# The Discovery of the Expanding Universe: Philosophical and Historical
Dimensions

Patrick M. Duerr1,2 and Abigail Holmes3,4

( 1Faculty of Philosophy, University of Oxford, Radcliffe Humanities,
Woodstock Road, Oxford, OX2 6GG, UK.
2 Martin Buber Society of Fellows for Advanced Research in the Humanities and
Social Sciences, Hebrew University, Mt Scopus Campus, Jerusalem, 91905, IL.
3 Department of Philosophy, University of Notre Dame, Notre Dame, IN, USA.
4 Reilly Center for Science, Technology, and Values, University of Notre Dame,
Notre Dame, IN, USA.
Contact<EMAIL_ADDRESS><EMAIL_ADDRESS>
)

###### Abstract

What constitutes a scientific discovery? What role do discoveries play in
science, its dynamics and social practices? Must every discovery be attributed
to an individual discoverer (or a small number of discoverers)? The paper
explores these questions by first critically examining extant philosophical
explications of scientific discovery—the models of scientific discovery,
propounded by Kuhn, McArthur, Hudson, and Schindler. As a simple, natural and
powerful alternative, we proffer the “change-driver model”: in a nutshell, it
takes discoveries to be cognitive scientific results that have epistemically
advanced science. The model overcomes the shortcomings of its precursors,
whilst preserving their insights. We demonstrate its intensional and
extensional superiority, especially with respect to the link between
scientific discoveries and the dynamics of science, as well as the award
system of science. Both as an illustration, and as an application to a recent
scientific and political controversy, we apply the considered models of
discovery to one of the most momentous discoveries of science: the expansion
of the universe. We oppose the 2018 proposal of the International Astronomers’
Union as too simplistic vis-à-vis the historical complexity of the episode.
The change-driver model yields a more nuanced and circumspect verdict: (i) The
redshift-distance relation shouldn’t be named the “Hubble-Lemaître Law”, but
“Slipher-Lundmark-Hubble-Humason Law”; (ii) Its interpretation in terms of an
expanding universe, however, Lemaître ought to be given credit for; but (iii)
The establishment of the expansion of the universe, as an evidentially
sufficiently warranted result, is a communal achievement, emerging in the
1950s or 1960s.

Keywords: Discovery, Kuhn, theory dynamics, progress, expansion of the
universe

###### Contents

  1. 1 Introduction
  2. 2 Extant models of discovery
    1. 2.1 Kuhn: discoveries and the dynamics of science
    2. 2.2 Hudson: Materially demonstrated base descriptions
    3. 2.3 McArthur: Discoveries for the structural realist
    4. 2.4 Schindler: Discovery as essence identification
    5. 2.5 General shortcomings
  3. 3 The change-driver model: scientific discoveries as drivers of scientific advances
    1. 3.1 The change-driver model of scientific discovery
    2. 3.2 Three types of discovery: the discovery of X
    3. 3.3 Merits
    4. 3.4 Problem cases and responses
  4. 4 Illustration: the discovery of the expanding universe
    1. 4.1 Historical overview
    2. 4.2 The view from extant accounts
    3. 4.3 Applying the change-driver account
      1. 4.3.1 Empirical-material discoveries of the expanding universe
      2. 4.3.2 Theoretical discoveries concerning expanding universes
      3. 4.3.3 Synthetic discoveries of the expanding universe
  5. 5 Summary and conclusion

##  1 Introduction

Discoveries indubitably lie at the heart of science. Staple examples comprise
a diverse array: the phases of the Venus, gravitational waves, Archaeopteryx,
Pauli’s exclusion principle, the Lascaux Cave Paintings, the double helix
structure of the DNA, $E=mc^{2}$, complex numbers, isomerism, X-rays, pulsars,
the theory of continental drift, HIV as the cause of AIDS, Lorentz attractors
in chaos theory, the cosmic microwave background, Wiles’ proof of Fermat’s
Last Theorem, or the Immortal Jellyfish’s immortality.

Intertwined with the notion of a scientific discovery are major descriptive
and historiographical, as well as normative and epistemological-methodological
questions. A bit more in detail, it figures centrally in key facets of
science: its internal dynamics, with discoveries viewed as the shining
achievements of science (think of Human Genome Project, or the images of Black
Holes) and hallmarks of progress (think of penicillin, or mind-boggling
accuracy of discoveries in particle physics or high-precision cosmology), and
several of its social practices, with honours (such as the Nobel Prize) heaped
upon illustrious discoverers, and pedagogy, with scarcely any textbook or
popular science story not revelling in the adventures and vicissitudes of
science’s heroes, discoverers.

But what exactly does “discovery” mean? What does it include, and what does
the notion exclude? Should we regard the term as a passe-partout concept,
applicable to anything that might preoccupy a person’s intellectual/mental
life, e.g. artistic inspiration, stumbling on a piquant photo of the Queen’s
manicurist, a solution to a crossword puzzle, an eccentric philosophical or
theological brainchild, any scientific or technological break-through or what
have you? Or ought we, at least in the context of science, to reserve the term
for a more specific usage? If so, how to construe it? And how is it related to
the various features of science?111Nickles (2000, p.85) provides—without
answering them—a list of salient questions: “(w)hat constitutes a scientific
discovery? How do we tell when a discovery has been made by whom and whom to
credit? Is making a discovery (always) the same as solving a problem? […] May
discovery require a long, intricate social process? Could it be an
experimental demonstration? How do we tell exactly what has been discovered,
given that old discoveries are often recharacterized in very different ways by
succeeding generations? What kinds of items can be discovered, and how? Is the
discovery of a theory accomplished in much the same way as the discovery of a
new comet, or is discovery an inhomogeneous domain of items or activities
calling for quite diverse accounts? Must a discovery be both new and true? How
is discovery related to (other?) forms of innovation, such as invention and
social construction?”

Given the ubiquity222Of late, the need for conceptual clarification has become
especially acute. The notion of scientific discovery—or rather: the idea of an
individual discoverer within the commonsense way of thinking about
discoveries—has come under pressure in at least two regards.
First, we live in an era of Big Data science; research is often conducted
within large-scale collaborations. Over one-third of the paper announcing the
detection of the Higgs boson, for instance, is taken up by the author list
(ATLAS, 2012). Papers that result from these collaborations are often
referenced by the name of the collaboration, not the first author or PI. Can
large collaborations as a whole be discoverers? Can present accounts of
discovery make sense of the large scale and collaborative nature of much of
modern science? Credit, such as in the form of awards, is often not given to
these collaborations as a whole, but rather to a select few individuals. The
Nobel Prize committee, in particular, limits its prizes to three people.
Secondly, the use of AI in science, leading to discoveries, raises the
question of agency: whom to ascribe agency in the discovery to? Is the AI just
a tool (with whom as its user?) or may it qualify as a discoverer sui generis?
These intriguing questions lie outside of the present paper’s ambit; we’ll not
be concerned with the question of attribution of a discovery—i.e. the
identification of a discoverer (see however Clark & Khosrowi, 2022). It’s
clear, however, that these challenges to our received way of thinking about
discoveries are grist for our mills: the notion of scientific discovery calls
for re-examination! of talk about discoveries in science, one is dumbfounded
by the paucity of philosophical attention devoted to it (cf. Michel, 2022,
especially sect.1&2): attempts at conceptually clarifying the notion are
bafflingly rare. One might perhaps hope to find a more fleshed-out
reconstruction of it and the role of discoveries in science in the loci
classici—Popper’s (1983; 2002a; 2002b) _Logic of Scientific Discovery_ ,
Hanson’s (1958) _Patterns of Discovery_ , and Kuhn’s (1996) _The Structure of
Scientific Revolutions_. Alas, one would look there somewhat in vain.333The
otherwise excellent Stanford Encyclopedia entry (Schickore, 2022) is a case in
point. As is Nickles (2000), despite raising the most pertinent questions (see
fn.1 above)! An exception is Blackwell’s (1969) largely neglected monograph,
on which we’ll draw for our account in §3. Relying on strong assumptions and
being unduly restricted in their domain of applicability, the few recent
examples (inspected in §2) turn out to be unpersuasive.

The present paper seeks to develop a more satisfactory, philosophical model of
the notion in its multifarious dimensions, hinted at above: our goal is to
provide an explication of discovery—in the sense of Carnap (1950, pp.5): a
simple, intensionally and extensionally adequate, and fertile precisification.

The discovery of the expanding universe marks the birth of modern cosmology.
The techniques developed to measure the expansion remain essential to
cosmology. They drove the later, and only slightly less revolutionary
discovery of our own times: that of “dark energy”—phenomena associated with
the accelerated expansion of the universe (see e.g. Durrer, 2011). In spite of
its profound importance—or quite possibly because of it—the attribution of
credit for the revelation that the universe is undergoing expansion continues
to be a topic of ongoing debate. Historical accounts of the discovery (e.g.
Kragh & Smith, 2003 or Nussbaumer & Bieri, 2009) primarily impugn the received
wisdom: both dispute the previously recognised discoverers, Edwin Hubble and
Alexander Friedmann, and forefront the contributions of Georges Lemaître.
Likewise, in 2018 the International Astronomical Union voted to rename the
former “Hubble Law” (which characterises the present expansion rate of the
Universe) to the “Hubble-Lemaître Law”. This was done in order to honour
Lemaître’s role in the discovery. Yet, without a more rigorous philosophical
conception of discovery, it’s difficult to argue where the credit is due—or
why getting the record straight even matters. The significance of this
discovery, and the continuing debate over how to distribute credit, make the
expanding universe a fruitful case for philosophical analysis.

We will proceed as follows. §2 will critically examine the extant models of
discoveries, found in the literature, beginning with Kuhn’s account and
continuing with philosophical elaborations to it. Having distilled from those
analyses lessons about what a philosophical explication of the notion should
achieve—and what to shun—we’ll present and discuss, in §3, a natural and
simple alternative, the “change-driver model”. §4 will apply it to the
historical case of the discovery of the expanding universe—and juxtapose our
model’s verdict with those of the other accounts. The main findings of our
paper are summarised in §5.

##  2 Extant models of discovery

Here, we’ll take stock of the previous literature that provides an account of
scientific discovery, critically examining in turn Kuhn’s (§2.1), Hudson’s
(§2.2), McArthur’s (§2.3), and Schindler’s (§2.4). §2.5 will cull general
shortcomings of all existing accounts. This will cast into sharper relief the
desiderata of a more satisfactory model, as sketched in §3.

###  2.1 Kuhn: discoveries and the dynamics of science

Kuhn’s oeuvre (1962; 1977; 1996) is one of the earliest systematic
explorations of discovery. Subsequent analyses, including those that we’ll
inspect in §2.2-§2.4, build upon his ideas. It’s therefore apposite to
commence our review of accounts of discovery with Kuhn.

Kuhn distinguishes between two types of scientific discoveries: “what-that”
and “that-what” discoveries (in Schindler’s (2015) evocative terminology). In
“what-that”-discoveries, a theoretical framework (which, notoriously, Kuhn
refers to as a paradigm) predicts—or induces the expectation of—a new fact or
phenomenon: what is supposed to exist precedes the empirical confirmation that
it exists. Classic cases of predictions fall into this class: “the neutrino,
radio waves, and the elements which filled empty spaces in the periodic table”
(Kuhn, 1962, p.761). By contrast, in “that-what”-discoveries, such as that of
Uranus (observed by a number of astronomers, on multiple occasions, but
eventually classified/identified as a planet by Lexell, see Kuhn, 1996,
pp.115) or that of X-rays, the temporal order is reversed: a fact or
phenomenon is observed in advance of its satisfactory conceptualisation within
a theory or framework; thus the discovery isn’t expected.

Each type impacts science in different ways. “What-that”-discoveries occur
with a theoretical-conceptual framework in place (in Kuhn’s historiographical
model: within “normal science”444“(N)ormal science, an enterprise that, as we
have already seen, aims to refine, extend, and articulate a paradigm that is
already in existence” (Kuhn, 1996, p.122). In the parlance of Kuhn’s
postscript (op.cit., pp.174), successful “what-that”-discoveries figure
centrally in the elaboration of the paradigm’s disciplinary matrix.). They
yield “mere additions or increments to the growing stockpile of scientific
knowledge” (Kuhn, 1962, p.763). By corroborating anticipations—expectations
buttressed by other successes of the framework—they solidify and deepen
knowledge. Usually, the assimilation of “what-that”-discoveries by the adopted
theoretical framework requires the latter’s further refinement, e.g. the
development of new computational techniques, more detailed or de-idealised
models, etc. Successful “what-that”-discoveries thus afford a “measure of
progress” (ibid.), achieved within the theoretical framework.

Much more viscerally “that-what”-discoveries “act back upon what has
previously been known […]” (ibid.). They therefore have the potential for
greater disruption or “subversion” (op.cit, p.5; 1962, p.362): “(a) discovery
like that of oxygen or X-rays does not simply add one more item to the
population of the scientist’s world” (Kuhn, 1996, p.7). A “sense that
something was amiss” (op.cit., p.56) dawns on the scientist—a mismatch between
the received theoretical framework and the phenomenon. “That awareness of
anomaly opens a period in which conceptual categories are adjusted until the
initially anomalous has become the anticipated” (op.cit., p.64). The anomaly’s
“assimilation” or its “digestion” (Lakatos) by the framework—the phenomenon’s
conceptualisation—requires profound conceptual and theoretical re-adjustments
in the existing theories. Such discoveries can thereby trigger scientific
revolutions, a “qualitative transformation and quantitative enrichment of
fundamental novelties” (cf. ibid.).

