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7 Conclusion: Theoretical Case-Based Philosophical Practice
T. Knuuttila and A. Loettgers
2016) does not lend credence to the idea that they argue for their philosophical
claims by simply confronting them with historical cases—or constructing the cases
according to their preferred theory (cf. Pitt 2001). Does this mean that historical
case studies in philosophy of science should be understood as interpretative activity
investigating scientific concepts, norms and practices, as Schickore has suggested?
Our answer to this question is positive, but we do not see that it would need to
imply either rejecting the evidential role of case studies (cf. Schickore 2011), or
compromising, or lessening, their evidential value (cf. Kinzel 2015). In our view,
philosophers of science usually use case studies as vehicles of theoretical reflection,
as resources in examining, questioning, and developing philosophical concepts and
accounts. In that use evidential and hermeneutic roles go hand in hand, informing
each other. Thus the three case studies presented in this paper serve as examples of
case-based theoretical philosophical practice that is underlined by the way each of
them uses the strategy of contrasting partially similar, and partially different scientific
examples. The use of the contrasting example highlights the conceptual distinctions
How should one, then, understand the philosophical case-based theoretical practice? The first thing to notice is that it is difficult to recognize it, if one approaches
philosophy as an activity that aims only at a general/rational reconstruction of scientific activity (although that would also need historical and empirical knowledge,
if only to recognize what constitutes, in fact, successful science). It seems that this
kind of conception of the philosophy of science lies behind the various iterations
of the claims that scientific case studies cannot give evidential support for philosophical positions. But clearly, philosophical theorizing also contains an important
descriptive component as well as being often more local and tentative in nature—as
the practice-oriented philosophy of science has recently shown.
If one looks at the use of historical case studies as vehicles for philosophical theorizing, nothing very special seems to be going on there. Also in scientific research
using case studies as a resource for investigation one has to negotiate the relationship
between the generalizable insights and the context-specific details. Even in the physical sciences single cases and experiments are sufficient for theorizing, as ShraderFrechette and McCoy (1994) point out in their study of case-based reasoning within
ecological sciences. According to them, ecologists often prefer case-specific knowledge coupled with conceptual and methodological analysis to “ecological theorizing
based on untestable principles and deductive inferences drawn from mathematical
models” (p. 244). The case-specific local knowledge allows various kinds of inferences: they can be local to local, or local to many. In local to many reasoning, the
local knowledge is desituated to a more generic level, or used to construct typical
representatives or exemplars (see Morgan 2014).
What needs to be recognized is that most scientific knowledge is local, or constructed from the local knowledge, being subject to various initial conditions and
environmental contexts. Moreover, while case studies provide a springboard for theorizing and generalization, they are often also used to question earlier held theoretical
views, or their generality. The case study methodology has also advantages that spring
forth from the way the evidential is woven together with theoretical. A historical case
8 Contrasting Cases: The Lotka-Volterra Model Times Three
study typically presents “a complex, often narrated, account that ... contains some
of the raw evidence as well as its analysis and that ties together many different bits
and pieces in the study” (Morgan 2012, p. 668). Thus narrative becomes a way to
deal with what Morgan calls “evidential density,” which contributes to theoretical
development by offering rich resources for a critical study of different theoretical
perspectives. This evidential richness is clearly one of the benefits of case studies:
many relevant factors do not need to be abstracted away or shielded, as with laboratory studies and mathematical modeling. Consequently, it seems a mistake to try
to tease the evidential dimension of case studies apart from their conceptual and
interpretative content. Both are woven together in the theoretical narrative that aims
to integrate different kinds and bits of evidence by showing their interdependence
(Morgan 2012, p. 675). This theoretical-cum-conceptual modality of case studies is
so strong that even when case studies succeed to identify a novel interesting phenomenon, like the “street corner society” (Whyte 1943), “the community’s response
was to understand the phenomena revealed as potentially generic” (Morgan 2012,
It is our claim, then, that the key to the epistemic value of case studies, in philosophy of science, like in both natural and social sciences, lies in the way they
weave together different kinds of evidence with the conceptual analysis and theoretical development. The observation that the same cases may be interpreted differently does not seem to us so grave an objection, since, as pointed out by numerous
scholars, case studies often breed new interpretations of the same cases, as well
as attempts to confirm the results by new case studies and independent data (e.g.
