out that if this ... methodological and terminological analysis [for the thesis that there are no atoms] ... is strictly adhered to, even stars and microscopic objects are not physical things in a literal sense, but merely by courtesy of language and pictorial imagination. This might seem awkward. But when I look through a microscope, all I see is a patch of color which creeps through the field like a . hadow over a wall. And a shadow, though real, is certainly not a physical thing." 4 I should like to point out that it is also the case that if this analysis is strictly adhered to, we cannot observe physical things through opera glasses, or even through ordinary spectacles, and one begins to wonder about the status of what we see through an ordinary windowpane. And what about distortions due to temperature gradients-however small and, thus, always present-in the ambient air? It really does
  • 11. "seem awk- ward" to say that when people who wear glasses describe what they see they are talking about shadows, while those who employ unaided vision talk about physical things-or that when we look through a window- pane, we can oply infer that it is raining, while if w e raise the window, we may "observe directly" that it is. The point I am making is that there is, in principle, a continuous series beginning with looking through a vacuum and containing these as members: looking through a window- pane, looking through glasses, looking through binoculars, looking through a low-power microscope, looking through a high-power micro- ope, etc., in the order given. The important consequence is that, so far, we are left without criteria which would enable us to draw a non- nrbitrary line between "observation" and "theory." Certainly, we will ften find it convenient to draw such a to-some-extent-arbitrary line; but il position will vary widely from context to context. (For example, if w are determining the resolving characteristics of a certain microscope, w would certainly draw the line beyond ordinary spectacles, probably
  • 12. ' . Bergmann , " Outline of an Empiricist Philosophy of Physics," American Jour- 111 1 of Pliysics, 11 : 248- 258; 335-342 (1943), reprinted in Readings in the Philoso- /lli y f Science, JI. Feig! and M. Brodbeck, eds. (New York : Appleton-Century- :1orl , I 953 ) , pp . 262-287. 7 Grover Maxwell beyond simple magnifying glasses, and possibly beyond another micro- scope with a lower power of resolution.) But what ontological ice does a mere methodologically convenient observational-theoretical dichotomy cut? Does an entity attain physical thinghood and/or "real existence" in one context only to lose it in another? Or, we may ask, recalling the con- tinuity from observable to unobservable, is what is seen through pecta- cles a "little bit less real" or does it "exist to a slightl y less extent" than what is observed by unaided vision? 5 However, it might be argued that things seen through sp tacles and binoculars look like ordinary physical objects, while those seen through microscopes and telescopes look like shadows and patches of li ght. I can
  • 13. only reply that this does not seem to me to be the case, p::irticularly when looking at the moon, or even Saturn, through a telescope or when looking at a small, though "directly observable," physical objc t thro ugh a low-power microscope. Thus, again, a continuity appears. "But," it might be objected, "theory tells us that wh::it we ce by means of a microscope is a real image, which is certainly clistin t from the object on the stage." Now first of all, it should be remark d that it seems odd that one who is espousing an austere empiri ism which re- quires a sharp observational-language/theoretical-langua g di tinction (and one in which the former language has a privileged ta u ) hould need a theory in order to tell him what is observable . But, l lling this pass, what is to prevent us from saying that we still ob erve th object on the stage, even though a "real image" may be involved? therwise, we shall be strongly tempted by phenomenalistic demons, and at this point we are considering a physical-object observation language rather than a sense-datum one. (Compare the traditional puzzles: o I see one physical object or two when I punch my eyeball? Does one obj ec t split into two? Or do I see one object and one image? Etc.) Another argument for the continuous transition from the
  • 14. observable to the unobservable (theoretical) may be adduced from theoretical con- • r. am not attributing to Professor Bergmann the absurd views sugges ted by th ese q11 cs l1ons. Ile seems to take a sense-datum language as his observation language (the !ins' or wl ~nt he called " the empirical hi~rarchy") , and, in some ways, such a position is mor'~ difTi ult to refu te than one which purports to take an "observable-physical- ohjt•< I" vi ·w. I low •vcr, I beli eve that demolishing the straw men with which I am 11 ow <k1 11i11 f: umo1111 ls lo de irable preliminary "therapy." Some nonrealist interpreta- 11 1111 ol I h '<>ii« wld It mbody the presupposition that the observable- theoretical cli 111H I 1111 I 111 11 p 11 11 d ont ologi ally crucial seem to me to entail positions which < 111 1 !'~ po11tl lo 11 < It f1 uw 111 · 11 rn th r losely. THE ONTOLOGICAL STATUS OF THEORETICAL ENTITIES siderations themselves. For example, contemporary valency theory tells us that there is a virtually continuous transition from very small mole- cules (such as those of hydrogen) through "medium-sized" ones (such as those of the fatty acids, polypeptides, proteins, and viruses) to ex- tremely large ones (such as crystals of the salts, diamonds, and lumps of polymeric plastic). The molecules in the last-mentioned group are
  • 15. macro, "directly observable" physical objects but are, nevertheless, genu- ine, single molecules; on the other hand, those in the first mentioned group have the same perplexing properties as subatomic particles (de Broglie waves, Heisenberg indeterminacy, etc.). Are we to say that a large protein molecule (e.g., a virus) which can be "seen" only with an electron microscope is a little less real or exists to somewhat less an ex- tent than does a molecule of a polymer which can be seen with an optical microscope? And does a hydrogen molecule partake of only an infinitesimal portion of existence or reality? Although there certainly is a continuous transition from observability to unobservability, any talk of such a continuity from full-blown existence to nonexistence is, clearly, nonsense. Let us now consider the next to last modified position which was adopted by our fictional philosophers. According to them, it is only those entities which are in principle impossible to observe that present special problems . What kind of impossibility is meant here? Without going into a detailed discussion of the various types of impossibility, about which there is abundant literature with which the reader is no
  • 16. doubt familiar, I shall assume what usually seems to be granted by most philosophers who talk of entities which are unobservable in principle- i.e., that the theory ( s) itself (coupled with a physiological theory of perception, I would add) entails that such entities are unobservable. We should immediately note that if this analysis of the notion of un- observability (and, hence, of observability) is accepted, then its use as n means of delimiting the observation language seems to be precluded for those philosophers who regard theoretical expressions as elements of calculating device-as meaningless strings of symbols. For suppose they wi bed to determine whether or not 'electron' was a theoretical term . Fir t, they must see whether the theory entails the sentence 'Electrons r unobservable.' So far, so good, for their calculating devices are said to be able to select genuine sentences, provided they contain no theo- ti l terms. But what about the selected "sentence" itself? Suppose 9
  • 17. Grover Maxwell that 'electron' is an observation term. It follows that the expression is a genuine sentence and asserts that electrons are unobservable. But this entails that 'electron' is not an observation term. Thus if 'electron' is an observation term, then it is not an observation term. Therefore it is not an observation term. But then it follows that 'Electrons are un- observable' is not a genuine sentence and does not assert that electrons are unobservable, since it is a meaningless string of marks and does not assert anything whatever. Of course, it could be stipulated that when a theory "selects" a meaningless expression of the form 'Xs are unobserv- able,' then 'X' is to be taken as a theoretical term. But this seems rather arbitrary. But, assuming that well-formed theoretical expressions are genuine sentences, what shall we say about unobservability in principle? I shall begin by putting my head on the block and argue that the present-day status of, say, electrons is in many ways similar to that of Jones' crobes before microscopes were invented. I am well aware of the numerous theoretical arguments for the impossibility of observing electrons. But
  • 18. suppose new entities are discovered which interact with electrons in such a mild manner that if an electron is, say, in an eigenstate of posi- tion, then, in certain circumstances, the interaction does not disturb it. Suppose also that a drug is discovered which vastly alters the human perceptual apparatus-perhaps even activates latent capacities so that a new sense modality emerges. Finally, suppose that in our altered state we are able to perceive (not necessarily visually) by means of these new entities in a manner roughly analogous to that by which we now see by means of photons. To make this a little more plausible, suppose that the energy eigenstates of the electrons in some of the compounds pres- ent in the relevant perceptual organ are such that even the weak inter- action with the new entities alters them and also that the cross sections, relative to the new entities, of the electrons and other particles of the gases of the air are so small that the chance of any interaction here is negligible. Then we might be able to "observe directly" the position and possibly the approximate diameter and other properties of some elec- tron s. It would follow, of course, that quantum theory would have to b alt r d in some respects, since the new entities do not conform to
  • 19. rill ils prin ipl s. But however improbable this may be, it does not, I 111ni11Lni11 , involv any logical or conceptual absurdity. Furthermore, the 10 THE ONTOLOGICAL STATUS OF THEORETICAL ENTITIES modification necessary for the inclusion of the new entities would not necessarily change the meaning of the term 'electron.' 6 Consider a somewhat less fantastic example, and one which does not involve any change in physical theory. Suppose a human mutant is born who is able to "observe" ultraviolet radiation, or even X rays, in the same way we "observe" visible light. Now I think that it is extremely improbable that we will ever observe electrons directly (i.e., that it will ever be reasonable to assert that we have so observed them). But this is neither here nor there; it is not the purpose of this essay to predict the future development of scientific theories, and, hence, it is not its business to decide what actually is ob- servable or what will become observable (in the more or less intuitive sense of 'observable' with which we are now working). After all, we are operating, here, under the assumption that it is theory, and thus
  • 20. science itself, which tells us what is or is not, in this sense, observable (the 'in principle' seems to have become superfluous). And this is the heart of the matter; for it follows that, at least for this sense of 'observable,' there are no a priori or philosophical criteria for separating the observable from the unobservable. By trying to show that we can talk about the possi- bility of observing electrons without committing logical or conceptual blunders, I have been trying to support the thesis that any ( nonlogical) term is a possible candidate for an observation term. There is another line which may be taken in regard to delimitation f the observation language. According to it, the proper term with which l work is not 'observable' but, rather 'observed.' There immediately mes to mind the tradition beginning with Locke and Hume (No idea without a preceding impression!), running through Logical Atomism nd the Principle of Acquaintance, and ending (perhaps) in contempo- ry positivism. Since the numerous facets of this tradition have been tensively examined and criticized in the literature, I shall limit myself re to a few summary remarks.
