## 1. Introduction



One of the most vigorous philosophical debates of the century broke
out among cosmologists during the 1930s and 1940s. At the peak of the
debate, 1936-37, many of the most prominent scientists in
Britain, as well as several leading philosophers of science, had
gotten themselves publicly involved. Their arguments, attacks and
rebuttals were chronicled in many of the leading scientific journals,
including a special edition of the foremost general scientific
journal, *Nature*, devoted entirely to philosophical arguments
and counter-arguments.



Methodology was the central issue of the debate, although metaphysical
questions also arose, particularly those concerning the actual reality
of certain structures and forces imputed to the Universe by the new
cosmological theories and observations. But in the end, methodology
was the real goad spurring on most of the participants.



At bottom, there were just two opposing positions in the debate, each
of which comprised a two-point stance. On one side were those
scientists who had their roots mostly in the experimental side of
natural science. To them, there was one and only one legitimate method
for science. Theory construction, they believed, involved two
closely-linked steps. First, one began from the *empirical
observations*, that is, from measurements, manipulations,
experiments, whose results were evident to the human senses; this is
classic *empiricist* epistemology. Observational results would
then suggest possible hypotheses to examine via further empirical
testing. When enough data concerning the hypothesis had been gathered,
*logical generalization* could be carried out, thereby
producing a theory; this is classic *inductivist* logic.



Opposing these inductive-empiricist scientists were those whose roots
were mostly in the theoretical side of natural science, most
especially mathematical physics. To them, there was another, more
logically sound, method to construct theories. First,
*hypotheses* could be generated in any fashion, although most
believed that imagining hypotheses which were based upon very general,
very reasonable concepts--that the Universe's physical
processes had simple mathematical descriptions, for example--was
the best place to begin; this is classic *rationalist*
epistemology. Once the hypothesis had been generated, strict
analytical reasoning could be used to make predictions about
observations; this is classic *deductivist* logic. Scientists
who held this view came to be called
*hypothetico-deductivists*; their views about both hypothesis
generation and deductive predictions were each strongly opposed by the
inductive-empiricists.



Part of the controversy may be laid to the fact that cosmology was a
new science, and disputes about methodology in new sciences are not
rare in the history of the sciences. What is rare about this case,
however, is the vigor, sometimes even bitterness, with which the
philosophical controversy was waged. Another reason for the
controversy lies in the fact that cosmology is a data-poor science:
observations are hard-won and rare, and they frequently must be run
through elaborate theoretical manipulations and corrections in order
to make sense at all. With a paucity of data results, scientists must
rely upon philosophical argument to undergird their views about how
the scientific work should be done.



One final feature of the debate must be noted. The participants are
almost universally scientists, and not philosophers. Yet this does not
much affect the level of philosophical thinking going on; these
scientists knew their philosophy well, and they wielded
philosophy's weapons and defenses with great skill. In the end,
their debate shaped cosmology into the science we know today.



It will be useful to look briefly at the history of cosmology leading
up to the debate.


## 2. The Lead-up to the Debate



Since about 1700 theories about the nature and structure of the
Universe were derived from Newtonian theory, most especially his
theory of gravitation, which was used to account for the behavior of
heavenly bodies and their systems. Newton's theory hypothesized
a force--gravitation--acting upon material bodies, free to
move over time within the passive, inert 'container' of
three-dimensional space. Bodies, paths, and space itself exemplified
the classical geometry of Euclid. All these features changed with the
publication of Einstein's General Theory of Relativity,
1915-17.


### 2.1 Einstein's General Theory of Relativity



Einstein's intended his theory to replace Newton's theory
of gravitation completely. In Einstein's view, gravity was not a
force existing independently of the spatial 'container';
rather, gravitation arises as a curvature of the space (and time,
which is necessarily connected to space in the new theory), which
means that geometry and gravity and astronomical behavior are all
intimately connected. For example, near the sun the geometrical
structure, the curvature, of spacetime changes radically, which
expresses itself as an increasing velocity of incoming orbiting bodies
such as comets or satellites. One immediate, and to some, puzzling,
consequence of Einstein's theory is that the geometry of the
Universe is no longer taken to be Euclidean. Although there are
several different candidates for the actual geometry of space, it was
not known which is correct.



It was not recognized at first that the General Theory of Relativity
could be applied to the Universe as a single, whole, individual
object, thereby producing a new cosmological theory, one completely
different from its predecessors. Although the mathematics involved are
extremely difficult, two solutions, one by Einstein himself, the other
by the Dutch astronomer Willem de Sitter, were produced in just a
short time in 1917. Unfortunately, the universes predicted by the two
solutions were extreme: Einstein's universe would be densely
packed with matter, whereas de Sitter's would be essentially
empty.



Obviously, the universe as observed by astronomers did not conform at
all to the description provided by either solution, a fact many found
troubling. Moreover, no additional solutions were forthcoming (even
though both Friedmann and LeMaitre had developed alternatives,
they remained unknown and unnoticed). For nearly twelve years, the new
cosmology appeared to be going nowhere. Then Hubble at
California's Mt. Palomar made public his astonishing
observations of a cosmic Doppler shift, a shift toward the red in the
color of light coming from the most distant star systems.


### 2.2 Hubble's Expanding Universe



Most cosmologists--with the interesting exception of Hubble
himself--came to the immediate conclusion that the red shift
could only mean that the universe was expanding. Immediately the
relativity theorists were able to interpret the expansion as a
continuous change in the geometry of spacetime, which was thoroughly
accounted for by the General Theory of Relativity. After over a decade
of stagnation in face of the meager choice between just two models of
the cosmos, Hubble's observations spurred theorists on to the
construction of a melange of new models, each vying in competition
with the other.