Kuhn’s treatment of discoveries has a surprising, and indeed untoward,
consequence: as far as “that-what”-discoveries (Schindler, 2015, pp.125) are
concerned555“(O)nly when all the relevant conceptual categories are prepared
in advance, in which case the phenomenon would not be of a new sort, can
discovering that and discovering what occur effortlessly, together, and in an
instant” (Kuhn, 1996, pp.55). In other words, “what-that”-discoveries often
lack a significant time dimension, and do admit of unique identifications of a
discoverer. , “[…] any attempt to date the discovery or to attribute it to an
individual must inevitably be arbitrary. Furthermore, it must be arbitrary
just because discovering a new sort of phenomenon is necessarily a complex
process which involves recognizing both that something is and what it is”
(1962, p.762; verbatim: 1996, p.55). The recognition of what a phenomenon is
isn’t only a temporally extended process. According to Kuhn, it also involves
a significant refashioning of the conceptual-theoretical background. Such a
process tends to be convoluted, with contributions from sundry agents (cf.
Arabatzis, 1996). In this regard, Kuhn makes three claims:

  1. 1.

the absorption of discoveries is marked by a murky and prolonged conceptual-
theoretical re-adjustment process;

  2. 2.

the “distinction between discovery and invention, or between fact and theory”
(1996, p.52) is “exceedingly artificial”—in other words: empirical discovery
is theory-laden, with an inseparable mixing of theoretical and empirical
elements;

  3. 2*.

the (semantic) incommensurability of paradigms leads to the the impossibility
of comparing theoretical (or, in conjunction with (2): scientific) claims
couched in different frameworks, due to their radical shifts in meaning.

(1) usually complicates the unambiguous spatiotemporal localisation of a
discovery act (and a discoverer). It’s a practical hindrance for the working
historian—not an in-principle impediment. Likewise (2) is merely a practical
challenge: an enlightening comparison of theoretical descriptions that utilise
different conceptual frameworks is typically a non-trivial task. It often
requires judicious analysis;666For a successful example of such a
comparison—in fact a rebuttal of one of Kuhn’s explicit examples for (2*)—see
Beisbart & Jung’s (2004) analysis of pre-relativistic and relativistic notions
of mass. occasionally even new conceptual-semantic or mathematical-formal
tools need to be developed.777For an example—again a rebuttal of one of Kuhn’s
examples for (2*)—see Fletcher (2019). On both points, (1) and (2), we largely
concur. With the more fine-grained taxonomy of discoveries, presented in §3.2,
we’ll show that these tenets of Kuhn’s—which, given their fairly
uncontroversial nature, we’ll treat as philosophical insights—can be retained,
without inescapably curtailing the ability to ascertain when and by whom a
“that-what”-discovery was made.

For Kuhn, the clincher for this latter claim pivots on (2*). Recall that (for
reasons we’ll clarify shortly) conceptualisations for Kuhn are prerequisites
for a discovery. As per (2), they are inseparably entrenched in a theoretical
framework. Rivalling frameworks, however, differ so radically that those
conceptualisations lack a common measure; semantically, they are mutually
opaque. With their conceptualisations being incommensurable, talk of
discoveries (both ”that-what”-discoveries, as well as “what-that”-discoveries)
that belong to, or inaugurate, different theoretical frameworks/paradigms is
inane; a discovery is inherently framework-indexed, i.e. meaningfully defined
only relative to a framework. In order to coherently talk about variegated
discoveries in one breath, one must adopt the same theoretical framework for
their conceptualisation. As a historian, though, Kuhn is loath to single out
any such framework; to privilege those of our present state-of-the art, in
particular, would be tantamount to anachronism—a historiographical blunder.
Consequently, a discovery remains eo ipso a perspectival construct. In short,
Kuhn’s incommensurability thesis strips the notion of a scientific discovery
of an objective sense: for the historian—as a matter of principle—it’s
impossible to unequivocally study discoveries. This is surely a rebarbative
conclusion (indeed one that Kuhn doesn’t spell out explicitly). It hinges on
(2*), Kuhn’s incommensurability thesis. The authors discussed in §2.2-§2.4
forgo it, and rescue an objective notion of discovery, by jettisoning the
incommensurability thesis. Instead, they postulate a form of continuity (of
varying strengths) between successful theories.

Blackwell (1969, p.86) rightly “(emphasises) that Kuhn does not intend to
develop a theory of discovery as such. His is the wider question of the growth
and development of science”. Herein, we maintain, lies indeed the most
important insight we glean from Kuhn’s analysis: Kuhn highlights the
connection between discoveries and the progressive dynamics of science;
discoveries and the modus operandi of science, its historical evolution, are
essentially interlaced. We regard this as a key lesson—one that other models
of discovery don’t sufficiently heed: the notion of a scientific discovery
must, we urge (§2.5), be embedded in the dynamics of science.

This is precisely what Kuhn accomplishes with his distinction between the two
types of discoveries (as Schindler (2015, p.124) rightly observes). Each plays
a slightly different role within the dynamics of science (see especially Kuhn,
1962, pp.363). Decisively for this link, Kuhn ties the notion of a discovery
to some kind of conceptualisation: “observation and conceptualization, fact
and assimilation of fact, are inseparably linked, in the discovery of
scientific novelty.” (1962, p.762). “What-that”-discoveries presuppose a
prerequisite framework; the discovery must, more or less, fit into its
conceptual-theoretical resources. Any residual mismatch is the source of
innovation: via modifications, additions, and/or refinements within the
existing framework, one seeks to minimise that mismatch. Thereby, the
successful resolution makes the framework more sophisticated, enhancing its
accuracy, range of applications, versatility, etc. “That-what”-discoveries, by
contrast, burst the confines of the old framework: relative to the latter,
they are anomalous. The resolution must come from a new framework: if the
tension between the existing framework and the discovery becomes too
pronounced, it “(necessitates) paradigm change” (op.cit., p.58). The “that-
what”-discovery has shaken, and led to a re-configuration of, the web of
orthodox belief; it has thereby advanced science in a fundamentally more
innovative way than its “what-that”-counterpart.

Later commentators on Kuhn (§2.2-§2.4) tie the notion of a discovery to a more
demanding kind of prerequisite conceptualisation—problematically so (as we’ll
see). Our alternative model of discovery (§3) shows how Kuhn’s insight into
the intimate connection between discoveries and the dynamics of science can be
salvaged—without subscribing to such a gratuitously strong link, nor without
rendering the dating of a certain kind of discovery, and the identity of its
discoverer, necessarily futile.

###  2.2 Hudson: Materially demonstrated base descriptions

On Hudson’s (2001) model of scientific discovery, four criteria must be
satisfied for the discovery of an object X (by an individual, the discoverer
D):

  1. 1.

Base description: D must provide what Hudson calls a “base description” for X.
This denotes “a description of the object that suffices to identify it:
something that satisfies this description is the object being considered”
(p.77).

  2. 2.

Material demonstration: D “succeeds in demonstrating materially that this base
description is satisfied” (p.79).

  3. 3.

Novelty condition: D “finds something which is novel relative to a particular
social community […]” (ibid.).

  4. 4.

Truth condition: “The object described and materially demonstrated is, _in
fact_ , X […]” (ibid., our emphasis)

Before delving into a critical evaluation, a few comments are in order. First,
the level of detail and accuracy required of a base description “is not hard
and fast” (p.78); it varies from (historical) context to context. Hudson
deliberately refrains from further specification. What matters, he argues, is
that given the knowledge available to D, a base description can fulfil two
functions. First, it serves as a means of (re-)identification, as an indicator
for X: “(t)o have discovered an object one need _only possess enough
conceptual resources to recognize its presence in a fairly reliable manner_ ,
and such resources are what base descriptions provide for us” (p.78, our
emphases). The same dependence on D’s context, the background knowledge of
their time in particular, applies to the level of accuracy required of the
material demonstration. A second function of the base description (touched on
only in passing) is to instil in D at least an idea of her or his discovery’s
significance: “(Hudson) (takes) the act of discovery to be a reflective event,
one that impresses itself upon the discoverer as significant and informative”
(ibid.).

Secondly, Hudson (p.81) stresses “[…] the contextualized nature of the novelty
condition: novelty is socially dependent […]. Thus, priority will sometimes
depend on who gets included in the relevant ambient social group.” Note
furthermore that for Hudson, relative to the relevant social group, the
novelty condition is a temporal absolute, detached from social realities: it
doesn’t require that D’s work and priority actually be recognised.

Thirdly, how do commonplace discoveries (of, say, the watch of one’s
grandfather in the attic) differ from scientific discoveries? According to
Hudson (op.cit., pp.81, our emphases), “(s)uch _commonplace items are
familiar_ to us and well-understood, whereas _scientific kinds on their
initial discovery are quite unfamiliar_ and sometimes even exotic in their
properties […]. What will count as an adequate base description or material
demonstration will be less certain and so more contestable. […] We are
admitting that scientific discoveries are _not of a different kind_ than
commonplace discoveries, but _differ only in the order of complexity_
regarding the sorts of base descriptions that are used and the sorts of
material demonstrations that need to be performed” (pp.81).

What to make of Hudson’s model? Although the model has some useful features,
our overall verdict is to dismiss it as untenable.

Commendably, the model aspires to a natural desideratum: unlike Kuhn’s model,
it seeks to clearly label individuals as discoverers. This practice, together
with the usually attendant bestowal of honours and rewards, belongs to the
social aspects of the notion (as we’ll elaborate in §3). It’s desirable that a
philosophical explication reflect them.

One may however question that the desideratum is successfully realised:
Hudson’s model asks for both too little and too much. First, Hudson’s
flexibility towards what a base description must deliver exacts the price of
vagueness. This isn’t merely troublesome in its own right. It also prompts a
quandary: is there a limit not only to how accurate in detail a discoverer’s
base description must be, but also to how much inaccuracy (or how much
falsehood in the description) is still tolerable (cf. Schindler, 2015, p.128)?
Analogous worries can be voiced about the material demonstration. Hudson’s
gestured-at minimal answer—that the base description and material
demonstration should suffice to rule out a sufficient number of relevant
alternatives (p.78)—is glaringly hand-waving. Moreover, it flies in the face
of both contemporary and historical queries (e.g. Laudan, 1981; Psillos, 1999,
Ch.5 & 6; cf. McArthur, 2011, sect. 3). Amongst the latter, the luminiferous
ether stands out as theoretically indispensable prior to 1905, and likewise
amply “materially demonstrated” (see e.g. Torretti, 2009). Hudson doesn’t take
up this historical challenge (the challenge that, as expounded in §2.1, led
Kuhn to his incommensurability thesis).

Contemporary challenges stem from the usage of idealisations, and stark
simplifications, omnipresent in science (e.g. the thermodynamic limit, in
which both the number of, and volume occupied by, the constituents in an
ensemble of gas atoms are taken to infinity, or the Hardy-Weinberg model in
population genetics, which assumes absence of both mutations and selection).
Such toy models are known to be drastic distortions—sometimes even physical
impossibilities—of their target systems (see e.g. Norton, 2012; Luczak, 2017).
Wouldn’t reliance on them preclude, on Hudson’s model, the making of a genuine
discovery—contrary to widespread practice and intuition?

At the same time, Hudson’s model asks for too much: why insist that a
discoverer D possess both a sufficiently accurate base description and
material demonstration? Sometimes, as in the case of gravitational waves or
Bose-Einstein condensation, discoveries can be—prima facie—purely theoretical,
with their material demonstrations (i.e. empirical confirmations)
significantly delayed. Vice versa, as in the case of ultra-high energy rays in
the cosmic radiation or dark energy, sometimes empirical discoveries precede
an adequate “base description”.888Bartels (2021, Ch.3.7) discusses the
illuminating example of a phenomenological discovery, still awaiting its
accurate “base description”: Alzheimer’s disease. It strikes us as plausible
to treat both kinds as distinct discoveries in their own right (as §3.2 will
elaborate).

A second defect of Hudson’s model concerns its scope: given both Hudson’s
elaborations, as well as his examples, it’s manifestly limited to the
discovery of objects. This contravenes bona fide examples of discoveries
concerning other types of entities: superconductivity (a _property_ of certain
materials), isospin (a quantum number related to a _symmetry_ of nucleons),
the photoelectric effect or seafloor spreading (a quantum mechanical and
geological _process_ , respectively). One may also be wary of the restriction
to _material_ objects (cf. also McArthur, 2011, pp.368): that implausibly
precludes otherwise bona fide discoveries from the mathematical and
theoretical sciences, e.g. the discovery of the Casimir effect of quantum
field theory (op.cit., sect.4), the Bell inequalities in the foundations of
quantum mechanics, or Turing’s proof of the _Entscheidungsproblem_.

Thirdly, Hudson expressly allows for the continuity between commonplace
discoveries and scientific ones. A modicum of continuity seems indeed an
attractive feature of the model. Yet, his demarcation criterion strikes us as
wrong-footed: familiarity—apart from being yet another problematically woolly
notion—is too contingent a psychological-subjective condition to base the
distinction between scientific and non-scientific discoveries on.999While
perhaps the demarcation between science and non-science can’t be drawn rigidly
(cf. Laudan, 1996, Ch. 11), we don’t believe that it lacks any basis other
than a psychological-subjective hunch, such as “familiarity”.