  • 21. Again, let us consider at this point only observation languages which ntnin ordinary physical-object terms (along with observation predi- s, etc., of course). Now, according to this view, all descriptive terms tu observation language must refer to that which has been observed. • F r nrgumcnts that it is possible to alter a theory without altering the meanings t t m1 , see my "Meaning Postulates in Scientific Theories," in Current Issues in 1 I lJ1il p l1 y of Science, Feig! and Maxwell, eds . 11 Grover Maxwell How is this to be interpreted? Not too narrowly, presumably, otherwise each language user would have a different observation language. The name of my Aunt Mamie, of California, whom I have never seen, would not be in my observation language, nor would 'snow' be an observation term for many Floridians. One could, of course, set off the observation language by means of this awkward restriction, but then, obviously, not being the referent of an observation term would have no bearing on the
  • 22. ontological status of Aunt Mamie or that of snow. Perhaps it is intended that the referents of observation terms must be members of a kind some of whose members have been observed or in- stances of a property some of whose instances have been observed. But there are familiar difficulties here. For example, given any entity, we can always find a kind whose only member is the entity in question; and surely expressions such as 'men over 14 feet tall' should be counted as observational even though no instances of the "property" of being a man over 14 feet tall have been observed. It would seem that this approach must soon fall back upon some notion of simples or determinables vs. determinates. But is it thereby saved? If it is held that only those terms which refer to observed simples or observed determinates are observation terms, we need only remind ourselves of such instances as Hume's no- torious missing shade of blue. And if it is contended that in order to be an observation term an expression must at least refer to an observed de- terminable, then we can always find such a determinable which is broad enough in scope to embrace any entity whatever. But even if these diffi- culties can be circumvented, we see (as we knew all along) that this
  • 23. approach leads inevitably into phenomenalism, which is a view with which we have not been concerning ourselves . Now it is not the purpose of this essay to give a detailed critique of phenomenalism. For the most part, I simply assume that it is untenable, at least in any of its translatability varieties.7 However, if there are any unreconstructed phenomenalists among the readers, my purpose, insofar as they are concerned, will have been largely achieved if they will grant what I suppose most of them would stoutly maintain anyway, i.e., that theoretical entities are no worse off than so-called observable physical object. ' Th r ad r is no doubt familiar with the abundant literature concerned with this i ~ 11 • S ·,, f r xnmple, Sellars' "Empiricism and the Philosophy of Mind," which nl , o 011 l n 111 ~ r f r ·nee to other pertinent works. 12 THE ONTOLOGICAL STATUS OF THEORETICAL ENTITIES Nevertheless, a few considerations concerning phenomenalism and re- lated matters may cast some light upon the observational - theoretical dichotomy and, perhaps, upon the nature of the "observation language."
  • 24. As a preface, allow me some overdue remarks on the latter. Although I have contended that the line between the observable and the unobserv- able is diffuse, that it shifts from one scientific problem to another, and that it is constantly being pushed toward the "unobservable" end of the spectrum as we develop better means of observation-better instruments -it would, nevertheless, be fatuous to minimize the importance of the observation base, for it is absolutely necessary as a confirmation base for statements which do refer to entities which are unobservable at a given time. But we should take as its basis and its unit not the "observational term" but, rather, the quickly decidable sentence. (I am indebted to Feyerabend, Joe. cit., for this terminology.) A quickly decidable sentence (in the technical sense employed here) may be defined as a singular, nonanalytic sentence such that a reliable, reasonably sophisticated lan- guage user can very quickly decide 8 whether to assert it or deny it when he is reporting on an occurrent situation. 'Observation term' may now . be defined as a 'descriptive (nonlogical) term which may occur in a quickly decidable sentence,' and 'observation sentence' as a 'sentence whose only descriptive terms are observation terms.'
  • 25. Returning to phenomenalism, let me emphasize that I am not among those philosophers who hold that there are no such things as sense con- tents (even sense data), nor do I believe that they play no important role in our perception of "reality." But the fact remains that the refer- nts of most (not all) of the statements of the linguistic framework u ed in everyday life and in science are not sense contents but rather l hysical objects and other publicly observable entities. Except f~r pains: dors, "inner states," etc., we do not usually observe sense contents; and lthough there is good reason to believe that they play an indispensable l in observation, we are usually not aware of them when we visually tactilely) observe physical objects. For example, when I observe a 'storted, obliquely reflected image in a mirror, I may seem to be seeing l nby elephant standing on its head; later I discover it is an image of 11 le harles taking a nap with his mouth open and his hand in a · uliar position. Or, passing my neighbor's home at a high rate of ' W may . say "~oninferent~lly" decide, provided this is interpreted liberally n h to avoid startmg the entire controversy about observability all over again.
  • 26. 13 Grover Maxwell speed, I observe that he is washing a car. If asked to report th ·s · oh · r vations I could quickly and easily report a baby elephant and n wn sliin of a car; I probably would not, without subsequent obsc rvaliou s, h • uhl to report what colors, shapes, etc. (i.e., what sense data) w •r · involv •<1. Two questions naturally arise at this point. How is ii tl111l w · ran (sometimes) quickly decide the truth or falsity of a pert i 11 •111 oh1.t•1 vn tion sentence? and, What role do sense contents play in Iii · app1opdnl · tokening of such sentences? The heart of the matter is tlrnl 111 . ., · 111 primarily scientific-theoretical questions rather than "p 111 ·ly 1011it1 1' ," "purely conceptual," or "purely epistemological." If the r I i · ii I l1 y~i<'s, psychology, neurophysiology, etc., were sufficiently advan •cl , W(' ('()11 ld give satisfactory answers to these questions, using, in all Ii k ·lil1ood , 111 physical-thing language as our observation language and tr "" i 111: ,(" 11 ~ :1 · tions, sense contents, sense data, and "inner states" as t/1 ·c11 ·t i(':i/ ( l'S,
  • 27. theoretical!) entities.9 It is interesting and important to note that, even bcf or · W(' i:iw <'<1 111 pletely satisfactory answers to the two questions consid ·1 ·cl 1hoV<', w · can, with due effort and reflection, train ourselves lo "obs ·1 v<• di11 ·c t ly" what were once theoretical entities-the sense conlcnls (C'o lo1 M' 11 1 d 1011 s, etc.)-involved in our perception of physical things. As !i ns 1>1· ·11 po11il ·d out before, we can also come to observe other kind s of 1·111ii1<' wl11d1 were once theoretical. Those which most readil y c 111 • lo 111111d 111volv · the use of instruments as aids to observation . Ind · d, """I: 011 1 pain· fully acquired theoretical knowledge of the world, w co 1111· lo I'<' lliul we "directly observe" many kinds of so-called thcor ·li ·1 1' 111111 1: . All ·r listening to a dull speech while sitting on a hard h ncli , W<' liq:111 Io h • come poignantly aware of the presence of a consid •rahly . 11011111:111viln· tional field, and as Professor Feyerabend is fond of poi111i111: rnll , ii w were carrying a heavy suitcase in a changing gravi tali o11 11 I flC'lcl , we• c 011ld observe the changes of the Gµ.v of the metric tensor. I conclude that our drawing of the obscrvatio1111l I li c011·1111 1' li111• at any given point is an accident and a function of 0111 pl1 wloi: r 11 11111k .