In the end, it was the Belgian astronomer Georges
LeMaitre's theory of an expanding, three-stage universe
that came to be accepted. LeMaitre's model was publicly
proclaimed as appropriate and generally correct by de Sitter at the
end of a special session of the British Association for the
Advancement of Science, 31 Oct 1931. Modern scientific cosmology had
been officially born; because of its birth within the context of
Einstein's theory of relativity, the new cosmology became
quickly and broadly known as *Relativistic Cosmology*. The
model of this cosmology is most famously that of the blowing up of a
balloon painted with dots to represent galaxies. Over time, the radius
of the model's spherical space (the balloon) increases, thereby
decreasing the curvature of the space (the balloon's skin), and
increasing the distance between the dots.



Although cosmologists came from Europe and America as well as Britain,
most of the work in theoretical cosmology took place in London,
Cambridge and Oxford. Americans Hubble, Tolman and Robertson did their
work at CalTech in Pasadena, but were frequently in England; and most
of the European and British workers cycled through Pasadena at one
time or another. De Sitter, from Holland, and LeMaitre, from
Belgium, spent important periods in England, as did various of the
German workers. Thus, even though cosmology was done throughout the
Western world, its major concentrating point was England; our focus in
what follows will be the same.


## 3. Cosmology and its philosophy



Because it represented such a radical departure from previous
scientific thinking about the Universe, relativistic cosmology needed
to work out its philosophical underpinnings, most especially in regard
to its methodology. 'How is this new science to be
conducted?' was thus a compelling question. But method, of
course, is always linked to metaphysics and epistemology. A full-blown
philosophical discussion was evidently required. It came soon enough:
within a span of less than a year, a vigorous debate between two
philosophically opposed camps developed. The debate required nearly
two decades to reach its full resolution. But, with the resolution,
cosmology had philosophically certified its methodology within the
context of a consensus metaphysics and epistemology. Before going into
the details of the debate, however, several general points should be
noted. Let us turn to the details of the origin of the debate.


### 3.1 Relativistic Cosmology: the majority philosophy



To begin with, the cosmological thinking of the majority of
scientists--including Eddington, de Sitter, Robertson, Tolman,
and their colleagues--had betrayed a relatively unexamined, and
apparently uncontroversial cluster of philosophical perspectives: on
the metaphysical side they held a modest sort of *explanatory
realism*--if an accepted theory referred to entity
*x*, then *x* was acceptable as a genuinely, physically
real object; to this metaphysical stance was coupled a methodology
exhibiting a classic sort of *inductive
empiricism*--scientific knowledge consisted of
generalizations built up from individual empirical observations. But
this cluster of views did not go long unchallenged. In early July
1932, just nine months after relativistic cosmology became the
consensus during the British Association meeting, Oxford
astrophysicist E. A. Milne published a short article in
*Nature* which directly attacked the current philosophical
tenets, proposing their replacement by a new cluster of views, one as
radical as the new science it purported to undergird.


### 3.2 Milne's Philosophical Challenge



Milne's metaphysical views were based in positivism, most
especially in *operationalism*: only those objects whose
properties could be directly revealed by some observational procedure,
or operation, were to be counted among the real. Thus, for Milne,
reality did not contain the usual relativistic cosmology referents
"curved space", "expanding space" or even
"four-dimensional spacetime", simply because none of these
entities were operationalizable. Milne held that 'what you see
is what you get'; since "curved space" of various
geometries couldn't be observed, space was just as it
looked--Euclidean. In the same way, the expanding of the Universe
was a genuine expanding--each galaxy was retreating from each
other--not just a change in the geometry of the curvature, as it
was for the relativists. Moreover, in place of relativistic
cosmology's inductive empiricism, Milne opted for a
*hypothetico-deductive rationalism*. Cosmologists, Milne
believed, were bound to dream up any and all possible models of a
universe, and then deduce what, if any, observable consequences
followed from their hypotheses. Hypothesizing could be based upon just
about anything, although Milne believed that certain very general
rational principles derived from aesthetic beliefs about universal
order and regularity would be the most fruitful. His
'*cosmological principle*', namely, that every
cosmologist in the universe should look out upon the same cosmos, was
the prime example of such thinking. Later, Bondi would found
Steady-state Cosmology on an even more general version of
Milne's principle, which he called the '*perfect*
cosmological principle.'


### 3.3 Kinematic Relativity--an alternative cosmology



Milne's philosophy of cosmology came with a closely associated
cosmological model, *kinematic relativity*, so-called because
of its tight links to the kinematics of Einstein's Special
Theory of Relativity. Kinematics, in Einstein's Special Theory,
is especially concerned with observers trying to make measurements of
the behavior of objects moving in systems relative to themselves.
According to Milne's understanding, these measurements could
only be made by the observers signalling among themselves using light
or other electromagnetic radiation, using clocks to time the signals.
In the end, all measurement--even space and
velocity--reduced to timing the signals as they went from one
observer to another. This idea of measurement represented a
revolutionary simplification of previous ideas, and held philosophical
interest for that reason alone. There were practical consequences as
well. As Bondi later remarked, "Milne's idea led
straightaway to the radar speed gun!"



Milne's kinematic relativity and its underlying philosophy both
immediately brought careful scrutiny, not to mention controversy.


## 4. The Great Cosmological Debate Begins: 1933-1934



Eddington was the first to attack Milne's views. In a series of
lectures given at Harvard in late 1932 and published early in the new
year as *The Expanding Universe*, Eddington denied the efficacy
of both operationalism and hypothetico-deductivism, and not only
defended explanatory realism, but strengthened his ontological
position heroically: the theoretical entities of relativistic
cosmology were not just plausible, they were so necessary to
understanding the universe, that cosmological knowledge was
essentially impossible without them (Eddington 1933, p. 19).


### 4.1 Dingle's First Attacks



Few others would ever go so far as Eddington's ontological
heroism; yet epistemological and methodological heroism in the fight
against Milne was not rare. Chief hero in this aspect of the attack on
Milne was Herbert Dingle, a highly respected astrophysicist, and
then-secretary of the Royal Astronomical Society. Dingle's
initial foray appeared as a response to Milne's first detailed
presentation of kinematic relativity (Milne 1933). After claiming that
while kinematic relativity did not differ appreciably from
relativistic cosmology in its mathematical formalism or observable
consequences, Dingle asserted that, on the other hand, it invited
special criticism because it renounced "the fundamental
principles of scientific method", namely, "Newton's
principle of induction from phenomena" (Dingle 1933, p. 178).
Dingle was never to relent in his attacks upon Milne's
hypothetico-deductivism, at all times rejecting the methodology as
even a possible candidate for acceptance by genuine science.