Finally, Hudson rightly underlines the relevance of a discovery’s social
context. Via the novelty condition, Hudson’s model indeed achieves an
important desideratum: it rules out that, say, undergraduates in chemistry lab
classes discover oxygen. Regrettably, his incorporation of a discovery’s
social dimension remains unsatisfactory. Hudson doesn’t address the dilemma it
entails: doesn’t the community-relativity imply a form of relativism? What
makes one community more suitable, or relevant, than another: one’s academic
school/tradition? one’s tribe? one’s country? one’s language community? What
about “independent researchers”? Hudson intimates awareness of the problem. As
a remedy, he proposes that “(i)n scientific cases, one might argue that the
ambient social group is the entirety of the human race, or more generally, all
Earth-bound rational beings over the course of all time. But the group is not
very likely any larger than this” (p.81, our emphasis). Such an expansion of
the allegedly relevant community seems overblown. It surely detracts neither
from the scientific value or significance nor the impressiveness of a
discoverer’s achievements, if in another part of the world her discovery had
been made by someone else—so long as their two communities and cultures are
sufficiently isolated. (They might not even know of each other’s existence!)
Accordingly, Hudson’s novelty condition appears to be an unduly strong fiat,
devoid of a convincing argument. In the same vein, Hudson’s model precludes,
by definition, simultaneous discoveries—a pervasive phenomenon in science (see
Lamb, 1984).101010 It even has a wikipedia-entry of its own:
https://en.wikipedia.org/wiki/List_of_multiple_discoveries! Again, this
consequence seems unduly prohibitive. It rubs against common practice (where
simultaneous, independent discoverers are typically given shared credit).

###  2.3 McArthur: Discoveries for the structural realist

McArthur (2011) “(works) out some revisions to [Hudson’s] account by drawing
from a structural realist view of theory change” (p.361). Structural realists
(of the epistemic stripe, see e.g. Votsis, 2020) contend that scientific
knowledge primarily resides in the patterns and relationships amongst
observable entities, information encoded in a theory’s structural-mathematical
content, its equations. Judgements about the nature of the entities that a
theory appears to postulate, by contrast, ought to be suspended. Viewing its
structural content as what is “essential” (McArthur, 2011, p.371) to a base
description, McArthur relaxes Hudson’s demands on the discoverer’s epistemic
grasp of it: a discoverer needn’t possess an approximately accurate base
description, as a scientific realist would interpret it (i.e. as a base
description that, when read “at face value”, is approximately true); instead,
for McArthur, a discoverer must only identify the discovery’s approximately
true structural content. Rather than a “ _literally_ ” (van Fraassen, 1980,
esp. Ch. 1&2) approximately true base description, she or he must possess a
base description that is structurally approximately true.

More in detail, for an individual D to qualify as the discoverer of an
entity111111While McArthur isn’t explicit about this extension of what kinds
of entities can be discovered, our more permissive reading is buttressed by
both his prime example, the Casimir effect, which isn’t naturally interpreted
as an object, as well as the structural-realist agnosticism about the nature
of entities per se, and its epistemic restriction to relations and patterns
amongst entities. X (an object, process, event, etc.), McArthur stipulates
three conditions:

  1. 1.

Base description: D must possess a base description of X (in the form of a
minimal theoretical description/conceptualisation).

  2. 2.

Novelty condition: D must be the first to provide such a base description.

  3. 3.

Structural adequacy condition: This base description for X must be
structurally adequate; its relevant structural content has already been
corroborated.

Many features—and shortcomings—carry over from Hudson’s model. For our
purposes, it will be instructive to zoom in on two.

First, McArthur rightly remarks that Hudson’s model is predicated on “an
inadequate account of theory change” (p.366): it presupposes an interpretation
of the base description in scientific-realist terms, assuming that the base
description deserves to be understood as (approximately) “ _literally_ true”.
Such a strong premise is, as we saw in §2.2, indeed pricklish. As a structural
realist, McArthur bypasses that problem: structural realism posits a weaker
sense of conceptual and referential continuity between past and present
science. The structural content of empirically and explanatorily successful
theories, structural realists avow, survive theory change.

Because of his commitment to structuralism, McArthur’s proposal remains
unconvincing, though. It sensitively relies on a specific (and as such
controversial) position within the scientific realism debate. A more robust
model of scientific discovery seems preferable. Here, we won’t rehearse the
general complaints about epistemic structural realism (see e.g. Psillos, 1999,
Ch.7, 2001; Chang, 2003; Ainsworth, 2014). In the present context, one problem
in particular stands out: structural realism is limited to theories admitting
of a _sufficiently mathematised_ form. But mathematised theories outside of
the mathematical-physical sciences are rare! Should we therefore, as
McArthur’s model would seem to imply, deny the possibility of discoveries in,
say, biology, psychology or medicine (e.g. the discovery of horizontal gene
transfer, a vaccine for polio, false memories, or the discovery of mirror
neurons)? This strikes us as eminently implausible.121212For the mathematised
sciences, an additional problem arises: several contemporary and historical
theories contain inconsistencies (Vickers, 2013). Therefore, the deduction of
a structurally adequate base description required of a discoverer can be
knotty: ex falso quodlibet! For example, are ad-hoc methods for circumventing
those inconsistencies acceptable in derivations?

A second shortcoming of McArthur’s model is inherited from Hudson’s: it
precludes (more) “purely” theoretical131313Curiously, despite initially
proclaimed intentions to allow for “purely mathematical discoveries” (p.368),
it’s clear that McArthur’s model remains limited to discoveries as results
within the empirical sciences. or (more) “purely” empirical discoveries; on
McArthur’s account, both components must be present for a genuine discovery.
This seems gratuitously austere: why veto—contrary to widespread practice—more
purely theoretical (e.g. mathematical) discoveries, or more purely empirical-
experimental discoveries as distinct, but nonetheless genuine, types of
discovery?

Without such a distinction, one runs into an unpalatable consequence—even
within the empirical sciences. Often, novel predictions draw on structural
properties of a theory that haven’t received independent empirical
confirmation yet, even if other aspects of the theory have. The historical
examples of Dirac’s prediction of antimatter, or Einstein’s predictions of
gravitational waves, or the prediction of the Higgs boson, respectively spring
to mind. All three antedated evidence by about half a century! It’s natural to
view these incontrovertible break-throughs as discoveries: they are novel
features entailed by a theory which otherwise had already proven its mettle.
However, the usual candidate (co-)discoverers would be barred on McArthur’s
model: the latter requires of a discoverer to be “the first to use some of
[the theory’s] _already-confirmed_ relations to provide the base description
of the effect that was later exploited in experiments” (2011, p.374, our
emphasis).

###  2.4 Schindler: Discovery as essence identification

Schindler’s (2015) model strengthens Hudson’s account of discovery by
demanding that the base description capture, at least in part, the discovered
phenomenon’s essence:

> A discovery of X requires observing X or its direct effects […] and the
> correct conceptualisation of those of X’s essential properties that suffice
> (epistemically) to individuate X at time t […] (op.cit., p.132, emphases in
> the original).

For a discovery, the phenomenon’s (materially demonstrated) base
description—in Hudson’s terminology—must contain at least some true beliefs
about X’s characteristic features, defining what X is. Moreover, a discoverer
needs to possess enough knowledge of them such that, against her background
knowledge, she can discriminate X from other conceivable entities with similar
effects. Thanks to such robust partial knowledge about X, according to
Schindler, the phenomenon has been sufficiently comprehended—both empirically
(qua material demonstration) as well as theoretically (qua the identification
of its (partial) essence)—to licence the title of a discovery.

Through the insistence on essential properties in the base description,
Schindler tries to overcome what he perceives as the main shortcoming of
Hudson’s model (which Hudson (2001, p.78) in turn animadverts upon in
Kuhn’s)—the double “what-indeterminacy”-problem (p.128): how _accurate_ does a
base description have to be for a discovery? And how much _in_ accuracy or
_in_ completeness is permissible? The identification of some of X’s essential
properties is supposed to address the first; the epistemic background—enabling
the distinction between X and alternative entities—is supposed to take care of
the second question.

In our assessment of Schindler’s proposal, we’ll concentrate on his employment
of essential properties.141414Since his account is intended as a debugged
version of Hudson’s (and Kuhn’s) with respect to the “what-
determinacy”-problem, it inherits several of their shortcomings. In
particular, Schindler merely gestures at the link between scientific
discoveries and the progress or growth of science (p.127)—to our minds, a
crucial desideratum of any adequate model of discoveries. Note also how
Schindler expressly brackets questions of priority, or any of the communal
aspects of scientific discovery; his is “an account intended to capture the
nature of discovery. It therefore does without any reference to people making
the discovery” (p.132, emphasis in the original). We likewise regard this
neglect of communal aspects as a defect of the model’s adequacy (§2.5).

Schindler strongly invites a reading of his proposal at face value (see, inter
alia, the literature he cites, see p.132, fn14): he seems committed to
essences, as discussed in the metaphysics literature—that is, properties that
define an object’s nature or identity, and that the object can’t lack without
ceasing to exist. Regrettably, Schindler elucidates neither his understanding
of essences nor the kind of essentialism he has in mind. In light of the
sizable literature (see e.g. Roca-Royes, 2011; Bird, 2009; 2018; Ishii &
Atkins, 2020 for reviews) on, and proliferating varieties of, essentialism,
this omission makes Schindler’s proposal tricky to evaluate.

It doesn’t bode well, though. Already at a general level, three arguments
militate against an appeal to essences in this strong sense.

First, one may simply shy away from such a controversial metaphysical notion.
In fact, “it is not obvious how best to characterize the notion of essential
property, nor is it easy to give conclusive arguments for the essentiality of
a given property” (Roca-Royes, 2011, p.65). A fortiori, one may be leery of
tying one’s understanding of scientific discoveries—a high-level notion
permeating scientific practice in all disciplines—to such a specific (and
notoriously vexed) idea in metaphysics.

Secondly, accounts of essentialism typically stipulate a tight definitional
link between essentiality and metaphysical necessity (see e.g. Ishii & Atkins,
2020, esp. sect.1-3). Necessity here is construed in terms of truth in all
possible worlds.151515Also Schindler explicitly endorses a (modal) definition
of essences: “(p)resumably, there is a list of properties that are
(metaphysically speaking) necessary and sufficient for the individuation of
electrons”(p.132). Whether science has much to say about such modal
speculations is questionable (cf. Norton, 2021). Accordingly, one may doubt
the relevance of essentialism for understanding science in general, and
scientific discoveries in particular. But even if one grants this relevance,
an epistemological worry looms: how to ensure that science attains knowledge
of essences? Schindler (implicitly) presumes that discoveries have actually
been made in science. Given his account’s commitment to essences, Schindler
thus professes an epistemic optimism about science—the sanguine hope that it
has uncovered at least some salient essences. Such triumphalism many will
repudiate as panglossian.

Thirdly, essentialism sits uneasily with the special sciences, such as
geology, biology, or social psychology. Due to their inherent complexity,
fuzzy conceptual boundaries, variability and dependence on specific
circumstances and interests of the inquirer, talk of essential properties for
the objects of those disciplines faces well-rehearsed challenges. That, on
Schindler’s account, would compromise the possibility of discoveries in those
disciplines. This strikes us as inordinately restrictive—as Schindler’s (2015,
sect. 4.1) own discussion of a bona fide discovery in geology illustrates, or
more dramatically: the discovery of anthropogenic climate change (see
Friedrich, 2022).161616Other examples are easily multiplied: think of the
discovery of extremophiles, or Harvey’s discovery of the circulatory system
with the heart’s function as a pump. Both significantly expanded our
understanding of life, and the human body, respectively. Yet, one would be
hard-pressed to argue why the properties of those discovered objects should
qualify as essential in any of the standard metaphysical senses.

Although clearly envisaging the foregoing strong metaphysical reading in terms
of essentialism, Schindler also contemplates a weaker reading (p.132., fn14):
“(a)nti-essentialists may plug in their preferred notion of natural kinds
here.” On this weaker reading, discoveries require the observation of X (or
its direct effects), in tandem with a sufficiently correct classification of
X’s natural kind.

The world, its objects and processes, adherents of natural kinds opine, admits
of natural groupings—a division into said natural kinds (see Dupré, 2000; Bird
& Tobin, 2023; Brzović, 2018 for further details); the latter are supposed to
carve nature at its joints. The most prominent proposal for such
classification or categorisation in terms of natural kinds is indeed
essentialism: natural kinds are anchored in (sufficiently similar) essences.
Other approaches are metaphysically less fastidious and more pluralistic: they
conceive of natural kinds as groupings on the basis of clusters of properties,
i.e. family resemblance.

Again, Schindler’s omission of further details hampers a deeper analysis of
how these alternate accounts apply to his model. At first blush, though, it’s
far from clear that they are compatible with his further commitment to a
“realist stance” (p.123). First, Schindler’s invocation of essences, or
natural kinds, is designed to underwrite an _objective_ distinction between
essential and accidental properties—properties that are necessary for a
discovery’s prerequisite conceptualisation, and those that aren’t. One may
wonder, however, whether groupings based on family-resemblance (rather than
putative essences) can deliver that: instead, the taxonomic lines of
demarcation tend to depend on the context (see e.g. Ruphy (2010) for stellar
classifications, relevant also for our case study in §4) —and the _subjective_
interests of the inquirers (as is frequently explicitly acknowledged in the
non-essentialist approaches to natural kinds). Secondly, and relatedly,
Schindler seems implicitly committed to semantic realism: his insistence on “
_correct_ conceptualisation” of a phenomenon (reiterated passim)—up to “at
least some false and incomplete beliefs about X” (p.128)—is naturally read in
realist terms (cf. Psillos, 1999, esp. Ch.1)—as an assertion about the
(partial) literal truth of a theory’s unobservable theoretical
content.171717It deserves to be stressed that Schindler erroneously imputes
such semantic realism to Kuhn (p.128): Kuhn is emphatically _not_ a realist.
With his (semantic) incommensurability thesis, and his rejection of a
correspondence theory of truth, in tandem with his rejection of a model of
progress in terms of increasing truth-likeness, it’s difficult to see what a “
_correct_ conceptualisation” within Kuhn’s thinking might even mean. Prima
facie, however, such semantic-realist ambitions—whilst underwritten by
essentialism—are at odds with a context-dependent classification and
categorisation of the world into natural kinds.