  • 28. •C f. Sellars, "Empiricism and the Philosophy of Mi11 I " A 1 1 111f1,~111 S •llnrs points out, this is the crux of the "other-minds" p1ohlc111 , Sr n 111 1111 1111tl 111111 tut e (r~lativc to nn i'.~tcrsubjc~ti~~ observation l:mgu:iric, I w1111ld 11 dd) 1111 11111111 t 111 1 t•n. ~111.cs (n 11d 1·h.'Y. really exist ) and not mer ly o ·111 11 l 1111d/111 "'~~l tit l11l111v111 S111 ly 1t is 11 ~ · 1111w1ll111gncss to countena nce th or lira I ·111 it 1·~ I 11 1111111 t 11111 1·vny ·n· t ·1.1c· 1 ~ I 11111slatnhl '. 11 01'. on ly int? som ohsc1~11 t i ~> 11 li111111111H• li11t 11111 t 111 phyNi1. l· I h111 g !:11.11:11111: wh1 ·h 1s r ·spons1blc for th 10111< 111 lir l111 v 111 - 111 " 111 1111 11ro Witt· fll' n ~ I t•11 11 1 111 ~ . THE ONTOLOGICAL STATUS OF THEORETICAL ENTITIES up, our current state of knowledge, and the instruments we happen to have available and, therefore, that it has no ontological significance what- ever. What If We COULD Eliminate Theoretical Terms? Among the candidates for methods of eliminating theoretical terms, three have received the lion's share of current attention: explicit defin- ability, the Ramsey sentence,10 and implications of Craig's theorem.11 Today there is almost (not quite) universal agreement that not all theo- retical terms can be eliminated by explicitly defining them in
  • 29. terms of observation terms . It seems to have been overlooked that even if this could be accomplished it would not necessarily avoid reference to un- observable (theoretical) entities. One example should make this evident. Within the elementary kinetic theory of gases we could define 'mole- cules' as 'particles of matter (or stuff), not large enough to be seen even with a microscope, which are in rapid motion, frequently colliding with each other, and are the constituents of all gases.' All the ( nonlogical) terms in the definiens are observation terms, and still the definition it- self, as well as kinetic theory (and other theoretical considerations), im- plies that molecules of gases are unobservable (at least for the present). It seems to me that a large number-certainly not all, however; for example, 'photon,' 'electromagnetic field,' 'if-function'-of theoretical terms could be explicitly defined wholly in terms of observation terms, but this would in no way avoid a reference to unobservable entities. This important fact seems to have been quite generally overlooked. It is an important oversight because philosophers today are devoting so much nltention to the meaning of theoretical terms (a crucially important
  • 30. pr blem, to be sure), while the ontological stomach-aches (ultimately unjustifiable, of course) concerning theories seem to have arisen from I h • fact that the entities rather than the terms were nonobservational. Implicit, of course, is the mistaken assumption that terms referring to 1111ob crvable entities cannot be among those which occur in the ob- c'IVnlion language (and also, perhaps, the assumption that the referent of 11 defined term always consists of a mere "bundle" of the entities ~ Iii ·h nrc referents of the terms of the definiens). '" l•' 111nk P. Ramsey, The Foundations of Mathematics (New York: Humanities 11111 ) . , " Wlllinrn rnig, "Replacement of Auxiliary Expressions," Philosophical Review r1 Ill ~~ ( 1956). ' 15 Grover Maxwell Surprisingly nough, both the Ramsey sentence and Craig's theorem provid e us with gen uine (in principle) methods for eliminating theo- reti al term s provided we are interested only in the deductive
  • 31. "observa- ti nal" onscq uences of an axiomatized theory. That neither can provide a viable method for avoiding reference to theoretical entities has been pointed out clearly by both Hempel and Nagel.1 2 I shall discuss these two devices only briefly.13 The first step in forming the Ramsey sentence of a theory is to take the conjunction of the axioms of the theory and conjoin it with the so-called correspondence rules (sentences containing both theoretical and observational terms-the "links" between the "purely theoretical" and the observational). This conjunction can be represented as follows: ---P---Q--- . . . where the dashes represent the sentential matrixes (the axioms and C- rules) containing the theoretical terms (which are, of course, almost always predicates or class terms) 'P,' 'Q,' ' .. .';the theoretical terms are then "eliminated" by replacing them with existentially quantified vari- ables . The resulting "Ramsey sen tence" is represented, then, by (3f)(3g) ... (---f---g--- . .. ) . Or, consider an informal illustration. Let us represent
  • 32. schematically an oversimplified axiomatization of kinetic theory by All gases are composed entirely of molecules. The molecules are in rapid motion and are in frequent collision, etc., etc. And for simplicity's sake, suppose that 'molecules' is the only theoretical term. The Ramsey sentence would be something like the following: There is a kind of entity such that all gases are composed entire- ly of these entities . They are in rapid motion and are in frequent collision, etc., etc. Now it is a simple matter to demonstrate that any sentence containing only observation (and logical) terms which is a deductive consequence of the original theory is also a deductive consequence of its Ramsey sentence (see, for example, Rozeboom's article in this volume); thus, :is for as any deductive systemization is concerned, any theory may be " nrl ,. IT mp I, "The Theoretician's Dilemma," in Minnesota Studies in Phi- losoi11ty I. i nee, Vol. II, Feig!, Scriven, and Maxwell, eds. Nagel, Joe. cit. ' For nn · l nd d nsiderntion of the Ramsey sentence see Professor William
  • 33. Hoi ·hoo111' s ny 111 thi volume. 16 THE ONTOLOGICAL STATUS OF THEORETICAL ENTITIES eliminated and its Ramsey sentence used instead. However, it is also easy to prove (if indeed it is not obvious) that if a given theory (or a theory together with other considerations, theoretical or observational) entails that there exist certain kinds of unobservable entities, then the appropriate Ramsey sentence will also entail that there exist the same number of kinds of unobservable entities.14 Although, insofar as deduc- tive systemization is concerned, the Ramsey sentence can avoid the use of theoretical terms; it cannot, even in letter, much less in spirit (Hem- pel, Ioc. cit., was too charitable), eliminate reference to unobservable (theoretical) entities. The Craig result, like the Ramsey sentence, provides a " method" of reaxiomatizing a postulate set so that any arbitrarily selected class of terms may be eliminated, provided one is interested only in those theo- rems which contain none of these terms . Its "advantages" over the Ramsey sentence are that it does not quantify over predicates and class
  • 34. terms and that its final reaxiomatization eliminates reference both in spirit and in letter to unobservable entities. However, its shortcomings (for the purposes at hand) render it useless as an instrument of actual scientific practice and also preclude its having, even in principle, any implications for ontology. The resulting number of axioms will, in gen- eral, and particularly in the case of the empirical sciences, be infinite in number and practicably unmanageable. But if the practical objections to the use of Craig's method as a means for elimination of theoretical terms are all but insurmountable, there are objections of principle which are even more formidable. Both Craig's method and the Ramsey device must operate upon theories (containing, of course, theoretical terms) which are "already there." They eliminate theoretical terms only after these terms have already been used in inter- " The proof may be sketched as follo ws: Let 'T' designate the theory (conjoined, i( nc essary, with other statements in the accepted body of knowledge ) which entails Iii 1t the kinds of entities C, D, ... are not observable, i.e ., T entails that (3 x)( 3 y) ... (Cx·Dy .. . xis not observable•y is not observable . . . ) which in turn entails
  • 35. (3f)(3 g) . .. (3x)(3y) ... (fx•gy ... x is notobservable•yisnot observable . . . ) . Ramsey result holds for any arbitrary division of nonlogical terms into two 1 l.1, r , 6 we may put 'observable' into the class with the observation terms, so that lltr h1 tt <•r formalized statement may be treated as an "observational" consequence 111 ' I' ( I 111 itivity of entailment). But then it is also a consequence of the Ramsey 111 l 1 1H' f T . Q. • .D. 17 Grover Maxwell mediary steps. Neither provides a method for axio1n ut izu ti n ab initio or a recipe or guide for invention of new theo ri es. 0 11 . qn •11tly neither provides a method for the elimination of th co rcli ul I •rn1 s in the all- important "context of discovery." 1 5 It might be argu cl th ut t- hi s objec- tion is not so telling, after all, for we also lack any re ·i I f r lh c inven- tion of theories themselves, and it is logically poss ibl lh:it w should discover, without the use of theories as intermediari es, Rams ·y se n tences or Craig end products which are just as useful for xpl ai nin a nd pre- dicting observations as the theories which we happ 11 to ha ve
  • 36. (acci- dently) adduced. It might be added that it is al so logica ll y poss ible that we should discover just those observation statement ( in cl ncl iu g pre- dictions, etc.) which happen to be true without th e use of a 11 y i nstru- mental intermediaries. We must reply that the accomplished fact that it is th eo ri es, referrin g to unobservables, which have been invented for thi s pmposc and tl1 at many of them serve it so admirabl y-this fa ct, itself, cri es out for expl anation. To say that theories are designed to accompli sh thi task is no r pl y un- less at least a schema of an instrum entalist recipe for su h cl signin g is provided. As far as I know thi s has not been don . Th e th sis t·hat theo- retical entities are "really" just "bundles" of obscrva hl bj ts or of sense data would, if tru e, p~ovicle an explanati on; but it is not taken very seriously by most philosophers today- for th e very good r ason tha t it seems to be fal se. The only reasonable explanati on for th e success of theories of which I am aware is that well-confirmed th eo ri es arc con- junctions of well-confirmed, genuine statements and that th e cn ti ti c to which they refer, in all probability, exist. That it is psychologica ll y pos- sible for us to invent such theories is explained by the fa ct that