Dingle's article appeared back-to-back with an appraisal of
kinematic relativity by the important American cosmologist H. P.
Robertson (Robertson 1933a). Robertson focussed upon Milne's
hypothetico-deducivism as well, noting that the cosmological principle
in kinematic relativity functions as an *a priori* rule, rather
than as an empirical generalization, its status in relativistic
cosmology. Robertson otherwise is not especially taken with
Milne's theory, limiting himself to remarks suggesting that,
where they can be compared, kinematic relativity and relativistic
cosmology apparently are similar in physical content. As we shall
shortly see, Robertson's later work strongly belied this earlier
apparent indifference to Milne's theory.


### 4.2 Two Ways to Disagree with Milne



Right from the start, cosmologists differed in their opinions about
both the physical content of Milne's theory, and its underlying
philosophy. Dingle disliked Milne's methods, but found the
theory itself of not much interest. Robertson initially agreed with
Dingle, but within a short time had significant changes of heart.
Eddington disliked both the theory and its philosophy, finding them
far too deviant from what was typical, i.e., relativistic cosmology
and its mainstream philosophy. Younger cosmologists such as McVittie
and McCrea, students, respectively, of Eddington and Whittaker, soon
joined the fray. McVittie initially found the physics of kinematic
relativity quite interesting, and quite different from the physics of
relativistic cosmology (McVittie 1933b). But Milne's philosophy
was something else; the strict empiricism McVittie had earlier
revealed (McVittie 1933a) made him equally unhappy with both
Milne's rationalism and his hypothetico-deductivism.



McCrea's remarks were among the most perceptive and favorable
(Kermack and McCrea 1933). While he thought that Milne's
operationalist criticisms of curved and expanding space were of little
import, McCrea was the first to notice the parsimony and elegance of
Milne's strictly kinematic solution to the problem of the origin
of the universe's expansion. Since a search for such a solution
had vexed relativistic cosmology for several years (McVittie 1931),
McCrea suggested that Milne's mechanism should be immdiately
shown to be part of relativistic cosmology (Kermack and McCrea 1933 p.
529).



Clearly, the so-recently won consensus about relativistic cosmology
and its philosophy had dissolved into confusion and controversy over
Milne and his methods.


### 4.3 Milne Makes Philosophical Improvements



Over the next year or so, Milne made strenuous efforts to elucidate
both kinematic relativity's physics and its philosophy,
beginning, as would be his wont, with the philosophy. In October,
Milne addressed the Philosophical Association, giving an explicit and
detailed analysis not only of his philosophical views, but also of
their history, which, he claimed, extended back to Locke and Hume
(Milne 1934a) His description of the two opposed
methods--inductive empiricism vs.
hypothetico-deductivism--is quite clear and useful:



> 
> Strictly speaking, physics has no philosophy. It has method...Now
> the methods of theoretical physics seem to be reducible to two
> species, the method of starting with concepts and the method of
> starting with things observed. ...When a subject is developed
> from concepts the concepts play the part of the terms occurring in the
> axioms of geometry.... The concepts are undefined save as being
> governed by propositions of which they are subjects.
> 



Milne's commitment to axiomatization is notable here. It was
based in his earlier admiration for the work of Whitehead and Russell
(Crowther 1970); commitment to axiomatization in cosmology, once
having been initiated by Milne, would be an enduring hallmark of the
work of many, including both Robertson and Walker.



Three weeks after this address, Milne spoke on related topics at the
monthly meeting of the Royal Astronomical Society. His main point was
that theories differed only insofar as their concepts could be cashed
out in observations deduced from them. Eddington took strong exception
to Milne's arguments, claiming in response that kinematic
relativity and relativistic cosmology differed more importantly in
their ontology than in their consequences. Eddington was especially
concerned with differences in the spacetime-geometry each theory
ascribed to the world. For Eddington and his colleagues, the
equivalence of gravitation and spacetime geometry was a genuine
reality, a feature of the physical world, just as real as suns and
moons and stars.


### 4.4 A Major Philosophical Issue: What makes a scientific theory 'good'?



Milne was having none of it. In the next month's
*Observatory*--the informal monthly publication of the
Royal Astronomical Society--he took Eddington and his
theoretical-realist colleagues to task, concluding that
"theories differ simply and solely when their predictions as to
phenomena differ"; most importantly, "this method of
comparison avoids all reference to distance-assignments,
world-geometry, schemes of projection or the like" (Milne
1934b). In other words, metaphysics was to be avoided in cosmology;
space, spacetime, geometry and the like were to be rejected as
scientific realities, replaced by reference simply and solely to
observations. The only realities, according to Milne, were what could
be reported among observers about light signals and clocks.



During 1934 Milne worked together with his new student A.G. Walker.
Walker never evinced much interest in the philosophical aspects of
kinematic relativity, choosing instead to focus tightly upon working
out the physical details of the theory itself. He had immediate
success (Walker 1934). One of his important conclusions was that other
authors, specifically McVittie and Robertson, were wrong to conclude
that the physics of Milne's theory ultimately corresponded to
relativistic cosmology: "*Milne's system is
fundamentally different from that of general relativity*"
(Walker 1934 p. 489; emphasis in original).


### 4.5 How to Choose Among Theories and Philosophies?



In an important review of the entire confused situation between
kinematic relativity and relativistic cosmology, McVittie confessed
that "experimentally it seems hopeless to discriminate between
them...at present the choice is almost entirely a matter of
personal taste" (McVittie 1934 p. 29). At almost the same time,
de Sitter took on Milne in serious fashion (de Sitter 1934).
Responding to Milne's methodological challenge, he showed that,
indeed, it is possible to formulate relativistic cosmology in
axiomatic fashion, just as Milne had formulated kinematic relativity
"from concepts." But de Sitter explicitly rejected
Milne's philosophical use of the cosmological principle,
"which asserts that statistically the world pictures of two
different observers must be the same." His objection is founded
on the matter-of-fact that "we have, however, no means of
communicating with other observers, situated on faraway stars, or
moving with excessive velocities" (de Sitter 1934 p. 598). So
much for rational principles as hypotheses!