###  2.5 General shortcomings

We’ll now step back to compile a handful of general inadequacies of the
foregoing models of discovery. By way of negative examples, they’ll sharpen
our sense of what a satisfactory model should achieve—paving the way for our
task in §3.

First, the scope of the extant models is expressly restricted to material
objects. As pointed out, this a priori limitation is unconvincing. Rather,
it’s desirable that an account of discovery not impose such constraints: not
only material objects—but also properties, processes, events, etc. can
plausibly be discovered. Moreover, in view of routine practice of nomenclature
and the ground-breaking significance of some of them for science, likewise a
limitation to material entities seems unduly narrow: also, say, physical laws,
or mathematical theorems, can plausibly be discovered.

Secondly, all three post-Kuhnian accounts (i.e. McArthur’s, Hudson’s, and
Schindler’s) overtly evince bias towards realism: each presupposes substantial
realist premises.

An alternative that isn’t hostage to such—invariably controversial—assumptions
would be desirable (especially for historians of science, see Arabatzis,
2001): a satisfactory model of scientific discovery ought not to depend on
specific positions in the realism/anti-realism debate.

One reason for the pro-realist bias lies in warding off a consequence of
Kuhn’s account (of which the other three models are intended as improvements):
Kuhn’s incommensurability thesis spoils the objectivity of the notion of a
discovery across major theory-change. One is then stuck with the catch-22 of
having to choose between either an anachronistic theoretical framework, or of
swallowing relativism about discoveries. Neither option is attractive. The
extant accounts seek to dodge the dilemma by blocking the incommensurability
by pro-realist assumptions. As we’ll see in the next section, it’s
possible—and plausible—to renounce the former, without subscribing to the
latter.

The pro-realist bias has, however, a second source of motivation. Its prima
facie plausibility musters intuitions independent of one’s philosophical
penchants for scientific realism. One may likely want to eschew talk of the
discovery of entities (e.g. ether drag, or the creation of mercuric oxide via
calx), today discarded as scientifically obsolete. By the same token, the pro-
realist bias is, we conjecture, also driven by the hunch that what makes a
scientific discovery valuable is its enduring value: we appear to prize
discoveries—and confer honours upon their discoverers (see below)—because they
constitute lasting achievements, hard-won but solid insights. Such reasoning
lures one towards an approach to discoveries that ab initio privileges our
current understanding of science. Past scientific achievements would
consequently have to exhibit sufficient continuity with it in order to qualify
as discoveries. From a scholarly perspective, however, such a bias towards
triumphalist presentism (“Whiggism”, Butterfield, 1931) is disconcerting; it’s
a dubious historiographic doctrine.181818And, in fact, the sustained target of
Kuhn’s writings (see Hoyningen-Huene, 2012). It’s desirable that a model of
discovery overcome such a bias. The challenge is to achieve this whilst doing
justice to the intuitions that drive the two arguments. (Our more fine-grained
taxonomy of discoveries (§3.2) delivers that.)

Thirdly, the three philosophical accounts pay insufficient attention to two
key facets of scientific discoveries:

  1. 1.

Their connection with theory dynamics: how are discoveries and the advancement
of science related? How do discoveries and science interact?

  2. 2.

Their communal dimension, and the various social-institutional practices
surrounding it: what makes discoveries scientifically valuable?191919Note the
entanglement of this question and our above comments on the Whiggish bias of
the extant philosophical accounts. Why do textbooks extol the achievements of
discoverers? What rationale—if any—underlies the idea of awards and other
signs of recognition for discoverers?

Kuhn’s account puts discoveries at the heart of his conception of the
evolution and progress of science. The advocates of the other models reject
Kuhn’s conception of the dynamics of science. Nonetheless, they try to improve
on his account of discoveries. Vis-$\grave{a}$-vis this tension, they remain
largely silent on (1), the significance of discoveries for the dynamics of
science.

Those authors follow Kuhn, however, in setting aside the questions under (2).
They explicitly elide the reward system of science in particular—with its
premium on priority. Presumably, we surmise, such issues are relegated to the
sociology of science—and viewed as a haphazard, messy, extraneous element of
science, of little concern to epistemology.

This neglect of central features of discoveries is problematic: a satisfactory
explication of the notion of a discovery, we contend, ought to reconstruct
both a natural link between discoveries and theory dynamics, as well as
between discoveries and the sociological dimension of science—a link that,
ideally, dovetails the historical and current social reality of science.

Finally, the tension between the goal of emending Kuhn’s model, and the
rejection of Kuhn’s larger framework for the dynamics of science spawns
another problem (closely related to the preceding point (1)): why do Hudson,
McArthur or Schindler weld the notion of a discovery to the need for the
discovered phenomenon’s conceptualisation? What speaks against (more or less)
_purely_ observational discoveries (of, say, sun-spots or place cells), or
(more or less) _purely_ theoretical-conceptual-interpretative discoveries
(e.g. of the existence of quasi-stable orbits in dynamical systems within KAM-
theory, or Dirac’s proof of the equivalence between Heisenberg’s matrix
mechanics and Schrödinger’s wave mechanics)? Within Kuhn’s two-phase framework
of science, the link is clear: no scientific result without a paradigm, either
the received one, or a new and revolutionary one. But since those authors
(rightly!) distance themselves from Kuhn’s framework, why insist on a
sufficiently detailed conceptualisation—and a fortiori a sufficiently accurate
one!—as a sine qua non for a discovery? As we’ll see in the next section, we
agree that qua scientific results, discoveries must be integrated into the
wider body of scientific knowledge; this requires _some_ kind of
conceptualisation. But we disagree with the extant models that this
conceptualisation must necessarily be sufficiently “accurate” or “reliable”.

##  3 The change-driver model: scientific discoveries as drivers of scientific
advances

This section will canvass an alternative account of scientific discoveries,
the “change-driver model”. §3.1 will introduce the model. §3.2 will present a
more fine-grained typology of scientific discoveries which naturally arises
within it. We’ll then (§3.3) discuss the merits of the model . Finally, in
§3.4, we’ll inspect, and rebut, some prima facie challenges.

###  3.1 The change-driver model of scientific discovery

Combining ideas of Popper (1983; 2002a; 2002b) and Kuhn (1962; 1996), we
propose to conceptualise discoveries in a way that puts them (again) at the
heart of science’s dynamics. Owing to its emphasis on how discoveries propel
science, we’ll dub our account the “change-driver model”. It elaborates
Blackwell’s (1969) remark that “(t)he word ‘discovery’ is a rather generic
term that includes quite diverse instances of the advancement of human
knowledge” (p. 96). For that, “to be counted as a discovery, [a new idea] must
be integrated in the accepted body of scientific knowledge. This acceptance
may be friendly or disruptive, depending on the impact of the new idea on
former views” (p.53).

A scientific discovery, we submit, is

  1. 1.

a cognitive scientific result (observational or experimental finding, theorem,
prediction, etc.)

  2. 2.

that has significantly advanced the scientific field in question.

The objects of a scientific discovery, as per (1), are what scientists traffic
in: empirical results (e.g. the detection of the cosmic microwave background,
or the first observation of a quasar), proofs (e.g. Poincaré’s discovery of
the chaotic dynamical behaviour in the three-body problem of celestial
mechanics, or Boltzmann’s H-theorem), an application of a theory that yields
novel predictions (e.g. the application of basic quantum mechanics and general
relativity to white dwarfs or neutron stars), a novel formulation of a theory
(e.g. Feynman’s path-integral formulation of quantum mechanics, or the
Hamiltonian (“ADM”) formulation of general relativity), the articulation of a
new and powerful conceptual or taxonomic framework (e.g. Mendeleev’s periodic
table), a new interpretation of a known result (as in the case of Special
Relativity, see e.g. Janssen, 2002, or the various interpretations of quantum
mechanics), etc. No a priori restrictions are imposed on what may in principle
be discovered: discoveries can pertain to material or immaterial entities
(e.g. exoplanets or axiomatisation of set theory), objects (e.g. archaea or
elementary particles), structures (e.g. violations of CPT invariance),
properties (e.g. superfluidity) or states (e.g. a false vacuum or Bose-
Einstein condensation), or processes (e.g. photosynthesis or CNO/Bethe-
Weizsäcker cycle).

We add the rider “cognitive” as a rough-and-ready further requirement that the
scientific result pertain to science’s cognitive aims: it ought to be related
to, and further, understanding and knowledge. By contrast, the devising of,
say, the telescope or the bubble chamber concerns more technological and
practical aspects. It yields knowledge that informs practical applications.
The guiding intuition here is that such applications don’t per se expand our
knowledge or understanding: pending further research, they can (but needn’t)
be used as tools for that. Sensu stricto, these inventions wouldn’t count as
cognitive scientific results.202020Nonetheless, the distinction between
cognitive and technological results lies on a continuum (see e.g. Shaw, 2022).
This parallels the blurry line that marks practical from theoretical
knowledge.

The second clause, (2) prescribes that a scientific discovery play a
distinguished role for knowledge within a scientific field. In an unusual way,
it contributed to scientific progress. Thanks to the discovery, our knowledge
grew—either in a temporally more discrete form, a “leap” forward, or over a
more extended period with continuous progress, culminating in a break-through
result.

The significance condition demarcates not only discoveries from _non-
discoveries_ (such as successfully answering an exam question). It also
demarcates scientific discoveries from _non-scientific_ ones (such as
discovering one’s love for Rumi’s poetry, or a wart on one’s toe). We’ll
return to both points below.

In preparation of our discussion in §3.3 and §3.4, it will prove profitable to
adumbrate three themes already in the offing at this juncture.

First, science requires a scholarly community within which it operates:
science has _essentially_ a communal dimension—a profound Kuhnian lesson (cf.
also Longino, 1990 and Solomon, 2001). Scientific discoveries, qua aspects of
science, can’t happen in isolation; they must conform to the organisational
and normative structures of science as a community.

Secondly, the model doesn’t impose any restrictions, neither directly nor
indirectly, on the discipline in question. As far as we can see, the change-
driver model can be applied to all fields in the physical, social and
mathematical sciences.212121 In principle, to our minds, nothing precludes
advances in, say, history. Plausibly, historical knowledge can grow.
Discoveries in history that seem to fit the change-driver model’s
characterisation concern the Rosetta Stone or the Cairo genizah.

Thirdly, our second requirement, (2), refers to the advancement or progress of
science. How to construe this? What is meant by the growth of knowledge, to
which a discovery is supposed to redound? Lest our model be taken hostage to
partisan views,222222We use “progress” in a loose and permissive sense, with
no specific commitment to any position in the debate (see e.g. Niiniluoto,
2019; Dellsén, 2019).  we’ll adopt a pluralist and permissive attitude:
science makes significant advances whenever a result has exceptionally
expanded, deepened or rectified our theoretical or empirical knowledge.
Knowledge can, of course, also grow through negative insights: we gain
knowledge by figuring out which ideas don’t work or which facts aren’t the
case. Hence negative discoveries are possible, as we’ll elaborate below.

What counts as a _significant_ advance lies on a continuum (more on this in
§3.3). Moreover, we regard it as a question that historians of science must
adjudicate: their scholarly expertise—rather than philosophical apriori
reasoning—should apprise us of which developments in science were particularly
influential and important. 232323NB: Any plausible account must necessarily
rely on historical expertise, if one wishes to apply it to actual—and ipso
facto historical—discoveries. Our model merely makes this reliance explicit.
We thereby don’t deny the objective existence of a historical record:
historical events and data concern matters of fact. Their interpretation and
grasp within a wider horizon of significance, however, will be mediated by
historians’ assessments. To be sure, consensus on discoveries can’t lay claim
to being an infallible authority: misjudgements (as evaluated
vis-$\grave{a}$-vis historical expertise) are possible. In line with Chang
(2009, 2021), the change-driver model is compatible with a pluralist approach
to the history of science.

Before unpacking the implications of the model, let’s ponder: what does it
mean to make _a particular_ discovery?

###  3.2 Three types of discovery: the discovery of X

So far, we have only characterised what counts as a discovery in general: the
model of §3.1 delimits criteria for declaring a finding a scientific
discovery. Often, however, we want to know something more specific about a
particular discovery—say, of the neutrino or fractal geometry.

For particular discoveries, we must disambiguate what _exactly_ the question
is when asking about the discovery of X. Scientific results may be grouped
into three broad types.242424The taxonomy equally applies to negative
discoveries. Null-results of violations of Lorentz invariance for high-energy
particles, or the non-observation of magnetic monopoles (as predicted by
typical grand-unified theories) are examples of negative physical-material
discoveries. The non-renormalisability of General Relativity is an example of
a negative theoretical discovery. And the coincidence of the speed of
gravitational and electromagnetic waves is an example for a negative synthetic
discovery about TeVeS (an alternative to General Relativity that predicted a
small discrepancy, see e.g. Abelson, 2022). Accordingly, should such a result
X significantly advance science, we can, on the change-driver model,
understand “the discovery of X” in (at least) three different ways: 252525 The
taxonomy is in no problematic way tied to realism (except in its
metaphysical—viz. anti-idealist—dimension, i.e. in regards to assuming a mind-
independent reality—a benign assumption that few anti-realists will contest).
Physical-material discoveries only rely on a sense of empirical adequacy, and
its anti-idealist interpretation as reflecting _something_ in a mind-
independent, material-physical reality. Theoretical discoveries are inherently
theory-relative/internal: they are made within a given theoretical framework,
refraining from inferences about any putative external material-physical
world. Synthetic discoveries needn’t be interpreted in problematically
substantive realist terms either: all they require are standards of
evidential-epistemic support. Anti-realists (except for radical sceptics and
relativists) typically don’t deny the existence of such standards of theory
appraisal vis-à-vis observational data. (They merely contest the realist
interpretation of the theory in toto, i.e. also with respect to all of its
theoretical claims.)