Shrader-Frechette and McCoy 1994). The three cases provide a good example of
this practice of presenting related case studies. As we have argued, they are largely
in agreement concerning Volterra’s work,23 and the theoretical and interpretative
element can most clearly be located to how Volterra’s work is contrasted with the
work of other scholars: Mendeleev, Darwin, and Lotka.
Finally, we remain skeptical of the idea that to justify case study methodology,
the cases should be typical of their kind—how do we know the typical without
any cases?—or somehow important or critical. The scientific record does not seem
to lend support to these kinds of claims either. Ankeny (2012) argues concerning
developmental biology that many model organisms used as kind of “cases” are now
regarded as presenting typical patterns of phenomena, while they were often originally selected for study for other reasons, such as convenience or ease of experimental
manipulation. And even when they turned out atypical, they still continued to provide a focal point in the field, permitting investigation of variations in phenomena or
processes. We see this kind phenomenon taking shape also with the three case studies
on Volterra, each of which presents variations on the theme of modeling, delineated
with the help of contrasting Volterra’s work with that of other theorists.
23 Even though the differences between the three case studies with respect to Volterra’s work were
more substantial, such underdetermination of theories by data would be a common feature of other
scientific practices, too.
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Gone Till November: A Disagreement in
Abstract The present paper examines an episode from the historiography of the genesis of general relativity. Einstein rejected a certain theory in the so-called “Zurich
notebook” in 1912–13, but he reinstated the same theory for a short period of time
in the November of 1915. Why did Einstein reject the theory at first, and why did
he change his mind later? The group of Einstein scholars who reconstructed Einstein’s reasoning in the Zurich notebook disagree on how to answer these questions.
According to the “majority view”, Einstein was unaware of so-called “coordinate
conditions”, and he relied on so-called “coordinate restrictions”. John Norton, on
the other hand, claims that Einstein must have had coordinate conditions all along,
but that he committed a different mistake, which he would repeat in the context of
the famous “hole argument”. After an account of the two views, and of the reactions
by the respective opponents, I will probe the two views for weaknesses, and try to
determine how we might settle the disagreement. Finally, I will discuss emerging
The present paper examines an episode from the historiography of general relativity
(GR) that exhibits methodological problems of history and philosophy of science.
These problems emerge because there are two competing accounts of an important
episode from Einstein’s long path to GR.1 The fact that two competing accounts exist
is not particularly exciting in itself—many episodes from the history of science have
been retold in many, often incompatible ways, and a plurality of accounts need not
be a sign of fundamental methodological problems. Plurality can be due to different
sources; sometimes new sources are discovered; the same episode can be presented
from different vantage points, and approached with different questions; new scientific
articles relevant to the present paper can be found in Janssen et al. (2007a, b).
T. Räz (B)
Universität Konstanz, FB Philosophie, 78457 Konstanz, Germany
© Springer International Publishing Switzerland 2016
T. Sauer and R. Scholl (eds.), The Philosophy of Historical Case Studies,
Boston Studies in the Philosophy and History of Science 319,
knowledge can deepen our understanding of an episode, making previous accounts
obsolete. This will lead to different accounts of the same historical episode in a
natural and unsurprising manner.
The present case is different. The two competing views of the episode exhibit
a considerable unity in perspective, methods, and sources. The Einstein scholars
defending the diverging views worked over a period of ten years on a reconstruction
and interpretation of one of the most important sources of Einstein scholarship, the
“Zurich notebook”.2 This long and close collaboration—I will call it the “genesis
collaboration”—resulted in a jointly authored book, the four-volume opus magnum
on the genesis of GR, Renn (2007). Despite the close collaboration, diverging views
of crucial turning points of the genesis of GR have emerged. A contribution by John
Norton defends a “minority view” of the episode in question, while the rest of the
genesis collaboration, notably Jürgen Renn, Tilman Sauer and Michel Janssen defend
what I will call the “majority view”.