The year in cosmology ended almost as confused as it had begun, with
one exception: Milne had gotten much clearer about his philosophical
views, and was applying them to an exhaustive presentation of his
cosmology, theory and philosophy. His book *Relativity, Gravitation
and World Structure* (Milne 1935) would be published in just a few
months.


## 5. The Triumph of Milne's Methods 1935-36.



The new year marked a sudden change. In short order, McCrea, Walker
and Robertson succumbed to Milne's methodological
recommendations: first, to carry out an operationalist paring of
non-observational concepts, then, secondly, to embed the resulting
minimalist concept set in an axiomatic hypothetical-deductive
structure. Thus was the famous Robertson-Walker spacetime metric
born.


### 5.1 McCrea, Walker and Robertson Adopt Milne's Methods



McCrea's effort operationalized the concept of
"distance", principally and originally by comparison of
certain elements of Newtonian cosmology and de Sitter's
axiomatized version of relativistic cosmology (McCrea 1935).
Walker's paper specifically eschewed use of "any
indefinable concepts", in particular, he did not assume that the
"associated metric [of relativistic cosmology] has any *a
priori* physical significance" (Walker 1935).
Robertson's article, the first of three, is the most important,
both in its content, and in the signal it sends, namely, that one of
the original mainstream relativistic cosmology proponents has adopted
a major element of Milne's new philosophy for cosmology
(Robertson 1935). Robertson's conclusion exhibits this point
clearly and explicitly:



> 
> We have examined, from the operational standpoint, the problem of
> determining the most general kinematical background suitable for an
> idealized universe in which the cosmological principle holds. Allowing
> the fundamental observers the use only of clocks and theodolites, and
> granting them the possibility of sending and receiving we have shown
> that for each given mode of motion *x(t)* there necessarily
> exists a quadratic line element which is invariant, in form as well as
> in fact, under transformation from one fundamental observer to
> another. (Robertson 1935 p. 300)
> 



Unlike de Sitter, Robertson accepts the cosmological principle,
replete with its observers on far-separated particles. Moreover, as
this statement shows, Robertson is intimately familiar with
Milne's latest operationalist reduction: space is to be reduced
to time measurements given by clock readings on signals exchanged
between observers. Robertson gets this idea from Milne's book,
which he had earlier reviewed (but which was only subsequently
published) for *Astrophysical Journal* (Robertson 1936).


### 5.2 But Eddington Scoffed...



Eddington disparages these same methods. In his scathing
*Nature* review of Milne's book, he rejects Milne's
hypothetico-deductivism, his cosmological principle, and, above all,
his operationalism: "When I visit the Cavendish Laboratory, I do
not find its occupants engaged in flashing light-signals at each
other, but I find practically everyone employing rigid scales or their
equivalent" (Eddington 1935, p. 636). Whittaker's review
was not so negative as Eddington's (Whittaker 1935). While the
senior physicist rejects Milne's operationalism and attacks upon
the geometrical commitments of relativistic proponents, he is
considerably more forgiving about Milne's
hypothetico-deductivism, and even goes so far as to remark
Milne's "brilliant record in astrophysical
discovery." Nonetheless, Milne's break with a tradition
including at least "Einstein, de Sitter, Friedmann,
LeMaitre, Weyl, Eddington, H.P. Robertson and others" is
to be regretted (Whittaker 1935 p. 179). Perhaps, along with
Eddington, Whittaker hopes that soon "Professor Milne will
return to orthodoxy" (Eddington 1935, p. 636).



But Whittaker's view on Milne must be put into the perspective
he held on the whole ongoing debate. As he saw it



> 
> ...a lively debate is in progress at the present moment between
> Sir Arthur Eddington and Dr Harold Jeffreys of Cambridge, Professor
> Milne of Oxford, Sir James Jeans, and Professor Dingle of the Imperial
> College, the subject being the respective shares of reason and
> observation in the discovery of the laws of nature. (Whittaker 1941,
> p. 160)
> 



But lively debate is far too gentlemanly a description for what now
occurred. After holding his ire somewhat in check for--as he saw
it--already far too long, Dingle finally erupted.


## 6. Dingle's Denoument



Controversy over Milne and his philosophy reached a crescendo in
mid-1937. Dingle, his stew having finally boiled over, wrote privately
to the editor of *Nature*, first castigating the rampant
cosmological 'mysticism' passing itself off for science,
and then offering to produce an article taking the sword to the
mystics themselves. His offer was immediately accepted. The result was
Dingle's notorious "Modern Aristotelianism", a
polemical diatribe chiefly against Milne, but aimed as well at
Eddington and Dirac on account of their "betrayal" of the
scientific method of Newton and his fellow members of the Royal
Society (Dingle 1937).


### 6.1 Modern Aristotles?



The article is remarkable both for its style and for its content.
Dingle's style in the article is vituperative. Thus,
emotionally-loaded terms such as "paralysis of reason",
"intoxication of the fancy", "'Universe'
mania", and the like frequently appear, these to be topped only
by references to "delusions", "traitors", and,
of course, "treachery", each associated with one or more
of the guilty parties (Dingle 1937, p. 786).