  1. 1.

_Empirical-material_ discovery of X.
The object of an empirical-material discovery concerns the physical-material
reality of a phenomenon. To discover X in this sense means to discover the
existence of a phenomenon which is referred to, or empirically adequately
described, by dint of X. Here, X may be a (possibly even heavily) theory-laden
term.

The discovery of various phenomenological laws (e.g. the Snell-Descartes-ibn-
Sahl law of refraction, or Zipf’s law of word distributions), the Doppler
effect, tool-use in chimpanzees, or the Miller-Urey experiment are cases in
point, as _relatively_ theory-free observational regularities. An example
implicating more theory-ladenness in an empirical-material discovery concerns
that of gravitational waves: if one refers to them as “ripples of spacetime
curvature”, one relies on General Relativity.262626Albeit the standard theory
for describing gravitational physics, empirically indistinguishable
alternatives exist that don’t conceive of gravitational radiation in terms of
spacetime curvature (e.g. Hohmann et al, 2020). The phenomena into whose
discovery—in its physical-material sense—we inquire when asking about the
discovery of “ripples of spacetime curvature” are gravitational effects that
propagate in a wave-like manner.

  1. 1.

_Theoretical_ discovery of X.
The object of theoretically discovering X is to discover X qua _theoretical_
scientific result (i.e. as treated within a given theoretical context). X may
be, for instance, a theorem proven to be entailed within a theory, the
proposal of an (at least pro tem speculative) idea or theory as a solution to
various problems, etc.

Theoretical discoveries—remarkable, cognitively impactful ideas “stumbled on”
or laboriously arrived at within a theoretical framework, in a manner similar
to empirical discoveries—include, for instance, the Nash equilibrium in game
theory, the spin-statistics theorem in relativistic quantum field theory,
super-symmetry (as a speculative proposal to solve, inter alia, the hierarchy
problem, implement an aesthetically pleasing symmetry, and as a prerequisite
for the consistency of string theory), singularity theorems as mathematical
facts within relativity theory, or Weyl’s discovery of the gauge principle
(which laid the foundation for the standard model of particle physics, but was
developed for a theory quickly discarded as empirically unviable, see e.g.
O’Raifeartaigh, 2000).

  1. 1.

_Synthetic_ discoveries about X.
Synthetic discoveries express a relation between X as a theoretical
concept/conceptualisation and the world. They combine elements of the two
other forms of discovery. To synthetically discover X means to discover that
X, as a theoretical idea, latches onto something in the physical-material
world: X can be successfully used to explain, model or accommodate certain
phenomena. The synthetic discovery about X consists in demonstrating some
epistemic-evidential warrant for taking X, and its theoretical framework,
seriously.

Synthetic discoveries often take the form of corroborations (e.g. Brownian
motion as a confirmation of the kinetic theory of heat, or Frisch’s
deciphering of the bees’ waggle-dance) or falsification (e.g. the detection of
neutrino oscillations as refuting the original assumption of the neutrino’s
masslessness, or the various forms of counterevidence to kinship selection).
To deflect the suspicion that one here succumbs to realist temptations, we
hasten to add that a synthetic discovery can be agnostic with respect to
realism: the metaphysical quarrel between realists and anti-realists seldom
stymies agreement on which theory to regard as the most explanatory or
empirically best-supported (e.g. the standard model of particle physics, or
the modern evolutionary synthesis). Synthetic discoveries concern such theory
appraisals.272727Proofs-of-concept—preliminary demonstrations or experimental
evidence that support the feasibility and in-principle viability of a
scientific theory, hypothesis, or modelling approach, and that serve as
initial validation that the proposed concept or idea has the potential to
work—can likewise be plausibly interpreted as synthetic discoveries. They are
particularly interesting in the present context because, owing to their
preliminary nature, they don’t lend themselves to a realist interpretation.
Schelling’s dynamical segregation model, which shows how collective
discriminatory social facts can inadvertently emerge from small individual
preferences and, in the main, individual tolerance, is a case in point (see
Bartels, 2021, Ch.3.8). Likewise germane are psychological—and, in particular,
psychiatric—disease patterns (op.cit., Ch. 3.7).

The three types of discoveries are clearly distinct.282828Needless to say:
insofar as, following e.g. Quine (1950), one disputes the analytic/synthetic
distinction, a clear-cut distinction between empirical and theoretical
distinction is likewise blurred at a fundamental level. Typically, though, in
specific historical/scientific contexts at least pragmatically it can be
fruitfully upheld. Theoretical results can be seminal, even ground-
breaking—and thus, according to the change-driver model, discoveries proper
(theoretical discoveries in the sense of (2), that is). Yet, their relevance
for physical reality (and hence status as empirical-material discoveries in
the sense of (1)) may remain (at best) controversial. Cases in point are
Hawking radiation (i.e. the creation of particle/antiparticle pairs near a
black hole that annihilate each other, resulting in the black hole’s gradual
evaporation) or the holographic principle (a conjectured map/correspondence
between a higher-dimensional gravitational theory, and a lower-dimensional
quantum field theory, exemplified e.g. by the AdS/CFT correspondence).
Conversely, it’s possible to have genuine physical-material discoveries whose
adequate theoretical conceptualisation—their theoretical or synthetic
discovery—is still pending.292929Caneva (2001, 2005) illustrates the relevance
of the distinctions for several cases in the history of science: “[…] what a
scientist is typically credited with having discovered often differs
significantly from the way in which the scientist himself characterized his
work” (Caneva, 2001, p.1). A spectacular example of our times concerns Dark
Matter (see Martens, 2021). A multitude of robust empirical phenomena is
known—empirically-materially discovered by, inter alios, Kapteyn, Oort and
Zwicky (see Bertone & Hooper, 2018). A plethora of possible models—each a
theoretical discovery in its own right—exist to account for them. Notoriously,
however, no conclusive synthetic discovery is forthcoming: evidentially-
epistemically, contemporary cosmology and astrophysics are stuck in an
impasse.303030Cosmic inflation provides a nuanced example, worth pointing out
because of its—with respect to our taxonomy—hybrid status. Historically, it
started off as a theoretical discovery, as a common solution to a few well-
known puzzling (so-called fine-tuning) facts of the inflation-less standard
model of cosmology, before physical-material discoveries (most importantly
related to the power spectrum of the cosmic microwave background) accumulated;
inflation makes novel predictions that were subsequently borne out. This
gradually shifted its status (see e.g. Smeenk, 2005, 2017). Yet, a _fully_
satisfactory synthetic discovery—a sufficiently warranted, specific model of
inflation—is still pending.

This taxonomy cuts natural distinctions, tracking intuitively different kinds
of discovery. The history of the electron with its manifold theories
exemplifies this (cf. Norton, 2000; Bains & Norton, 2001): the “discovery of
the electron” is a polysemous umbrella term that encompasses empirical
phenomena (e.g. the results of Millikan’s oil drop-experiment establishing the
existence of an elementary unit of charge, or the photoelectric findings of
Lenard’s cathode ray experiments), theoretical triumphs (e.g. the natural
incorporation of spin via Dirac’s theory of the electron, or the development
of Feynman diagrammes) and extraordinary evidential-epistemic accomplishments
(e.g. the stunningly accurate prediction of the electron’s gyromagnetic ratio
in quantum electrodynamics). Each of these results—to name only a few!—was a
ground-breaking discovery in its own right, tokens of the types of discovery
(1)-(3).

A subtlety concerning theoretical and synthetic discoveries merits attention.
Eis ipsis, they may involve potentially strong theoretical—that is, strongly
theory-laden—assumptions about their objects; to describe the latter, they
presuppose theoretical apparatus that can’t be easily severed. Einstein’s
discovery of a static universe solution to his gravitational field equations
(§4.1), or Gödel’s theoretical discovery of general-relativistic time-travel
(i.e. spacetimes with closed time-like curves), for instance, are inextricably
interwoven with the theoretical framework of General Relativity; likewise, a
characterisation of the Higgs mechanism for explaining the origins of mass in
particle physics can’t be disentangled from the quantum field theoretical
framework.313131In the case of logico-mathematical discoveries—a special case
of theoretical ones—such as the discovery of fractal geometries, Lie groups,
or complex numbers, the very notion of a discovery requires formulating a
mathematical theory (Bartels, 2021, Ch.3.9).

An analysis of theoretical and synthetic discoveries harbours conceptual-
semantic challenges. How similar to the theoretical framework in which X is
described does X’ have to be in order to qualify as an antedating theoretical
discovery? How similar does the evidential-epistemic warrant for—how similar
do the arguments in favour of—X and X’ have to be for X’ to qualify as an
earlier synthetic discovery? Both problems are especially poignant when we
phrase the question about the discovery of X in terms heavily leaning on
_current_ theoretical understanding, e.g. when talking about particles (see
e.g. Falkenburg, 2010) or light (see e.g. Hentschel, 2023), concepts that have
drastically evolved over the past century. As arguably typical of assessments
of similarities, they depend on various contextual factors. This we also take
to be the case here: the extent to which X and X’ resemble each other
conceptually-semantically and epistemically-evidentially can vary; it depends
on the concepts in question (X and X’, respectively), and the specific aspects
of the comparison one inspects. Fortunately, in the case of the expanding
universe these complications affect an analysis only marginally.

In conclusion, the question about the discovery of X requires specification of
which sense of discovery (1)-(3) one is interested in; the choice typically
determines the answer. Our analysis of the discovery of the expanding universe
in §4 will illustrate this.

Before weighing the benefits of the change-driver model, it is crucial to
discuss the role of the discoverer. To which entity should we ascribe agency
in the discovering process? Who or what makes a discovery— an individual or a
group (e.g. the scientific community as a whole)? The model remains neutral on
this: it is compatible with either option, as well as a case-dependent hybrid.
While Clark & Khosrowi (2022) have convincingly argued against the received
individual agent-view, we’ll adopt a more permissive view that allows for
case-dependent continuity: some discoveries are attributable to individuals,
others to a collective, and yet others (in varying degrees) to both, as
illustrated in §4.3. The model doesn’t necessarily presuppose the existence of
an individual discoverer. Rather, we’ll treat it as an open question—one that
historical analysis has to answer—whether one can be identified for the
specific discovery under discussion.

###  3.3 Merits

Its simplicity and commonsensical ring notwithstanding, the model of
discoveries as change-drivers is surprisingly powerful. It overcomes the flaws
of the received models, synthesises several of their respective advantages,
and effortlessly realises a number of further desiderata for a satisfactory
explication of “discovery”.

We begin with its most patent advantage: its inherent connection with theory
dynamics. This is built into the model ab initio via the requirement (2): a
scientific discovery must have contributed non-negligibly to the advancement
of science; its significance should jut out against the epistemic “background
noise”. Discoveries are thus integral to the healthy—progressive—development
of science. On the change-driver model, this link is essential. On the other
models it comes out as either accidental, or dependent on potentially
problematic further assumptions.

Merging the insights of Kuhn and Popper (especially in their contributions to
Lakatos & Musgrave, 1970), scientific discoveries advance science in three
major ways:

  1. 1.

They _expand_ our knowledge. Physical-material discoveries increase our
factual-empirical knowledge about the world. Theoretical ones increase our
theoretical-formal knowledge about, and understanding of, a given theory, its
logical content, potential applications, relation to other espoused beliefs,
etc.; more generally, they typically broaden our intellectual-conceptual
horizon and enrich our conceptual-theoretical resources. Synthetic discoveries
increase what we know (have epistemically warranted beliefs), and understand
(gain cognitive control over, cf. McCoy, 2022) about the world.

  2. 2.

No less importantly, discoveries in their various forms can also _confirm,
corroborate or solidify_ existing knowledge. Discoveries can deepen our
understanding of a theory, both “internally”, as well as with respect to
_other_ theories, and theory’s empirical relation to the world. Thereby, they
refine and improve the epistemic quality of our expectations and beliefs.

  3. 3.

Discoveries can also _challenge_ existing theories and beliefs—by exposing
problems and anomalies (as eloquently expressed in the quotes cited in
Schindler, 2015, sect. 4.2; cf. Laudan, 1977, esp. Ch. 1&2 for a systematic
elaboration). Theoretical discoveries can disclose problems, contradictions or
even conceptual-logical inconsistencies. Physical-material discoveries can
constitute empirical anomalies, or even refute theories. Synthetic discoveries
of this ilk flag gaps in our knowledge, e.g. applications for which our
established knowledge breaks down. The upheaval that scientific discoveries
wreak—through revealing gaps, inadequacies, consistencies, conflicts with
other theories etc.—calls for a revision, and/or extension of established
beliefs. Challenging discoveries thus elicit innovation.

As a second major advantage, the change-driver model divorces the notion of a
scientific discovery from the realism/anti-realism debate: the change-maker
model remains neutral.323232As a litmus test: an advocate of Turner’s (2007)
“Natural Historical Attitude” can embrace it. It doesn’t rely on substantive
premises germane to that debate. Compatible with a pluralist approach to
progress, it’s not tied either to any specific position regarding global
notions of progress.333333It’s natural, but by no means inevitable, to adopt
Laudan’s (1977) view of progress as problem-solving. In particular, the model
isn’t tied to construing progress in terms of verisimilitude (i.e. increasing
truth-likeness—the most common realist model for progress).