  • 37. many of th e entities to which they refer resemble in many respects (although . ',: T he Ramsey sentence is intuitively tractable enough so that ve ry simple " theo- ri es . might be mvented as full-blown Ramsey sentences without the use of inter- mec!1ary ~crms. However'. Craig's theorem provides no means of operating ab initio. ra 1g points out ( Joe. cit. ) that once the original theory is " there," reference in I ·11 ·r, 1·0 theoret ical e.ntities in the application of his method may be avoided by u; ing l!ll' ,11 11 111 ·s of t~1 coret1 ca l terms rather t~an using the terms themselves (i.e . by men- l1011111 g, lh ·or l1 cnl term s ra ther than usmg them) . But surely only a diehard instru- 11 1 c· 11 l 1 il 1 ~ I • 111 l:ik : more than very scant comfort from this. The qu es tion would still 11' 11 1111 11 : h ·r did th theory come fr om in th e first place, and why are the names ol th C' ~ ci p11il i(o 11l 11 I ·n 11s arra ng cl in this particu lar ma nn er such admirable "instru- 11 11•11I H" 101 <• p l 11 11 1 ~ 1 ion . nn I pr ·di tio1.1 of ob crvat ions? Whatever ontological im- pl 111 11011 I I ii ~ 111 odif1 c11 11 011 of t he ra1g m ·thod may have, they seem to be exactly t li 1 11 11 1 11 lh <l'I(' of i11 Nl1 u111 ·nt: il is111 pr p •r. 18 THE ONTOLOGICAL STATUS OF THEORETICAL ENTITIES they may differ radically from them in others) the entities which
  • 38. we have already observed. It should also be remembered, at this point, that theories, even as instruments, are important not only for deductive systemization but also for inductive systemization (see Hempel, Joe. cit.) . We often reason theoretically using induction, and the conclusions may be either obser- vational or theoretical. Thus we might infer from the facts that a certain substance was paramagnetic, that it catalyzed the recombination of free radicals, and that it probably contained a " one-electron" bond; and we might go on to infer, again inductively, that it would probably catalyze the conversion of orthohydrogen to parahydrogen. The Craig result ap- plies only to deductive systemization and, thus, cannot, even in its Pick- wickian fashion, eliminate theoretical terms where inductive theoretical reasoning is involved . Although Craig's theorem is of great interest for formal logic, we must conclude, to use Craig's (Joe. cit.) own words, "[as far as] the meaning [and, I would add, the referents] of such ex- pressions [auxiliary expressions (theoretical terms)] . . . [is concerned] the method . . . fails to provide any . . . clarification." We have seen that the elimination of theoretical terms, even by
  • 39. ex- -' plicit definition, would not necessarily eliminate reference to theoretical (unobservable) entities. We have also seen that, even if reference to theoretical entities could be eliminated after the theories themselves have been used in such an elimination (for example, by a device such n Craig's), the reality (existence) of the theoretical entities is not there- by militated against. But the most crucial point follows. Even if we do me up with a gimmick-a prediction machine or "black box" -into whi ch we can feed data and grind out all the completely veridical ob- N rvational predictions which we may desire, the possibility-I should 1y the likelihood-of the existence of unobserved causes for the ob- •rv cl events would still remain . For unless an explanation of why any lL li ction machine or " calculating device" in terms of the established ... ul · of explanation, confirmation, etc., were forthcoming, the task of ·i •n c would still be incomplete. 'fltis brings us to another mistaken assumption that has been responsi- k. f r much mischief in considerations concerning the cognitive status tl1 · ries-th e assumption that science is concerned solely with
  • 40. the '' tutful" orga ni za tion of observational data or, more specifically, with · ·ss fnl predi ction. Surel y the main concerns of, say, a theoretical 19 Grover Maxwell physicist involve such things as the actual properties and vari ties of subatomic particles rather than the mere predictions abo ut where and how intense a certain spectral line will be. The instrum ntalist has the picture entirely reversed; as far as pure science is con crned, most ob- servational data-most predictions-are mere instrum ents and are of value only for their roles in confirming theoretical principles. Even if we obtain the prediction machine, many of the theoric ex tant today are well confirmed enough to argue strongly for the reality of th eoretical entities. And they are much more intellectually satisfactory, for they pro- vide an explanation of the occurrence of the observational events which they predict. And-equally important-an explanation for th e fact that theories "work" as well as they do is, as already noted, also
  • 41. forth coming; it is simply that the entities to which they refer exist. "Criteria" of Reality and i nstrum en talism It was pointed out in the beginning of this article that Professor Ernest Nagel considers the dispute between realists and instrumentalists to be merely a verbal one.16 There follows here a brief and what I hope is a not too inaccurate summary of his argument. Various criteria of 'real' or 'exist' (runs the argument) are employed by scientists, philoso- phers, etc., in their considerations of the "reality problem." (Among these. criteria-some of them competing, some compatible with each other-are public perceivability, being mentioned in a generally accepted law, being mentioned in more than one law, being mentioned in a "causal" law, and being invariant "under some stipulated set of trans- formation, projections, or perspectives." 17 ) Since, then (it continues) any two disputants will, in all probability, be using 'real' or 'exist' in two different senses, such disputes are merely verbal. Now someone might anticipate the forthcoming objections to this argument by pointing out that the word 'criteria' is a troublesome one and that perhaps, for Nagel, the connection between criteria and reality or existence is a con tingent
  • 42. one rather than one based on meaning. But a mom ent's reA tion makes it obvious that for Nagel's argument to have for e, ' rit ri,' must be tak n in the latter sense; and, indeed, Nagel xpli ·itl y 1 ak for the 0 1111 1·i n between criteria and th e "sen es [ i I] f ' r nl' r 'exist.' " 18 •• p. it., pp . 141- 152 . "Nn11 ·I, op. it., pp . 145- 150. ,. p. it., p. 151. 2 THE ONTOLOGICAL STATUS OF THEORETICAL ENTITIES n fore proceeding to a criticism of these arguments, let me point out that Professor Gustav Bergmann, completely independently, treats ontologi- al questions in a similar manner. Rather than criteria, he speaks of "pat- terns," although he does say that he "could instead have spoken of riteria," and he makes explicit reference to various "uses" of 'exist.' 19 There are two main points that I wish to make regarding this kind of approach to ontological issues. First, it seems to me that it commits the Id mistake of confusing meaning with evidence. To be sure, the
  • 43. fact that a kind of entity is mentioned in well-confirmed laws or that such entities are publicly perceptible, etc.-such facts are evidence (very good evidence!) for the existence or "reality" of the entities in question. But I cannot see how a prima-facie-or any other kind of-case can be made for taking such conditions as defining characteristics of existence. The second point is even more serious . One would hope that (Pro- fess or Norman Malcolm notwithstanding) over nine hundred years of debate and analysis have made it clear that existence is not a property. Now surely the characteristics of being mentioned in well - confirmed laws, being publicly perceptible, etc ., are properties of sorts; and if these omprised part of the meaning of 'exists,' then 'existence' would be a predicate (and existence a property) . Thus it is seen that the issue between instrumentalism and realism ' an be made into a merely verbal one only by twisting the meanings of 'existence' and 'reality,' not only beyond their "ordinary" meaning but, al o, far beyond any reasonable meanings which these terms might be •iven. In fact, it seems not too much to say that such an
  • 44. interpretation f the "reality problem" commits a fallacy closely akin to that of the ntological Argument. What can be said about the meanings of 'real' and 'exists'? I submit 1hnt in "ordinary language," the most usual uses of these terms are such Iha <I>. are real =dr <I>. exist md that <I>. exist = dr there are <I> 8 ll l l that the meanings of these definiens are clear enough so that no 111 lh r xplication is seriously needed . (In most "constructed languages," ''l'h are iJl.' would, of course, be expressed by ' ( 3x) ( <I>x) .') Thus, if ••" Phy i ond Ontology," Pl1ilosopl1y of Science, 28 : 1-14 ( 196 1). 21 Grover Maxwell we have a well-confirmed set of statements (laws or theories plus initial conditions) which entail the statement 'There are cf!.' (or ' ( 3x)
  • 45. ( cf!x )'), then it is well confirmed that cf!. are real-full stop! In summary, let us recall three points concerning instrumentalism. First, as is shown above, it cannot be excused on the grounds that it differs from realism only in terminology. Second, it cannot provide an explanation as to why its "calculating devices" (theories) are so success- ful. Realism provides the very simple and cogent explanation that the entities referred to by well-confirmed theories exist. Third, it must be acutely embarrassing to instrumentalists when what was once a " purely" theoretical entity becomes, due to better instruments, etc., an observ- able one.20 The Ontological Status of Entities-Theoretical and Otherwise As I have stated elsewhere (see the second reference in footnote 22), the key to the solution of all significant problems in ontology can be found in Carnap's classic article, "Empiricism, Semantics, and Ontol- ogy.''21 Taking this essay as our point of departure, we may say that in order to speak at all about any kind of entities whatever and thus, a for- tiori, to consider their existence or nonexistence, one must first accept the "linguistic framework" which ... troduces the entities." 22