Above and beyond his extreme language, Dingle makes certain
substantive claims bearing directly upon central philosophical
questions. The issue, as he sees it, is nothing more than the question
"Whether the *foundation* of science shall be observation
or invention" (Dingle 1937, p. 786). As always, talk about
'foundations' is philosophical talk. The two opposing
positions Dingle here calls "foundational" involve views
on both method and epistemology, suitably tangled together. Dingle
delineates the opposed alternatives as follows. The way of true
science, he claims, shows that "the first step in the study of
Nature should be sense observation, no general principles being
admitted which are not derived by induction therefrom" (Dingle
1937, p. 784). Stated more explicitly, Dingle here argues that
authentic science is **empiricist** in epistemology
(scientific knowledge is founded in sensory observation), and
**inductivist** in method (general principles are reached
via inductive logic). Opposed to this view, he argues, is "the
doctrine that Nature is the visible working-out of general principles
known to the human mind apart from sense perception" (Dingle
1937, p. 787). As representative of this latter view Dingle cites
Milne, and refers in particular to Milne's claim that "it
is, in fact, possible to derive the laws of dynamics
rationally...without recourse to experience" (Milne 1937,
p. 329). Obviously, Dingle is here arguing against the view,
Milne's view, that authentic science may be
**rationalist** in epistemology (scientific knowledge is
founded in pure theoretical reasoning apart from sense perception),
and **hypothetico-deductive** in method (general
principles are justified by their deductively implying correct
observations).



Along with Milne, Dingle indicts Eddington, and, by implication,
Dirac, all three of whom, Dingle believes, are guilty of inventing
scientific hypotheses by free mental imaginings rather than by strict
immersion in observations and observational data.


### 6.2 Dingle as 'True Believer'



What is going on here? Put bluntly, Dingle is an old-fashioned
empiricist and inductivist. He believes that the only way to do true
science is to first collect data, then, and only then, to hypothesize
on the basis of that data. Observation, then hypothesis. As he sees
it, Eddington, Milne and Dirac have got it exactly backwards. They
first (as he terms it) assume an hypothesis, then, and only then, go
about collecting data. Except, according to his lights, the data
isn't ever collected: "to [the Aristotelians']
modern representatives it seems as though a fancy is no sooner in the
head than it is on paper and sent for publication" (Dingle 1937,
p. 785). Obviously Dingle is simply wrong; it never occurred to his
opponents that hypotheses would **not** be followed
immediately by attempts at deductive prediction of observational
consequences. But it was enough, in Dingle's mind, that they
didn't use induction, for them to come under blame.


### 6.3 Wrong from the Very Start



But there is something else at work here as well. Dingle doesn't
object solely to his opponents' lack of inductive logic. Of
equal importance is the fact that they find the source of their
hypotheses in fairly general principles, wide-ranging rational
proposals about the structure of the universe at large. These
principles Dingle takes to be *a priori*, in the most
pejorative sense of that term. They are phantasms,
"chimeras" he calls them, which seduce the imaginations of
his opponents, and lead them and their dumb-struck admirers away from
the genuine, authentic method of science. **This** is
what really sticks in Dingle's craw. In turn, Eddington, Milne
and Dirac are chastised, each for something slightly different, but at
bottom the same, namely, they one and all "appear as a victim of
the great 'Universe' mania" (Dingle 1937, p. 786).
In the end, Dingle believes, the danger of this new
'methodology' is real, and serious. As he notes in
conclusion:



> 
> Nor are we dealing with a mere skin disease which time itself will
> heal. Such ailments are familiar enough; every age has its delusions
> and every cause its traitors. But the danger here is radical. Our
> leaders themselves are bemused, so that treachery can pass unnoticed
> and even think itself fidelity. It is the noblest minds that are
> o'erthrown...the very council of the elect can violate its
> charter and think it is doing science service. (Dingle 1937, p. 786)
> 



Here Dingle obviously goes over the top. Yet overblown as it is, there
is no doubting his sincerity: Milne and the other cosmologists have
betrayed the true science bequeathed them by their ancestors in the
Royal Society.



How could Dingle be answered?


### 6.4 The Debate Goes Very Public



The response arrived three months later, on 12 June. On this
particular Saturday in June, *Nature* published a fifteen-page
special supplement as No. 3528. Contained within were contributions
from sixteen "representative investigators", as the editor
referred to them, each responding to "Modern
Aristotelianism" *Nature*'s Editor, R.A. Gregory,
introduces the occasion by noting that "in *Nature* of
May 8, we published an article by Dr. Herbert Dingle entitled
'Modern Aristotelianism'". Because the article, as
Gregory goes on to say, "created considerable interest",
*Nature* "decided to invite further contributions on the
subject from a number of representative investigators."



"Created considerable interest" is, to understate the
issue, an understatement. Some of the contributors were quite
obviously livid with rage and other volatile emotions. Others, such as
Milne himself, who had come in for particularly scathing criticism in
Dingle's article, were patient and careful in rebuttal. Each of
the sixteen contributors to the special article chose a side in the
controversy, either pro Dingle's inductive empiricism, and con
Milne et al.'s rationalist hypothetico-deductivism, or vice
versa. Remarks made by the participants exhibit the full diversity of
philosophy of science in their contemporary community. Dingle's
views, in particular, were not without favor.



Harold Jeffreys, F.R.S., noted geologist and astronomer, and author of
a well-regarded philosophy of science book *Scientific
Inference* (1957), led off with a nice *ad hominem*:
"Without using induction, Milne and Eddington could not order
their lives for a day, and what they are really asserting is that they
are entitled to use special axioms in physics, for which no need has
been shown." Jeffreys' criticism here of course ignores
the role of deductive observations in justifying the
"special" axioms. The problem, as Jeffreys sees it,
originates in the perpetrators' "belief that there is some
special virtue in mathematics." L.N.G. Filon, F.R.S.,
vice-chancellor of the University of London agrees on this point,
noting that "some men of science appear to think that they can
solve the whole problem of Nature by some all-inclusive mathematical
intuition." R.A. Sampson, the Astronomer Royal, focusses upon
the rationalistic aspects of the 'modern Aristotelians',
to wit, for their "framing a theory independent of experience,
such as is denounced in Dr. Dingle's article", which
produces work not unlike that "of a poet or other humanist, who
gives us at most a number of illustrative cases."