Due to its link with theory dynamics, the change-driver model provides a
unified account of “that-what” and “what-that”-discoveries. Physical-material
discoveries that precede their satisfactory conceptualisation and theoretical
grasp, as well as “material demonstrations” of such
conceptualisations—synthetic discoveries in our taxonomy— _both_ qualify as
discoveries sui generis. By contrast, owing to their insistence on a suitable
“conceptualisation” (Schindler) or “base descriptions” (Hudson), Schindler’s
and Hudson’s models only admit “mixed” scientific discoveries; _purely_
theoretical or (primarily) empirical ones flout their requirements.

What these authors got right is a key point stressed (in a complementary way,
with each lop-sidedly fixating on one aspect) by Kuhn and Popper: in order for
an observational or theoretical result to acquire and fully unfold its
scientific significance, it must cohere with our wider web of beliefs (see
Blackwell, 1969, esp. Pp. 140 for details; also Bonjour, 1985 for an in-depth
study of the broader epistemological point). We try to make sense of the
discovery against the backdrop of our prior knowledge.

Note that the latter comprises _both_ empirical-factual knowledge, as well as
theoretical knowledge. Hence, “what-that”-discoveries—phenomena hitherto
materially not yet demonstrated, but entailed by our background
beliefs—generate no less a tension in the total web of beliefs than “that-
what”-discoveries. Scientific efforts to confirm the former serve to alleviate
that tension—just like efforts to fathom enigmatic “what-that”-discoveries,
anomalies resisting comprehension within our old background knowledge. In
rough approximation of Kuhn’s account (§2.1), this process of integration
happens in two principal manners: through more conservative inclusion in, or
absorption by the existing body of background knowledge (with suitable,
“small-scale”, more cumulative modifications), or through larger-scale
revisions in our theoretical background. The tension that triggers the
subsequent integrative process is what Kuhn (1959) aptly calls “the essential
tension” for science, one of the main motors of scientific progress (cf.
Turner, 2018 for the specific case of cosmology). The urge to lessen the
tension, and the attendant need for integration, whereby coherence is restored
in our knowledge-_cum_ -discovery, constitutes the unifying thread of all
types of discoveries; it’s the common function in virtue of which motley
scientific results can be meaningfully subsumed under the umbrella term
“discovery”.

In the same vein, the change-driver model seamlessly subsumes _negative_
discoveries—in contrast to the rivalling accounts: the non-observation of a
predicted phenomenon (null-results e.g. for magnetic monopoles, or certain
particle Dark Matter candidates), impossibility proofs (e.g. G$\ddot{o}$del’s
incompleteness theorems), a counterexample, implausible consequences (e.g.
“ghosts” in particle-physics, or dynamical instabilities), etc. Due to their
negative content, such discoveries sit uncomfortably with the other
philosophical models. The change-driver model naturally accommodates them.
Negative findings of that sort not rarely are even more important than
positive ones—as Popper never tired of haranguing about.

Within the change-driver model, the problem besetting the standard accounts
that we monikered the “Problem of Theoretical Continuity” doesn’t arise. We
neither have to make strong and overly optimistic assumptions about what
science can and does discover (or what current science _has_ discovered) nor
does the model privilege our present scientific knowledge as the arbiter of
what to classify as a real discovery. The need lapses to postulate a strong
link between the scientific discovery in its historical understanding, and the
discovery as _we_ interpret it.

What advances science is—with details and specific judgements up to the
historians’ discretion—a historiographical question: whether, say, the
observations indicating the existence of galaxies outside of the Milky Way
impacted astronomy and cosmology must be investigated through historical
studies. Our present knowledge and conceptualisation/understanding of
discoveries stand in a loose and motley relationship to how the discoveries
were understood at the time (see also Chang, 2003).343434We don’t deny that
some continuity between past and present science can typically be identified
(see e.g. Bain & Norton, 2002). Our point is merely, in line with its non-
partisan position in the realism/anti-realism debate, that the change-driver
model of discovery is independent of any specific continuity thesis.  The
change-driver model purges the notion of discovery from residual “Whiggism” in
the other models: in judging what counts as a discovery, circumspect _history_
of science—not necessarily, let alone exclusively, contemporary scientific
understanding—matters.

The change-driver model is historically sensitive: to classify a scientific
result as a discovery doesn’t commit us to anachronisms; a result can be
granted that status on terms natural to its historical context. It allows us
to honour past theories’ achievements (without indulging in Whiggism). The
ether theory, for instance, entailed several genuine physical-material
discoveries (see e.g. Janssen & Stachel, 2004), as did Bohr’s model of the
atom. In the same vein, we can recognise the various explanatory and
evidential successes of now-defunct, but formerly rightly cherished theories,
such as the caloric theory (see e.g. Chang, 2003) or the Steady-State Theory
(see Kragh, 1996), as synthetic discoveries. 353535The latter case is
illuminating because it illustrates how a series of synthetic discoveries—a
complex and prolonged back-and-forth between positive and negative synthetic
discoveries about the Steady-State Theory—ultimately shifted evidential-
epistemic superiority from the Steady-State Theory to the Big Bang model.

An appealing by-product of this historical sensitivity is its modesty with
respect to current, more speculative research: without (prematurely) taking
sides, it’s consistent and natural to speak of theoretical discoveries in
string theory (e.g. in the context of what Dawid (2013) calls the unexpected
explanatory coherence argument for string theory), of material-physical
discoveries in MONDian phenomenology (see e.g. Merritt, 2021), or of—even if
perhaps evidentially not (yet) compelling—synthetic discoveries in
inflationary cosmology (see e.g. Guth, 2004).

The change-driver model of discoveries not only remedies shortcomings of the
extant accounts. It also has several _additional_ benefits.

What, according to the model, constitutes a scientific discovery lies on a
continuum. Assessing the significance of a scientific advance (or a particular
contribution to it) is ineluctably a somewhat vague affair. Typically, it
hinges on a historian’s particular perspective. Siding with a pluralist
approach to history (and philosophy) of science, we don’t consider this a
particular problem. It simply mirrors the complexity of history of science, as
well as that of science itself.

At the same time, continuity of discoveries doesn’t divest the change-driver
model of the ability to draw salient distinctions. The invocation of both
advances and the significance of certain results does rule out intuitive
cases. On the one hand, consider the case of students in curricular lab
classes, or when hitting on solutions of their assignments: they don’t make
scientific discoveries. These cases don’t advance our scientific knowledge
(although ideally they ought to advance the individual students’ knowledge);
they serve training purposes. A similarly unambiguous classification is
obtained for homely discoveries, such discovering that a marten has been
nesting in the attic over the summer. These are _mundane, not scientific_
discoveries; for the most part, they are irrelevant for science.

When it comes to _research_ , the picture becomes less clear-cut. Thereby, to
our minds, it gains in being realistic. Contributions can span a wide-range as
far as regards advancing science; the significance of contributions lies on a
spectrum. (Think of, say, nuclear fission vs. the recent discovery that viagra
cures jetlag in hamsters.) The extent to which a particular result contributes
to the advance of science—the extent to which the change-driver model’s second
clause is satisfied—is a problem that only historians of science (and363636In
the spirit of Chang’s (2004, 2008, 2016) “complementary science”, the
distinction between scientists and historians of science is, at best, blurry.
Historical analyses of scientific episodes can be, and often are,
contributions to science. scientists themselves) are competent to answer. It’s
incumbent on them to reconstruct the development of science in a coherent
manner; that reconstruction, then, substantiates the discovery’s significance.

This continuum aspect of scientific discoveries, together with the change-
driver’s science-inherent link to the social recognition and reward system for
discoveries (more on this below), also _explains_ another phenomenon that, on
the other models, looks puzzling—an apparently contingent, sociological fact:
why _aren’t_ all scientific discoveries celebrated equally? In particular, why
does the glory associated with a scientific discovery seem to be correlated
with the scientific impact it makes? The first discovered exoplanet, for
instance, made a big splash (with credit being assigned, discoverers’ names
being remembered, plenty of discussion and media attention, etc., see e.g.
Winn, 2023). Now discoveries of exoplanets are a dime-a-dozen; the reaction to
discovering a new one has calmed down. The change-maker model easily explains
this in a science-internal manner, vindicating the rationality underlying the
social practice: a discovery is, in the main, celebrated according to its
scientific value, its significance. The first exoplanet discovered validated a
range of observational techniques, instrumentation, theory; determining its
properties like mass, radius, composition, etc presented new problems to
solve. By the 5,000th exoplanet, the flurry of activity following such a
discovery has subsided; in terms of significance, scientific results of the
same kind have diminishing returns. On the change-driver model, their status
as discoveries pales—and concomitantly the occasion for accolades. For the
other accounts, by contrast, the discovery of the first and million-th
exoplanet are both discoveries. Nothing more, it seems, can be said—nothing in
particular about the rewards meted out to the discoverer.

With its emphasis on the progress of _science_ , the change-driver model has
ab origine a communal dimension: science is essentially a communal endeavour
(cf. Duerr, 2023 for a Popperian perspective). Accordingly, scientific
discoveries are advances within, and for, a scientific community. This
complements our above discussion of mundane and scientific discoveries: the
marten in the attic—no matter how personally momentous—constitutes a discovery
disconnected from the (any) scientific community.

An interesting problem case (other variants of which we’ll elaborate in more
detail in §3.4) concerns privately made discoveries, _potential_ scientific
discoveries, even of ground-breaking relevance— _had they had_ broader impact
(but didn’t, say, because the discoverer prescinded from publishing her
results). On the change-driver model, they fail to meet the criteria for
scientific discoveries: as such they require the connection with the actual
development of science; else they remain discoveries simpliciter. To our
minds, this consequence is plausible: it follows from the communal and
organisational structure of science, as an institutionalised practice, rather
than an intellectual activity of isolated individuals (see e.g. Ziman, 2002).

The model’s in-built communal dimension has two noteworthy corollaries; both
are germane to blemishes in Hudson’s account (§2.2). The first concerns the
priority condition. Discoverers are usually assumed to fulfil it. But why
demand that a discoverer be the first to make the discovery? Rather than
stipulating by fiat, the change-driver model can, to some extent, _derive_ it.

According to the model, temporal priority is, strictly speaking, inessential
for a scientific discovery: what matters instead is that the result in
question increases knowledge of the scientific community—and usually sparks
off further developments. More often than not, this is going to be correlated
with temporal priority. Nonetheless, the correlation doesn’t always hold:
unpublished work or publication in obscure journals may later be found to have
presaged a claimed scientific discovery. We bite the bullet that adverse
circumstances, or fatal decisions on the side of the researcher, can prevent
such discoveries simpliciter from becoming scientific ones (or, if one prefers
the modal paraphrase: they can prevent _potential_ scientific discoveries from
becoming _actual_ ones).

Secondly, recall one of our quibbles about Hudson’s account: which social
group is supposed to be relevant for judgments of temporal priority? In light
of the stunning scientific achievements of, say, Chinese science and the
Islamic world the question becomes especially pressing (with worries about
unacceptable eurocentrism looming). Hudson’s model ended up with a slightly
outr$\acute{e}$ answer; the other models skirted the question altogether. The
change-maker model, with its explicit community-relativity, embraces a
pluralism of communities: the notion of a scientific discovery is always
relative to a scientific community—i.e. relative to a local network of
inquirers with strong information links and a somewhat institutionalised form
of critical exchange, rather than to any _arbitrarily selected_ social group,
or (pace Hudson) to “all Earth-bound rational beings over the course of all
time”.373737To be sure, insofar as science has always been global (see e.g.
Poskett, 2022), any talk of local scientific communities remains, to some
extent, an idealisation that belies the more complex historical reality; ideas
and knowledge have (fortunately) always travelled across borders. Yet, this
idealisation underlying orthodox historiography of science has, we think,
value in at least a rough-and-ready sense. It’s beyond the present paper’s
ambit to question it.

Thanks to its in-built communal dimension, the change-driver model allows a
rational reconstruction of the normative aspects surrounding scientific
discoveries. We take this to amount to another score on the model’s
intensional adequacy.

First, let’s wonder: what underlies the general appreciation of scientific
discoveries? What makes them, in line with the prevalent attitude amongst
scientists, valuable? Bracketing all normative issues, the extant accounts
remain silent on that. The change-driver model, by contrast, gives a simple
answer: it’s arguably an intrinsic aim of science as an activity to
advance—which, as per the second clause, (2), of the model (§3.1), is what
scientific discoveries purvey!

Secondly, the change-driver model sheds light on the credit/recognition
practices regarding scientific discoveries: discoverers deserve credit for
having advanced science. The other models, by contrast, consign those
practices to the contingent side of science, white noise of human hustle and
bustle: they are traditionally banished to its “external history”, not
susceptible to further rational analysis—and maybe “of great interest to
empirical psychology; but […] irrelevant to the logical analysis of scientific
knowledge” (Popper, 2002b, pp.7). Construing scientific discoveries as drivers
of change yields a different verdict: these practices implement the “normative
structure of science” (Merton, 1942; see also Ziman, 2002), the complex set of
institutionalised action-guiding rules, aimed at the realisation of the aims
of science.