What is the disagreement? Einstein rejected a certain theory in the Zurich notebook
in 1912–13, while the very same theory was reinstated for a short period of time in the
November of 1915. Why did Einstein reject the theory in the notebook, and why did
he change his mind in November 1915? The majority claims that there is one major
difference between the first and the second period, Einstein’s awareness of so-called
“coordinate conditions”. This is a now-standard mathematical procedure for bringing
the field equations of GR into correspondence with Newtonian gravitational theory.
The majority argues that Einstein was unaware of coordinate conditions at the time of
the notebook, and that he relied on so-called “coordinate restrictions”, which severely
limited the generality of the field equations and made the theory unacceptable. Only
when he became aware of coordinate conditions did the theory become acceptable
again. Norton finds this story implausible. He claims that Einstein must have had the
modern notion of coordinate condition all along, but that he committed a different,
more elaborate mistake. Importantly, this is a mistake that Einstein would repeat in
the context of the famous “hole argument”, a major roadblock on the path to the final
theory of GR.
I will discuss methodological issues that arise from this non-trivial disagreement.
Is this a dispute that cannot be settled despite a unity of evidence and methods?
There is hope, I will argue, that we can dissolve the dispute. We can do better in
the interpretation of the available evidence, in the reconstruction of the scientific
and mathematical context of Einstein’s struggle, and we can challenge the internal
consistency of the two views. However, there are also fundamental methodological
problems that we have to navigate. There are boundary conditions of rationality that
enter into the reconstruction of historical episodes, for which there is no clear-cut
I provide a short introduction to the history of GR and to the most important
concepts in the upcoming section. I have tried to make the technical subject-matter
of the episode accessible to non-specialists as much as possible. I then give an account
the introduction in Janssen et al. (2007a) for remarks on the collaboration between Jürgen
Renn, Tilman Sauer, Michel Janssen, John D. Norton, and John Stachel.
9 Gone Till November: A Disagreement in Einstein Scholarship
of the two views, and of the reactions to the views by the respective opponents. After
reviewing the arguments, I will probe the two views for weaknesses, and try to
determine how we might settle the disagreement based on the available evidence,
and on other considerations. Finally, I will discuss emerging methodological issues
based on the previous discussion, and on methodological remarks by the parties
9.2 A Bird’s Eye View of the Episode
The story of the genesis of GR can be told in the form of a drama in three acts.3 The
main character is Einstein, with appearances by other famous physicists and mathematicians, notably his friend Marcel Grossmann, as well as various mathematical
and physical theories and concepts. The premise of the drama is that not all is well
in the house of gravitational physics. There is tension between the new theory of
special relativity (SR), which constrains all physical theories and has a built-in finite
speed of light, and the old Newtonian gravitational theory (NGT), which works by
instantaneous action-at-a-distance. NGT will have to change, but how?
Enter Einstein, who sets out to reconcile the two theories by formulating a relativistic theory of gravitation. The core piece of the new theory will be field equations
that generalize the gravitational Poisson equation. Gravitational field equations tell
us how gravitation and matter, energy, and momentum hang together. The first two
acts of the drama go relatively smoothly. In the first act, Einstein formulates the
equivalence principle, which establishes a connection between accelerated reference
frames and gravitational fields. In the second act, he finds that the best way to represent the gravitational potential in the field equations is by the metric tensor, which
generalizes the notion of distance in Euclidean space to distance in space-times with
At the beginning of act three, Einstein has learned how to represent distance in
space-time by the metric tensor, and he knows that energy-momentum can be represented using the energy-momentum tensor.4 All that is left to do is to find the
gravitational field equations, which tell us how space-time is influenced by the distribution of matter, energy, and momentum. Mathematically, the missing element of
the field equations is a differential operator, which acts on the metric and thereby tells
us how the metric and the energy-momentum tensor hang together. An appropriate
differential operator generalizes the Laplace operator of the Poisson equation. This is
where the reversal of fortune sets in. Einstein tests various candidates, straightforward
generalizations of the Laplace operator, and also other candidates. However, none of
them fits the bill. In a state of desperation, Einstein turns to Marcel Grossmann, his
mathematician friend, for help.