### 6.5 The Counterattack



But Milne, Eddington, and Dirac had their supporters as well. N.R.
Campbell, whose theory of science was already well-known, makes an
uncontroversial interpretation of the affair. "Science" he
begins, "(or at least physics) has long consisted of two
distinct but complementary activities", one of which is
experimental and empirical; "its procedure is induction."
The other activity attempts to provide explanations of scientific
laws, which explanations have the "pecularity" that
"they often (not always) predict new laws in addition to
explaining old ones." Campbell cannot resist ending on an *ad
hominem* of his own: "If he [Dingle] does not deem it
important to observe the distinction between what is and what is not
demonstrable experiment, surely he should welcome a movement to
amalgamate the Royal with the Aristotelian Society." Indeed.



G.J. Whitrow, then a young lecturer at Christ Church, Oxford, returns
to the mathematical theme. Dingle, he argues, "not only attacks
the particular methods adopted by contemporary mathematical
investigators in relativistic cosmology, but even refuses to admit
that this subject is worthy of scientific investigation as it is based
not only on experience but also on reason." Hypotheses, by this
light, may originate rationalistically as well as any other way,
certainly there is no problem with this.


### 6.6 The Coolest Voice



The clearest, most temperate description of the issues at hand is
given by young cosmologist William McCrea, then professor of
mathematics at Queen's, Belfast, and editor of the
R.A.S.'s *Observatory*. Not to be outdone by Jeffreys,
McCrea begins with an *ad hominem* of his own: "Dr. H.
Dingle's objection to 'modern Aristotelianism' seems
to be itself what he would call Aristotelian rather than
Galilean." In other words, Dingle raises a non-empirical
objection about Milne *et al*.'s non-empiricism! But
McCrea soon gets to the heart of the matter, the role of
hypothetico-deductivism in mathematical physics:



> 
> What Dr. Dingle has done is to reopen the question of the relation of
> mathematical physics to experimental physics, since he claims to
> detect a new and perverted point of view in the former. Now a system
> of mathematical physics, apart from the alleged perversion, is the
> working out of the mathematical consequences of certain hypotheses.
> The worth of the theory is judged...by the closeness of the
> agreement of its predictions with the results of observation, and also
> the number of phenomena which it can so predict from the one set of
> hypotheses. The scientific attitude is, not to cavil at the attempt,
> but to see if it is successful.
> 



This is an absolutely standard interpretation of how the H-D method
works. Throughout his own writings, beginning right from his inaugural
lecture in Oxford (Milne 1929), Milne had subscribed to precisely the
same interpretation of the Hypothetico-Deductive (H-D) method.
Whatever the controversy is about, the issue is not how to interpret
hypothetico-deductivism. That much is evident.



Moreover, it is quite clear that Dingle *et al*. are not
mounting opposition to something we, today, would consider
philosophically radical; rather, they are objecting to what, today,
would be considered completely unobjectionable. Given today's
acceptance of the H-D method, yet its rejection by otherwise
well-regarded scientists at that time, it seems to follow that it was,
at least in part, this debate and its followup which settled the
issue. In any case, Dingle and his supporters generally went silent,
restricting their activities for the most part to books, or relatively
positive statements of their own positions (A.D.R. 1938, Dingle 1938).
Things settled down, just in time for the War.


## 7. The Calm Between the Storms



During the next several years, it became evident that Milne's
methods, and kinematic relativity as well, had reached respectability.
One important sign of this progress was exhibited at an early 1939
joint meeting between the Royal Astronomical Society and the Physical
Society of London, The meeting had as its goal a thorough review of
the situation in cosmology. McVittie was chosen to present the
observational situation; his report was soon published (McVittie,
1939). Reviewing the theoretical situation was George Temple, one of
the most highly respected mathematicians of the time. Temple's
report saw print almost immediately (Temple 1939). Within a short
time, Temple's paper took on the role of successor to
Robertson's definitive 1933 "Relativistic Cosmology"
(Robertson 1933b).


### 7.1 Two Equal Competitors



Both McVittie and Temple presented kinematic relativity and
relativistic cosmology as equal competitors in accounting for the
cosmological observations. Unfortunately, as McVittie noted,
observations could not, at that time, discriminate between the two
theories. Temple's analysis of Milne's work praises its
simplicity and elegance, and refers in particular to its
operationalism and axiomatization, which "start from a
completely novel discussion of the correlation of measurements made by
different observers in terms of light signals only" (Temple
1939, p. 468). Throughout the rest of his discussion of the two
theories, Temple utilizes Milne's light-signal correlation
method, explicitly rejecting rigid-rod transport for distance
measurement. Milne's methods have triumphed.



Later that year McCrea published an important paper in *Philosophy
of Science* (McCrea 1939). Put most simply, the paper starts out
to defend Milne's methods, but ends up by presenting a
full-blown and interesting, although quite unhistorical, account of
the evolution and structure of physical theories.


### 7.2 The Origin and Evolution of Theories



McCrea's overall view is that theories are set up to be
hypothetico-deductive in structure. His account is based on his view
of the evolution of theories of space-time and mechanics, beginning
with Newton, through the General Theory of Relativity and ending in
kinematic relativity. His argument reduces to the claim that, insofar
as Milne and e.g., Newton, can be shown to follow the same procedure,
any attack upon Milne is also an attack upon Newton. First, he states
his goals in the paper.



The first goal is to emphasise how each theory leaves us in a position
in which the succeeding one appears as a perfectly natural next step
in the development of ideas (McCrea 1939, p. 137). McCrea embeds this
argument in an account of how analogue models (a la Campbell)
are used to set up new theories--this is essentially an account
of how discovery might proceed in linking an older theory with its
successor. The second goal is to show how, in spite of superficial
differences in character, the theories in question all necessarily
possess the same general structure constituted by the presence of
hypotheses, from which certain general mathematical relations are
deduced, which in their turn are used to predict relations between
observable quantities. As McCrea notes, "this study may claim an
interest of its own, but it is presented also for a further
reason" namely, that



> 
> it has been contended [by Dingle, most especially] that theories like
> Milne's represent a fundamentally new outlook on the part of
> some theorists, in that such theories are purely mental constructs
> divorced from experience of the physical world. We shall see that on
> the contrary Milne's theory is easily brought into line with the
> others in such a way that this criticism is neither more nor less true
> of it than of the rest. (McCrea 1939, p. 138)
> 



In McCrea's discussion of the theories he asserts that
"the consituents [of the theories themselves] which are of
physical significance are sets of mathematical relations, coupled with
sets of rules of interpretation" which yield, "after
observational test, descriptions rather than explanations of physical
phenomena." According to McCrea, one real advantage of his view
is that it "leads to simple criteria for comparing the merits of
different theories." Finally, on the metaphysics of the original
hypotheses, McCrea claims that "the initial hypotheses from
which the mathematical relations are deduced do not ultimately have
any direct physical significance."