Most directly connected with the importance of scientific discoveries, visible
at the social level—in priorities disputes, and the general reward system
(prestige, prizes, and eponymy in particular)—are two norms of that “ethos of
science”, the institutionalised “complex of values and norms which is held to
be binding on the man of science” (Merton, 1973, pp.268). One norm is
originality, or the novelty of insights. A premium on a scientific result’s
originality incentivises researchers to strive for innovation. In order to
advance science, however, novel ideas in science must necessarily be
accompanied by “communism” or ”communalism”: they must be made publicly
available. Results can only unfold their potential for scientific progress if
disseminated in the scientific community (last not least, for further critical
scrutiny). Both norms, originality and communism, thus explain the
credit/recognition system in a science-_internal_ manner: those practices
reflect the norms inherent to science; through their institutionalised
implementation, they promote scientific progress. The change-driver model
hence is not only tied to the social practices surrounding scientific
discoveries. It also anchors them and their rationality in science itself (see
Merton, 1957 for a detailed analysis along those lines): _given_ the
institutional values and norms of science, scientific discoveries are indeed
worthy of applause.

Our account also facilitates the integration of discoveries into science
education. Kuhn (1962, ch. 11) points out that science textbooks often present
a simplistic and linear-cumulative history of scientific progress. In that
Whiggish narrative, individuals make discoveries at specific times
contributing to the steady, inexorable march of science towards its present-
day climax. Such textbook mythology fails to capture the complexity of the
history of science. Yet, despite the misleading nature of “great men of
science”-histories, even Kuhn notes that identifying “heroes” is often
expedient in science education (ibid. 139).

The change-driver model steers a middle course between the two extremes. On
the one hand, although an element of presentism lingers in identifying who
discovered the various features of _present_ science, this needn’t be the
tidied-up “textbook science” Kuhn warns against. First, while we are happy to
label individuals as discoverers, our account is also inherently communal. To
be a change-maker is to change something about one’s community; it’s not an
epiphany of, nor for, lonely geniuses (see also Michel, 2022, sect.2.5.2).
Further, since it’s the historian of science who has to identify the change-
makers of scientific progress, the model has the flexibility to be as complex,
rooted in historical context, and messy as required to convey the true
significance of each discovery.

On the other hand, the model recognises that discoverers, who made exceptional
contributions to the field, can serve as role models and exemplars (a point
stressed especially by Duhem, see e.g. Stump, 2007). In line with Chang’s
(2021) plea for pluralism in the history of science, we are also sympathetic
to using (without, obviously, distorting the facts!) historical figures and
episodes to illustrate exemplary use of methods, ideas and practices that
current science still employs. A presentist approach to history is a possible
perspective amongst many. And even if their methods and practices have become
outdated, those discoverers’ attitudes, behaviours, and sagacity and other
intellectual (as well as moral) virtues are of pedagogical/didactic interest.
Teaching such exemplars is arguably indeed “crucial to maintaining the values
of the institution of science—the specificity and unique character of
knowledge it produces, for example” (Pestre in: Caneva, 2001, p.20, fn.59).

###  3.4 Problem cases and responses

We’ll close our discussion of the change-driver model by inspecting potential
problem cases for—prima facie implausible or repugnant consequences of—the
model, and proffer rebuttals.

The fine-graining problem. Doesn’t our account demote discoveries to fleeting
surface phenomena that disappear once one looks into greater details? The more
closely one zooms in on an episode in the history of science, the worry goes,
the more continuity with earlier (and later) research is revealed—the more
elusive a discovery’s significance becomes. Consequently, the notion of a
scientific discovery, as in the change-maker model, would seem to fade away
into an artefact of a surface-level description, denuded of deeper substance.

Our response is that this fine-graining problem is a variant of the problem of
special sciences (Fodor, 1974, 1991): the fine-graining problem presumes that
the macro-historical details can be reduced to micro-historical details—that
macro-historical descriptions lack autonomy as explanatory frameworks, and
that they are replaceable by micro-historical ones. We reject this premise as
reductionist (cf., for instance, Bunge, 2004). Macro-historical accounts in
the history of science (or other aspects of history) are illuminating in a way
that more fine-grained ones (insofar as they are even available) aren’t;
certain patterns are only visible at that higher, more coarse-grained level of
description. This, to our minds, suffices to take these descriptions
seriously. Scientific discoveries play a role in those descriptions, typically
contributing to explanations of a discipline’s historical trajectory.
Accordingly, discoveries are legitimate “higher-level” concepts, with
explanatory clout (cf. Dennett, 1991).

The omnipotent plagiarist. Take your favourite (bona fide) discovery. Imagine
that whom you consider its discoverer actually plagiarised her or his result
from an unknown original discoverer OD. The plagiariser effaced all traces of
his crime (obliterating his victim, OD, from the face of history). The
discovery subsequently made an impact on the scientific community—falsely
giving credit to the cunning plagiarist P. Did P, on the change-driver model,
make the discovery then–rather than OD? The answer is—no! For the chain of
developments leading to the scientific advances originates _in OD’s_
discovery: P _learnt about_ the result in question from OD, and then resolved
to assassinate OD and erase all traces. OD made the scientific discovery—even
though no one (apart from the plagiariser) would ever know. That history of
science spuriously identifies the plagiariser P as the discoverer discloses no
defect of the change-maker model. It merely reflects the fallibility of
historical knowledge—an insuperable limitation of our general epistemic
predicament.

Scientific discoveries amidst Orwellian totalitarianism. Consider state-
enforced négationnisme about some particular scientific discovery, say in an
Orwellian state where that discovery which gainsays the ruling ideology is
effectively suppressed. Doesn’t the change-driver model grant the powers-that-
be the ability to determine what counts as a discovery? Isn’t, in short, the
change-driver model too sensitive to vagaries of political power?

We regard this merely a feature, not a bug of the model: what the scenario
illustrates is that science can only flourish in societies with a modicum of
freedom. Political power structures can prevent a scientific result from
advancing science. Thereby the discovery is prevented from becoming a
scientific one. What makes such an act of successful _n
$\acute{e}$gationnisme_ so pernicious is less that it deprives a discovery
from its elevation to a fully scientific one (or that it robs the scientists
of their well-earned recognition). Rather, it’s that the act damages science
itself—by stifling its progress, viz. by obviating the possibility of
discoveries. We descry no implausibility in this.

Swampman scenarios (cf. Davidson, 1987). Someone, P, after laborious years of
continued efforts, is just on the verge of making a great discovery—when a
lightning hits them, annihilating all traces. A few seconds later another
lightning strikes someone else P’. Instead of annihilating her or him, this
time the lightning infuses in them—a flash of inspiration—all the requisite
details for duplicating the discovery that the just-annihilated person was
about to make. The discovery is disseminated, and makes a significant
contribution to the advancement of science. According to the change-maker
model, P’ made a discovery—rather than P.

Should one demur at this conclusion? We don’t think so. True—P’ was lucky,
whereas P was damn unlucky. Lamentably, that—the ineliminability of a quantum
of luck for the heroes of science and, often, bad luck for those more tragic
figures whose toils don’t bear fruit—is a generic feature of science and
scientific discovery (see also Copeland, 2018). Any model of discoveries faces
this element of fate; the change-maker model is no worse off than other
accounts.

The discovery of America. Imagine an ibn-Batūtta-like explorer E, embarking on
a daring mission to map unexplored continents and conduct ethno-
anthropological research.383838 We can make the example even more vivid by
imagining E to discover a scientifically highly developed exra-terrestrial
civilisation on an exoplanet. As she lands on a populated continent never
before visited by anyone from her culture back home, E diligently records the
location, and shares her studies with her community. Now, does E genuinely
discover the continent and its indigenous population? One might hesitate to
answer affirmatively: the indigenous inhabitants are obviously well-acquainted
with their own land and culture!

But this is the verdict of the change-driver model: the continent and its
population have been discovered—a scientific result for geography and
anthropology of E’s scientific community. Recalling the communal nature of
science, we find nothing objectionable in this consequence. While E’s work
might have not changed anything in the science of the native people (assuming
that they practise science), it _would_ impact E’s scientific community.

##  4 Illustration: the discovery of the expanding universe

The change-driver model purports to take history seriously. What better
episode to apply it to in order to showcase the model’s virtues than “one of
the major milestones in the development of the science of astronomy during the
last 100 years, […] one of the founding pillars of modern cosmology” (IAU,
2018): that the universe expands. However, who—if anyone—made this discovery
remains contentious. After reviewing the main historical developments393939We
follow the presentations in North (1965, Ch.5-7); Smith (1983, Ch.5); Ellis
(1989); Kragh (2007, Ch.3), and Nussbaumer & Bieri (2009), to which we refer
the interested reader for details. (§4.1) we’ll here compare the verdicts of
the extant accounts of discovery for the case of the expanding universe
(§4.2). §4.3 will apply the change-driver model’s perspective.

###  4.1 Historical overview

The gates to modern theoretical cosmology were flung open in 1917, when—less
than two years after completing his new theory of gravity, general relativity
(GR)—Einstein applied it to the universe as a whole (see e.g. O’Raifeartaigh
et al., 2017 for details). This was the first cosmological model, an exact
solution of GR’s field equations for the cosmos at large. In it, Einstein
assumed, matter was distributed uniformly (i.e. homogeneously and
isotropically), and the universe as a whole finite (i.e. its spatial geometry
closed). Einstein’s model quickly stimulated further investigations—the
pioneering work of modern cosmology’s founding fathers (amongst them,
Friedmann, de Sitter, Eddington, and Lemaître, about whom we’ll hear more
momentarily).

Two peculiarities of Einstein’s result are worth adverting to. First,
Einstein’s primary motivation wasn’t to apply GR to a new domain—one where one
might perhaps expect incisive discrepancies with Newtonian theory. He didn’t
intend his model as a realistic description of the universe, apt for empirical
tests (nor was Einstein even particularly informed about the state of the art
in astronomy). “Instead, Einstein’s foray into cosmology was a final attempt
to guarantee that a version of ‘Mach’s Principle’ holds” (Smeenk, 2013,
p.228), i.e. the idea that inertia is fully determined by matter. In that
regard, de Sitter’s work soon dashed Einstein’s hopes.

Secondly, and of key relevance for our purposes, Einstein’s model was, by
fiat, static: the universe it represented stays the same across time. In order
to balance out the gravitational attraction of matter, and thereby to achieve
the demanded staticity, Einstein had to modify his original field equations of
1915—by including the cosmological constant term $\Lambda$ (introducing a free
parameter). “Although he originally treated this as only a simplifying
assumption, Einstein later brandished the requirement that any reasonable
solution must be static to rule out an anti-Machian cosmological model
discovered by de Sitter. Thus […] Einstein was blind to the more dramatic
result that his new gravitational theory naturally leads to dynamical models.
Even when expanding universe models had been described by Alexander Friedmann
and Georges Lemaître, Einstein rejected them as physically unreasonable”
(op.cit., p.229). In clinging to the static nature of the universe Einstein
conformed to the prevailing consensus, rooted in the time-honoured doctrine of
the immutability of the heavens404040It’s imperative to appreciate how
different the received wisdom about the universe was in 1917: recall that
Einstein was writing two years before “The Great Debate” over the size of the
Milky Way and the existence of “nebulae”, i.e. extragalactic systems (see e.g.
Smith, 1983, Ch.1-3)!—and a tenuous observational basis in “the small
velocities of stars” (Einstein, 1917, p.139).

Throughout 1916 and 1917, de Sitter propounded his own model of a homogeneous
and isotropic universe (de Sitter 1916a; 1916b; 1917). In contrast to
Einstein’s model, it was devoid of matter; the model contained only a
cosmological constant $\Lambda$. Likewise in contrast to Einstein, de Sitter
“took his model seriously enough to study its observational consequences, as
we will see” (Smeenk, 2013, p.244).

Over the next decade, Einstein’s and de Sitter’s models remained the only
well-known relativistic models of the universe; most cosmological
investigations focused on those two rivalling models. “The major conceptual
innovation introduced by Einstein was the very possibility of a mathematical
description of the universe as a whole, but it was not immediately clear what
observational and physical content these abstract models possessed” (op.cit.,
pp.242).

De Sitter makes two points important for our story. First, unlike Einstein, he
countenanced a dynamical universe as a physical possibility: “(i)n [de
Sitter’s model—in contrast to Einstein’s] […], if there is more than one
material particle these _cannot be at rest_ , and if the whole world were
filled homogeneously with matter, this could not be at rest without internal
pressure or stress” (1917, p.18, our emphasis). This wasn’t quite tantamount
to entertaining an expanding universe; the de Sitter model was generally
considered a static solution. De Sitter’s spacetime metric didn’t contain a
time-dependent scale factor (describing the change of physical spatial
distances across time). In 1922, however, Lanczos showed how the de Sitter
model could, through a change of coordinates, be interpreted as an expanding
universe with a (time-dependent) hyperbolic, spatial geometry.414141In his
first article on cosmology (1925), Lemaître also introduced new coordinates
that rendered the de Sitter metric dynamical (with vanishing spatial
curvature, and an exponentially increasing scale factor). That it actually
wasn’t a static model took a surprisingly long time to realise. The waters
were muddied by confusion over artefacts due to coordinates (a common ailment
of early work in relativistic physics, see e.g. Kennefick, 2007, Ch. 4&5).