  • 46. This sim- ply means that in order to understand considerations concerning the existence of any kind of entities one must understand the meanings of the linguistic expressions (sentences and terms) referring to them-and that such expressions have no meaning unless they are given a place in a linguistic framework which "talks about the world" and which has at least a minimum of comprehensiveness . (Since I am interested, here, primarily in empirical science, I neglect universes of discourse containing only "purely mathematical" or "purely logical" entities.) Although wide latitude in choosing and constructing frameworks is permissible, any satisfactory framework will embody, at the very least, • 20 ".'-!though I cannot agree with all the conclusions of Professor Feycrabend 's essay 111 this volume, the reader 1s referred to it for an interesting critique of instrumen- talism . " R. a map, Meaning and Necessity, 2nd ed. (Chicago: Univers ity of Chicago Pr ss, 19 59 ) . " fo'or n mor cl ctailccl discussion of linguistic frameworks as well as th eir releva nce
  • 47. for nn tn lop i(•nl probl ms, sec Carnap, ibid .; and G . Maxw II , "Theories, Frameworks, 11 11 <1 )11tolor,y,' Pl1ilosop hy of Science, vol. 28 (1961 ). For an elaboration of the li11 11 11i NI i · I Ii ·scs pr •s 11ppos d by th e fatter article and, to some extent, by this essay, 22 THE ONTOLOGICAL STATUS OF THEORETICAL ENTITIES I h ' f II owing features: ( 1) the usual L ( ogical )-formation and L-trans- fo1 n1ation rules and the corresponding set of L-true sentences which I Ii y generate; ( 2) a set of confirmation rules, whose nature I shall not di · n s here but which I shall assume are quite similar to those actually 11 , d in the sciences; ( 3) a set of sentences whose truth value is quickly d idable on other than purely linguistic grounds-these correspond to "s i11 gular observation statements," but, of course, as we have seen, it is 11 ithcr necessary nor desirable that such statements be incorrigible or i11dubitable or that a sharp distinction between observation and theory h ' drawn; and ( 4) a set of law like sentences, which, among other things, provide that component of meaning which is nonostensive for every d s riptive ( nonlogical) term of the framework. (I have argued in the 1· •f rcnces given in footnote 22 that every descriptive term has
  • 48. a mean- i11 omponent which is nonostensive.23 Even a term such as 'red' has I art of its meaning provided by, for example, the lawlike sentence 'No snrfoce can be both red and green all over at the same time.' Such a vi •w is sometimes stigmatized by the epithet 'holism.' But if there is 111 y holi sm involved in the view I am advocating, it is completely con- ptual or epistemological and not ontological. Just what relations are pr ' nt, or absent, between the actual entities of the "real world" is an ·111pirical question and must be decided by considerations within a de- s ·ri ptivc linguistic framework rather than by consideration about such f1t11n works.) this point, two views may be mentioned . I will omit consideration o xpli citly defined terms, since they are, in principle, always eliminable. · · rcling to one view, it is always a proper subset of the lawlike sen- t · 11 ontaining a given term which contributes to the term's meaning. ' I 'Ii · s n tcnces in this subset are A-true 24 (analytic in a broad sense) 111d :ir · totally devoid of any factual content-their only function is to I 1 ovid part of the meaning of the term in question. The
  • 49. situation is 111111 ·n cly com plicated by the fact that when actual usage is considered, 11 •• Maxwell and H. F eig!, "Why Ordinary Language Needs Reforming," Journal 11/ l '/1ilosop hy, 58: 488-498 (1961); G. Maxwell, "Meaning Postulates in Scientific ' l'll('oii ·s," in Current Issues in the Philosophy of Science, Feigl and Maxwell, eds.; and 111 hd •f nrti le, "Th e N ecessary and the Contingent," in this volume. r. nlso the writi ngs of Wilfrid Sellars, for example in "Some Reflections on I .111111111H a mes," Pl1iloso pl1y of Science, 21 : 204-228 ( 1954 ). 1 S • · ll. amnp, " Bcobachtun gsprache und theoretisch Sprache," Dialectica, I ~ 2<18 ( 1957); as we ll as the referen ces in fn . 22 . 23 Grover Maxwell a sentence which is A-true in one context may be contingent in another and that even in a given context it is, more often than not, not clear, unless the context is a rational reformation, whether a given sentence is being used as A-true or as contingent. This confusion can be avoided
  • 50. by engaging in rational reformation, i.e., by stipulating (subject to cer- tain broad and very liberal limitations) which sentences are to be taken as A-true and which as contingent. Needless to say, this is the viewpoint which I prefer. The complication just mentioned, however, has led many philoso- phers, including Professor Putnam 25-to say nothing of W. V. Quine- to the other viewpoint. According to it, no segregation of the relevant lawlike sentences into A-true and contingent should be attempted; each law like sentence plays a dual role : ( 1) it contributes to the meanings of its descriptive terms and (2) it provides empirical information. For- tunately, we do not have to choose between these two viewpoints here, for the thesis of realism which I am advocating is (almost) equally well accommodated by either one. Now when we engage in any considerations about any kinds of en- tities and, a fortiori, considerations about the existence of theoretical entities, it is to the lawlike sentences mentioning the entities-for theo- retical entities, the theoretical postulates and the so-called correspond- ence rules-to which we turn. These sentences tell us, for example, how
  • 51. theoretical entities of a given kind resemble, on the one hand, and differ from, on the other, the entities with which we happen to be more fa- miliar. And the fact that many theoretical entities, for example those of quantum theory, differ a great deal from our ordinary everyday physical objects is no reason whatever to ascribe a questionable ontological status to them or to contend that they are merely "calculating devices." After all, the very air we breathe as well as such things as shadows and mir- ror images are entities of quite different kinds from chairs and tables, but this provides no grounds for impugning their ontological status. The fa ct that molecules, atoms, etc., cannot be said in any non- Pickwickian sense to have a color has given some philosophers ontological qualms. But, of course, the air has no color (unless we invoke the color of the sky); and a transparent object whose refractive index was the same as t li a t of air would be completely invisible, although it would have all • S h is essay in this volume. 24 THE ONTOLOGICAL STATUS OF THEORETICAL ENTITIES I he other properties of ordinary physical objects. Molecules,
  • 52. for exam- pl e, are in about the same category; they are physical things which pos- ' some but not all of the properties of everyday physical things. A : Do molecules exist? B: Certainly. We have an extremely well-confirmed theory, which when conjoined with other true sentences such as 'There are gases' entails that there are molecules. A: But are they real? B: What do you mean? A: Well, I'm not sure. As a starter : Are they physical objects? B: Certainly the large ones are. Take, for example, that dia- mond in your ring. As for those which are submicroscopic but still large enough to have large quantum numbers, it seems that in almost any reasonable reformation they would be classified as physical objects. It would seem unjustifiable to withhold from them this status simply because they can- not be said to have a color in any straightforward fa shion . In fact, I would even be inclined to call the smallest, the molecule of hydrogen, a physical object. It has mass, a reasonably determinate diameter, and, usually, something which approximates simple location, etc. A: How about electrons? B : The decision here is more difficult. We might find it neces - sary to try several reformations, taking into account many facets of contemporary physical theory, before we arrived at the most satisfactory one. It would also be helpful to have a more specific problem in view than the one which we are now considering. At any rate, we might begin by
  • 53. pointing out that electrons do have mass, even rest mass. 111ey can be simply located at the expense of refraining from ascribing to them a determinate momentum . They ca~ be said to causally interact with "bona fide" physical ob1 ec ts, even by those who have a billiard-ball notion of ca usality. The important point is that the question 'Are elec- tron s physical objects?' is a request for a rational reformation of a very thoroughgoing variety. For most purposes, a ra- tion al reformation would not need to answer it. For your purposes, wh y not be content to learn in what ways elec- trons are similar to, and in what ways they differ from , what yo u would call "ordinary physical objects"? This will enable you to avoid conceptual blunders. A: Perh aps you are right. However, I am genuinely puzzled nhoul fi eld s, and even photons. 25 Grover Maxwell B: Take the last first. We would probably never call them physical objects. For example, they have no rest mass and it would be a conceptual mistake to ask, except in a Pick- wickian sense, What is their color? However, it would be reasonable to say that they are a sort of physical continuant; and they can even interact with electrons in a billiard-ball manner. At any rate, we must agree, speaking loosely, that they are "every bit as real" as electrons. The concepts of field theories are so open textured that it is difficult to decide what kinds of reformations one should adopt here. And it is virtually impossible to find similar kinds of entities with which one is prescientifically familiar. Perhaps these theories will someday be enriched until decisions concerning the
  • 54. most appropriate rational reformations are easier to make- perhaps not. But even here, the meanings of the terms in- volved are usually sufficiently clear to avoid conceptual blunders and ontological anxieties. You might like to con- sider the "lines of force," which are often spoken of in con- nection with fields. These are often used as a paradigm of the "convenient fiction" by those who hold such a view of theories. 26 But though convenient, lines of force are not fictions. They "really exist." Let me try to make this a little more plausible. Consider the isobars of meteorology, or the isograms which connect points of equal elevation above sea level. Now at this very moment, the 1017 millibar isobar, i.e., the line along which the barometric pressure is 1017 millibars, exists right here in the United States. Its location can even be determined "operationally." And all of this is true whether anyone ever draws, or ever has drawn, a weather map. Since a well-confirmed theory (plus, perhaps, other "°Cf. B. Mayo, "The Existence of Theoretical Entities," Science News, 32: 7-18 (1954), and "More about Theoretical Entities," ibid., 39:42-55 (1956) . For a critique of these articles and for excellent constructive remarks concerning theoretical entities, see J. J. C . Smart, "The Reality of Theoretical Entities," Austrafasian Journal of Philosophy, 34 :1-12 (1956). In connection with convenient fictions, we might consider such entities as ideal gases and bodies uninfluenced by external forces. These actually are fictions. But no theory (or theory plus true sentences) entails that there are such things . To under- sta nd their function, we need only recourse to the notion of a limit, often used in