McCrea's paper, published in the leading philosophy of science
journal of the time, is the final imprimateur on Milne's
views.


### 7.3 Milne's Ultimate Success



Three years later, Milne was awarded the James Scott prize, the most
prestigious award for 'natural philosophy' in the
Anglophone world. Milne's lecture title is telling:
"Fundamental Concepts of Natural Philosophy" (Milne 1943).
Although Milne does concede to Dingle that he no longer believes that
it is possible to deduce physics completely in the absence of
reference to phenomena, for the most part his award lecture is a long
reiteration of his previous twelve years' work in cosmology.



One year later, Milne received his ultimate accolade, election as
president of the Royal Astronomical Society. In his inaugural lecture,
Milne again reviews his work, but adds two remarks of interest. First,
he modifies his earlier view that theories are acceptable solely on
the basis of their successful predictive power; to this, he now adds
that a theory cannot be accepted as satisfactory unless it is
philosophically satisfying (Milne 1943, p. 120). Secondly, on a
personal note, he admits that he is still amazed at the outcry that
his theory and its philosophy caused. Milne here is being a bit
disingenuous. In many places in his letters he not only recognizes the
outcry, he delights in it, and seeks to provoke it even more (Milne
1932-37, 12 May 35; 28 Jul 36).



From this point onward, cosmology's philosophy is no longer
directly influenced by Milne himself. Moreover, kinematic relativity
began to stagnate as a research programme; except for Whitrow, Milne
had no new students, and failed to attract any new converts to the
theory (Whitrow, 1996). His personal philosophical work was done.



But although his personal philosophical work was done, and kinematic
relativity seemed moribund as a research program, in the late 1990s it
was rediscovered, and *Milne's model*, as it was
christened, came into renewed interest as a source of predictions for
cosmological behaviour such as rates of cosmic expansion, and
production of cosmological strings. (Moncy, 2016; Russo, 2003).



But even though Milne himself retreated into the background, his
philosophical influence didn't end, in fact it wasn't to
crest until the end of the 40s in the work of another man, Hermann
Bondi. Again, however, a storm was generated by Milne's methods,
even though they were now in the hands of another.


## 8. Steady-state Cosmology



In 1948, a young mathematician, Herman Bondi, in concert with two
close friends Thomas Gold and Fred Hoyle, proposed a radical new
cosmological theory, the *Steady State* theory. This theory
differs from the basic picture shared by both kinematic relativity and
relativistic cosmology, namely, that of a universe with a definite
origin in a small, dense knot, followed by evolution into the universe
we have today. According to Bondi's theory, the universe as far
back into the past as we might look would always look the same; there
was no evolution, there could be no "fossils", as Bondi
called putative evidence of a universe different in the past from our
present one. What we observe today is the same state of a universe
that has been and always will be steady. Bondi came to his notion of
the steady state primarily from his commitment to the philosophical
components of Milne's work, most especially the methodology of
rationalism plus hypothetico-deductivism; additionally, Bondi coupled
to these Milnean notions some ideas taken directly from the philosophy
of Karl Popper.


### 8.1 Bondi's Philosophical Origins



Bondi reveals his philosophical commitments in several ways. First, he
argues against induction and extrapolation from small-scale
experiment, that is, against the inductive empiricism of Dingle *et
al*. Secondly, he argues in favor of hypothesis and deduction,
that is, in favor of Milne *et al*. Finally, he specifically
remarks the excellence of Milne's Methods, and the
theory--kinematic relativity--created therefrom, and remarks
the significance of these elements in the creation of his version of
the new steady-state cosmology.



From the very beginning Bondi admits the validity of both positions in
the methodological debate:



> 
> In particular, there are two important approaches to the subject
> [cosmology] so different from each other that it is hardly surprising
> that they lead to different answers...The contrast between the
> 'extrapolating' and the 'deductive' attitudes
> to cosmology is very great indeed. (Bondi 1960), p. 3-5)
> 



The *extrapolating* approach, which Bondi sometimes calls the
*empirical school*, is represented by Dingle, McVittie, and
their colleagues. Opposed to the extrapolative approach is the
*deductive* approach, which "is reached from
investigations in the borderland between physics and
philosophy." Milne is obviously the major proponent of this
view. Although Bondi finds good points in both approaches, he also
finds problems in both approaches. In the end, cosmology is the worse
for excesses from **either** end of the spectrum:



> 
> Just as some adherents of the 'empirical' school tend to
> regard cosmology as a testing ground for their extrapolations and as a
> legitimate playground for the geometers, so some adherents of the
> deductive approach appear to regard cosmology as a purely logical
> subject. (Bondi 1960, p. 7)
> 



In this latter case, the deductive extremists, in their mathematical
zeal, seem to forget that cosmology, after all,
**should** have some relation to observation: "To
them all that is of interest in a theory is its logical character, not
its relevance to the interpretation of observational data."
Obviously, this danger must be avoided: according to Bondi,
deductivism can be a ***scientific*** approach in
cosmology only if its postulates (or axioms) are candidates for
disproof.


