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7 Conclusion: Theoretical Case-Based Philosophical Practice

7 Conclusion: Theoretical Case-Based Philosophical Practice

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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,

p. 673).

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.


T. Knuuttila and A. Loettgers


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Chapter 9

Gone Till November: A Disagreement in

Einstein Scholarship

Tim Räz

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

methodological issues.

9.1 Introduction

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

1 Most

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

e-mail: tim.raez@gmail.com

© 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,

DOI 10.1007/978-3-319-30229-4_9



T. Räz

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

2 See

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

variable curvature.

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.

3 Stachel

(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).


T. Räz

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

5 The

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.

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