  • 55. mathematics. Roughly speaking, what we actually do when we use theories involving s11 ch "fictions" is to assume, for example, that the influence of external forces on the body in question is very, very small, or that the behavior of the gas with which we :11 011 ·crnccl is approximately given by 'PV = nRT,' or, in early kinetic theory, that t Ii ~· di:1111 ·1 ·r of ~ molecule is very, very small compa red to the distance between mole- c·11l<·s. Nol· th nt lind van clcr Waals taken the calculating- device or convenient-fiction vi •w, Ii · p1ohahly wou ld not ha ve developed his equation which embodies a correction for th · d i n ·! d11l0 lo Ili c finite (greater than zero) diameter of molecules. 26 THE ONTOLOGICAL STATUS OF THEORETICAL ENTITIES well-confirmed sentences) entails that there are lines of force, lines of force exist. To be sure, they are very different from everyday physical objects. But as long as we are clear about this, what metaphysical-what ontological-problems re- main? ne of the exciting aspects of the development of science has been I It emergence of reference to strikingly new kinds of entities. This is p:irticularly true in field theories and quantum theory. The great differ- •ncc between these and the old, familiar categories seems to have caused
  • 56. 111any philosophers and philosophically inclined scientists to despair of ·ff cting a satisfactory conceptual analysis of these powerful new con- . ptual tools. The attitude too often has been, "Let us proceed to use I ho e new devices and, if necessary for heuristic reasons, even to behave is it they consisted of genuine sta~ements about real entities. But let us 1 ·member that, in the last analysis, they are only meaningless calculating I 'vices, or, at best, they talk only of convenient fictions, etc. The only r •nl entities are the good old familiar ones which we sense directly every- da y." To turn the purpose of a saying of Bertrand Russell's almost com- pl Lely about-face: such a view has advantages-they are the same as I hose of theft over honest toil. The compulsion toward metaphysical 1s ·p is which appears to have been the motivation for the espousal of 1rn1n y of these reductionistic philosophies seems, itself, to have arisen I 10111 a preoccupation with metaphysical pseudo problems, e.g., the con- j ·t ion that there are very few ontologically legitimate kinds of entities, l •rhaps only one. 27 03.jpg04.jpg06.jpg08.jpg10.jpg12.jpg14.jpg16.jpg18.jpg20.jpg2
  • 57. 2.jpg24.jpg26.jpg 80 Scientific American, August 2011 Fractals, such as this stack of spheres created using 3-D modeling software, are one of the mathematical structures that were invent- ed for abstract reasons yet manage to capture reality. © 2011 Scientific American August 2011, ScientificAmerican.com 81Illustration by Tom Beddard Mario Livio is a theoretical astrophysicist at the Space Telescope Science Institute in Baltimore. He has studied a wide range of cosmic phenomena, ranging from dark energy and super nova explosions to extrasolar planets and accretion onto white dwarfs, neutron stars and black holes. Is math invented or discovered? A leading astrophysicist suggests that the answer to the millennia-old question is both By Mario Livio
  • 58. M ost of us take it for granted that math works—that sci- entists can devise formulas to describe subatomic events or that engineers can calcu- late paths for space craft. We accept the view, initially es- poused by Galileo, that mathematics is the language of science and expect that its grammar explains experi- mental results and even predicts novel phenomena. The power of mathematics, though, is nothing short of astonishing. Consider, for example, Scottish physicist James Clerk Maxwell’s famed equations: not only do these four expressions summarize all that was known of electromagnetism in the 1860s, they also anticipat- ed the existence of radio waves two decades before German physicist Heinrich Hertz detected them. Very few languages are as effective, able to articulate vol- umes’ worth of material so succinctly and with such precision. Albert Einstein pondered, “How is it possi­ ble that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?” As a working theoretical astrophysicist, I encoun- ter the seemingly “unreasonable effectiveness of math­ ematics,” as Nobel laureate physicist Eugene Wigner called it in 1960, in every step of my job. Whether I am struggling to understand which progenitor systems produce the stellar explosions known as type Ia super- novae or calculating the fate of Earth when our sun ul- timately becomes a red giant, the tools I use and the models I develop are mathematical. The uncanny way
  • 59. I N B R I E F The deepest mysteries are often the things we take for granted. Most people never think twice about the fact that scientists use mathematics to describe and explain the world. But why should that be the case? Math concepts developed for purely ab- stract reasons turn out to explain real phe- nomena. Their utility, as physicist Eugene Wigner once wrote, “is a wonderful gift which we neither understand nor deserve.” Part of the puzzle is the question of wheth- er mathematics is an invention (a creation of the human mind) or a discovery (some- thing that exists independently of us). The author suggests it is both. Math P H I L O S O P H Y O F S C I E N C E Works Why © 2011 Scientific American 82 Scientific American, August 2011 ED W
  • 60. A RD C H A RL ES L E G RI CE G et ty Im ag es that math captures the natural world has fascinated me through- out my career, and about 10 years ago I resolved to look into the issue more deeply. At the core of this mystery lies an argument that mathemati- cians, physicists, philosophers and cognitive scientists have had for centuries: Is math an invented set of tools, as Einstein be-
  • 61. lieved? Or does it actually exist in some abstract realm, with hu- mans merely discovering its truths? Many great mathemati- cians—including David Hilbert, Georg Cantor and the group known as Nicolas Bourbaki—have shared Einstein’s view, associ- ated with a school of thought called Formalism. But other illustri- ous thinkers—among them Godfrey Harold Hardy, Roger Pen- rose and Kurt Gödel—have held the opposite view, Platonism. This debate about the nature of mathematics rages on today and seems to elude an answer. I believe that by asking simply whether mathematics is invented or discovered, we ignore the possibility of a more intricate answer: both invention and dis- covery play a crucial role. I posit that together they account for why math works so well. Although eliminating the dichotomy between invention and discovery does not fully explain the un- reasonable effectiveness of mathematics, the problem is so pro- found that even a partial step toward solving it is progress. INVENTION AND DISCOVERY mathematics is unreasonably effective in two distinct ways, one I think of as active and the other as passive. Sometimes scientists create methods specifically for quantifying real-world phenome- na. For example, Isaac Newton formulated calculus for the pur- pose of capturing motion and change, breaking them up into in- finitesimally small frame-by-frame sequences. Of course, such ac- tive inventions are effective; the tools are, after all, made to order. What is surprising, however, is their stupendous accuracy in some cases. Take, for instance, quantum electrodynamics, the mathe- matical theory developed to describe how light and matter inter-
  • 62. act. When scientists use it to calculate the magnetic moment of the electron, the theoretical value agrees with the most recent experimental value—measured at 1.00115965218073 in the ap- propriate units in 2008—to within a few parts per trillion! Even more astonishing, perhaps, mathematicians sometimes develop entire fields of study with no application in mind, and yet decades, even centuries, later physicists discover that these very branches make sense of their observations. Examples of this kind of passive effectiveness abound. French mathematician Évariste Galois, for example, developed group theory in the early 1800s for the sole purpose of determining the solvability of polynomial equations. Very broadly, groups are algebraic structures made up of sets of objects (say, the integers) united under some operation (for instance, addition) that obey specific rules (among them the existence of an identity element such as 0, which, when added to any integer, gives back that same integer). In 20th-century phys- ics, this rather abstract field turned out to be the most fruitful way of categorizing elementary particles—the building blocks of matter. In the 1960s physicists Murray Gell-Mann and Yuval Ne’eman independently showed that a specific group, referred to as SU(3), mirrored a behavior of subatomic particles called had- rons—a connection that ultimately laid the foundations for the modern theory of how atomic nuclei are held together. The study of knots offers another beautiful example of passive effectiveness. Mathematical knots are similar to everyday knots,
  • 63. except that they have no loose ends. In the 1860s Lord Kelvin hoped to describe atoms as knot- ted tubes of ether. That misguid- ed model failed to connect with reality, but mathematicians con- tinued to analyze knots for many decades merely as an esoteric arm of pure mathematics. Amaz- ingly, knot theory now pro vides important insights into string theory and loop quantum gravi- ty—our current best attempts at articulating a theory of space- time that reconciles quantum mechanics with general relativi- ty. Similarly, English mathemati- Similarly, English mathemati-Similarly, English mathemati- cian Hardy’s discoveries in num­ ber theory advanced the field of cryptography, despite Hardy’s earlier proclamation that “no one has yet discovered any warlike purpose to be served by the theo- ry of numbers.” And in 1854 Bernhard Riemann described non­ Euclidean geo met ries— curious spaces in which parallel lines converge or diverge. More than half a century later Einstein in- voked those geometries to build his general theory of relativity. A pattern emerges: humans invent mathematical concepts by way of abstracting elements from the world around them— shapes, lines, sets, groups, and so forth—either for some specific purpose or simply for fun. They then go on to discover the con-