### 8.2 Enter Popper



Clearly, with this reference to the connection between science and
disproof, Bondi has added a distinctly Poppererian element to the
deductivist methodology, one which had not previously appeared in the
works of any of the earlier members of the hypothetico-deductive
school. According to Popper's philosophy of science, a theory
can legitimately be called "scientific" only if that
theory makes a prediction that, in principle, can be shown to be
false, or *falsified*, to use Popper's own term. Thus
astrology, for example, fails to be a scientific theory because it
cannot be falsified: although astrology seems to make predictions,
these statements about the future are so vague, so general and
abstract, that they cannot be tied down to definite claims about
observations to be made at a definite time and place. Hence there is
no explicit observation to be made in falsification. Astronomy, in
comparison, makes explicit, specific predictions about what will occur
in the sky on such-and-such a date, in such-and-such a place. If the
prediction fails, then we know that the element of astronomical theory
which made the prediction is deficient, maybe even false.



Cosmology is a borderline case: since observations of cosmological
significance are so rare and hard-won--Hubble's observation
of the red shift was one of the first solid ones--it is very
difficult, not to mention brave, to tie one's cosmological
theory to Popper's falsificationist principle as a guarantee of
scientific acceptability. But this is exactly what Bondi did.



Much later Bondi was to make explicit his debt to Popper:



> 
> I think the person from whom we had most help on the philosophical
> side was Popper. His analysis of science encouraged one to be
> imaginative, and encouraged one to go for something that was very
> rigid and therefore empirically disprovable. (Bondi 1990, p. 194)
> 


### 8.3 But It's Milne In the End



Yet Bondi's major philosophical debt was to Milne. According to
Bondi, Milne's theory was through and through deductive, which
was reason enough for some of his colleagues to condemn it:



> 
> The aim of this discipline [= kinematic relativity] is to deduce as
> much as possible merely from the cosmological principle and the basic
> properties of space, time and the propagation of light. The beauty of
> this, as indeed of any deductive theory, rests on the rigour of the
> arguments and the small number of the axioms required...When the
> theory was first developed it met with great hostility and was
> criticized very severely, often unjustly, and sometimes frivolously.
> (Bondi 1960), p. 123)
> 



In addition to his admiration of Milne's H-D methodology, Bondi
has high praise as well for Milne's operationalism, particularly
its use in defining distance:



> 
> Imperfect as Milne's definition of distance may be, it is very
> much better than the 'rigid ruler' one used in most other
> theories...Milne's definition of distance, by no means
> perfect as it is, is probably the best yet devised. (Bondi 1960, p.
> 126-9)
> 



In the end, Bondi sums up Milne's contributions with no
uncertain praise:



> 
> The foregoing brief description will have indicated the remarkable
> success of kinematic relativity in attempting to use the cosmological
> principle not only for the construction of the substratum but as chief
> guide in formulating ordinary physics. In this respect it differs
> greatly from all other cosmologies which either rely on a
> conventionally obtained body of physics or have not yet succeeded in
> drawing conclusions of local interest from the cosmological principle.
> (Bondi 1960, p. 136)
> 


### 8.4 Return of the Cosmological Principle



Here Bondi speaks of Milne's cosmological principle. According
to Milne's principle, every observer in the universe should get
the same world picture, that is, should make precisely the same
observations of the universe at the same moment as any other observer
(Milne 1934b). Uniformity over spatial slices is guaranteed by
Milne's invoking of the principle. Yet Milne's universe
evolves, it changes its form over time. Hence it has no temporal
uniformity. Bondi felt that this raised the possibility that physics
itself might change over time. Because of this risk, Bondi generalized
Milne's cosmological principle into what he called the
*perfect cosmological principle* [= PCP]. According to this
principle, all observers at all places and **at all
times** will look out upon the same unchanging, unevolving,
universe. Such a universe is a universe in a steady-state--hence
the name.



Clearly, PCP is a daring, indeed heroic, interpretation of a
methodological necessity. Forty years after the fact, Bondi described
the "philosophical attitude" which underlay his
"implausible" PCP:



> 
> But the essential point of the philosophy was and is that if the
> universe was evolving and changing, then there is no reason to trust
> what we call the laws of physics, established by experiments performed
> here and now, to have permanent validity. (Bondi 1990, p. 192)
> 



Hence, or so Bondi's argument goes, since there is reason
**not** to trust the laws of physics if the universe is
evolving, let us presume that the universe is **not**
evolving and changing; that is, let us presume PCP. Although the
principle (and the theory which results from it--steady state
cosmology) is, as McVittie remarked, "much more restrictive than
general relativity"; (McVittie 1990, p. 45) it is this very
restrictiveness which satisfies Bondi's Popperian wishes:



> 
> For the correct argument has always been that the steady state model
> was the one that could be disproved most easily by observation,
> Therefore, it should take precedence over other less disprovable ones
> until it has been disproved. (Bondi and Kilmister 1959, p. 55-6)
> 



In another place, Bondi makes a similar point: "Comparison with
observation becomes then possible and renders the PCP liable to
observational disproof. This possibility of a clear-cut disproof
establishes the scientific status of PCP" (Bondi 1957, p. 198).
Comments such as this make clear Bondi's committment to a
Popperian addition to the basic deductive methodology he inherited
from Milne.


### 8.5 A Popperian Conclusion



In the end, the philosophical purity of Bondi's steady state
theory served him, and cosmology, well. Of course, the usual suspect,
Dingle, and others of his ilk, such as McVittie in particular, were
outraged, and loudly, at Bondi's extension of Milne's
methods. A passage from Dingle's R.A.S. Presidential Address
suffices to show the tenor of the debate's declining days:



> 
> Even idle speculation may not be quite valueless if it is recognized
> for what it is. If the new cosmologists would observe this proviso,
> calling a spade a spade and not a perfect agricultural principle,
> one's only cause for regret would be that such great talents
> were spent for so little profit. (Dingle 1953, p. 406)
> 



But PCP and the theory which it engendered were exactly as described:
eminently falsifiable. No matter the extent of Dingle *et
al*'s disdain, Steady State theory stayed right out in
front, ready for whatever empirical observations might be slung at it.
As Bondi said "Show me some fossils from an evolving universe,
and I'll give it up." In 1965, the fossils arrived,
courtesy of the observations of the 3deg K remnant microwave
radiation.



And Bondi, true to his philosophy, gave it up.