(2007) has given an account of the genesis of GR in this form. The present section serves
as an introduction; technical details are mostly relegated to footnotes.
4 A detailed account of how the third act unfolded can be found in Renn and Sauer (2007).
Grossmann is indeed able to help.5 He finds a mathematical theory, the “absolute differential calculus”, proposed by the Italian mathematicians Gregorio RicciCurbastro and Tullio Levi-Civita; this calculus is a framework that provides candidate
differential operators for the field equations. The candidates are generally covariant,
i.e., they keep their form under arbitrary coordinate transformations. The single most
important object is the Riemann tensor; every possible generally covariant differential operator can be constructed from it. At the end of the drama, in November 1915,
it will turn out that the absolute differential calculus and gravitational theory were
right for each other all along. However, in 1912, Einstein and Grossmann do not
realize this and the final, correct field equations have to wait behind the scenes.
Einstein and Grossmann use the Riemann tensor to derive the so-called Ricci
tensor, a promising candidate.6 However, Einstein soon rejects the Ricci tensor as
unsuitable for the field equations. This is a mistake, because the reasons for the
rejection are ill conceived. The root of the problem has to do with the correspondence
principle: The new field equations have to be put in correspondence with the old,
classical gravitational field equation—the classical case should be recovered as a
limiting case of the new, general theory. In order to do this, one has to consider other,
intermediate cases, such as weak gravitational fields. At this point, Einstein is already
experienced in handling such intermediate cases, but this experience does not serve
him well: It generates wrong expectations about the form that special cases should
take. The rejection of the Ricci tensor is a consequence of these wrong expectations.
Einstein then turns to the so-called “November tensor”,7 a little brother of the
Ricci tensor. The November tensor can be found by decomposing the Ricci tensor
into two summands—one of these is the November tensor. It is not a generally
covariant object, but its covariance group still includes some accelerated reference
frames. At this point, the drama gets confusing. Einstein is able to show that the
November tensor does not run into the same difficulties that had led him to eliminate
the Ricci tensor. Despite this apparent progress, Einstein eliminates the November
tensor as well, and it is not considered any further in the Zurich notebook. What
prevented Einstein from investigating the November tensor further? What is more,
years later, in November 1915, he returned to the November tensor and used it to
formulate a version of general relativity. What made the November tensor acceptable
again in November 1915? In later recollections, Einstein stated reasons for rejecting
collaboration between Einstein and Grossmann resulted in several publications, most importantly the so-called “Entwurf” (“outline”) theory (Einstein and Grossmann 1995), which contains
the first detailed exposition of tensor calculus in the context of GR. The Entwurf theory does not yet
formulate the final, correct field equations of GR; see Sauer (2014) for an account of Grossmann’s
contribution to GR.
6 From here on, the story can only be reconstructed on the basis of the Zurich notebook. This part of
the drama is now well understood thanks to the genesis collaboration; see Janssen et al. (2007a, b).
The following account of Einstein’s struggle is based on Norton (2007, Sect. 1).
7 The name was coined by the genesis collaboration; the November tensor became prominent in
November 1915. It first appears on p. 22R of the Zurich notebook; see Fig. 9.1. I use the standard
pagination; see Janssen et al. (2007a), Klein et al. (1995) for a facsimile of the notebook and Janssen
et al. (2007b) for the commentary. Note that a facsimile of the Zurich notebook is also available
online at Einstein Archive Online.