  • 64. nections among those concepts. Because this process of inventing and discovering is man-made—unlike the kind of discovery to which the Platonists subscribe—our mathematics is ultimately based on our perceptions and the mental pictures we can conjure. For instance, we possess an innate talent, called subitizing, for in- stantly recognizing quantity, which undoubtedly led to the con- cept of number. We are very good at perceiving the edges of indi- vidual objects and at distinguishing between straight and curved lines and between different shapes, such as circles and ellipses— abilities that probably led to the development of arithmetic and geometry. So, too, the repeated human experience of cause and ef- fect at least partially contributed to the creation of logic and, with it, the notion that certain statements imply the validity of others. SELECTION AND EVOLUTION michael atiyah, one of the greatest mathematicians of the 20th century, has presented an elegant thought experiment that re- veals just how perception colors which mathematical concepts we embrace—even ones as seemingly fundamental as numbers. Ger- man mathematician Leopold Kronecker famously declared, “God created the natural numbers, all else is the work of man.” But imagine if the intelligence in our world resided not with human- kind but rather with a singular, isolated jellyfish, floating deep in the Pacific Ocean. Everything in its experience would be
  • 65. continu- ous, from the flow of the surrounding water to its fluctuating tem- perature and pressure. In such an environment, lacking individu- al objects or indeed anything discrete, would the concept of num- ber arise? If there were nothing to count, would numbers exist? Like the jellyfish, we adopt mathematical tools that apply to The universe has regularities, known as symmetries, that let physicists describe it mathematically. And no one knows why. © 2011 Scientific American August 2011, ScientificAmerican.com 83 our world—a fact that has undoubtedly contributed to the per- ceived effectiveness of mathematics. Scientists do not choose an- alytical methods arbitrarily but rather on the basis of how well they predict the results of their experiments. When a tennis ball machine shoots out balls, you can use the natural numbers 1, 2, 3, and so on, to describe the flux of balls. When firefighters use a hose, however, they must invoke other concepts, such as volume
  • 66. or weight, to render a meaningful description of the stream. So, too, when distinct subatomic particles collide in a particle accel- erator, physicists turn to measures such as energy and momen- tum and not to the end number of particles, which would reveal only partial information about how the original particles collid- ed because additional particles can be created in the pr ocess. Over time only the best models survive. Failed models—such as French philosopher René Descartes’s attempt to describe the motion of the planets by vortices of cosmic matter—die in their infancy. In contrast, successful models evolve as new information becomes available. For instance, very accurate measurements of the precession of the planet Mercury necessitated an overhaul of Newton’s theory of gravity in the form of Einstein’s general rela- tivity. All successful mathematical concepts have a long shelf life: the formula for the surface area of a sphere remains as correct to- day as it was when Archimedes proved it around 250 b.c. As a re- sult, scientists of any era can search through a vast arsenal of for- malisms to find the most appropriate methods. Not only do scientists cherry-pick solutions, they also tend to select problems that are amenable to mathematical treatment. There exists, however, a whole host of phenomena for which no accurate mathematical predictions are possible, sometimes not even in principle. In economics, for example, many variables— the detailed psychology of the masses, to name one—do not easily lend themselves to quantitative analysis. The predictive value of any theory relies on the constancy of the underlying relations
  • 67. among variables. Our analyses also fail to fully capture systems that develop chaos, in which the tiniest change in the initial condi- tions may produce entirely different end results, prohibiting any long-term predictions. Mathematicians have developed statistics and probability to deal with such shortcomings, but mathematics itself is limited, as Austrian logician Gödel famously proved. SYMMETRY OF NATURE this careful selection of problems and solutions only partially accounts for mathematics’s success in describing the laws of na­ ture. Such laws must exist in the first place! Luckily for mathema- ticians and physicists alike, universal laws appear to govern our cosmos: an atom 12 billion light-years away behaves just like an atom on Earth; light in the distant past and light today share the same traits; and the same gravitational forces that shaped the universe’s initial structures hold sway over present­day galaxies. Mathematicians and physicists have invented the concept of sym- metry to describe this kind of immunity to change. The laws of physics seem to display symmetry with respect to space and time: They do not depend on where, from which an- gle, or when we examine them. They are also identical to all ob- servers, irrespective of whether these observers are at rest, mov- ing at constant speeds or accelerating. Consequently, the same laws explain our results, whether the experiments occur in Chi- na, Alabama or the Andromeda galaxy—and whether we con- duct our experiment today or someone else does a billion years from now. If the universe did not possess these symmetries, any attempt to decipher nature’s grand design—any mathematical model built on our observations—would be doomed because we
  • 68. would have to continuously repeat experiments at every point in space and time. Even more subtle symmetries, called gauge symmetries, prevail within the laws that describe the subatomic world. For instance, because of the fuzziness of the quantum realm, a giv- en particle can be a negatively charged electron or an electri- cally neutral neutrino, or a mixture of both—until we measure the electric charge that distinguishes between the two. As it turns out, the laws of nature take the same form when we inter- change electrons for neutrinos or any mix of the two. The same holds true for interchanges of other fundamental particles. Without such gauge symmetries, it would have been very diffi- cult to provide a theory of the fundamental workings of the cosmos. We would be similarly stuck without locality—the fact that objects in our universe are influenced directly only by their immediate surroundings rather than by distant phenomena. Thanks to locality, we can attempt to assemble a mathematical model of the universe much as we might put together a jigsaw puzzle, starting with a description of the most basic forces among elementary particles and then building on additional pieces of knowledge. Our current best mathematical attempt at unifying all inter- actions calls for yet another symmetry, known as supersymme- try. In a universe based on supersymmetry, every known parti- cle must have an as yet undiscovered partner. If such partners are discovered (for instance, once the Large Hadron Collider at CERN near Geneva reaches its full energy), it will be yet another triumph for the effectiveness of mathematics. I started with two basic, interrelated questions: Is mathemat- ics invented or discovered? And what gives mathematics its ex- planatory and predictive powers? I believe that we know the an- swer to the first question. Mathematics is an intricate fusion of
  • 69. inventions and discoveries. Concepts are generally invented, and even though all the correct relations among them existed before their discovery, humans still chose which ones to study. The sec- ond question turns out to be even more complex. There is no doubt that the selection of topics we address mathematically has played an important role in math’s perceived effectiveness. But mathematics would not work at all were there no universal fea- tures to be discovered. You may now ask: Why are there univer- sal laws of nature at all? Or equivalently: Why is our universe governed by certain symmetries and by locality? I truly do not know the answers, except to note that perhaps in a universe without these properties, complexity and life would have never emerged, and we would not be here to ask the question. M O R E T O E X P L O R E The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Eugene Wigner in Communications in Pure and Applied Mathematics, Vol. 13, No. 1, pages 1–14; February 1960. Pi in the Sky: Counting, Thinking, and Being. John D. Barrow. Back Bay Books, 1992. Creation v. Discovery. Michael Atiyah in Times Higher Education Supplement; Septem- ber 29, 1995. Is God a Mathematician? Mario Livio. Simon & Schuster, 2010. SCIENTIFIC AMERICAN ONLINE Is mathematics invented, discovered, both or neither? See examples of remarkable math- ematical structures that invite this question at ScientificAmerican.com/aug11/livio © 2011 Scientific American
  • 70. McMullin’s Inference: A Case for Realism? with Bas C. van Fraassen, “Scientific Realism and the Empiricist Challenge: An Introduction to Ernan McMullin’s Aquinas Lecture”; and Ernan McMullin, “The Inference that Makes Science” SCIENTIFIC REALISM AND THE EMPIRICIST CHALLENGE: AN INTRODUCTION TO ERNAN MCMULLIN’S AQUINAS LECTURE by Bas C. van Fraassen Abstract. In The Inference That Makes Science, Ernan McMullin recounts the clear historical progress he saw toward a vision of the sciences as conclusions reached rationally on the basis of empirical evidence. Distinctive of this vision was his view of science as driven by a specific form of inference, retroduction. To understand this properly, we need to disentangle the description of retroductive inference from the claims made on its behalf. To end I will suggest that the real rival to McMullin’s vision of science is not the methodologies he criticizes so successfully but a more radical empiricist alternative in epistemology.