Secondly, whereas Einstein adamantly spurned non-static models as unphysical,
de Sitter (seconded, in 1925, by Lemaître) hailed the dynamical character of
his model as an avenue for further research (e.g. 1917, p.28): might it, he
mulled, explain the receding motion of spiral nebulae? Indeed, de Sitter
(1917, sect. 7) predicted a distance-dependent redshift in the spectral lines
of far-away objects. Using available data, he even calculated the effect.
Moreover, also methodically, he “took an important step in suggesting that the
movements of the spiral nebulae rather than the stars (which Einstein had
focused on) should be used as gauges of cosmic structure on the largest
scales. The nature of the redshift effect and the precise functional
dependence of redshift on distance for the De Sitter model were both matters
of substantial controversy for the following decade and a half” (Smeenk, 2013,
p.249). De Sitter initially derived—erroneously—a _quadratic_ dependence of
redshift on distance. Later, Weyl (1923) claimed that if test particles were
introduced on geodesics emanating from a common point in the past, objects
would appear to recede approximately according to a _linear_ redshift-distance
relation. Introducing matter in a different manner would lead to different
predictions. Improving on Weyl’s result, Robertson (1928) confirmed the linear
redshift-distance relation.

The prospect of predicting redshifts was enticing. De Sitter’s model “soon
became a foundation for further theoretical work, among both astronomers and
mathematicians” (Kragh, 2007, p.136)—including Eddington and Weyl. In 1909,
Slipher had begun measuring redshifts at the Lowell Observatory, taking the
spectra of spiral nebulae. In 1917, he published his results: all 25 spiral
nebulae exhibited quite large blueshifts or redshifts. The high radial
velocities invited an interpretation as recession velocities, resulting from
the (standard) Doppler effect. The redshifts, Slipher averred, may have been
the result of the Earth’s motion through space: the nebulae we moved towards
would be blueshifted; the ones we moved away from would be redshifted. But by
the early 1920s, the redshift observations of spiral nebulae “left little
doubt that there was a systematic recession. [….] (F)rom about 1920 there
developed a minor industry based on the [Einstein’s and de Sitter’s
respective] models. It was predominantly a mathematical industry” (Kragh,
2007, p.136). The next milestone would be to build a bridge to physics, and
astronomical observations in particular. “The question of the relationship
between cosmology and the observed redshifts remained unresolved for a decade
or so, for other reasons, because it was difficult to distinguish a
cosmological redshift (the de Sitter effect) from gravitational redshifts and
the Doppler shifts caused by relative motion” (ibid.).

For some time, the Einstein and de Sitter cosmologies were the only well-
developed cosmological solutions to GR. Two papers, one in 1922 and the other
in 1924 (as well as in a semi-popular book of 1923, in Russian), ventured
further. In them, Friedmann disclosed a much larger class of solutions: its
members corresponded to matter-filled universes that _expanded_. Friedmann
procured nothing short of “a complete and systematic analysis of the solutions
of Einstein’s cosmological equations that went beyond earlier analysis”
(Kragh, 2007, p.141). The Einstein and de Sitter model turned out to be
special cases of a richer space of solutions; these solutions demonstrate “the
possibility of a world in which the curvature of space is independent of the
three spatial coordinates but does depend on time” (Friedmann, 1922, p.377).
Specifically, Friedmann had solved Einstein’s field equations of GR for open
and closed homogeneous and isotropic universes with time-_dependent_ radii of
curvature. For different values of $\Lambda$, Friedmann explored the
consequences of cyclical models: the universe, in those solutions,
periodically expand and contract, undergo accelerated expansion, or contract
back into a point. With Friedmann, dynamical cosmological models of GR were
squarely on the table—as mathematical possibilities. Friedmann _explicitly_
didn’t connect his models with astronomical observations: “(o)ur information
is completely insufficient to carry out numerical calculations and to
distinguish which world our universe is” (ibid., pp.385-386). No references to
astronomical data are included in Friedmann’s papers. For Friedmann, his
analysis seems to have been first and foremost a _mathematical_ exercise (see
also Kragh & Smith, 2003, pp.146). Did Einstein and others overlook
Friedmann’s work? Not at all: he, like most others, simply didn’t attribute to
Friedmann’s non-static cosmological models any physical significance.
Friedmann had ushered in an “unnoticed revolution” (Kragh, 2007, p.140). Still
in 1927, firmly in the grip of the ruling paradigm of a static universe,
Einstein unabashedly dismissed non-static cosmological models as, from a
physical perspective, “tout $\grave{a}$ fait abominable”.

The occasion for Einstein’s aspersion was a meeting with Lemaître. It
concerned cosmological models for an expanding universe. They had been the
subject of an article by the latter a few months earlier (1927) that “a friend
had made (Einstein) read” (Lemaître as quoted in Luminet, 2013, p.1625). Its
agenda Lemaître had already foreshadowed two years earlier: “Eddington [1923]
writes […]: ‘It is sometimes urged against de Sitter’s world that it becomes
non-statical as soon as any matter is inserted in it. But this property is
perhaps rather in favor of de Sitter’s theory than against it.’ Our treatment
evidences this non-static character of de Sitter’s world which gives one
possible interpretation of the mean receding motion of spiral nebulae”
(Lemaître, 1925, p.41). Unravelling this thought, Lemaître’s 1927 _opus
eximium_ “combines the advantages of the Einstein world and the de Sitter
world” (Kragh, 2018, p.1334) in order to find a solution to the Einstein field
equations that satisfactorily accounts for both the redshifts and the
existence of matter. This led Lemaître to a cosmological model with a _time-
dependent_ radius of curvature—corresponding to an expanding, homogeneous and
isotropic closed universe. In the main424242A qualification is due: Lemaître
included thermodynamic aspects. “Whereas Friedmann had ignored the radiation
pressure, it was an important quantity in Lemaître’s more physical and
ambitious project” (op.cit., p. 1338). Lemaître’s formal results duplicated
Friedmann’s; to his work Lemaître was only alerted in the above-mentioned
meeting with Einstein. The crucial innovation, as far as the physical thrust
of Lemaître’s paper is concerned, was his renunciation of the ruling paradigm
of staticity: Lemaître—“in stark contrast to Friedmann” (op.cit.,
p.1334)—audaciously suggested that _our_ universe _in fact_ grew in size.
“What distinguished Lemaître’s paper over Friedmann’s was in particular his
analysis of the galactic redshifts and his clear recognition that they were
caused solely by the expansion of space” (op.cit., p.1338)—that is, the
realisation “that the redshifts were caused not by galaxies moving _through_
space, but by galaxies being carried _with_ the expanding space” (Kragh, 2007,
p.144).

Theoretically, Lemaître derived an approximately linear relationship between
the distances and recession velocities of extragalactic nebulae (i.e.
galaxies)—in the form still used today (i.e. with the proportionality constant
given by the “Hubble-parameter”, the ratio between the rate of change of the
scale factor, and the scale factor). He then connected his solution to
astronomical observations. Relying on averaged data for the ratio between
radial velocities (through data due to Str$\ddot{o}$mberg and Slipher) and
distances (through data due to Hubble), Lemaître calculated a rough estimate
of the “Hubble-parameter”. What, in other words, Lemaître thereby did
accomplish was to empirically determine the proportionality coefficient of his
theoretically derived linear distance-velocity relationship; he thus made a
genuine prediction—that, once sufficiently accurate data were available, it
would corroborate that linear relationship (roughly with the proportionality
coefficient Lemaître had determined). By contradistinction, what he _didn’t_
do was to provide original empirical evidence for that relationship; he
didn’t, and couldn’t yet, verify his prediction.

“Lemaitre’s prediction of an expanding universe made no more impact than did
Friedmann’s work. On the contrary, his paper seems to have been almost
completely unknown and to have received no citations from other scientists
until 1930” (ibid.). The reasons plausibly lie in the relative obscurity of
the journal, the _Annales de la Soci $\acute{e}$t$\acute{e}$ Scientifique de
Bruxelles_, in which he had decided to publish it (in French).434343Luminet
(2013, p.1625) locates the “main obstacle to a larger diffusion of Lemaître’s
article” in the fact “that most of the physicists at the time, such as
Einstein and Hubble, could not accept the idea of a non-static universe.”
According to O’Raifeartaigh (2020, p.9), “it is very plausible that the
observational data cited by Lemaître in support of his model were not
sufficiently robust to cause Eddington and others to consider expanding
cosmologies.” Through the hands of Eddington, three years after the paper’s
appearance, the tide would turn for Lemaître’s fame. But first someone else
would step into the limelight: the very person usually, but contentiously,
credited with having discovered the expanding universe.

During the mid-1920s, Hubble had ascended to international renown as an
astronomer at the world’s most powerful telescope, the Mt. Wilson Observatory.
His meticulous observations conclusively refuted the hitherto prevailing view
that nebulae were part of the Milky Way; being too far away, the nebulae
formed galaxies in their own right.

Hubble was thus well-prepared for the next problem he tackled—the redshifts of
galaxies. As we saw above, both theoretically and observationally, a
correlation had been postulated between redshifts and distance of
extragalactic nebulae: they appeared to flee from earth the faster, the
farther away they were. But no consensus existed as to the functional
relationship—or even the reliability of such a systematic correlation between
observed redshifts and distances (see also O’Raifeartaigh,
2020).444444Especially noteworthy amongst these early empirical endeavours
prior to Hubble was the work of Wirtz (1922, 1924). Despite too insignificant
a sample size for further conclusions, he was able to demonstrate (upon
suitable grouping of the data) a systematic positive correlation between
redshift and distance (and interpreted this as a confirmation of de Sitter’s
model), see Duerbeck & Seitter, 1990 for details. A similar result was
achieved by Lundmark (1924, 1925), who drew on Slipher’s velocity measurements
and his own distance measurements.  At a meeting of the Astronomical Union
1928, Hubble probably learnt from conversations with de Sitter and others how
his previous work and expertise might be relevant for on-going work in
theoretical cosmology. The study Hubble embarked on would, Hubble hoped, also
enable a critical test between Einstein’s and de Sitter’s model of the
universe.

A significant leap forward came with the discovery that Cepheid variable stars
can function as ‘standard candle’ distance indicators:“a formidable obstacle
had to be overcome before securing a relation between redshift and distance
that would be convincing to the majority of astronomers: the accurate
determination of the distances to the [spiral galaxies]. But in 1923 and 1924
this barrier was in part removed when Hubble discovered Cepheid variables in
nearby spiral nebulae. Before Hubble’s observations of Cepheids, astronomers
had been restricted almost entirely to the crude distance indicators provided
by the novae, the apparent luminosities and the apparent diameters of
extragalactic nebulae” (Smith, 1983, p. 175).

Cepheids denote a group of stars with a variable brightness, pulsating with a
well-defined, stable period. Leavitt (1908) (and Leavitt & Pickering, 1912)
had shown that the length of a Cepheid’s period is correlated with its
intrinsic luminosity: the longer the period, the brighter the Cepheid.
Together with Hertzsprung’s (1913) calculation of the zero-point luminosity
and calibration of the period-luminosity relation (by measuring the distance
to Cepheids in the Milky Way through parallax), Cepheids could thus be
utilised as so-called standard candles, i.e. as means for determining cosmic
distances. Hubble hadn’t observed Cepheids in every galaxy he had redshift
data for. (Individual Cepheids are difficult to resolve at high distances, and
don’t occur in all galaxies.) So he calibrated other assumed standard candles,
such as the brightest star in a galaxy or the total brightness of a galaxy, to
determine the distance to galaxies without observed Cepheids.

Plotting the distances of the galaxies (measured by himself) against their
velocities (essentially drawing on measurements by Slipher and Humason),
Hubble (1929) “(established) a roughly linear relation between velocities and
distances among nebulae for which velocities have been previously published”
(p.173). “(M)any commentators have noted that the quality and quantity of the
data shown on Hubble’s graph only marginally supported his conclusion of
linear relation between redshift and distance for the nebulae […]. However,
the graph marked an important turning point […]” (O’Raifeartaigh, 2019, p.9).
The data on which Lemaître had relied in 1927, in particular, was contaminated
by significant uncertainties due to scatter. The linear redshift-distance
relation dimly discernible in Hubble’s data could at best count as
preliminary: “the nebular distances were established using a method that was
prone to large errors” (op.cit., pp.8). Hubble’s subsequent paper, co-authored
with Humason (Hubble & Humason, 1931) dispelled lingering scepticism. “The
linear correlation between redshift and distance seemed to be even clearer
than before and effectively ended the debate on the existence of a linear
relation” (Kragh & Smith, 2003, p.150).

How did Hubble interpret the empirical finding? He never—throughout his
life—unambiguously championed its interpretation as evidence of an expanding
universe (see op.cit., pp.151 for details). In 1929, Hubble had little to say
on the interpretation of his data except that it could be a manifestation of
the “de Sitter effect” (p.173): “(i)n the de Sitter cosmology, displacements
of the spectra arise from two sources, an apparent slowing down of atomic
vibrations and a general tendency of material particles to scatter. […] The
relative importance of these two effects should determine the form of the
relation between distances and observed velocities” (ibid.). No mention is
made of an expanding universe. Also later on, Hubble remained, at best,
agnostic about that now-standard interpretation; deferring its interpretation
to others (as he expressly wrote in a letter to de Sitter, quoted in e.g.
Luminet, 2015, p.5), he was wont to underscore the empirical/phenomenological
nature of the linear redshift-distance relation.454545Indeed, that
interpretation ran into a chronic embarrassment: the age problem. As implied
by that interpretation, given Hubble’s measurements, the cosmos would be
younger than the Earth (as inferred from radioactive decay) or the oldest
known stars—a glaring absurdity (see also Grøn, 2018, p.13). In line with
this, Hubble “was not aware that the proportionality factor between redshift
and distance, wrongly named the ‘Hubble constant’ was not a constant since it
varies with time” (ibid.)—a variation that follows directly from interpreting
the redshift-distance relation in terms of an expanding universe.

Hubble’s paper fell on fertile soil. By and large, it had dawned on the
astronomy community that Einstein’s and de Sitter’s cosmologies might be
inadequate. The question of making sense of the redshift-distance relation