  • 71. Keywords: abduction; empiricism; induction; Ernan McMullin; retroduction; scientific realism In The Inference That Makes Science, Ernan McMullin takes us on a fabulous journey through the history of philosophy of science, displaying clear progress toward a vision of the sciences as conclusions reached rationally on the basis of empirical evidence.1 This is McMullin’s vision, distinctively his, though in large outlines shared by the twentieth-century philosophers to whom he refers, in the last few pages, as scientific realists. And surely, in large outlines, though with characteristic qualifications, it is also shared by those to whose contrasting points of view he refers there as instrumentalist. For on all hands, the empirical sciences are accepted as a paradigm of rational inquiry into what our world is like. But the title itself announces what is distinctive of McMullin’s view: the sciences are driven by a specific form of inference that accounts for Bas C. van Fraassen is a professor of philosophy at San Francisco State University and may be contacted at the Department of Philosophy, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA 94132, USA; e-mail: [email protected] Unless otherwise noted, page references will be to the text of The Inference That Makes
  • 72. Science (originally McMullin 1992) which is reprinted in this issue of Zygon: Journal of Religion and Science. [Zygon, vol. 48, no. 1 (March 2013)] C© 2013 by the Joint Publication Board of Zygon ISSN 0591- 2385 www.zygonjournal.org 131 132 Zygon their success, and is indeed the hallmark of the scientific approach to any subject. As the history unfolds we see the attempts, one after the other found wanting, to identify that form of inference, until its final articulation as a process of (as McMullin decides to call it) retroductive inference. Aristotle, Grosseteste, Aquinas, Galileo, Zabarella, the late me- dieval nominalists and Francis Bacon, Isaac Newton’s methodological vacillations, . . . the story reads as well and as fluently as a mystery novel, and is as engaging. What I shall comment on here is not McMullin’s excursions into history, however, though they were certainly for me the most fascinating part. My concern will instead be with McMullin’s project, the project to characterize the sciences as, in essence, a practice identified
  • 73. by a form of inference. CONTRASTING MCMULLIN’S VISION WITH RIVAL EPISTEMOLOGIES McMullin does enough to discredit some alternative projects with a similar aim, such as attempts to define induction as a method for science. Today other projects of that sort exist as well, drawing in one way or another on the concept and theories of probability, notably varieties of Bayesianism or a more liberal probabilism. It would be of interest to ask how, or to what extent, such alternatives could do justice to the insights that support McMullin’s concept of retroduction as the crucial or central form of scientific inference. I will leave that aside as well. The more interesting question, for me, is rather whether scientific practice, the enterprise of science, is best characterized in that sort of form at all. McMullin does not have an overriding ambition in this project. He emphasizes that it was “not intended to furnish a criterion of demarcation between science and non science [ . . . .] retroductive inference makes use of ingredients that are commonplace in human reason generally” (144). In good human reasoning to be sure; McMullin mentions approvingly the detective and the journalist. But retroduction is easily discerned
  • 74. in not so good human reasoning as well, when conspiracy theorists are retroductively inferring from the facts in evidence to their weird or wonderful causal explanation. So it seems at least at first blush as if the hallmark of scientific inquiry will not be that the form of inference is different, but rather how well it is employed: What is distinctive about the way in which explanatory theories are constructed and tested in natural science is the precision, as well as the explicitness, with which retroductive inference is deployed. (146) But that is too modest. It is not just a matter of doing it better, not just a matter of greater precision and explicitness, because McMullin emphasized features of the practice that are not captured by such earlier accounts as Bas C. van Fraassen 133 were focused on deduction, induction, or even Peircean abduction. The details emerge for McMullin after a long scrutiny of errors and insights accumulating through some twenty centuries of reflection on the matter, and they are not simple or neat, let alone algorithmic.
  • 75. As a process of inference, retroduction “is not rule-governed as deduction is, nor regulated by technique as induction is” (183). McMullin elaborates on this elsewhere, indicating a strong difference from another rival that was much in the limelight in the closing decades of the twentieth century: retroduction [ . . . ] is not a strict form of rule-governed reasoning, or at least, it is not as long as it isn’t equated with the easily-criticized “inference to best explanation.” [ . . . .] The vulnerability of such an inference need hardly be emphasized. (McMullin 2007, 175) These are important differences, and it is a characteristically twentieth- century insight that rational change in view is not a matter of rule following, that rules of right reason cannot be dictates, only guidelines. But something is needed beyond this negative point. MCMULLIN’S ACCOUNT OF RETRODUCTIVE INFERENCE It is in fact not easy to disentangle the points that allow us to recognize a process of retroductive inference from the claims McMullin makes concerning this sort of inference. We must concentrate on the definitive account that McMullin provides in the last 5 pages (in the reprint that follows) of The Inference That Makes Science, but it may help
  • 76. to look first at a formulation McMullin provided in a later publication, as a short summary: Retroduction, argument from observed data to an explanatory causal structure which may itself be unobserved though not necessarily unobservable is of its essence tentative. It terminates in likelihood (in the everyday sense of that term, not the sense given it in probability theory). It allows for the gradual mounting of evidence of all sorts: increasingly troublesome anomalies eliminated, ambiguities resolved, new evidence successfully incorporated, and the rest. Above all, under certain circumstances it encourages more and more persistent questioning of the assumption that the paradigm in possession is beyond challenge or that a potential rival is, on the face of it, absurd. There is a lot of room here between strict reason and credo quia absurdum, the room afforded by an ever- increasing likelihood that may begin from a very low level indeed. (McMullin 2007, 176) To what extent is this a description, such as a neutral observer of scientific practices might give, and to what extent does it involve claims about the adequacy or rationality or truth-conduciveness of this form of inference? First: that in such an inference we are “led backwards” from effect
  • 77. to cause, for example, we can read as merely describing the form (from premises about what happens to conclusions about what causes them). But we can also read it as a claim that what happens is al ways in fact an 134 Zygon effect, that is, an event that has causes, and in addition that these causes are discovered by retroductive inference. That this composite claim is in fact part of what McMullin maintains becomes quickly evident toward the end of his Aquinas lecture. That McMullin is making a strong claim on behalf of this form appears also earlier in his critique of Newton, whom he describes as having been misled by the “quasi-demonstrative” form of his own writings, and as having had a distorting influence on eighteenth century methodological reflection, which was to have negative repercussions for decades to come, until the atoms and ether- vibrations of the early nineteenth century once and for all showed causal inference to underlying structure to be indispensable to the work of the physical scientist. (180)
  • 78. Second: one feature McMullin lists, which clearly distinguishes this retroductive inference, is the creation of new concepts. We can imagine a situation in which all attempts at explanation fail, within the conceptual framework that has been actualized so far. In that case—and surely there are famous historical cases of this sort—a smaller or larger conceptual revolution is the only way forward. As a distinguishing mark of retroductive inference, though, it has its limits; for this feature is one that may be present, and certainly is not always involved. Once again, Newton furnishes the bad example of a misdirected empiricism. The need for new concepts and new language appears to be ruled out by Newton’s Third Rule of Reasoning which postulated that the relevant properties of all bodies would be those accessible to the human senses. And this was not incidental, Newton “needed this restriction . . . in order that induction might be, as he claimed, the all-sufficient method of natural science” (185). Third: that the product of retroduction is a theory which presents a causal explanation, distinct from the sort of empirical law that registers a regularity, is crucial. We can perhaps typically see the feature of causal
  • 79. “explanatoriness” at a glance, and if so it can serve as a hallmark to recognize retroduction. But even here a claim of adequacy or efficacy, not just something offered as description, is entangled with the description: The language here is, of course, that of scientific realism. It is because the cause is, in some sense however qualified, affirmed as real cause, that retroduction functions as a distinct form of inference. (184) Here, after all, Newton appears as on the side of the angels. For this phrasing echoes Newton’s First Rule of Reasoning, the “vera causa” principle. What I will suggest though is that inductivism in the naı̈ ve form that Newton may have preached, if not practiced, is in any case not the most important rival to McMullin’s view of science. Bas C. van Fraassen 135 AN ANALOGY, TO ARRIVE AT WHAT MAY BE DISTINCTIVELY DIFFERENT As an analogy, suppose that someone wanted to construct an account not of what science is but of business, commerce. If someone starts a business, he will begin by amassing some capital, acquire a place of
  • 80. business, equipment, inventory, employees, and begin to advertise. As the business gets going he has to look ahead, plan replenishing his stock, have reserve funds for repair and for salary, including his own, when receipts are lagging. What is the inference that makes business? Certainly inference is involved. Evidence of demand for his goods or services needs to be available before he can set out at all. A record of the expenses and receipts, and the timing of each, forms a growing base of evidence that he needs to consult continually, not simply to assess how well he is doing but to assess what is needed to go on. This assessment is a process of arriving at some conclusion that, though perhaps not logically derivable from that evidence, is at least sufficiently likely to him in the light of that evidence. That process is a process of inference. So yes, inference is involved. But this we could say of almost any form of intentional activity or practice. In order to characterize business in a way that distinguishes it from other human practices, is looking for a distinctive form of the sort of inference involved the right thing to do? Is business distinguished by a special form of inference? Is engaging in that sort of inference
  • 81. precisely what it is to do business? McMullin’s concentration on inference in developing his view of science, in continuation with the tradition he explores, suggests that we should assume science to be distinguished from such other practices as business and commerce in these terms. Science, not business or commerce or the like, is distinguished by a special form of inference. But it takes patience and willingness to look for differences, partly differences of degree and partly of kind, to elucidate what is special about that special form. We can go back at this point to the early pages of McMullin’s Aquinas lecture and remember that the ingredients of retroductive inference, as present in science, are commonplace in human reason generally. That all sorts of rational ways to reach conclusions are involved in business, and that this should be a common feature of business practice and scientific practice, should come as no surprise. It may well be in addition that in business sometimes the way to victory over rivals, to commercial success, can only come through the creation of new, novel concepts. A new invention, conceptually novel, may open an opportunity for a business to take on